HITZER, Eckhard MS
2002-01-01
This paper treats the fundamentals of the vector differential calculus part of universal geometric calculus. Geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. In order to make the treatment self-contained, I first compile all important geometric algebra relationships,which are necesssary for vector differential calculus. Then differentiation by vectors is introduced and a host of major ve...
Differential Calculus on Quantum Spheres
Welk, Martin
1998-01-01
We study covariant differential calculus on the quantum spheres S_q^2N-1. Two classification results for covariant first order differential calculi are proved. As an important step towards a description of the noncommutative geometry of the quantum spheres, a framework of covariant differential calculus is established, including a particular first order calculus obtained by factorization, higher order calculi and a symmetry concept.
Paragrassmann differential calculus
International Nuclear Information System (INIS)
Filippov, A.T.; Isaev, A.P.; Kurdikov, A.V.
1993-01-01
This paper significantly extends and generalizes the paragrassmann calculus previous paper. Explicit general constructions for paragrassmann calculus with one and many vaiables are discussed. A general construction of many-variable differentiation algebras is given. Some particular examples are related to multi-parametric quantum deformation of the harmonic oscillators
Putting Differentials Back into Calculus
Dray, Tevian; Manogue, Corrine A.
2010-01-01
We argue that the use of differentials in introductory calculus courses is useful and provides a unifying theme, leading to a coherent view of the calculus. Along the way, we meet several interpretations of differentials, some better than others.
A primer on exterior differential calculus
Directory of Open Access Journals (Sweden)
Burton D.A.
2003-01-01
Full Text Available A pedagogical application-oriented introduction to the calculus of exterior differential forms on differential manifolds is presented. Stokes' theorem, the Lie derivative, linear connections and their curvature, torsion and non-metricity are discussed. Numerous examples using differential calculus are given and some detailed comparisons are made with their traditional vector counterparts. In particular, vector calculus on R3 is cast in terms of exterior calculus and the traditional Stokes' and divergence theorems replaced by the more powerful exterior expression of Stokes' theorem. Examples from classical continuum mechanics and spacetime physics are discussed and worked through using the language of exterior forms. The numerous advantages of this calculus, over more traditional machinery, are stressed throughout the article. .
Differential calculus on deformed E(2) group
International Nuclear Information System (INIS)
Giller, S.; Gonera, C.; Kosinski, P.; Maslanka, P.
1997-01-01
Four dimensional bi-covariant differential *-calculus on quantum E(2) group is constructed. The relevant Lie algebra is obtained and covariant differential calculus on quantum plane is found. (author)
Covariant differential calculus on the quantum hyperplane
International Nuclear Information System (INIS)
Wess, J.
1991-01-01
We develop a differential calculus on the quantum hyperplane covariant with respect to the action of the quantum group GL q (n). This is a concrete example of noncommutative differential geometry. We describe the general constraints for a noncommutative differential calculus and verify that the example given here satisfies all these constraints. We also discuss briefly the integration over the quantum plane. (orig.)
The absolute differential calculus calculus of tensors
Levi-Cività, Tullio
1926-01-01
Written by a towering figure of twentieth-century mathematics, this classic examines the mathematical background necessary for a grasp of relativity theory. Tullio Levi-Civita provides a thorough treatment of the introductory theories that form the basis for discussions of fundamental quadratic forms and absolute differential calculus, and he further explores physical applications.Part one opens with considerations of functional determinants and matrices, advancing to systems of total differential equations, linear partial differential equations, algebraic foundations, and a geometrical intro
Calculus of tensors and differential forms
Sinha, Rajnikant
2014-01-01
Calculus of tensors and differential forms is an introductory-level textbook. Through this book, students will familiarize themselves with tools they need in order to use for further study on general relativity and research, such as affine tensors, tensor calculus on manifolds, relative tensors, Lie derivatives, wedge products, differential forms, and Stokes' theorem. The treatment is concrete and in detail, so that abstract concepts do not deter even physics and engineering students. This self contained book requires undergraduate-level calculus of several variables and linear algebra as prerequisite. Fubini's theorem in real analysis, to be used in Stokes' theorem, has been proved earlier than Stokes' theorem so that students don't have to search elsewhere.
Series expansion in fractional calculus and fractional differential equations
Li, Ming-Fan; Ren, Ji-Rong; Zhu, Tao
2009-01-01
Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this theorem, in this paper we introduce fractional series expansion method to fractional calculus. We define a kind of fractional Taylor series of an infinitely fractionally-differentiable function. Further, based on our definition we generalize hypergeometric functio...
Introduction to Differential Calculus Systematic Studies with Engineering Applications for Beginners
Rohde, Ulrich L; Poddar, Ajay K; Ghosh, A K
2011-01-01
Enables readers to apply the fundamentals of differential calculus to solve real-life problems in engineering and the physical sciences Introduction to Differential Calculus fully engages readers by presenting the fundamental theories and methods of differential calculus and then showcasing how the discussed concepts can be applied to real-world problems in engineering and the physical sciences. With its easy-to-follow style and accessible explanations, the book sets a solid foundation before advancing to specific calculus methods, demonstrating the connections between differential calculus
Covariant differential calculus on quantum spheres of odd dimension
International Nuclear Information System (INIS)
Welk, M.
1998-01-01
Covariant differential calculus on the quantum spheres S q 2N-1 is studied. Two classification results for covariant first order differential calculi are proved. As an important step towards a description of the noncommutative geometry of the quantum spheres, a framework of covariant differential calculus is established, including first and higher order calculi and a symmetry concept. (author)
On paragrassmann differential calculus
International Nuclear Information System (INIS)
Filippov, A.T.; Isaev, A.P.; Kurdikov, A.B.
1992-01-01
The paper significantly extends and generalizes our previous paper. Here we discuss explicit general constructions for paragrassmann calculus with one and many variables. For one variable nondegenerate differentiation algebras are identified and shown to be equivalent to the algebra of (p+1)x(p+1) complex matrices. For many variables we give a general construction of the differentiation algebras. Some particular examples are related to the multiparametric quantum deformations of the harmonic oscillators. 18 refs
Differential calculus and its applications
Field, Michael J
2013-01-01
Based on undergraduate courses in advanced calculus, the treatment covers a wide range of topics, from soft functional analysis and finite-dimensional linear algebra to differential equations on submanifolds of Euclidean space. 1976 edition.
QPFT operator algebras and commutative exterior differential calculus
International Nuclear Information System (INIS)
Yur'ev, D.V.
1993-01-01
The reduction of the structure theory of the operator algebras of quantum projective (sl(2, C)-invariant) field theory (QPFT operator algebras) to a commutative exterior differential calculus by means of the operation of renormalization of a pointwise product of operator fields is described. In the first section, the author introduces the concept of the operator algebra of quantum field theory and describes the operation of the renormalization of a pointwise product of operator fields. The second section is devoted to a brief exposition of the fundamentals of the structure theory of QPT operator algebras. The third section is devoted to commutative exterior differential calculus. In the fourth section, the author establishes the connection between the renormalized pointwise product of operator fields in QPFT operator algebras and the commutative exterior differential calculus. 5 refs
Higher order differential calculus on SLq(N)
International Nuclear Information System (INIS)
Heckenberger, I.; Schueler, A.
1997-01-01
Let Γ be a bicovariant first order differential calculus on a Hopf algebra A. There are three possibilities to construct a differential N 0 -graded Hopf algebra Γcirconflex which contains Γ as its first order part. In all cases Γcirconflex is a quotient Γcirconflex = Γ x /J of the tensor algebra by some suitable ideal. We distinguish three possible choices u J, s J, and w J, where the first one generates the universal differential calculus (over Γ) and the last one is Woronowicz' external algebra. Let q be a transcendental complex number and let Γ be one of the N 2 -dimensional bicovariant first order differential calculi on the quantum group SL q (N). Then for N ≥ 3 the three ideals coincide. For Woronowicz' external algebra we calculate the dimensions of the spaces of left-invariant and bi-invariant k-forms. In this case each bi-invariant form is closed. In case of 4D ± calculi on SL q (2) the universal calculus is strictly larger than the other two calculi. In particular, the bi-invariant 1-form is not closed. (author)
DIFFERENTIAL AND INTEGRAL CALCULUS. A TENTATIVE CURRICULUM GUIDE.
BRANT, VINCENT; GERARDI, WILLIAM
A GUIDE FOR A 1-YEAR COURSE IN DIFFERENTIAL AND INTEGRAL CALCULUS PREREQUISITED KNOWLEDGE IN ALGEBRA, ANALYTIC TRIGONOMETRY, AND ELEMENTARY ANALYSIS. EACH ASSIGNMENT CONTAINED BOTH NEW AND REVIEW WORK TO REINFORCE THE NEW WORK. THERE WERE ELEVEN UNITS OF STUDY USING THE FOLLOWING FOUR BOOKS--"CALCULUS AND ANALYTIC GEOMETRY, THIRD…
Malliavin Calculus With Applications to Stochastic Partial Differential Equations
Sanz-Solé, Marta
2005-01-01
Developed in the 1970s to study the existence and smoothness of density for the probability laws of random vectors, Malliavin calculus--a stochastic calculus of variation on the Wiener space--has proven fruitful in many problems in probability theory, particularly in probabilistic numerical methods in financial mathematics.This book presents applications of Malliavin calculus to the analysis of probability laws of solutions to stochastic partial differential equations driven by Gaussian noises that are white in time and coloured in space. The first five chapters introduce the calculus itself
About the differential calculus on the quantum groups
International Nuclear Information System (INIS)
Bernard, D.
1992-01-01
Given a solution R of the Yang-Baxter equation admitting a quasi-triangular decomposition we define a quasi-triangular quantum Lie algebra. We describe how to any quasi-triangular quantum Lie algebra U(G R ) is associated a Hopf algebra F(G R ) with a differential calculus on it such that the algebra of the quantum Lie derivatives is the algebra U(G R ). This allows us to make the connection between the differential calculus on quantum groups and the exchange algebras of the algebraic Bethe ansatz. (orig.)
Covariant differential calculus on the quantum exterior vector space
International Nuclear Information System (INIS)
Parashar, P.; Soni, S.K.
1992-01-01
We formulate a differential calculus on the quantum exterior vector space spanned by the generators of a non-anticommutative algebra satisfying r ij = θ i θ j +B kl ij θ k θ l =0 i, j=1, 2, ..., n. and (θ i ) 2 =(θ j ) 2 =...=(θ n ) 2 =0, where B kl ij is the most general matrix defined in terms of complex deformation parameters. Following considerations analogous to those of Wess and Zumino, we are able to exhibit covariance of our calculus under ( 2 n )+1 parameter deformation of GL(n) and explicitly check that the non-anticommutative differential calculus satisfies the general constraints given by them, such as the 'linear' conditions dr ij ≅0 and the 'quadratic' condition r ij x n ≅0 where x n =dθ n are the differentials of the variables. (orig.)
Differential calculus for q-deformed twistors
International Nuclear Information System (INIS)
Akulov, V.P.; Duplij, S.A.; Chitov, V.V.
1998-01-01
Brief type of q-deformed differential calculus at light cone with using of twistor representation is suggested. Commutative relations between coordinates and moments are obtained. Considered quasiclassical limit gives exact form of vanish from mass shell
Multivariable calculus and differential geometry
Walschap, Gerard
2015-01-01
This text is a modern in-depth study of the subject that includes all the material needed from linear algebra. It then goes on to investigate topics in differential geometry, such as manifolds in Euclidean space, curvature, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.
Differentiated Instruction in a Calculus Curriculum for College Students in Taiwan
Chen, Jing-Hua; Chen, Yi-Chou
2018-01-01
Objectives: To explore differentiated instruction within a calculus curriculum. For college students to learn concentration, motivation and the impact of academic achievement; explore the attitudes and ideas of students on differentiated instruction within a calculus curriculum; build up the diversity of mathematics education within varied…
On the algebraic structure of differential calculus on quantum groups
International Nuclear Information System (INIS)
Rad'ko, O.V.; Vladimirov, A.A.
1997-01-01
Intrinsic Hopf algebra structure of the Woronowicz differential complex is shown to generate quite naturally a bicovariant algebra of four basic objects within a differential calculus on quantum groups - coordinate functions, differential forms, Lie derivatives, and inner derivatives - as the cross-product algebra of two mutually dual graded Hopf algebras. This construction, properly taking into account Hopf-algebraic properties of Woronowicz's bicovariant calculus, provides a direct proof of the Cartan identity and of many other useful relations. A detailed comparison with other approaches is also given
Differential calculus in normed linear spaces
Mukherjea, Kalyan
2007-01-01
This book presents Advanced Calculus from a geometric point of view: instead of dealing with partial derivatives of functions of several variables, the derivative of the function is treated as a linear transformation between normed linear spaces. Not only does this lead to a simplified and transparent exposition of "difficult" results like the Inverse and Implicit Function Theorems but also permits, without any extra effort, a discussion of the Differential Calculus of functions defined on infinite dimensional Hilbert or Banach spaces.The prerequisites demanded of the reader are modest: a sound understanding of convergence of sequences and series of real numbers, the continuity and differentiability properties of functions of a real variable and a little Linear Algebra should provide adequate background for understanding the book. The first two chapters cover much of the more advanced background material on Linear Algebra (like dual spaces, multilinear functions and tensor products.) Chapter 3 gives an ab ini...
Equivariant calculus in the differential envelope
Energy Technology Data Exchange (ETDEWEB)
Kastler, D. (Centre National de la Recherche Scientifique, 13 - Marseille (France). Centre de Physique Theorique)
1991-01-01
The author shows how Z/2-graded cyclic cohomology is related to the equivariant calculus of S. Klimek, W. Kondracki, and A. Lesniewski (HUTMP 90/B247 (1990)). He uses the differential envelope of a complex unital differential algebra. After a presentation of fiber-preserved operators on equivariant functions valued in this algebra on a group he considers certain operators on this algebra. Finally he discusses explicitly the case G=Z/2. (HSI).
Equivariant calculus in the differential envelope
International Nuclear Information System (INIS)
Kastler, D.
1991-01-01
The author shows how Z/2-graded cyclic cohomology is related to the equivariant calculus of S. Klimek, W. Kondracki, and A. Lesniewski (HUTMP 90/B247 (1990)). He uses the differential envelope of a complex unital differential algebra. After a presentation of fiber-preserved operators on equivariant functions valued in this algebra on a group he considers certain operators on this algebra. Finally he discusses explicitly the case G=Z/2. (HSI)
Differential calculus on quantized simple Lie groups
International Nuclear Information System (INIS)
Jurco, B.
1991-01-01
Differential calculi, generalizations of Woronowicz's four-dimensional calculus on SU q (2), are introduced for quantized classical simple Lie groups in a constructive way. For this purpose, the approach of Faddeev and his collaborators to quantum groups was used. An equivalence of Woronowicz's enveloping algebra generated by the dual space to the left-invariant differential forms and the corresponding quantized universal enveloping algebra, is obtained for our differential calculi. Real forms for q ε R are also discussed. (orig.)
Ritow, Ira
2003-01-01
This brief introductory text presents the basic principles of calculus from the engineering viewpoint. Excellent either as a refresher or as an introductory course, it focuses on developing familiarity with the basic principles rather than presenting detailed proofs.Topics include differential calculus, in terms of differentiation and elementary differential equations; integral calculus, in simple and multiple integration forms; time calculus; equations of motion and their solution; complex variables; complex algebra; complex functions; complex and operational calculus; and simple and inverse
The bicovariant differential calculus on the κ-Poincare and κ-Weyl groups
International Nuclear Information System (INIS)
Przanowski, K.
1997-01-01
The bicovariant differential calculus on four-dimensional κ-Poincare group and corresponding Lie-algebra-like structure for any metric tensor are described. The bicovariant differential calculus on four-dimensional κ-Weyl group and corresponding Lie-algebra-like structure for any metric tensor in the reference frame in which g 00 = 0 are considered. (author). 6 refs
Differential calculus on quantized simple Lie groups
Energy Technology Data Exchange (ETDEWEB)
Jurco, B. (Dept. of Optics, Palacky Univ., Olomouc (Czechoslovakia))
1991-07-01
Differential calculi, generalizations of Woronowicz's four-dimensional calculus on SU{sub q}(2), are introduced for quantized classical simple Lie groups in a constructive way. For this purpose, the approach of Faddeev and his collaborators to quantum groups was used. An equivalence of Woronowicz's enveloping algebra generated by the dual space to the left-invariant differential forms and the corresponding quantized universal enveloping algebra, is obtained for our differential calculi. Real forms for q {epsilon} R are also discussed. (orig.).
International Nuclear Information System (INIS)
Carow-Watamura, U.; Schlieker, M.; Watamura, S.
1991-01-01
We construct a differential calculus on the N-dimensional non-commutative Euclidean space, i.e., the space on which the quantum group SO q (N) is acting. The differential calculus is required to be manifestly covariant under SO q (N) transformations. Using this calculus, we consider the Schroedinger equation corresponding to the harmonic oscillator in the limit of q→1. The solution of it is given by q-deformed functions. (orig.)
Hermeneutics of differential calculus in eighteenth-century northern Germany.
Blanco, Mónica
2008-01-01
This paper applies comparative textbook analysis to studying the mathematical development of differential calculus in northern German states during the eighteenth century. It begins with describing how the four textbooks analyzed presented the foundations of calculus and continues with assessing the influence each of these foundational approaches exerted on the resolution of problems, such as the determination of tangents and extreme values, and even on the choice of coordinates for both algebraic and transcendental curves.
Differential reflectometry versus tactile sense detection of subgingival calculus in dentistry
Shakibaie, Fardad; Walsh, Laurence J.
2012-10-01
Detecting dental calculus is clinically challenging in dentistry. This study used typodonts with extracted premolar and molar teeth and simulated gingival tissue to compare the performance of differential reflectometry and periodontal probing. A total of 30 extracted teeth were set in an anatomical configuration in stone to create three typodonts. Clear polyvinyl siloxane impression material was placed to replicate the periodontal soft tissues. Pocket depths ranged from 10 to 15 mm. The three models were placed in a phantom head, and an experienced dentist assessed the presence of subgingival calculus first using the DetecTar (differential reflectometry) and then a periodontal probe. Scores from these two different methods were compared to the gold standard (direct examination of the root surface using 20× magnification) to determine the accuracy and reproducibility. Differential reflectometry was more accurate than tactile assessment (79% versus 60%), and its reproducibility was also higher (Cohen kappa 0.54 versus 0.39). Both methods performed better on single rooted premolar teeth than on multirooted teeth. These laboratory results indicate that differential reflectometry allows more accurate and reproducible detection of subgingival calculus than conventional probing, and supports its use for supplementing traditional periodontal examination methods in dental practice.
The bicovariant differential calculus on the κ-Poincare group and on the κ-Minkowski space
International Nuclear Information System (INIS)
Kosinski, P.; Maslanka, P.; Sobczyk, J.
1996-01-01
The bicovariant differential calculus on the four-dimensional κ-Poincare group and the corresponding Lie-algebra-like structure are described. The differential calculus on the n-dimensional κ-Minkowski space covariant under the action of the κ-Poincare group was constructed. 5 refs
Matlab differential and integral calculus
Lopez, Cesar
2014-01-01
MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Differential and Integral Calculus introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to givi
Boehme, Thomas K
1987-01-01
Operational Calculus, Volume II is a methodical presentation of operational calculus. An outline of the general theory of linear differential equations with constant coefficients is presented. Integral operational calculus and advanced topics in operational calculus, including locally integrable functions and convergence in the space of operators, are also discussed. Formulas and tables are included.Comprised of four sections, this volume begins with a discussion on the general theory of linear differential equations with constant coefficients, focusing on such topics as homogeneous and non-ho
Morris, Carla C
2015-01-01
Fundamentals of Calculus encourages students to use power, quotient, and product rules for solutions as well as stresses the importance of modeling skills. In addition to core integral and differential calculus coverage, the book features finite calculus, which lends itself to modeling and spreadsheets. Specifically, finite calculus is applied to marginal economic analysis, finance, growth, and decay. Includes: Linear Equations and FunctionsThe DerivativeUsing the Derivative Exponential and Logarithmic Functions Techniques of DifferentiationIntegral CalculusIntegration TechniquesFunctions
Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces
Meljanac, Stjepan; Krešić–Jurić, Saša; Martinić, Tea
2017-07-01
This paper investigates bicovariant differential calculus on noncommutative spaces of the Lie algebra type. For a given Lie algebra g0, we construct a Lie superalgebra g =g0⊕g1 containing noncommutative coordinates and one-forms. We show that g can be extended by a set of generators TAB whose action on the enveloping algebra U (g ) gives the commutation relations between monomials in U (g0 ) and one-forms. Realizations of noncommutative coordinates, one-forms, and the generators TAB as formal power series in a semicompleted Weyl superalgebra are found. In the special case dim(g0 ) =dim(g1 ) , we also find a realization of the exterior derivative on U (g0 ) . The realizations of these geometric objects yield a bicovariant differential calculus on U (g0 ) as a deformation of the standard calculus on the Euclidean space.
Klaf, A A
1956-01-01
This book is unique in English as a refresher for engineers, technicians, and students who either wish to brush up their calculus or find parts of calculus unclear. It is not an ordinary textbook. It is, instead, an examination of the most important aspects of integral and differential calculus in terms of the 756 questions most likely to occur to the technical reader. It provides a very easily followed presentation and may also be used as either an introductory or supplementary textbook. The first part of this book covers simple differential calculus, with constants, variables, functions, inc
GLq(N)-covariant quantum algebras and covariant differential calculus
International Nuclear Information System (INIS)
Isaev, A.P.; Pyatov, P.N.
1993-01-01
We consider GL q (N)-covariant quantum algebras with generators satisfying quadratic polynomial relations. We show that, up to some inessential arbitrariness, there are only two kinds of such quantum algebras, namely, the algebras with q-deformed commutation and q-deformed anticommutation relations. The connection with the bicovariant differential calculus on the linear quantum groups is discussed. (orig.)
The malliavin calculus and related topics
Nualart, David
1995-01-01
The Malliavin calculus (or stochastic calculus of variations) is an infinite-dimensional differential calculus on the Wiener space Originally, it was developed to prove a probabilistic proof to Hörmander's "sum of squares" theorem, but more recently it has found application in a variety of stochastic differential equation problems This monograph presents the main features of the Malliavin calculus and discusses in detail its connection with the anticipating stochastic calculus The author begins by developing analysis on the Wiener space, and then uses this to analyze the regularity of probability laws and to prove Hörmander's theorem Subsequent chapters apply the Malliavin calculus to anticipating stochastic differential equations and to studying the Markov property of solutions to stochastic differential equations with boundary conditions
International Nuclear Information System (INIS)
Sharma, C.S.; Rebelo, I.
1975-01-01
It is proved that a semilinear function on a complex banach space is not differentiable according to the usual definition of differentiability in the calculus on banch spaces. It is shown that this result makes the calculus largely inapplicable to the solution od variational problems of quantum mechanics. A new concept of differentiability called semidifferentiability is defined. This generalizes the standard concept of differentiability in a banach space and the resulting calculus is particularly suitable for optimizing real-value functions on a complex banach space and is directly applicable to the solution of quantum mechanical variational problems. As an example of such application a rigorous proof of a generalized version of a result due to Sharma (J. Phys. A; 2:413 (1969)) is given. In the course of this work a new concept of prelinearity is defined and some standard results in the calculus in banach spaces are extended and generalized into more powerful ones applicable directly to prelinear functions and hence yielding the standard results for linear function as particular cases. (author)
An outline of possible pre-course diagnostics for differential calculus
Directory of Open Access Journals (Sweden)
Aneshkumar Maharaj
2014-07-01
Full Text Available There is a view that many first-year students lack the basic knowledge and skills expected of them to study at university level. We examined the expected work habits and pre-course diagnostics for students who choose to take a course on differential calculus. We focused on the lecturer pre-course expectations of a student in the context of work habits, knowledge and technical skills. In particular, we formulated outcomes and then sample diagnostic questions to test whether the identified learning outcomes on expected work habits and learning are in place. If students are made aware of the expected learning outcomes and if they take the diagnostic test, they should be able to achieve greater success in their studies. The validity of this assumption will be the subject of a future paper which will report on the implementation of the learning outcomes and diagnostic questions that we formulated for pre-course diagnostics in differential calculus.
Differential calculus on quantum spaces and quantum groups
International Nuclear Information System (INIS)
Zumino, B.
1992-01-01
A review of recent developments in the quantum differential calculus. The quantum group GL q (n) is treated by considering it as a particular quantum space. Functions on SL q (n) are defined as a subclass of functions on GL q (n). The case of SO q (n) is also briefly considered. These notes cover part of a lecture given at the XIX International Conference on Group Theoretic Methods in Physics, Salamanca, Spain 1992
Essential calculus with applications
Silverman, Richard A
1989-01-01
Rigorous but accessible text introduces undergraduate-level students to necessary background math, then clear coverage of differential calculus, differentiation as a tool, integral calculus, integration as a tool, and functions of several variables. Numerous problems and a supplementary section of ""Hints and Answers."" 1977 edition.
Relativistic differential-difference momentum operators and noncommutative differential calculus
International Nuclear Information System (INIS)
Mir-Kasimov, R.M.
2011-01-01
Full text: (author)The relativistic kinetic momentum operators are introduced in the framework of the Quantum Mechanics in the relativistic configuration space (RCS). These operators correspond to the half of the non-Euclidean distance in the Lobachevsky momentum space. In terms of kinetic momentum operators the relativistic kinetic energy is separated from the total Hamiltonian. The role of the plane wave (wave function of the motion with definite value of momentum and energy) plays the generation function for the matrix elements of the unitary irreps of Lorentz group (generalized Jacobi polynomials). The kinetic momentum operators are the interior derivatives in the framework of the non-commutative differential calculus over the commutative algebra generated by the coordinate functions over the RCS
TENSOR CALCULUS with applications to Differential Theory of Surfaces and Dynamics
DEFF Research Database (Denmark)
Nielsen, Søren R. K.
The present outline on tensor calculus with special application to differential theory of surfaces and dynamics represents a modified and extended version of a lecture note written by the author as an introduction to a course on shell theory given together with Ph.D. Jesper Winther Stærdahl...
Bicovariant differential calculus on quantum groups and wave mechanics
International Nuclear Information System (INIS)
Carow-Watamura, U.; Watamura, S.; Hebecker, A.; Schlieker, M.; Weich, W.
1992-01-01
The bicovariant differential calculus on quantum groups defined by Woronowicz and later worked out explicitly by Carow-Watamura et al. and Jurco for the real quantum groups SU q (N) and SO q (N) through a systematic construction of the bicovariant bimodules of these quantum groups, is reviewed for SU q (2) and SO q (N). The resulting vector fields build representations of the quantized universal enveloping algebras acting as covariant differential operators on the quantum groups and their associated quantum spaces. As an application, a free particle stationary wave equation on quantum space is formulated and solved in terms of a complete set of energy eigenfunctions. (author) 15 refs
Complex quantum group, dual algebra and bicovariant differential calculus
International Nuclear Information System (INIS)
Carow-Watamura, U.; Watamura, Satoshi
1993-01-01
The method used to construct the bicovariant bimodule in ref. [CSWW] is applied to examine the structure of the dual algebra and the bicovariant differential calculus of the complex quantum group. The complex quantum group Fun q (SL(N, C)) is defined by requiring that it contains Fun q (SU(N)) as a subalgebra analogously to the quantum Lorentz group. Analyzing the properties of the fundamental bimodule, we show that the dual algebra has the structure of the twisted product Fun q (SU(N))x tilde Fun q (SU(N)) reg *. Then the bicovariant differential calculi on the complex quantum group are constructed. (orig.)
BRST-operator for quantum Lie algebra and differential calculus on quantum groups
International Nuclear Information System (INIS)
Isaev, A.P.; Ogievetskij, O.V.
2001-01-01
For A Hopf algebra one determined structure of differential complex in two dual external Hopf algebras: A external expansion and in A* dual algebra external expansion. The Heisenberg double of these two Hopf algebras governs the differential algebra for the Cartan differential calculus on A algebra. The forst differential complex is the analog of the de Rame complex. The second complex coincide with the standard complex. Differential is realized as (anti)commutator with Q BRST-operator. Paper contains recursion relation that determines unequivocally Q operator. For U q (gl(N)) Lie quantum algebra one constructed BRST- and anti-BRST-operators and formulated the theorem of the Hodge expansion [ru
Explicit Minkowski invariance and differential calculus in the quantum space-time
International Nuclear Information System (INIS)
Xu Zhan.
1991-11-01
In terms of the R-circumflex matrix of the quantum group SL q (2), the explicit Minkowski coordinate commutation relations in the four-dimensional quantum space-time are given, and the invariance of the Minkowski metric is shown. The differential calculus in this quantum space-time is discussed and the corresponding commutation relations are proposed. (author). 17 refs
Generalized vector calculus on convex domain
Agrawal, Om P.; Xu, Yufeng
2015-06-01
In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.
Balankin, Alexander S.; Bory-Reyes, Juan; Shapiro, Michael
2016-02-01
One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.
Noncommutative operational calculus
Directory of Open Access Journals (Sweden)
Henry E. Heatherly
1999-12-01
Full Text Available Oliver Heaviside's operational calculus was placed on a rigorous mathematical basis by Jan Mikusinski, who constructed an algebraic setting for the operational methods. In this paper, we generalize Mikusi'{n}ski's methods to solve linear ordinary differential equations in which the unknown is a matrix- or linear operator-valued function. Because these functions can be zero-divisors and do not necessarily commute, Mikusi'{n}ski's one-dimensional calculus cannot be used. The noncommuative operational calculus developed here,however, is used to solve a wide class of such equations. In addition, we provide new proofs of existence and uniqueness theorems for certain matrix- and operator valued Volterra integral and integro-differential equations. Several examples are given which demonstrate these new methods.
Fock space representation of differential calculus on the noncommutative quantum space
International Nuclear Information System (INIS)
Mishra, A.K.; Rajasekaran, G.
1997-01-01
A complete Fock space representation of the covariant differential calculus on quantum space is constructed. The consistency criteria for the ensuing algebraic structure, mapping to the canonical fermions and bosons and the consequences of the new algebra for the statistics of quanta are analyzed and discussed. The concept of statistical transmutation between bosons and fermions is introduced. copyright 1997 American Institute of Physics
Schaaf, William L
2011-01-01
Comprehensive but concise, this introduction to differential and integral calculus covers all the topics usually included in a first course. The straightforward development places less emphasis on mathematical rigor, and the informal manner of presentation sets students at ease. Many carefully worked-out examples illuminate the text, in addition to numerous diagrams, problems, and answers.Bearing the needs of beginners constantly in mind, the treatment covers all the basic concepts of calculus: functions, derivatives, differentiation of algebraic and transcendental functions, partial different
Ideas of Physical Forces and Differential Calculus in Ancient India
Girish, T. E.; Nair, C. Radhakrishnan
2010-01-01
We have studied the context and development of the ideas of physical forces and differential calculus in ancient India by studying relevant literature related to both astrology and astronomy since pre-Greek periods. The concept of Naisargika Bala (natural force) discussed in Hora texts from India is defined to be proportional to planetary size and inversely related to planetary distance. This idea developed several centuries prior to Isaac Newton resembles fundamental physical forces in natur...
Domingues, João Caramalho
2008-01-01
Silvestre François Lacroix (Paris, 1765 - ibid., 1843) was a most influential mathematical book author. His most famous work is the three-volume Traité du calcul différentiel et du calcul intégral (1797-1800; 2nd ed. 1810-1819) – an encyclopedic appraisal of 18th-century calculus which remained the standard reference on the subject through much of the 19th century, in spite of Cauchy's reform of the subject in the 1820's. Lacroix and the Calculus is the first major study of Lacroix’s large Traité. It uses the unique and massive bibliography given by Lacroix to explore late 18th-century calculus, and the way it is reflected in Lacroix’s account. Several particular aspects are addressed in detail, including: the foundations of differential calculus, analytic and differential geometry, conceptions of the integral, and types of solutions of differential equations (singular/complete/general integrals, geometrical interpretations, and generality of arbitrary functions). Lacroix’s large Traité... was a...
Calculus of bivariant function
PTÁČNÍK, Jan
2011-01-01
This thesis deals with the introduction of function of two variables and differential calculus of this function. This work should serve as a textbook for students of elementary school's teacher. Each chapter contains a summary of basic concepts and explanations of relationships, then solved model exercises of the topic and finally the exercises, which should solve the student himself. Thesis have transmit to students basic knowledges of differential calculus of functions of two variables, inc...
n=3 differential calculus and gauge theory on a reduced quantum plane
International Nuclear Information System (INIS)
El Baz, M.; El Hassouni, A.; Hassouni, Y.; Zakkari, E.H.
2003-01-01
We discuss the algebra of NxN matrices as a reduced quantum plane. A n=3-nilpotent deformed differential calculus involving a complex parameter q is constructed. The two cases, q 3rd and Nth root of unity are completely treated. As an application, we establish a gauge field theory for the particular cases n=2 and n=3
Grossman, Stanley I
1984-01-01
Calculus, Third Edition emphasizes the techniques and theorems of calculus, including many applied examples and exercises in both drill and applied-type problems.This book discusses shifting the graphs of functions, derivative as a rate of change, derivative of a power function, and theory of maxima and minima. The area between two curves, differential equations of exponential growth and decay, inverse hyperbolic functions, and integration of rational functions are also elaborated. This text likewise covers the fluid pressure, ellipse and translation of axes, graphing in polar coordinates, pro
An outline of possible pre-course diagnostics for differential calculus
Maharaj, Aneshkumar; Wagh, Vivek
2014-01-01
There is a view that many first-year students lack the basic knowledge and skills expected of them to study at university level. We examined the expected work habits and pre-course diagnostics for students who choose to take a course on differential calculus. We focused on the lecturer pre-course expectations of a student in the context of work habits, knowledge and technical skills. In particular, we formulated outcomes and then sample diagnostic questions to test whether the identified lear...
Testicular calculus: A rare case.
Sen, Volkan; Bozkurt, Ozan; Demır, Omer; Tuna, Burcin; Yorukoglu, Kutsal; Esen, Adil
2015-01-01
Testicular calculus is an extremely rare case with unknown etiology and pathogenesis. To our knowledge, here we report the third case of testicular calculus. A 31-year-old man was admitted to our clinic with painful solid mass in left testis. After diagnostic work-up for a possible testicular tumour, he underwent inguinal orchiectomy and histopathologic examination showed a testicular calculus. Case hypothesis: Solid testicular lesions in young adults generally correspond to testicular cancer. Differential diagnosis should be done carefully. Future implications: In young adults with painful and solid testicular mass with hyperechogenic appearance on scrotal ultrasonography, testicular calculus must be kept in mind in differential diagnosis. Further reports on this topic may let us do more clear recommendations about the etiology and treatment of this rare disease.
Ryan, Mark
2014-01-01
Slay the calculus monster with this user-friendly guide Calculus For Dummies, 2nd Edition makes calculus manageable-even if you're one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the ""how"" and ""why"" in plain English instead of math-speak. Through relevant instruction and practical examples, you'll s
On conservation laws for models in discrete, noncommutative and fractional differential calculus
International Nuclear Information System (INIS)
Klimek, M.
2001-01-01
We present the general method of derivation the explicit form of conserved currents for equations built within the framework of discrete, noncommutative or fractional differential calculus. The procedure applies to linear models with variable coefficients including also nonlinear potential part. As an example an equation on quantum plane, nonlinear Toda lattice model and homogeneous equation of fractional diffusion in 1+1 dimensions are studied
Algebraic differential calculus for gauge theories
International Nuclear Information System (INIS)
Landi, G.; Marmo, G.
1990-01-01
The guiding idea in this paper is that, from the point of view of physics, functions and fields are more important than the (space time) manifold over which they are defined. The line pursued in these notes belongs to the general framework of ideas that replaces the space M by the ring of functions on it. Our essential observation, underlying this work, is that much of mathematical physics requires only a few differential operators (Lie derivative, d, δ) operating on modules of sections of suitable bundles. A connection (=gauge potential) can be described by a lift of vector fields from the base to the total space of a principal bundle. Much of the information can be encoded in the lift without reference to the bundle structures. In this manner, one arrives at an 'algebraic differential calculus' and its graded generalization that we are going to discuss. We are going to give an exposition of 'algebraic gauge theory' in both ungraded and graded versions. We show how to deal with the essential features of electromagnetism, Dirac, Kaluza-Klein and 't Hooft-Polyakov monopoles. We also show how to break the symmetry from SU(2) to U(1) without Higgs field. We briefly show how to deal with tests particles in external fields and with the Lagrangian formulation of field theories. (orig./HSI)
Stochastic differential calculus for Gaussian and non-Gaussian noises: A critical review
Falsone, G.
2018-03-01
In this paper a review of the literature works devoted to the study of stochastic differential equations (SDEs) subjected to Gaussian and non-Gaussian white noises and to fractional Brownian noises is given. In these cases, particular attention must be paid in treating the SDEs because the classical rules of the differential calculus, as the Newton-Leibnitz one, cannot be applied or are applicable with many difficulties. Here all the principal approaches solving the SDEs are reported for any kind of noise, highlighting the negative and positive properties of each one and making the comparisons, where it is possible.
Covariant differential calculus on quantum Minkowski space and the q-analogue of Dirac equation
International Nuclear Information System (INIS)
Song Xingchang; Academia Sinica, Beijing
1992-01-01
The covariant differential calculus on the quantum Minkowski space is presented with the help of the generalized Wess-Zumino method and the quantum Pauli matrices and quantum Dirac matrices are constructed parallel to those in the classical case. Combining these two aspects a q-analogue of Dirac equation follows directly. (orig.)
Multivariable calculus with applications
Lax, Peter D
2017-01-01
This text in multivariable calculus fosters comprehension through meaningful explanations. Written with students in mathematics, the physical sciences, and engineering in mind, it extends concepts from single variable calculus such as derivative, integral, and important theorems to partial derivatives, multiple integrals, Stokes’ and divergence theorems. Students with a background in single variable calculus are guided through a variety of problem solving techniques and practice problems. Examples from the physical sciences are utilized to highlight the essential relationship between calculus and modern science. The symbiotic relationship between science and mathematics is shown by deriving and discussing several conservation laws, and vector calculus is utilized to describe a number of physical theories via partial differential equations. Students will learn that mathematics is the language that enables scientific ideas to be precisely formulated and that science is a source for the development of mathemat...
On the Lipschitz condition in the fractal calculus
International Nuclear Information System (INIS)
Golmankhaneh, Alireza K.; Tunc, Cemil
2017-01-01
In this paper, the existence and uniqueness theorems are proved for the linear and non-linear fractal differential equations. The fractal Lipschitz condition is given on the F"α-calculus which applies for the non-differentiable function in the sense of the standard calculus. More, the metric spaces associated with fractal sets and about functions with fractal supports are defined to build fractal Cauchy sequence. Furthermore, Picard iterative process in the F"α-calculus which have important role in the numerical and approximate solution of fractal differential equations is explored. We clarify the results using the illustrative examples.
Topology, calculus and approximation
Komornik, Vilmos
2017-01-01
Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...
n=3 differential calculus on a given reduced quantum plane and gauge theory
International Nuclear Information System (INIS)
Elbaz, M.; El Hassouni, A.; Hassouni, Y.; Zakkari, E.H.
2002-08-01
We discuss the algebra of NxN matrices that seems to be as a reduced quantum plane. A new deformed differential calculus involving a complex parameter q is introduced. The two cases, q generic and q N-th root of unity are completely treated. As an application, we give connection with gauge field theory for the particular cases n=2 and n=3. (author)
The two-parameter deformation of GL(2), its differential calculus, and Lie algebra
International Nuclear Information System (INIS)
Schirrmacher, A.; Wess, J.
1991-01-01
The Yang-Baxter equation is solved in two dimensions giving rise to a two-parameter deformation of GL(2). The transformation properties of quantum planes are briefly discussed. Non-central determinant and inverse are constructed. A right-invariant differential calculus is presented and the role of the different deformation parameters investigated. While the corresponding Lie algebra relations are simply deformed, the comultiplication exhibits both quantization parameters. (orig.)
International Nuclear Information System (INIS)
Schirrmacher, A.
1991-01-01
A n(n-1)/2+1 parameter solution of the Yang Baxter equation is presented giving rise to the quantum Group GL x;qij (n). Determinant and inverse are constructed. The group acts covariantly on a quantum vector space of non-commutative coordinates. The associated exterior space can be identified with the differentials exhibiting a multiparameter deformed differential calculus following the construction of Wess and Zumino. (orig.)
Introduction to the operational calculus
Berg, Lothar
2013-01-01
Introduction to the Operational Calculus is a translation of ""Einfuhrung in die Operatorenrechnung, Second Edition."" This book deals with Heaviside's interpretation, on the Laplace integral, and on Jan Mikusinki's fundamental work ""Operational Calculus."" Throughout the book, basic algebraic concepts appear as aids to understanding some relevant points of the subject. An important field for research in analysis is asymptotic properties. This text also discusses examples to show the potentialities in applying operational calculus that run beyond ordinary differential equations with constant
Fractional vector calculus and fractional Maxwell's equations
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2008-01-01
The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using a fractional generalization of the Fundamental Theorem of Calculus. We define the differential and integral vector operations. The fractional Green's, Stokes' and Gauss's theorems are formulated. The proofs of these theorems are realized for simplest regions. A fractional generalization of exterior differential calculus of differential forms is discussed. Fractional nonlocal Maxwell's equations and the corresponding fractional wave equations are considered
Advanced Placement Mathematics Calculus, Grade 12 Curriculum Guide.
Scharf, John; And Others
This document is a guide to the advanced placement program in calculus for grade 12 in the city schools in Warren, Ohio. The program covers analytic geometry, differential and integral calculus of algebraic functions, elementary transcendental functions, and applications of differentiation and integration. The philosophy and aims of the program…
Brownian motion, martingales, and stochastic calculus
Le Gall, Jean-François
2016-01-01
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested i...
Christensen, Mark J
1981-01-01
Computing for Calculus focuses on BASIC as the computer language used for solving calculus problems.This book discusses the input statement for numeric variables, advanced intrinsic functions, numerical estimation of limits, and linear approximations and tangents. The elementary estimation of areas, numerical and string arrays, line drawing algorithms, and bisection and secant method are also elaborated. This text likewise covers the implicit functions and differentiation, upper and lower rectangular estimates, Simpson's rule and parabolic approximation, and interpolating polynomials. Other to
Scale calculus and the Schroedinger equation
International Nuclear Information System (INIS)
Cresson, Jacky
2003-01-01
This paper is twofold. In a first part, we extend the classical differential calculus to continuous nondifferentiable functions by developing the notion of scale calculus. The scale calculus is based on a new approach of continuous nondifferentiable functions by constructing a one parameter family of differentiable functions f(t,ε) such that f(t,ε)→f(t) when ε goes to zero. This led to several new notions as representations: fractal functions and ε-differentiability. The basic objects of the scale calculus are left and right quantum operators and the scale operator which generalizes the classical derivative. We then discuss some algebraic properties of these operators. We define a natural bialgebra, called quantum bialgebra, associated with them. Finally, we discuss a convenient geometric object associated with our study. In a second part, we define a first quantization procedure of classical mechanics following the scale relativity theory developed by Nottale. We obtain a nonlinear Schroedinger equation via the classical Newton's equation of dynamics using the scale operator. Under special assumptions we recover the classical Schroedinger equation and we discuss the relevance of these assumptions
Differential calculus for Dirichlet forms: The measure-valued gradient preserved by image
Bouleau, Nicolas
2005-01-01
In order to develop a differential calculus for error propagation we study local Dirichlet forms on probability spaces with square field operator $\\Gamma$ -- i.e. error structures -- and we are looking for an object related to $\\Gamma$ which is linear and with a good behaviour by images. For this we introduce a new notion called the measure valued gradient which is a randomized square root of $\\Gamma$. The exposition begins with inspecting some natural notions candidate to solve the problem b...
Osserman, Robert
2011-01-01
The basic component of several-variable calculus, two-dimensional calculus is vital to mastery of the broader field. This extensive treatment of the subject offers the advantage of a thorough integration of linear algebra and materials, which aids readers in the development of geometric intuition. An introductory chapter presents background information on vectors in the plane, plane curves, and functions of two variables. Subsequent chapters address differentiation, transformations, and integration. Each chapter concludes with problem sets, and answers to selected exercises appear at the end o
Tensor Calculus: Unlearning Vector Calculus
Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita
2018-01-01
Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…
Restrictive metric regularity and generalized differential calculus in Banach spaces
Directory of Open Access Journals (Sweden)
Bingwu Wang
2004-10-01
Full Text Available We consider nonlinear mappings f:XÃ¢Â†Â’Y between Banach spaces and study the notion of restrictive metric regularity of f around some point xÃ‚Â¯, that is, metric regularity of f from X into the metric space E=f(X. Some sufficient as well as necessary and sufficient conditions for restrictive metric regularity are obtained, which particularly include an extension of the classical Lyusternik-Graves theorem in the case when f is strictly differentiable at xÃ‚Â¯ but its strict derivative Ã¢ÂˆÂ‡f(xÃ‚Â¯ is not surjective. We develop applications of the results obtained and some other techniques in variational analysis to generalized differential calculus involving normal cones to nonsmooth and nonconvex sets, coderivatives of set-valued mappings, as well as first-order and second-order subdifferentials of extended real-valued functions.
Teacher knowledge of error analysis in differential calculus
Directory of Open Access Journals (Sweden)
Eunice K. Moru
2014-12-01
Full Text Available The study investigated teacher knowledge of error analysis in differential calculus. Two teachers were the sample of the study: one a subject specialist and the other a mathematics education specialist. Questionnaires and interviews were used for data collection. The findings of the study reflect that the teachers’ knowledge of error analysis was characterised by the following assertions, which are backed up with some evidence: (1 teachers identified the errors correctly, (2 the generalised error identification resulted in opaque analysis, (3 some of the identified errors were not interpreted from multiple perspectives, (4 teachers’ evaluation of errors was either local or global and (5 in remedying errors accuracy and efficiency were emphasised more than conceptual understanding. The implications of the findings of the study for teaching include engaging in error analysis continuously as this is one way of improving knowledge for teaching.
Functional Fractional Calculus
Das, Shantanu
2011-01-01
When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with 'ordinary' differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematic
Applications of fractional calculus in physics
2000-01-01
Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus.This volume provides an introduction to fractional calculus for physicists, and co
Directory of Open Access Journals (Sweden)
Resat Yilmazer
2016-02-01
Full Text Available In this work; we present a method for solving the second-order linear ordinary differential equation of hypergeometric type. The solutions of this equation are given by the confluent hypergeometric functions (CHFs. Unlike previous studies, we obtain some different new solutions of the equation without using the CHFs. Therefore, we obtain new discrete fractional solutions of the homogeneous and non-homogeneous confluent hypergeometric differential equation (CHE by using a discrete fractional Nabla calculus operator. Thus, we obtain four different new discrete complex fractional solutions for these equations.
Differential Calculus on the Quantum Sphere and Deformed Self-Duality Equation
International Nuclear Information System (INIS)
Zupnik, B.M.
1994-01-01
We discuss the left-covariant 3-dimensional differential calculus on the quantum sphere SU q (2)/U(1). The SU q (2)-spinor harmonics are treated as coordinates of the quantum sphere. We consider the gauge theory for the quantum group SU q (2) x U(1) on the deformed Euclidean space E q (4). A q-generalization of the harmonic-gauge-field formalism is suggested. This formalism is applied for the harmonic (Twistor) interpretation of the quantum-group self-duality equation (QGSDE). We consider the zero-curvature representation and the general construction of QGSDE-solutions in terms of the analytic pre potential. 24 refs
Jukic Matic, Ljerka; Dahl, Bettina
2014-01-01
This paper reports a study on retention of differential and integral calculus concepts of a second-year student of physical chemistry at a Danish university. The focus was on what knowledge the student retained 14 months after the course and on what effect beliefs about mathematics had on the retention. We argue that if a student can quickly…
Ayres, Frank
1999-01-01
Students can gain a thorough understanding of differential and integral calculus with this powerful study tool. They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guide--more than 104,000 copies were bought of the prior edition--includes problems and examples using graphing calculators.
Izadi, F A; Bagirov, G
2009-01-01
With its origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. The topics covered here usually arise in many branches of science and technology, especially in discrete mathematics, numerical analysis, statistics and probability theory as well as in electrical engineering, but our viewpoint here is that these topics belong to a much more general realm of mathematics; namely calculus and differential equations because of the remarkable analogy of the subject to this branch of mathemati
Fluorescence detection of dental calculus
International Nuclear Information System (INIS)
Gonchukov, S; Sukhinina, A; Vdovin, Yu; Biryukova, T
2010-01-01
This work is devoted to the optimization of fluorescence dental calculus diagnostics in optical spectrum. The optimal wavelengths for fluorescence excitation and registration are determined. Two spectral ranges 620 – 645 nm and 340 – 370 nm are the most convenient for supra- and subgingival calculus determination. The simple implementation of differential method free from the necessity of spectrometer using was investigated. Calculus detection reliability in the case of simple implementation is higher than in the case of spectra analysis at optimal wavelengths. The use of modulated excitation light and narrowband detection of informative signal allows us to decrease essentially its diagnostic intensity even in comparison with intensity of the low level laser dental therapy
Fluorescence detection of dental calculus
Gonchukov, S.; Biryukova, T.; Sukhinina, A.; Vdovin, Yu
2010-11-01
This work is devoted to the optimization of fluorescence dental calculus diagnostics in optical spectrum. The optimal wavelengths for fluorescence excitation and registration are determined. Two spectral ranges 620 - 645 nm and 340 - 370 nm are the most convenient for supra- and subgingival calculus determination. The simple implementation of differential method free from the necessity of spectrometer using was investigated. Calculus detection reliability in the case of simple implementation is higher than in the case of spectra analysis at optimal wavelengths. The use of modulated excitation light and narrowband detection of informative signal allows us to decrease essentially its diagnostic intensity even in comparison with intensity of the low level laser dental therapy.
Stochastic Calculus and Differential Equations for Physics and Finance
McCauley, Joseph L.
2013-02-01
1. Random variables and probability distributions; 2. Martingales, Markov, and nonstationarity; 3. Stochastic calculus; 4. Ito processes and Fokker-Planck equations; 5. Selfsimilar Ito processes; 6. Fractional Brownian motion; 7. Kolmogorov's PDEs and Chapman-Kolmogorov; 8. Non Markov Ito processes; 9. Black-Scholes, martingales, and Feynman-Katz; 10. Stochastic calculus with martingales; 11. Statistical physics and finance, a brief history of both; 12. Introduction to new financial economics; 13. Statistical ensembles and time series analysis; 14. Econometrics; 15. Semimartingales; References; Index.
Fractional and multivariable calculus model building and optimization problems
Mathai, A M
2017-01-01
This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable ...
Calculus and analysis in Euclidean space
Shurman, Jerry
2016-01-01
The graceful role of analysis in underpinning calculus is often lost to their separation in the curriculum. This book entwines the two subjects, providing a conceptual approach to multivariable calculus closely supported by the structure and reasoning of analysis. The setting is Euclidean space, with the material on differentiation culminating in the inverse and implicit function theorems, and the material on integration culminating in the general fundamental theorem of integral calculus. More in-depth than most calculus books but less technical than a typical analysis introduction, Calculus and Analysis in Euclidean Space offers a rich blend of content to students outside the traditional mathematics major, while also providing transitional preparation for those who will continue on in the subject. The writing in this book aims to convey the intent of ideas early in discussion. The narrative proceeds through figures, formulas, and text, guiding the reader to do mathematics resourcefully by marshaling the skil...
Jones, Patrick
2014-01-01
Practice makes perfect-and helps deepen your understanding of calculus 1001 Calculus Practice Problems For Dummies takes you beyond the instruction and guidance offered in Calculus For Dummies, giving you 1001 opportunities to practice solving problems from the major topics in your calculus course. Plus, an online component provides you with a collection of calculus problems presented in multiple-choice format to further help you test your skills as you go. Gives you a chance to practice and reinforce the skills you learn in your calculus courseHelps you refine your understanding of calculusP
Generalized Cartan Calculus in general dimension
Wang, Yi-Nan
2015-07-01
We develop the generalized Cartan Calculus for the groups and SO(5 , 5). They are the underlying algebraic structures of d = 9 , 7 , 6 exceptional field theory, respectively. These algebraic identities are needed for the "tensor hierarchy" structure in exceptional field theory. The validity of Poincaré lemmas in this new differential geometry is also discussed. Finally we explore some possible extension of the generalized Cartan calculus beyond the exceptional series.
The Pendulum and the Calculus.
Sworder, Steven C.
A pair of experiments, appropriate for the lower division fourth semester calculus or differential equations course, are presented. The second order differential equation representing the equation of motion of a simple pendulum is derived. The period of oscillation for a particular pendulum can be predicted from the solution to this equation. As a…
Integration on supermanifolds and a generalized Cartan calculus
International Nuclear Information System (INIS)
Picken, R.F.; Sundermeyer, K.
1986-01-01
A suggestion by Berezin for a method of integration on supermanifolds is given a precise differential geometric meaning by assuming that a supermanifold is the total space of a fibre bundle with connection. The relevant objects for integration are identified as suitable horizontal/vertical projections of hyperforms. The latter are generalizations of differential forms having both covariant and contravariant indices. The exterior calculus of these projected hyperforms is developed, analogously to the Cartan calculus, by introducing appropriate derivations and determining their commutators, respectively anticommutators. (orig.)
Non-commutative differential calculus and the axial anomaly in Abelian lattice gauge theories
International Nuclear Information System (INIS)
Fujiwara, Takanori; Suzuki, Hiroshi; Wu, Ke
2000-01-01
The axial anomaly in lattice gauge theories has a topological nature when the Dirac operator satisfies the Ginsparg-Wilson relation. We study the axial anomaly in Abelian gauge theories on an infinite hypercubic lattice by utilizing cohomological arguments. The crucial tool in our approach is the non-commutative differential calculus (NCDC) which makes the Leibniz rule of exterior derivatives valid on the lattice. The topological nature of the 'Chern character' on the lattice becomes manifest in the context of NCDC. Our result provides an algebraic proof of Luescher's theorem for a four-dimensional lattice and its generalization to arbitrary dimensions
Stochastic integration by parts and functional Itô calculus
Vives, Josep
2016-01-01
This volume contains lecture notes from the courses given by Vlad Bally and Rama Cont at the Barcelona Summer School on Stochastic Analysis (July 2012). The notes of the course by Vlad Bally, co-authored with Lucia Caramellino, develop integration by parts formulas in an abstract setting, extending Malliavin's work on abstract Wiener spaces. The results are applied to prove absolute continuity and regularity results of the density for a broad class of random processes. Rama Cont's notes provide an introduction to the Functional Itô Calculus, a non-anticipative functional calculus that extends the classical Itô calculus to path-dependent functionals of stochastic processes. This calculus leads to a new class of path-dependent partial differential equations, termed Functional Kolmogorov Equations, which arise in the study of martingales and forward-backward stochastic differential equations. This book will appeal to both young and senior researchers in probability and stochastic processes, as well as to pract...
Partial differential equations and calculus of variations
Leis, Rolf
1988-01-01
This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory.
A TENTATIVE GUIDE, DIFFERENTIAL AND INTEGRAL CALCULUS.
BRANT, VINCENT; GERARDI, WILLIAM
THE COURSE IS INTENDED TO GO BEYOND THE REQUIREMENTS OF THE ADVANCED PLACEMENT PROGRAM IN MATHEMATICS AS DESIGNED BY THE COLLEGE ENTRANCE EXAMINATION BOARD. THE ADVANCED PLACEMENT PROGRAM CONSISTS OF A 1-YEAR COURSE COMBINING ANALYTIC GEOMETRY AND CALCULUS. PRESUPPOSED HERE ARE--A SEMESTER COURSE IN ANALYTIC GEOMETRY AND A THOROUGH KNOWLEDGE OF…
Miniature endoscopic optical coherence tomography for calculus detection.
Kao, Meng-Chun; Lin, Chun-Li; Kung, Che-Yen; Huang, Yi-Fung; Kuo, Wen-Chuan
2015-08-20
The effective treatment of periodontitis involves the detection and removal of subgingival dental calculus. However, subgingival calculus is more difficult to detect than supragingival calculus because it is firmly attached to root surfaces within periodontal pockets. To achieve a smooth root surface, clinicians often remove excessive amounts of root structure because of decreased visibility. In addition, enamel pearl, a rare type of ectopic enamel formation on the root surface, can easily be confused with dental calculus in the subgingival environment. In this study, we developed a fiber-probe swept-source optical coherence tomography (SSOCT) technique and combined it with the quantitative measurement of an optical parameter [standard deviation (SD) of the optical coherence tomography (OCT) intensity] to differentiate subgingival calculus from sound enamel, including enamel pearl. Two-dimensional circumferential images were constructed by rotating the miniprobe (0.9 mm diameter) while acquiring image lines, and the adjacent lines in each rotation were stacked to generate a three-dimensional volume. In OCT images, compared to sound enamel and enamel pearls, dental calculus showed significant differences (Pdental calculus.
On certain fractional calculus operators involving generalized Mittag-Leffler function
Dinesh Kumar
2016-01-01
The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators are the generalization of the Saigo fractional calculus operators. The established results provide ex...
Introduction to Integral Calculus Systematic Studies with Engineering Applications for Beginners
Rohde, Ulrich L; Poddar, Ajay K; Ghosh, A K
2011-01-01
An accessible introduction to the fundamentals of calculus needed to solve current problems in engineering and the physical sciences I ntegration is an important function of calculus, and Introduction to Integral Calculus combines fundamental concepts with scientific problems to develop intuition and skills for solving mathematical problems related to engineering and the physical sciences. The authors provide a solid introduction to integral calculus and feature applications of integration, solutions of differential equations, and evaluation methods. With logical organization coupled with cle
White noise calculus and Fock space
Obata, Nobuaki
1994-01-01
White Noise Calculus is a distribution theory on Gaussian space, proposed by T. Hida in 1975. This approach enables us to use pointwise defined creation and annihilation operators as well as the well-established theory of nuclear space.This self-contained monograph presents, for the first time, a systematic introduction to operator theory on fock space by means of white noise calculus. The goal is a comprehensive account of general expansion theory of Fock space operators and its applications. In particular,first order differential operators, Laplacians, rotation group, Fourier transform and their interrelations are discussed in detail w.r.t. harmonic analysis on Gaussian space. The mathematical formalism used here is based on distribution theory and functional analysis , prior knowledge of white noise calculus is not required.
Fractional calculus in bioengineering, part 3.
Magin, Richard L
2004-01-01
Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub
Stochastic calculus an introduction through theory and exercises
Baldi, Paolo
2017-01-01
This book provides a comprehensive introduction to the theory of stochastic calculus and some of its applications. It is the only textbook on the subject to include more than two hundred exercises with complete solutions. After explaining the basic elements of probability, the author introduces more advanced topics such as Brownian motion, martingales and Markov processes. The core of the book covers stochastic calculus, including stochastic differential equations, the relationship to partial differential equations, numerical methods and simulation, as well as applications of stochastic processes to finance. The final chapter provides detailed solutions to all exercises, in some cases presenting various solution techniques together with a discussion of advantages and drawbacks of the methods used. Stochastic Calculus will be particularly useful to advanced undergraduate and graduate students wishing to acquire a solid understanding of the subject through the theory and exercises. Including full mathematical ...
Cartan calculus on quantum Lie algebras
International Nuclear Information System (INIS)
Schupp, P.; Watts, P.; Zumino, B.
1993-01-01
A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum spaces we combine an exterior derivative, inner derivations, Lie derivatives, forms and functions au into one big algebra, the ''Cartan Calculus.''
Equations involving Malliavin calculus operators applications and numerical approximation
Levajković, Tijana
2017-01-01
This book provides a comprehensive and unified introduction to stochastic differential equations and related optimal control problems. The material is new and the presentation is reader-friendly. A major contribution of the book is the development of generalized Malliavin calculus in the framework of white noise analysis, based on chaos expansion representation of stochastic processes and its application for solving several classes of stochastic differential equations with singular data involving the main operators of Malliavin calculus. In addition, applications in optimal control and numerical approximations are discussed. The book is divided into four chapters. The first, entitled White Noise Analysis and Chaos Expansions, includes notation and provides the reader with the theoretical background needed to understand the subsequent chapters. In Chapter 2, Generalized Operators of Malliavin Calculus, the Malliavin derivative operator, the Skorokhod integral and the Ornstein-Uhlenbeck operator are introdu...
A primer on the calculus of variations and optimal control theory
Mesterton-Gibbons, Mike
2009-01-01
The calculus of variations is used to find functions that optimize quantities expressed in terms of integrals. Optimal control theory seeks to find functions that minimize cost integrals for systems described by differential equations. This book is an introduction to both the classical theory of the calculus of variations and the more modern developments of optimal control theory from the perspective of an applied mathematician. It focuses on understanding concepts and how to apply them. The range of potential applications is broad: the calculus of variations and optimal control theory have been widely used in numerous ways in biology, criminology, economics, engineering, finance, management science, and physics. Applications described in this book include cancer chemotherapy, navigational control, and renewable resource harvesting. The prerequisites for the book are modest: the standard calculus sequence, a first course on ordinary differential equations, and some facility with the use of mathematical softwa...
Multivariable dynamic calculus on time scales
Bohner, Martin
2016-01-01
This book offers the reader an overview of recent developments of multivariable dynamic calculus on time scales, taking readers beyond the traditional calculus texts. Covering topics from parameter-dependent integrals to partial differentiation on time scales, the book’s nine pedagogically oriented chapters provide a pathway to this active area of research that will appeal to students and researchers in mathematics and the physical sciences. The authors present a clear and well-organized treatment of the concept behind the mathematics and solution techniques, including many practical examples and exercises.
Quantum stochastic calculus associated with quadratic quantum noises
International Nuclear Information System (INIS)
Ji, Un Cig; Sinha, Kalyan B.
2016-01-01
We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus
Quantum stochastic calculus associated with quadratic quantum noises
Energy Technology Data Exchange (ETDEWEB)
Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr [Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju, Chungbuk 28644 (Korea, Republic of); Sinha, Kalyan B., E-mail: kbs-jaya@yahoo.co.in [Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore-64, India and Department of Mathematics, Indian Institute of Science, Bangalore-12 (India)
2016-02-15
We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus.
Renal vein thrombosis mimicking urinary calculus: a dilemma of diagnosis.
Wang, Yimin; Chen, Shanwen; Wang, Wei; Liu, Jianyong; Jin, Baiye
2015-07-02
Renal vein thrombosis (RVT) with flank pain, and hematuria, is often mistaken with renal colic originating from ureteric or renal calculus. Especially in young and otherwise healthy patients, clinicians are easily misled by clinical presentation and calcified RVT. A 38-year-old woman presented with flank pain and hematuria suggestive of renal calculus on ultrasound. She underwent extracorporeal shock wave lithotripsy that failed, leading to the recommendation that percutaneous lithotomy was necessary to remove the renal calculus. In preoperative view of the unusual shape of the calculus without hydronephrosis, noncontrast computed tomography was taken and demonstrated left ureteric calculus. However computed tomography angiography revealed, to our surprise, a calcified RVT that was initially thought to be a urinary calculus. This case shows that a calcified RVT might mimic a urinary calculus on conventional ultrasonography and ureteric calculus on noncontrast computed tomography. Subsequent computed tomography angiography disclosed that a calcified RVT caused the imaging findings, thus creating a potentially dangerous clinical pitfall. Hence, it is suggested that the possibility of a RVT needs to be considered in the differential diagnosis whenever one detects an uncommon shape for a urinary calculus.
On Flipping the Classroom in Large First Year Calculus Courses
Jungic, Veselin; Kaur, Harpreet; Mulholland, Jamie; Xin, Cindy
2015-01-01
Over the course of two years, 2012-2014, we have implemented a "flipping" the classroom approach in three of our large enrolment first year calculus courses: differential and integral calculus for scientists and engineers. In this article we describe the details of our particular approach and share with the reader some experiences of…
Modelling the Landing of a Plane in a Calculus Lab
Morante, Antonio; Vallejo, Jose A.
2012-01-01
We exhibit a simple model of a plane landing that involves only basic concepts of differential calculus, so it is suitable for a first-year calculus lab. We use the computer algebra system Maxima and the interactive geometry software GeoGebra to do the computations and graphics. (Contains 5 figures and 1 note.)
Zandy, Bernard V
2003-01-01
We take great notes-and make learning a snap When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core Calculus concepts-from functions, limits, and derivatives to differentials, integration, and definite integrals- and get the best possible grade. At CliffsNotes, we're dedicated to helping you do your best, no matter how challenging the subject. Our authors are veteran teachers and talented writers who know how to cut to the chase- and zero in on the essential information you need to succeed.
International Nuclear Information System (INIS)
He, Ji-Huan; Elagan, S.K.; Li, Z.B.
2012-01-01
The fractional complex transform is suggested to convert a fractional differential equation with Jumarie's modification of Riemann–Liouville derivative into its classical differential partner. Understanding the fractional complex transform and the chain rule for fractional calculus are elucidated geometrically. -- Highlights: ► The chain rule for fractional calculus is invalid, a counter example is given. ► The fractional complex transform is explained geometrically. ► Fractional equations can be converted into differential equations.
On flipping the classroom in large first year calculus courses
Jungić, Veselin; Kaur, Harpreet; Mulholland, Jamie; Xin, Cindy
2015-05-01
Over the course of two years, 2012--2014, we have implemented a 'flipping' the classroom approach in three of our large enrolment first year calculus courses: differential and integral calculus for scientists and engineers. In this article we describe the details of our particular approach and share with the reader some experiences of both instructors and students.
Fitzpatrick, Patrick M
2009-01-01
Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclide
Symbolic boundary calculus and feedback operators
DEFF Research Database (Denmark)
Pedersen, Michael
1991-01-01
The recent developments in microlocal analysis and pseudodifferential boundary calculus are well suited tools in the investigation of a large number of problems occurring in control theory for partial differential equations. We explain some of the basic ideas of a pseudodifferential model...
A MATLAB companion for multivariable calculus
Cooper, Jeffery
2001-01-01
Offering a concise collection of MatLab programs and exercises to accompany a third semester course in multivariable calculus, A MatLab Companion for Multivariable Calculus introduces simple numerical procedures such as numerical differentiation, numerical integration and Newton''s method in several variables, thereby allowing students to tackle realistic problems. The many examples show students how to use MatLab effectively and easily in many contexts. Numerous exercises in mathematics and applications areas are presented, graded from routine to more demanding projects requiring some programming. Matlab M-files are provided on the Harcourt/Academic Press web site at http://www.harcourt-ap.com/matlab.html.* Computer-oriented material that complements the essential topics in multivariable calculus* Main ideas presented with examples of computations and graphics displays using MATLAB * Numerous examples of short code in the text, which can be modified for use with the exercises* MATLAB files are used to implem...
Friedman, Menahem
2011-01-01
Another Calculus book? As long as students find calculus scary, the failure rate in mathematics is higher than in all other subjects, and as long as most people mistakenly believe that only geniuses can learn and understand mathematics, there will always be room for a new book of Calculus. We call it Calculus Light. This book is designed for a one semester course in ""light"" calculus -- mostly single variable, meant to be used by undergraduate students without a wide mathematical background and who do not major in mathematics but study subjects such as engineering, biology or management infor
Spinor calculus on 5-dimensional spacetimes
International Nuclear Information System (INIS)
Gomez-Lobo, Alfonso Garcia-Parrado; Martin-Garcia, Jose M
2010-01-01
We explain how Penrose's spinor calculus of 4-dimensional Lorentzian geometry is implemented in a 5-dimensional Lorentzian manifold. A number of issues, such as the essential spin algebra, the spin covariant derivative and the algebro-differential properties of the curvature spinors are discussed.
Friedman, Avner
2007-01-01
This rigorous two-part treatment advances from functions of one variable to those of several variables. Intended for students who have already completed a one-year course in elementary calculus, it defers the introduction of functions of several variables for as long as possible, and adds clarity and simplicity by avoiding a mixture of heuristic and rigorous arguments.The first part explores functions of one variable, including numbers and sequences, continuous functions, differentiable functions, integration, and sequences and series of functions. The second part examines functions of several
REA, Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Calculus III includes vector analysis, real valued functions, partial differentiation, multiple integrations, vector fields, and infinite series.
Larson, Ron
2014-01-01
The Larson CALCULUS program has a long history of innovation in the calculus market. It has been widely praised by a generation of students and professors for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.
Geron, B.; Geuvers, J.H.; de'Liguoro, U.; Saurin, A.
2013-01-01
Programs with control are usually modeled using lambda calculus extended with control operators. Instead of modifying lambda calculus, we consider a different model of computation. We introduce continuation calculus, or CC, a deterministic model of computation that is evaluated using only head
Impact of Calculus Reform in a Liberal Arts Calculus Course.
Brosnan, Patricia A.; Ralley, Thomas G.
This report describes the changes in a freshman-level calculus course that occurred as a consequence of adopting the Harvard Consortium Calculus text. The perspective is that of the lecturer. The course is intended as an introduction to calculus for liberal arts students, that is, students who will not be expected to use calculus as a mathematical…
Grossman, Stanley I
1981-01-01
Calculus, Second Edition discusses the techniques and theorems of calculus. This edition introduces the sine and cosine functions, distributes ?-? material over several chapters, and includes a detailed account of analytic geometry and vector analysis.This book also discusses the equation of a straight line, trigonometric limit, derivative of a power function, mean value theorem, and fundamental theorems of calculus. The exponential and logarithmic functions, inverse trigonometric functions, linear and quadratic denominators, and centroid of a plane region are likewise elaborated. Other topics
Roman, Steven
2005-01-01
Geared toward upper-level undergraduates and graduate students, this elementary introduction to classical umbral calculus requires only an acquaintance with the basic notions of algebra and a bit of applied mathematics (such as differential equations) to help put the theory in mathematical perspective. Subjects include Sheffer sequences and operators and their adjoints, with numerous examples of associated and other sequences. Related topics encompass the connection constants problem and duplication formulas, the Lagrange inversion formula, operational formulas, inverse relations, and binomial
Fluorescence-based calculus detection using a 405-nm excitation wavelength
Brede, O.; Schelle, F.; Krueger, S.; Oehme, B.; Dehn, C.; Frentzen, M.; Braun, A.
2011-03-01
The aim of this study was to assess the difference of fluorescence signals of cement and calculus using a 405 nm excitation wavelength. A total number of 20 freshly extracted teeth was used. The light source used for this study was a blue LED with a wavelength of 405nm. For each tooth the spectra of calculus and cementum were measured separately. Fluorescence light was collimated into an optical fibre and spectrally analyzed using an echelle spectrometer (aryelle 200, Lasertechnik Berlin, Germany) with an additionally bandpass (fgb 67, Edmund Industrial Optics, Karlsruhe, Germany). From these 40 measurements the median values were calculated over the whole spectrum, leading to two different median spectra, one for calculus and one for cementum. For further statistical analysis we defined 8 areas of interest (AOI) in wavelength regions, showing remarkable differences in signal strength. In 7 AOIs the intensity of the calculus spectrum differed statistically significant from the intensity of the cementum spectrum (p calculus and cement between 600nm and 700nm. Thus, we can conclude that fluorescence of calculus shows a significant difference to the fluorescence of cement. A differentiation over the intensity is possible as well as over the spectrum. Using a wavelength of 405nm, it is possible to distinguish between calculus and cement. These results could be used for further devices to develop a method for feedback controlled calculus removal.
Answers to selected problems in multivariable calculus with linear algebra and series
Trench, William F
1972-01-01
Answers to Selected Problems in Multivariable Calculus with Linear Algebra and Series contains the answers to selected problems in linear algebra, the calculus of several variables, and series. Topics covered range from vectors and vector spaces to linear matrices and analytic geometry, as well as differential calculus of real-valued functions. Theorems and definitions are included, most of which are followed by worked-out illustrative examples.The problems and corresponding solutions deal with linear equations and matrices, including determinants; vector spaces and linear transformations; eig
A Tutorial Review on Fractal Spacetime and Fractional Calculus
He, Ji-Huan
2014-11-01
This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.
The conceptual basis of mathematics in cardiology: (II). Calculus and differential equations.
Bates, Jason H T; Sobel, Burton E
2003-04-01
This is the second in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to
Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus
Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.
2015-05-01
We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.
Stoker, J J
2011-01-01
This classic work is now available in an unabridged paperback edition. Stoker makes this fertile branch of mathematics accessible to the nonspecialist by the use of three different notations: vector algebra and calculus, tensor calculus, and the notation devised by Cartan, which employs invariant differential forms as elements in an algebra due to Grassman, combined with an operation called exterior differentiation. Assumed are a passing acquaintance with linear algebra and the basic elements of analysis.
On varitional iteration method for fractional calculus
Directory of Open Access Journals (Sweden)
Wu Hai-Gen
2017-01-01
Full Text Available Modification of the Das’ variational iteration method for fractional differential equations is discussed, and its main shortcoming involved in the solution process is pointed out and overcome by using fractional power series. The suggested computational procedure is simple and reliable for fractional calculus.
Introduction to stochastic analysis and Malliavin calculus
Prato, Giuseppe
2014-01-01
This volume presents an introductory course on differential stochastic equations and Malliavin calculus. The material of the book has grown out of a series of courses delivered at the Scuola Normale Superiore di Pisa (and also at the Trento and Funchal Universities) and has been refined over several years of teaching experience in the subject. The lectures are addressed to a reader who is familiar with basic notions of measure theory and functional analysis. The first part is devoted to the Gaussian measure in a separable Hilbert space, the Malliavin derivative, the construction of the Brownian motion and Itô's formula. The second part deals with differential stochastic equations and their connection with parabolic problems. The third part provides an introduction to the Malliavin calculus. Several applications are given, notably the Feynman-Kac, Girsanov and Clark-Ocone formulae, the Krylov-Bogoliubov and Von Neumann theorems. In this third edition several small improvements are added and a new section devo...
The Initial Conditions of Fractional Calculus
International Nuclear Information System (INIS)
Trigeassou, J. C.; Maamri, N.
2011-01-01
During the past fifty years , Fractional Calculus has become an original and renowned mathematical tool for the modelling of diffusion Partial Differential Equations and the design of robust control algorithms. However, in spite of these celebrated results, some theoretical problems have not yet received a satisfying solution. The mastery of initial conditions, either for Fractional Differential Equations (FDEs) or for the Caputo and Riemann-Liouville fractional derivatives, remains an open research domain. The solution of this fundamental problem, also related to the long range memory property, is certainly the necessary prerequisite for a satisfying approach to modelling and control applications. The fractional integrator and its continuously frequency distributed differential model is a valuable tool for the simulation of fractional systems and the solution of initial condition problems. Indeed, the infinite dimensional state vector of fractional integrators allows the direct generalization to fractional calculus of the theoretical results of integer order systems. After a reminder of definitions and properties related to fractional derivatives and systems, this presentation is intended to show, based on the results of two recent publications [1,2], how the fractional integrator provides the solution of the initial condition problem of FDEs and of Caputo and Riemann-Liouville fractional derivatives. Numerical simulation examples illustrate and validate these new theoretical concepts.
An introduction to quantum groups and non-commutative differential calculus
International Nuclear Information System (INIS)
Azcarraga, J.A. de; Rodenas, F.
1995-01-01
An introduction to quantum groups and quantum spaces is presented, and the non-commutative calculus on them is discussed. The case of q-Minkowski space is presented as an illustrative example. A set of useful expressions and formulae are collected in an appendix. 45 refs
New trends in nanotechnology and fractional calculus applications
Baleanu, Dumitru; Machado, JA Tenreiro
2010-01-01
In recent years, fractional calculus has played a major role in various fields such as mechanics, electricity, biology and economics. This book presents the state-of-the-art in the study of fractional systems and the application of fractional differentiation.
R-Function Relationships for Application in the Fractional Calculus
Lorenzo, Carl F.; Hartley, Tom T.
2000-01-01
The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis. Relationships of the R-function to the common exponential function, e(t), and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, el, in terms of the R-function are developed. Also, some approximations for the R-function are developed.
Students' Difficulties with Vector Calculus in Electrodynamics
Bollen, Laurens; van Kampen, Paul; De Cock, Mieke
2015-01-01
Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven…
Quantum Stratonovich calculus and the quantum Wong-Zakai theorem
International Nuclear Information System (INIS)
Gough, John
2006-01-01
We extend the Ito(bar sign)-to-Stratonovich analysis or quantum stochastic differential equations, introduced by Gardiner and Collett for emission (creation), absorption (annihilation) processes, to include scattering (conservation) processes. Working within the framework of quantum stochastic calculus, we define Stratonovich calculus as an algebraic modification of the Ito(bar sign) one and give conditions for the existence of Stratonovich time-ordered exponentials. We show that conversion formula for the coefficients has a striking resemblance to Green's function formulas from standard perturbation theory. We show that the calculus conveniently describes the Markov limit of regular open quantum dynamical systems in much the same way as in the Wong-Zakai approximation theorems of classical stochastic analysis. We extend previous limit results to multiple-dimensions with a proof that makes use of diagrammatic conventions
The impact of taking a college pre-calculus course on students' college calculus performance
Sonnert, Gerhard; Sadler, Philip M.
2014-11-01
Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and four-year colleges continues to grow, and these courses are well-populated with students who already took pre-calculus in high school. We examine student performance in college calculus, using regression discontinuity to estimate the effects of taking college pre-calculus or not, in a national US sample of 5507 students at 132 institutions. We find that students who take college pre-calculus do not earn higher calculus grades.
Generalized calculus with applications to matter and forces
Campos, L M B C
2014-01-01
Combining mathematical theory, physical principles, and engineering problems, Generalized Calculus with Applications to Matter and Forces examines generalized functions, including the Heaviside unit jump and the Dirac unit impulse and its derivatives of all orders, in one and several dimensions. The text introduces the two main approaches to generalized functions: (1) as a nonuniform limit of a family of ordinary functions, and (2) as a functional over a set of test functions from which properties are inherited. The second approach is developed more extensively to encompass multidimensional generalized functions whose arguments are ordinary functions of several variables. As part of a series of books for engineers and scientists exploring advanced mathematics, Generalized Calculus with Applications to Matter and Forces presents generalized functions from an applied point of view, tackling problem classes such as: •Gauss and Stokes’ theorems in the differential geometry, tensor calculus, and theory of ...
Study on bioactive compounds of in vitro cultured Calculus Suis and natural Calculus Bovis.
Wan, Tien-Chun; Cheng, Fu-Yuan; Liu, Yu-Tse; Lin, Liang-Chuan; Sakata, Ryoichi
2009-12-01
The purpose of the study was to investigate bioactive compounds of in vitro cultured Calculus Suis and natural Calculus Bovis obtained as valuable by-products from animals used for meat production. The results showed that the components of natural Calculus Bovis were rich in bilirubin and biliverdin and had higher content of essential amino acids. The major amino acids of in vitro cultured Calculus Suis were identified as glycine, alanine, glutamic acid and aspartic acid, and those for natural Calculus Bovis were found to be glutamic acid, aspartic acid, proline, and arginine. The methionine and cysteine contents of precursors for glutathione in natural Calculus Bovis were significantly higher than those of in vitro cultured Calculus Suis. The mineral contents of zinc, iron and manganese of natural Calculus Bovis were significantly higher than those of in vitro cultured Calculus Suis. The major bile acids in both products were cholic acid and dehydrocholic acid, respectively. The chenodeoxycholic and ursodeoxycholic acid content of in vitro cultured Calculus Suis was significantly higher than that of natural Calculus Bovis.
Directory of Open Access Journals (Sweden)
Nilda Iglesias Domecq
2018-05-01
Full Text Available The current information society demands that civil engineers have an adequate command of the contents of Differential and Integral Calculus as a basis for their successful professional performance. However, there are many national and international reports of learning difficulties of these contents during the undergraduate training period. The objective of this article is to explain the interdisciplinary dynamic that underlies the teaching-learning process of Differential and Integral Calculus by Civil Engineering students. The research methods used were the content analysis of relevant theoretical sources and holistic-configurational modeling. The main result reveals the interdisciplinary logic established between the systematization and engineering functionality of the content of Differential and Integral Calculus and its projective-structural generalization, which constitutes an essential necessary condition for the development of competence for the application of the referred content to the resolution of projective-structural problems. Keywords: The current information society demands that civil engineers have an adequate command of the contents of Differential and Integral Calculus as a basis for their successful professional performance. However, there are many national and international reports of learning difficulties of these contents during the undergraduate training period. The objective of this article is to explain the interdisciplinary dynamic that underlies the teaching-learning process of Differential and Integral Calculus by Civil Engineering students. The research methods used were the content analysis of relevant theoretical sources and holistic-configurational modeling. The main result reveals the interdisciplinary logic established between the systematization and engineering functionality of the content of Differential and Integral Calculus and its projective-structural generalization, which constitutes an essential
Numerical convergence of discrete exterior calculus on arbitrary surface meshes
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi
2018-01-01
Discrete exterior calculus (DEC) is a structure-preserving numerical framework for partial differential equations solution, particularly suitable for simplicial meshes. A longstanding and widespread assumption has been that DEC requires special
van Doorn, Floris
2015-01-01
I formalize important theorems about classical propositional logic in the proof assistant Coq. The main theorems I prove are (1) the soundness and completeness of natural deduction calculus, (2) the equivalence between natural deduction calculus, Hilbert systems and sequent calculus and (3) cut elimination for sequent calculus.
Bergstra, J. A.; Ponse, A.; van der Zwaag, M. B.
2007-01-01
We introduce a calculus for tuplices, which are expressions that generalize matrices and vectors. Tuplices have an underlying data type for quantities that are taken from a zero-totalized field. We start with the core tuplix calculus CTC for entries and tests, which are combined using conjunctive composition. We define a standard model and prove that CTC is relatively complete with respect to it. The core calculus is extended with operators for choice, information hiding, scalar multiplicatio...
Ogawa, Shigeyoshi
2017-01-01
This book presents an elementary introduction to the theory of noncausal stochastic calculus that arises as a natural alternative to the standard theory of stochastic calculus founded in 1944 by Professor Kiyoshi Itô. As is generally known, Itô Calculus is essentially based on the "hypothesis of causality", asking random functions to be adapted to a natural filtration generated by Brownian motion or more generally by square integrable martingale. The intention in this book is to establish a stochastic calculus that is free from this "hypothesis of causality". To be more precise, a noncausal theory of stochastic calculus is developed in this book, based on the noncausal integral introduced by the author in 1979. After studying basic properties of the noncausal stochastic integral, various concrete problems of noncausal nature are considered, mostly concerning stochastic functional equations such as SDE, SIE, SPDE, and others, to show not only the necessity of such theory of noncausal stochastic calculus but ...
A transition calculus for Boolean functions. [logic circuit analysis
Tucker, J. H.; Bennett, A. W.
1974-01-01
A transition calculus is presented for analyzing the effect of input changes on the output of logic circuits. The method is closely related to the Boolean difference, but it is more powerful. Both differentiation and integration are considered.
A continuous time formulation of the Regge calculus
International Nuclear Information System (INIS)
Brewin, Leo
1988-01-01
A complete continuous time formulation of the Regge calculus is presented by developing the associated continuous time Regge action. It is shown that the time constraint is, by way of the Bianchi identities conserved by the evolution equations. This analysis leads to an explicit first integral for each of the evolution equations. The dynamical equations of the theory are therefore reduced to a set of first-order differential equations. In this formalism the time constraints reduce to a simple sum of the integration constants. This result is unique to the Regge calculus-there does not appear to be a complete set of first integrals available for the vacuum Einstein equations. (author)
Differential and Integral Calculus in careers of technical sciences. Specificities of their teaching
Directory of Open Access Journals (Sweden)
Iván Javier Villamar-Alvarado
2017-12-01
Full Text Available The Differential and Integral Calculus has great relevance for the professionals of the technical sciences since it provides them with a solid theoretical-conceptual body to process information, to use models that simulate real processes, to solve technical problems, to work in multidisciplinary projects and to communicate with precision. In spite of this relevance, there are numerous international dissatisfactions related to their learning by training engineers. The objective was to unveil the specificities of the teaching-learning process of this discipline that favor a successful appropriation of its content by the future engineers. The result was to unveil the didactic need to resolve the dialectical contradiction that manifests itself between the systematization of the engineering functionality of the aforementioned content and its contextualized interdisciplinary generalization. As a consequence, the need arises to create new didactic proposals that overcome this contradiction, as a way to perfect the teaching-learning process of this discipline in the engineering careers.
Directory of Open Access Journals (Sweden)
Bram Geron
2013-09-01
Full Text Available Programs with control are usually modeled using lambda calculus extended with control operators. Instead of modifying lambda calculus, we consider a different model of computation. We introduce continuation calculus, or CC, a deterministic model of computation that is evaluated using only head reduction, and argue that it is suitable for modeling programs with control. It is demonstrated how to define programs, specify them, and prove them correct. This is shown in detail by presenting in CC a list multiplication program that prematurely returns when it encounters a zero. The correctness proof includes termination of the program. In continuation calculus we can model both call-by-name and call-by-value. In addition, call-by-name functions can be applied to call-by-value results, and conversely.
Calculus & ordinary differential equations
Pearson, David
1995-01-01
Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.
Zegarelli, Mark
2012-01-01
An easy-to-understand primer on advanced calculus topics Calculus II is a prerequisite for many popular college majors, including pre-med, engineering, and physics. Calculus II For Dummies offers expert instruction, advice, and tips to help second semester calculus students get a handle on the subject and ace their exams. It covers intermediate calculus topics in plain English, featuring in-depth coverage of integration, including substitution, integration techniques and when to use them, approximate integration, and improper integrals. This hands-on guide also covers sequences and series, wit
Exterior calculus and two-dimensional supersymmetric models
International Nuclear Information System (INIS)
Sciuto, S.
1980-01-01
An important property of the calculus of differential forms on superspace is pointed out, and an economical way to treat the linear problem associated with certain supersymmetric two-dimensional models is discussed. A generalization of the super sine-Gordon model is proposed; its bosonic limit is a new model whose associate linear set has an SU(3) structure. (orig.)
Early Vector Calculus: A Path through Multivariable Calculus
Robertson, Robert L.
2013-01-01
The divergence theorem, Stokes' theorem, and Green's theorem appear near the end of calculus texts. These are important results, but many instructors struggle to reach them. We describe a pathway through a standard calculus text that allows instructors to emphasize these theorems. (Contains 2 figures.)
Trajectory Optimization for Differential Flat Systems
Kahina Louadj; Benjamas Panomruttanarug; Alexandre Carlos Brandao Ramos; Felix Mora-Camino
2016-01-01
International audience; The purpose of this communication is to investigate the applicability of Variational Calculus to the optimization of the operation of differentially flat systems. After introducingcharacteristic properties of differentially flat systems, the applicability of variational calculus to the optimization of flat output trajectories is displayed. Two illustrative examples are also presented.
Brownian motion and stochastic calculus
Karatzas, Ioannis
1998-01-01
This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large num...
Toward lattice fractional vector calculus
International Nuclear Information System (INIS)
Tarasov, Vasily E
2014-01-01
An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity. (papers)
Toward lattice fractional vector calculus
Tarasov, Vasily E.
2014-09-01
An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.
Spivak, Michael
2006-01-01
Spivak's celebrated textbook is widely held as one of the finest introductions to mathematical analysis. His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.
Calculus in physics classes at UFRGS: an exploratory study
Directory of Open Access Journals (Sweden)
Maria Cecilia Pereira Santarosa
2011-11-01
Full Text Available This study is part f a larger one whose general objective is to investigate and to develop a new strategy for teaching Differential and Integral Calculus I, specifically for physics majors, through a possible integration with the teaching of General and Experimental Physics I. With the specific objective of identifying physics problem-situations that may help in making sense of the mathematical concepts used in Calculus I, and languages and notations that might be used in the teaching of Calculus to favor physics learning, it was investigates, through an ethnographic study, the may mathematics is transposed to classes of General and Experimental Physics I, in classes of physics courses at the Federal University of Rio Grande do Sul (UFRGS. Some findings of this study confirmed those reported in the literature regarding the teaching and learning process in introductory college physics courses. These findings will subsidize the preparation of potentially meaningful instructional materials that will be used in a second stage of the research designed to investigate the learning of declarative and procedural knowledge in basic college physics under an approach that integrates problem-situation in physics and calculus mathematical concepts.
Calculus problems and solutions
Ginzburg, Abraham
2011-01-01
Ideal for self-instruction as well as for classroom use, this text helps students improve their understanding and problem-solving skills in analysis, analytic geometry, and higher algebra. More than 1,200 problems appear in the text, with concise explanations of the basic notions and theorems to be used in their solution. Many are followed by complete answers; solutions for the others appear at the end of the book. Topics include sequences, functions of a single variable, limit of a function, differential calculus for functions of a single variable, fundamental theorems and applications of dif
An introduction to differential geometry
Willmore, T J
2012-01-01
This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.
Fractional dynamic calculus and fractional dynamic equations on time scales
Georgiev, Svetlin G
2018-01-01
Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger’s basic theories on time scales and examines recent developments within the field of fractional calculus and fractional equations. Useful tools are provided for solving differential and integral equations as well as various problems involving special functions of mathematical physics and their extensions and generalizations in one and more variables. Much discussion is devoted to Riemann-Liouville fractional dynamic equations and Caputo fractional dynamic equations. Intended for use in the field and designed for students without an extensive mathematical background, this book is suitable for graduate courses and researchers looking for an introduction to fractional dynamic calculus and equations on time scales. .
Bergstra, J.A.; Ponse, A.; van der Zwaag, M.B.
2008-01-01
We introduce a calculus for tuplices, which are expressions that generalize matrices and vectors. Tuplices have an underlying data type for quantities that are taken from a zero-totalized field. We start with the core tuplix calculus CTC for entries and tests, which are combined using conjunctive
Lax, Peter D
2014-01-01
This new edition of Lax, Burstein, and Lax's Calculus with Applications and Computing offers meaningful explanations of the important theorems of single variable calculus. Written with students in mathematics, the physical sciences, and engineering in mind, and revised with their help, it shows that the themes of calculation, approximation, and modeling are central to mathematics and the main ideas of single variable calculus. This edition brings the innovation of the first edition to a new generation of students. New sections in this book use simple, elementary examples to show that when applying calculus concepts to approximations of functions, uniform convergence is more natural and easier to use than point-wise convergence. As in the original, this edition includes material that is essential for students in science and engineering, including an elementary introduction to complex numbers and complex-valued functions, applications of calculus to modeling vibrations and population dynamics, and an introduc...
Goodrich, Christopher
2015-01-01
This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...
Making Implicit Multivariable Calculus Representations Explicit: A Clinical Study
McGee, Daniel; Moore-Russo, Deborah; Martinez-Planell, Rafael
2015-01-01
Reviewing numerous textbooks, we found that in both differential and integral calculus textbooks the authors commonly assume that: (i) students can generalize associations between representations in two dimensions to associations between representations of the same mathematical concept in three dimensions on their own; and (ii) explicit…
Grossman, Stanley I
1986-01-01
Calculus of One Variable, Second Edition presents the essential topics in the study of the techniques and theorems of calculus.The book provides a comprehensive introduction to calculus. It contains examples, exercises, the history and development of calculus, and various applications. Some of the topics discussed in the text include the concept of limits, one-variable theory, the derivatives of all six trigonometric functions, exponential and logarithmic functions, and infinite series.This textbook is intended for use by college students.
Time scales: from Nabla calculus to Delta calculus and vice versa via duality
Caputo, M. Cristina
2009-01-01
In this note we show how one can obtain results from the nabla calculus from results on the delta calculus and vice versa via a duality argument. We provide applications of the main results to the calculus of variations on time scales.
The calculus lifesaver all the tools you need to excel at calculus
Banner, Adrian
2009-01-01
For many students, calculus can be the most mystifying and frustrating course they will ever take. The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it. All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of
The history of the calculus and its conceptual development
Boyer, Carl B
1959-01-01
Fluent description of the development of both the integral and differential calculus. Early beginnings in antiquity, medieval contributions, and a century of anticipation lead up to a consideration of Newton and Leibniz, the period of indecison that followed them, and the final rigorous formulation that we know today.
Fractional Calculus in Hydrologic Modeling: A Numerical Perspective
Energy Technology Data Exchange (ETDEWEB)
David A. Benson; Mark M. Meerschaert; Jordan Revielle
2012-01-01
Fractional derivatives can be viewed either as a handy extension of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Levy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Levy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus.
Vickers, Trevor
1992-01-01
On the Refinement Calculus gives one view of the development of the refinement calculus and its attempt to bring together - among other things - Z specifications and Dijkstra's programming language. It is an excellent source of reference material for all those seeking the background and mathematical underpinnings of the refinement calculus.
The Impact of Taking a College Pre-Calculus Course on Students' College Calculus Performance
Sonnert, Gerhard; Sadler, Philip M.
2014-01-01
Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and…
Applying π-Calculus to Practice
DEFF Research Database (Denmark)
Abendroth, Jorg
2003-01-01
The π-Calculus has been developed to reason about behavioural equivalence. Different notations of equivalence are defined in terms of process interactions, as well as the context of processes. There are various extensions of the π-Calculus, such as the SPI calculus, which has primitives...... modles are instantiated correctly. In this paper we will utilize the to π-Calculus reason about access control policies and mechanism. An equivalence of different policy implementations, as well as access control mechanism will be shown. Finally some experiences regarding the use of π-Calculus...
Differential participation in formative assessment and achievement in introductory calculus
Dibbs, Rebecca-Anne
2015-01-01
International audience; Prior formative assessment research has shown positive achievement gains when classes using formative assessment are compared to classes that do not. However, little is known about what, if any, benefits of formative assessment occur within a class. The purpose of this study was to investigate the achievement of the students in introductory calculus using formative assessment at the two different participation levels observed in class. Although there was no significant...
A generalized nonlocal vector calculus
Alali, Bacim; Liu, Kuo; Gunzburger, Max
2015-10-01
A nonlocal vector calculus was introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A formulation is developed that provides a more general setting for the nonlocal vector calculus that is independent of particular nonlocal models. It is shown that general nonlocal calculus operators are integral operators with specific integral kernels. General nonlocal calculus properties are developed, including nonlocal integration by parts formula and Green's identities. The nonlocal vector calculus introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) is shown to be recoverable from the general formulation as a special example. This special nonlocal vector calculus is used to reformulate the peridynamics equation of motion in terms of the nonlocal gradient operator and its adjoint. A new example of nonlocal vector calculus operators is introduced, which shows the potential use of the general formulation for general nonlocal models.
Elsgolc, L E; Stark, M
1961-01-01
Calculus of Variations aims to provide an understanding of the basic notions and standard methods of the calculus of variations, including the direct methods of solution of the variational problems. The wide variety of applications of variational methods to different fields of mechanics and technology has made it essential for engineers to learn the fundamentals of the calculus of variations. The book begins with a discussion of the method of variation in problems with fixed boundaries. Subsequent chapters cover variational problems with movable boundaries and some other problems; sufficiency
Smooth vectors and Weyl-Pedersen calculus for representations of nilpotent Lie groups
Beltita, Ingrid; Beltita, Daniel
2009-01-01
We present some recent results on smooth vectors for unitary irreducible representations of nilpotent Lie groups. Applications to the Weyl-Pedersen calculus of pseudo-differential operators with symbols on the coadjoint orbits are also discussed.
Extreme value problems without calculus: a good link with geometry and elementary maths
Ganci, Salvatore
2016-11-01
Some classical examples of problem solving, where an extreme value condition is required, are here considered and/or revisited. The search for non-calculus solutions appears pedagogically useful and intriguing as shown through a rich literature. A teacher, who teaches both maths and physics, (as happens in Italian High schools) can find in these kinds of problems a mind stimulating exercise compared with the standard solution obtained by the differential calculus. A good link between the geometric and analytical explanations is so established.
Modern calculus and analytic geometry
Silverman, Richard A
2012-01-01
A self-contained text for an introductory course, this volume places strong emphasis on physical applications. Key elements of differential equations and linear algebra are introduced early and are consistently referenced, all theorems are proved using elementary methods, and numerous worked-out examples appear throughout. The highly readable text approaches calculus from the student's viewpoint and points out potential stumbling blocks before they develop. A collection of more than 1,600 problems ranges from exercise material to exploration of new points of theory - many of the answers are fo
Polynomial Calculus: Rethinking the Role of Calculus in High Schools
Grant, Melva R.; Crombie, William; Enderson, Mary; Cobb, Nell
2016-01-01
Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in…
Calculus of Elementary Functions, Part IV. Teacher's Commentary. Preliminary Edition.
Herriot, Sarah T.; And Others
This teacher's guide is designed for use with the SMSG textbook "Calculus of Elementary Functions." It contains solutions to exercises found in Chapter 9, Integration Theory and Technique; Chapter 10, Simple Differential Equations; Appendix 5, Area and Integral; Appendix 6; Appendix 7, Continuity Theory; and Appendix 8, More About…
Advanced calculus a transition to analysis
Dence, Thomas P
2010-01-01
Designed for a one-semester advanced calculus course, Advanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis -- providing a mathematically sophisticated introduction to functional analytical concepts. The text is interesting to read and includes many illustrative worked-out examples and instructive exercises, and precise historical notes to aid in further exploration of calculus. Ancillary list: * Companion website, Ebook- http://www.elsevierdirect.com/product.jsp?isbn=9780123749550 * Student Solutions Manual- To come * Instructor
Tensors, differential forms, and variational principles
Lovelock, David
1989-01-01
Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques, with large number of problems, from routine manipulative exercises to technically difficult assignments.
Presymplectic current and the inverse problem of the calculus of variations
Khavkine, I.
2013-01-01
The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when horizontally closed on solutions, allows us to construct a
Maxima and Minima Without Calculus.
Birnbaum, Ian
1982-01-01
Approaches to extrema that do not require calculus are presented to help free maxima/minima problems from the confines of calculus. Many students falsely suppose that these types of problems can only be dealt with through calculus, since few, if any, noncalculus examples are usually presented. (MP)
The quantum probability calculus
International Nuclear Information System (INIS)
Jauch, J.M.
1976-01-01
The Wigner anomaly (1932) for the joint distribution of noncompatible observables is an indication that the classical probability calculus is not applicable for quantum probabilities. It should, therefore, be replaced by another, more general calculus, which is specifically adapted to quantal systems. In this article this calculus is exhibited and its mathematical axioms and the definitions of the basic concepts such as probability field, random variable, and expectation values are given. (B.R.H)
Schoenly, Joshua E.; Seka, Wolf; Romanos, Georgios; Rechmann, Peter
A desired outcome of scaling and root planing is the complete removal of calculus and infected root tissue and preservation of healthy cementum for rapid healing of periodontal tissues. Conventional periodontal treatments for calculus removal, such as hand instrument scaling and ultrasonic scaling, often deeply scrape the surface of the underlying hard tissue and may leave behind a smear layer. Pulsed lasers emitting at violet wavelengths (specifically, 380 to 400 nm) are a potential alternative treatment since they can selectively ablate dental calculus without ablating pristine hard tissue (i.e., enamel, cementum, and dentin). In this study, light and scanning electron microscopy are used to compare and contrast the efficacy of in vitro calculus removal for several conventional periodontal treatments (hand instruments, ultrasonic scaler, and Er:YAG laser) to calculus removal with a frequency-doubled Ti:sapphire (λ = 400 nm). After calculus removal, enamel and cementum surfaces are investigated for calculus debris and damage to the underlying hard tissue surface. Compared to the smear layer, grooves, and unintentional hard tissue removal typically found using these conventional treatments, calculus removal using the 400-nm laser is complete and selective without any removal of pristine dental hard tissue. Based on these results, selective ablation from the 400-nm laser appears to produce a root surface that would be more suitable for successful healing of periodontal tissues.
[Fluorescence control of dental calculus removal].
Bakhmutov, D N; Gonchukov, S A; Lonkina, T V; Sukhinina, A V
2012-01-01
The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In the frames of this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise detection of tooth-calculus interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing (as ultrasonic or laser devices).
A differential calculus for random matrices with applications to (max,+)-linear stochastic systems
Heidergott, B.F.
2001-01-01
We introducet he concept of weak differentiabilityf or randomm atricesa nd therebyo btain closedform analytical expressions for derivatives of functions of random matrices. More specifically, we develop a calculus of weak differentiationf or randomm atricest hat resembles the standardc alculus of
Cleaveland, Rance; Luettgen, Gerald; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
This paper presents the Logical Process Calculus (LPC), a formalism that supports heterogeneous system specifications containing both operational and declarative subspecifications. Syntactically, LPC extends Milner's Calculus of Communicating Systems with operators from the alternation-free linear-time mu-calculus (LT(mu)). Semantically, LPC is equipped with a behavioral preorder that generalizes Hennessy's and DeNicola's must-testing preorder as well as LT(mu's) satisfaction relation, while being compositional for all LPC operators. From a technical point of view, the new calculus is distinguished by the inclusion of: (1) both minimal and maximal fixed-point operators and (2) an unimple-mentability predicate on process terms, which tags inconsistent specifications. The utility of LPC is demonstrated by means of an example highlighting the benefits of heterogeneous system specification.
Arán Filippetti, Vanessa; Richaud, María Cristina
2017-10-01
Though the relationship between executive functions (EFs) and mathematical skills has been well documented, little is known about how both EFs and IQ differentially support diverse math domains in primary students. Inconsistency of results may be due to the statistical techniques employed, specifically, if the analysis is conducted with observed variables, i.e., regression analysis, or at the latent level, i.e., structural equation modeling (SEM). The current study explores the contribution of both EFs and IQ in mathematics through an SEM approach. A total of 118 8- to 12-year-olds were administered measures of EFs, crystallized (Gc) and fluid (Gf) intelligence, and math abilities (i.e., number production, mental calculus and arithmetical problem-solving). Confirmatory factor analysis (CFA) offered support for the three-factor solution of EFs: (1) working memory (WM), (2) shifting, and (3) inhibition. Regarding the relationship among EFs, IQ and math abilities, the results of the SEM analysis showed that (i) WM and age predict number production and mental calculus, and (ii) shifting and sex predict arithmetical problem-solving. In all of the SEM models, EFs partially or totally mediated the relationship between IQ, age and math achievement. These results suggest that EFs differentially supports math abilities in primary-school children and is a more significant predictor of math achievement than IQ level.
A Calculus for Context-Awareness
DEFF Research Database (Denmark)
Zimmer, Pascal
2005-01-01
In order to answer the challenge of pervasive computing, we propose a new process calculus, whose aim is to describe dynamic systems composed of agents able to move and react differently depending on their location. This Context-Aware Calculus features a hierarchical structure similar to mobile...... ambients, and a generic multi-agent synchronization mechanism, inspired from the join-calculus. After general ideas and introduction, we review the full calculus' syntax and semantics, as well as some motivating examples, study its expressiveness, and show how the notion of computation itself can be made...
Gibson, Megan
2013-01-01
Due in part to the growing popularity of the Advanced Placement program, an increasingly large percentage of entering college students are enrolling in calculus courses having already taken calculus in high school. Many students do not score high enough on the AP calculus examination to place out of Calculus I, and many do not take the…
Sutherland, Melissa
2006-01-01
In this paper we discuss manipulatives and hands-on investigations for Calculus involving volume, arc length, and surface area to motivate and develop formulae which can then be verified using techniques of integration. Pre-service teachers in calculus courses using these activities experience a classroom in which active learning is encouraged and…
The Vectorial $\\lambda$-Calculus
Arrighi, Pablo; Díaz-Caro, Alejandro; Valiron, Benoît
2013-01-01
We describe a type system for the linear-algebraic $\\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\\lambda$-calculus: it is able to statically describe the linear combinations of terms that will be obtained when reducing the programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. We prove that the resulting typed $\\lambda$-calculus is strongly normalising and fea...
Sauerheber, Richard D.
2012-01-01
Methods of teaching the Calculus are presented in honour of Sir Isaac Newton, by discussing an extension of his original proofs and discoveries. The methods, requested by Newton to be used that reflect the historical sequence of the discovered Fundamental Theorems, allow first-time students to grasp quickly the basics of the Calculus from its…
Anisotropic fractal media by vector calculus in non-integer dimensional space
Energy Technology Data Exchange (ETDEWEB)
Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)
2014-08-15
A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.
Anisotropic fractal media by vector calculus in non-integer dimensional space
Tarasov, Vasily E.
2014-08-01
A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.
Anisotropic fractal media by vector calculus in non-integer dimensional space
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2014-01-01
A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media
Towards Analysis-Driven Scientific Software Architecture: The Case for Abstract Data Type Calculus
Directory of Open Access Journals (Sweden)
Damian W.I. Rouson
2008-01-01
Full Text Available This article approaches scientific software architecture from three analytical paths. Each path examines discrete time advancement of multiphysics phenomena governed by coupled differential equations. The new object-oriented Fortran 2003 constructs provide a formal syntax for an abstract data type (ADT calculus. The first analysis uses traditional object-oriented software design metrics to demonstrate the high cohesion and low coupling associated with the calculus. A second analysis from the viewpoint of computational complexity theory demonstrates that a more representative bug search strategy than that considered by Rouson et al. (ACM Trans. Math. Soft. 34(1 (2008 reduces the number of lines searched in a code with λ total lines from O(λ2 to O(λ log2 λ , which in turn becomes nearly independent of the overall code size in the context of ADT calculus. The third analysis derives from information theory an argument that ADT calculus simplifies developer communications in part by minimizing the growth in interface information content as developers add new physics to a multiphysics package.
Dental Calculus Arrest of Dental Caries.
Keyes, Paul H; Rams, Thomas E
An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human teeth for the presence and location of dental caries, dental calculus, and dental plaque biofilms. A total of 1,200 teeth were preserved in 10% buffered formal saline, and viewed while moist by a single experienced examiner using a research stereomicroscope at 15-25× magnification. Representative teeth were sectioned and photographed, and their dental plaque biofilms subjected to gram-stain examination with light microscopy at 100× magnification. Dental calculus was observed on 1,140 (95%) of the extracted human teeth, and no dental carious lesions were found underlying dental calculus-covered surfaces on 1,139 of these teeth. However, dental calculus arrest of dental caries was found on one (0.54%) of 187 evaluated teeth that presented with unrestored proximal enamel caries. On the distal surface of a maxillary premolar tooth, dental calculus mineralization filled the outer surface cavitation of an incipient dental caries lesion. The dental calculus-covered carious lesion extended only slightly into enamel, and exhibited a brown pigmentation characteristic of inactive or arrested dental caries. In contrast, the tooth's mesial surface, without a superficial layer of dental calculus, had a large carious lesion going through enamel and deep into dentin. These observations further document the potential protective effects of dental calculus mineralization against dental caries.
Dental Calculus Arrest of Dental Caries
Keyes, Paul H.; Rams, Thomas E.
2016-01-01
Background An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human teeth for the presence and location of dental caries, dental calculus, and dental plaque biofilms. Materials and methods A total of 1,200 teeth were preserved in 10% buffered formal saline, and viewed while moist by a single experienced examiner using a research stereomicroscope at 15-25× magnification. Representative teeth were sectioned and photographed, and their dental plaque biofilms subjected to gram-stain examination with light microscopy at 100× magnification. Results Dental calculus was observed on 1,140 (95%) of the extracted human teeth, and no dental carious lesions were found underlying dental calculus-covered surfaces on 1,139 of these teeth. However, dental calculus arrest of dental caries was found on one (0.54%) of 187 evaluated teeth that presented with unrestored proximal enamel caries. On the distal surface of a maxillary premolar tooth, dental calculus mineralization filled the outer surface cavitation of an incipient dental caries lesion. The dental calculus-covered carious lesion extended only slightly into enamel, and exhibited a brown pigmentation characteristic of inactive or arrested dental caries. In contrast, the tooth's mesial surface, without a superficial layer of dental calculus, had a large carious lesion going through enamel and deep into dentin. Conclusions These observations further document the potential protective effects of dental calculus mineralization against dental caries. PMID:27446993
Fundamentals of tensor calculus for engineers with a primer on smooth manifolds
Mühlich, Uwe
2017-01-01
This book presents the fundamentals of modern tensor calculus for students in engineering and applied physics, emphasizing those aspects that are crucial for applying tensor calculus safely in Euclidian space and for grasping the very essence of the smooth manifold concept. After introducing the subject, it provides a brief exposition on point set topology to familiarize readers with the subject, especially with those topics required in later chapters. It then describes the finite dimensional real vector space and its dual, focusing on the usefulness of the latter for encoding duality concepts in physics. Moreover, it introduces tensors as objects that encode linear mappings and discusses affine and Euclidean spaces. Tensor analysis is explored first in Euclidean space, starting from a generalization of the concept of differentiability and proceeding towards concepts such as directional derivative, covariant derivative and integration based on differential forms. The final chapter addresses the role of smooth...
Pre-calculus workbook for dummies
Kuang, Yang
2011-01-01
Get the confidence and math skills you need to get started with calculus Are you preparing for calculus? This hands-on workbook helps you master basic pre-calculus concepts and practice the types of problems you'll encounter in the course. You'll get hundreds of valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every problem. You'll also memorize the most frequently used equations, see how to avoid common mistakes, understand tricky trig proofs, and much more. Pre-Calculus Workbook For Dummies is the perfect tool for anyone who wa
Initialized Fractional Calculus
Lorenzo, Carl F.; Hartley, Tom T.
2000-01-01
This paper demonstrates the need for a nonconstant initialization for the fractional calculus and establishes a basic definition set for the initialized fractional differintegral. This definition set allows the formalization of an initialized fractional calculus. Two basis calculi are considered; the Riemann-Liouville and the Grunwald fractional calculi. Two forms of initialization, terminal and side are developed.
Stochastic calculus in physics
International Nuclear Information System (INIS)
Fox, R.F.
1987-01-01
The relationship of Ito-Stratonovich stochastic calculus to studies of weakly colored noise is explained. A functional calculus approach is used to obtain an effective Fokker-Planck equation for the weakly colored noise regime. In a smooth limit, this representation produces the Stratonovich version of the Ito-Stratonovich calculus for white noise. It also provides an approach to steady state behavior for strongly colored noise. Numerical simulation algorithms are explored, and a novel suggestion is made for efficient and accurate simulation of white noise equations
Lei, Qian
2017-01-01
This book offers a comprehensive and systematic review of the latest research findings in the area of intuitionistic fuzzy calculus. After introducing the intuitionistic fuzzy numbers’ operational laws and their geometrical and algebraic properties, the book defines the concept of intuitionistic fuzzy functions and presents the research on the derivative, differential, indefinite integral and definite integral of intuitionistic fuzzy functions. It also discusses some of the methods that have been successfully used to deal with continuous intuitionistic fuzzy information or data, which are different from the previous aggregation operators focusing on discrete information or data. Mainly intended for engineers and researchers in the fields of fuzzy mathematics, operations research, information science and management science, this book is also a valuable textbook for postgraduate and advanced undergraduate students alike.
The stochastic quality calculus
DEFF Research Database (Denmark)
Zeng, Kebin; Nielson, Flemming; Nielson, Hanne Riis
2014-01-01
We introduce the Stochastic Quality Calculus in order to model and reason about distributed processes that rely on each other in order to achieve their overall behaviour. The calculus supports broadcast communication in a truly concurrent setting. Generally distributed delays are associated...... with the outputs and at the same time the inputs impose constraints on the waiting times. Consequently, the expected inputs may not be available when needed and therefore the calculus allows to express the absence of data.The communication delays are expressed by general distributions and the resulting semantics...
Nickerson, HK; Steenrod, NE
2011-01-01
""This book is a radical departure from all previous concepts of advanced calculus,"" declared the Bulletin of the American Mathematics Society, ""and the nature of this departure merits serious study of the book by everyone interested in undergraduate education in mathematics."" Classroom-tested in a Princeton University honors course, it offers students a unified introduction to advanced calculus. Starting with an abstract treatment of vector spaces and linear transforms, the authors introduce a single basic derivative in an invariant form. All other derivatives - gradient, divergent, curl,
The application of Regge calculus to quantum gravity and quantum field theory in a curved background
International Nuclear Information System (INIS)
Warner, N.P.
1982-01-01
The application of Regge calculus to quantum gravity and quantum field theory in a curved background is discussed. A discrete form of exterior differential calculus is developed, and this is used to obtain Laplacians for p-forms on the Regge manifold. To assess the accuracy of these approximations, the eigenvalues of the discrete Laplacians were calculated for the regular tesselations of S 2 and S 3 . The results indicate that the methods obtained in this paper may be used in curved space-times with an accuracy comparing with that obtained in lattice gauge theories on a flat background. It also becomes evident that Regge calculus provides particularly suitable lattices for Monte-Carlo techniques. (author)
Differential Calculus on h-Deformed Spaces
Herlemont, Basile; Ogievetsky, Oleg
2017-10-01
We construct the rings of generalized differential operators on the h-deformed vector space of gl-type. In contrast to the q-deformed vector space, where the ring of differential operators is unique up to an isomorphism, the general ring of h-deformed differential operators {Diff}_{h},σ(n) is labeled by a rational function σ in n variables, satisfying an over-determined system of finite-difference equations. We obtain the general solution of the system and describe some properties of the rings {Diff}_{h},σ(n).
Cui, Helen; Thomas, Johanna; Kumar, Sunil
2013-04-10
We present a case of a renal calculus treated solely with antibiotics which has not been previously reported in the literature. A man with a 17 mm lower pole renal calculus and concurrent Escherichia coli urine infection was being worked up to undergo percutaneous nephrolithotomy. However, after a course of preoperative antibiotics the stone was no longer seen on retrograde pyelography or CT imaging.
Reasoning about objects using process calculus techniques
DEFF Research Database (Denmark)
Kleist, Josva
This thesis investigates the applicability of techniques known from the world of process calculi to reason about properties of object-oriented programs. The investigation is performed upon a small object-oriented language - The Sigma-calculus of Abadi and Cardelli. The investigation is twofold: We......-calculus turns out to be insufficient. Based on our experiences, we present a translation of a typed imperative Sigma-calculus, which looks promising. We are able to provide simple proofs of the equivalence of different Sigma-calculus objects using this translation. We use a labelled transition system adapted...... to the Sigma-calculus to investigate the use of process calculi techniques directly on the Sigma-calculus. The results obtained are of a fairly theoretical nature. We investigate the connection between the operational and denotaional semantics for a typed functional Sigma-calculus. The result is that Abadi...
Baronti, Marco; van der Putten, Robertus; Venturi, Irene
2016-01-01
This book, intended as a practical working guide for students in Engineering, Mathematics, Physics, or any other field where rigorous calculus is needed, includes 450 exercises. Each chapter starts with a summary of the main definitions and results, which is followed by a selection of solved exercises accompanied by brief, illustrative comments. A selection of problems with indicated solutions rounds out each chapter. A final chapter explores problems that are not designed with a single issue in mind but instead call for the combination of a variety of techniques, rounding out the book’s coverage. Though the book’s primary focus is on functions of one real variable, basic ordinary differential equations (separation of variables, linear first order and constant coefficients ODEs) are also discussed. The material is taken from actual written tests that have been delivered at the Engineering School of the University of Genoa. Literally thousands of students have worked on these problems, ensuring their real-...
Kuang, Yang
2012-01-01
The fun and easy way to learn pre-calculus Getting ready for calculus but still feel a bit confused? Have no fear. Pre-Calculus For Dummies is an un-intimidating, hands-on guide that walks you through all the essential topics, from absolute value and quadratic equations to logarithms and exponential functions to trig identities and matrix operations. With this guide's help you'll quickly and painlessly get a handle on all of the concepts - not just the number crunching - and understand how to perform all pre-calc tasks, from graphing to tackling proofs. You'll also get a new appreciation for
Factors Associated with Success in College Calculus II
Rosasco, Margaret E.
2013-01-01
Students are entering college having earned credit for college Calculus 1 based on their scores on the College Board's Advanced Placement (AP) Calculus AB exam. Despite being granted credit for college Calculus 1, it is unclear whether these students are adequately prepared for college Calculus 2. College calculus classes are often taught from a…
Leveraging Prior Calculus Study with Embedded Review
Nikolov, Margaret C.; Withers, Wm. Douglas
2016-01-01
We propose a new course structure to address the needs of college students with previous calculus study but no course validations as an alternative to repeating the first year of calculus. Students are introduced directly to topics from Calculus III unpreceded by a formal review of topics from Calculus I or II, but with additional syllabus time…
Generalized Gaussian Error Calculus
Grabe, Michael
2010-01-01
For the first time in 200 years Generalized Gaussian Error Calculus addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. Since experimentalists realized that measurements in general are burdened by unknown systematic errors, the classical, widespread used evaluation procedures scrutinizing the consequences of random errors alone turned out to be obsolete. As a matter of course, the error calculus to-be, treating random and unknown systematic errors side by side, should ensure the consistency and traceability of physical units, physical constants and physical quantities at large. The generalized Gaussian error calculus considers unknown systematic errors to spawn biased estimators. Beyond, random errors are asked to conform to the idea of what the author calls well-defined measuring conditions. The approach features the properties of a building kit: any overall uncertainty turns out to be the sum of a contribution due to random errors, to be taken from a confidence inter...
On the Presentation of Pre-Calculus and Calculus Topics: An Alternate View
Davydov, Aleksandr; Sturm-Beiss, Rachel
2008-01-01
The orders of presentation of pre-calculus and calculus topics, and the notation used, deserve careful study as they affect clarity and ultimately students' level of understanding. We introduce an alternate approach to some of the topics included in this sequence. The suggested alternative is based on years of teaching in colleges within and…
What Do Croatian Pre-Service Teachers Remember from Their Calculus Course?
Jukic, Ljerka; Brückler, Franka Miriam
2014-01-01
This paper reports a study on retention of core concepts in differential and integral calculus by examining the knowledge of two pre-service mathematics students. The study is conducted using a mixed method approach and the obtained data were analyzed using theory of three worlds of mathematics. The results showed that having good understanding of…
Malinowska , Agnieszka B.; Torres , Delfim
2014-01-01
International audience; Introduces readers to the treatment of the calculus of variations with q-differences and Hahn difference operators Provides the reader with the first extended treatment of quantum variational calculus Shows how the techniques described can be applied to economic models as well as other mathematical systems This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of it...
Laparoscopic Cholecystectomy in Chronic Calculus Cholecystitis
Directory of Open Access Journals (Sweden)
Prakash Sapkota
2013-12-01
Full Text Available Introduction: Laparoscopic cholecystectomy has clearly become the choice over open cholecystectomy in the treatment of hepatobiliary disease since its introduction by Mouret in 1987. This study evaluates a series of patients with chronic calculus cholecystitis who were treated with laparoscopic and open cholecystectomy and assesses the outcomes of both techniques. Objective: To evaluate the efficacy of laparoscopic vs open cholecystectomy in chronic calculus cholecystitis and establish the out-comes of this treatment modality at Lumbini Medical College and Teaching Hospital. Methods: This was a retrospective analysis over a one-year period (January 1, 2012 to December 31, 2012, per-formed by single surgeon at Lumbini Medical College and Teaching Hospital located midwest of Nepal. 166 patients underwent surgical treatment for chronic calculus cholecystitis. Patients included were only chronic calculus cholecystitis proven histopathologocally and the rest were excluded. Data was collected which included patients demographics, medical history, presentation, complications, conversion rates from laparoscopic. cholecystectomy to open cholecystectomy, operative and postoperative time. Results: Patients treated with laparoscopic cholecystectomy for chronic calculus cholecystitis had shorter operating times and length of stay compared to patients treated with open cholecystectomy for chronic calculus cholecystitis. Conversion rates were 3.54% in chronic calculus cholecystitis during the study period. Complications were also lower in patients who underwent laparoscopic cholecystectomy versus open cholecystectomy for cholelithiasis. Conclusions: Laparoscopic cholecystectomy appears to be a reliable, safe, and cost-effective treatment modality for chronic calculus cholecystitis.
On the notion of Jacobi fields in constrained calculus of variations
Directory of Open Access Journals (Sweden)
Massa Enrico
2016-12-01
Full Text Available In variational calculus, the minimality of a given functional under arbitrary deformations with fixed end-points is established through an analysis of the so called second variation. In this paper, the argument is examined in the context of constrained variational calculus, assuming piecewise differentiable extremals, commonly referred to as extremaloids. The approach relies on the existence of a fully covariant representation of the second variation of the action functional, based on a family of local gauge transformations of the original Lagrangian and on a set of scalar attributes of the extremaloid, called the corners' strengths [16]. In dis- cussing the positivity of the second variation, a relevant role is played by the Jacobi fields, defined as infinitesimal generators of 1-parameter groups of diffeomorphisms preserving the extremaloids. Along a piecewise differentiable extremal, these fields are generally discontinuous across the corners. A thorough analysis of this point is presented. An alternative characterization of the Jacobi fields as solutions of a suitable accessory variational problem is established.
A κ-symmetry calculus for superparticles
International Nuclear Information System (INIS)
Gauntlett, J.P.
1991-01-01
We develop a κ-symmetry calculus for the d=2 and d=3, N=2 massive superparticles, which enables us to construct higher order κ-invariant actions. The method relies on a reformulation of these models as supersymmetric sigma models that are invariant under local worldline superconformal transformations. We show that the κ-symmetry is embedded in the superconformal symmetry so that a calculus for the κ-symmetry is equivalent to a tensor calculus for the latter. We develop such a calculus without the introduction of a wordline supergravity multiplet. (orig.)
An AP Calculus Classroom Amusement Park
Ferguson, Sarah
2016-01-01
Throughout the school year, AP Calculus teachers strive to teach course content comprehensively and swiftly in an effort to finish all required material before the AP Calculus exam. As early May approaches and the AP Calculus test looms, students and teachers nervously complete lessons, assignments, and assessments to ensure student preparation.…
Geometrical enhancement of the electric field: Application of fractional calculus in nanoplasmonics
Baskin, E.; Iomin, A.
2011-12-01
We developed an analytical approach, for a wave propagation in metal-dielectric nanostructures in the quasi-static limit. This consideration establishes a link between fractional geometry of the nanostructure and fractional integro-differentiation. The method is based on fractional calculus and permits to obtain analytical expressions for the electric-field enhancement.
The untyped stack calculus and Bohm's theorem
Directory of Open Access Journals (Sweden)
Alberto Carraro
2013-03-01
Full Text Available The stack calculus is a functional language in which is in a Curry-Howard correspondence with classical logic. It enjoys confluence but, as well as Parigot's lambda-mu, does not admit the Bohm Theorem, typical of the lambda-calculus. We present a simple extension of stack calculus which is for the stack calculus what Saurin's Lambda-mu is for lambda-mu.
DEFF Research Database (Denmark)
Ody, Heinrich; Fränzle, Martin; Hansen, Michael Reichhardt
2016-01-01
To formally reason about the temporal quality of systems discounting was introduced to CTL and LTL. However, these logic are discrete and they cannot express duration properties. In this work we introduce discounting for a variant of Duration Calculus. We prove decidability of model checking...... for a useful fragment of discounted Duration Calculus formulas on timed automata under mild assumptions. Further, we provide an extensive example to show the usefulness of the fragment....
A Formal Calculus for Categories
DEFF Research Database (Denmark)
Cáccamo, Mario José
This dissertation studies the logic underlying category theory. In particular we present a formal calculus for reasoning about universal properties. The aim is to systematise judgements about functoriality and naturality central to categorical reasoning. The calculus is based on a language which...... extends the typed lambda calculus with new binders to represent universal constructions. The types of the languages are interpreted as locally small categories and the expressions represent functors. The logic supports a syntactic treatment of universality and duality. Contravariance requires a definition...... of universality generous enough to deal with functors of mixed variance. Ends generalise limits to cover these kinds of functors and moreover provide the basis for a very convenient algebraic manipulation of expressions. The equational theory of the lambda calculus is extended with new rules for the definitions...
Synthesizing controllers from duration calculus
DEFF Research Database (Denmark)
Fränzle, Martin
1996-01-01
Duration Calculus is a logic for reasoning about requirements for real-time systems at a high level of abstraction from operational detail, which qualifies it as an interesting starting point for embedded controller design. Such a design activity is generally thought to aim at a control device...... the physical behaviours of which satisfy the requirements formula, i.e. the refinement relation between requirements and implementations is taken to be trajectory inclusion. Due to the abstractness of the vocabulary of Duration Calculus, trajectory inclusion between control requirements and controller designs...... for embedded controller design and exploit this fact for developing an automatic procedure for controller synthesis from specifications formalized in Duration Calculus. As far as we know, this is the first positive result concerning feasibility of automatic synthesis from dense-time Duration Calculus....
Mohamed, Mamdouh S.
2016-02-11
A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi
2016-05-01
A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.
Samtaney, Ravi; Mohamed, Mamdouh; Hirani, Anil
2015-11-01
We present examples of numerical solutions of incompressible flow on 2D curved domains. The Navier-Stokes equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. A conservative discretization of Navier-Stokes equations on simplicial meshes is developed based on discrete exterior calculus (DEC). The discretization is then carried out by substituting the corresponding discrete operators based on the DEC framework. By construction, the method is conservative in that both the discrete divergence and circulation are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step. Numerical examples include Taylor vortices on a sphere, Stuart vortices on a sphere, and flow past a cylinder on domains with varying curvature. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1401-01.
Pseudo-differential operators on manifolds with singularities
Schulze, B-W
1991-01-01
The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics. The applications and concrete models from engineering and physics are often classical but the modern structure calculus was only possible since the achievements of pseudo-differential operators. This led to deep connections with index theory, topology and mathematical physics. The present book is devoted to elliptic partial differential equations in the framework of pseudo-differential operators. The first chapter contains the Mellin pseudo-differential calculus on R+ and the functional analysis of weighted Sobolev spaces with discrete and continuous asymptotics. Chapter 2 is devoted to the analogous theory on manifolds with conical singularities, Chapter 3 to manifolds with edges. Employed are pseudo-differential operators along edges with cone-operator-valued symbols.
Directory of Open Access Journals (Sweden)
Alberto Carraro
2013-03-01
Full Text Available We introduce a functional calculus with simple syntax and operational semantics in which the calculi introduced so far in the Curry-Howard correspondence for Classical Logic can be faithfully encoded. Our calculus enjoys confluence without any restriction. Its type system enforces strong normalization of expressions and it is a sound and complete system for full implicational Classical Logic. We give a very simple denotational semantics which allows easy calculations of the interpretation of expressions.
Improving student learning in calculus through applications
Young, C. Y.; Georgiopoulos, M.; Hagen, S. C.; Geiger, C. L.; Dagley-Falls, M. A.; Islas, A. L.; Ramsey, P. J.; Lancey, P. M.; Straney, R. A.; Forde, D. S.; Bradbury, E. E.
2011-07-01
Nationally only 40% of the incoming freshmen Science, Technology, Engineering and Mathematics (STEM) majors are successful in earning a STEM degree. The University of Central Florida (UCF) EXCEL programme is a National Science Foundation funded STEM Talent Expansion Programme whose goal is to increase the number of UCF STEM graduates. One of the key requirements for STEM majors is a strong foundation in Calculus. To improve student learning in calculus, the EXCEL programme developed two special courses at the freshman level called Applications of Calculus I (Apps I) and Applications of Calculus II (Apps II). Apps I and II are one-credit classes that are co-requisites for Calculus I and II. These classes are teams taught by science and engineering professors whose goal is to demonstrate to students where the calculus topics they are learning appear in upper level science and engineering classes as well as how faculty use calculus in their STEM research programmes. This article outlines the process used in producing the educational materials for the Apps I and II courses, and it also discusses the assessment results pertaining to this specific EXCEL activity. Pre- and post-tests conducted with experimental and control groups indicate significant improvement in student learning in Calculus II as a direct result of the application courses.
Malinowska, Agnieszka B
2014-01-01
This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of its results is that they are able to deal with nondifferentiable (even discontinuous) functions, which are important in applications. Possible applications in economics are discussed. Economists model time as continuous or discrete. Although individual economic decisions are generally made at discrete time intervals, they may well be less than perfectly synchronized in ways discrete models postulate. On the other hand, the usual assumption that economic activity takes place continuously, is nothing else than a convenient abstraction that in many applications is far from reality. The Hahn quantum calculus helps to bridge the gap between the two families of models: continuous and discrete. Quantum Variational Calculus is self-contained and unified in presentation. It provides an opportunity for an introduction to the quantum calculus of variations fo...
Hill, Gregory
2013-01-01
Earn College Credit with REA's Test Prep for CLEP* Calculus Everything you need to pass the exam and get the college credit you deserve.Our test prep for CLEP* Calculus and the free online tools that come with it, will allow you to create a personalized CLEP* study plan that can be customized to fit you: your schedule, your learning style, and your current level of knowledge.Here's how it works:Diagnostic exam at the REA Study Center focuses your studyOur online diagnostic exam pinpoints your strengths and shows you exactly where you need to focus your study. Armed with this information, you
Null-strut calculus. II. Dynamics
International Nuclear Information System (INIS)
Kheyfets, A.; LaFave, N.J.; Miller, W.A.
1990-01-01
In this paper, we continue from the preceding paper to develop a fully functional Regge calculus geometrodynamic algorithm from the null-strut-calculus construction. The developments discussed include (a) the identification of the Regge calculus analogue of the constraint and evolution equations on the null-strut lattice, (b) a description of the Minkowski solid geometry for the simplicial blocks of the null-strut lattice, (c) a description of the evolution algorithm for the geometrodynamic scheme and an analysis of its consistency, and (d) a presentation of the dynamical degrees of freedom for a simplicial hypersurface and the description of an initial-value prescription. To demonstrate qualitatively this new approach to geometrodynamics, we present the most simple application of null-strut calculus that we know of---the Friedmann cosmology using the three-boundary of a 600-cell simplicial polytope to model the simplicial hypersurface
A Higher-Order Calculus for Categories
DEFF Research Database (Denmark)
Cáccamo, Mario José; Winskel, Glynn
2001-01-01
A calculus for a fragment of category theory is presented. The types in the language denote categories and the expressions functors. The judgements of the calculus systematise categorical arguments such as: an expression is functorial in its free variables; two expressions are naturally isomorphic...... in their free variables. There are special binders for limits and more general ends. The rules for limits and ends support an algebraic manipulation of universal constructions as opposed to a more traditional diagrammatic approach. Duality within the calculus and applications in proving continuity are discussed...... with examples. The calculus gives a basis for mechanising a theory of categories in a generic theorem prover like Isabelle....
Giant calculus: review and report of a case.
Woodmansey, Karl; Severine, Anthony; Lembariti, Bakari S
2013-01-01
Dental calculus is a common oral finding. The term giant calculus is used to describe unusually large deposits of dental calculus. Several extreme cases have been reported in the dental literature. The specific etiology of these cases remains uncertain. This paper reviews previously reported cases, and presents another extreme example of giant calculus.
Treiman, Jay S
2014-01-01
Calculus with Vectors grew out of a strong need for a beginning calculus textbook for undergraduates who intend to pursue careers in STEM. fields. The approach introduces vector-valued functions from the start, emphasizing the connections between one-variable and multi-variable calculus. The text includes early vectors and early transcendentals and includes a rigorous but informal approach to vectors. Examples and focused applications are well presented along with an abundance of motivating exercises. All three-dimensional graphs have rotatable versions included as extra source materials and may be freely downloaded and manipulated with Maple Player; a free Maple Player App is available for the iPad on iTunes. The approaches taken to topics such as the derivation of the derivatives of sine and cosine, the approach to limits, and the use of "tables" of integration have been modified from the standards seen in other textbooks in order to maximize the ease with which students may comprehend the material. Additio...
Dental calculus detection using the VistaCam.
Shakibaie, Fardad; Walsh, Laurence J
2016-12-01
The VistaCam® intra-oral camera system (Dürr Dental, Bietigheim-Bissingen, Germany) is a fluorescence system using light emitting diodes that produce a 405-nm violet light. This wavelength has potential application for detection of dental calculus based on red emissions from porphyrin molecules. This study assessed the digital scores obtained for both supragingival and subgingival calculus on 60 extracted teeth and compared these with lesions of dental caries. It has also examined the effect of saliva and blood on the fluorescence readings for dental calculus. VistaCam fluorescence scores for both supragingival (1.7-3.3) and subgingival calculus (1.3-2.4) were higher than those for sound root surfaces (0.9-1.1) and dental caries (0.9-2.2) ( p calculus samples were not affected by the presence of saliva or blood. These results suggest that the use of violet light fluorescence could be a possible adjunct to clinical examination for deposits of dental calculus.
Differential form representation of stochastic electromagnetic fields
Haider, Michael; Russer, Johannes A.
2017-09-01
In this work, we revisit the theory of stochastic electromagnetic fields using exterior differential forms. We present a short overview as well as a brief introduction to the application of differential forms in electromagnetic theory. Within the framework of exterior calculus we derive equations for the second order moments, describing stochastic electromagnetic fields. Since the resulting objects are continuous quantities in space, a discretization scheme based on the Method of Moments (MoM) is introduced for numerical treatment. The MoM is applied in such a way, that the notation of exterior calculus is maintained while we still arrive at the same set of algebraic equations as obtained for the case of formulating the theory using the traditional notation of vector calculus. We conclude with an analytic calculation of the radiated electric field of two Hertzian dipole, excited by uncorrelated random currents.
On Some Syntactic Properties of the Modalized Heyting Calculus
Muravitsky, Alexei
2016-01-01
We show that the modalized Heyting calculus introduced by Leo Esakia admits a normal axiomatization. Then, we prove that the inference rules $\\square\\alpha/\\alpha$ and $\\square\\alpha\\rightarrow\\alpha/\\alpha$ are admissible in this calculus. Finally, we show that this calculus and intuitionistic propositional calculus are assertorically equipollent, which leads to a variant of limited separation property for the modalized Heyting calculus.
Differential forms and the geometry of general relativity
Dray, Tevian
2015-01-01
Differential Forms and the Geometry of General Relativity provides readers with a coherent path to understanding relativity. Requiring little more than calculus and some linear algebra, it helps readers learn just enough differential geometry to grasp the basics of general relativity.The book contains two intertwined but distinct halves. Designed for advanced undergraduate or beginning graduate students in mathematics or physics, most of the text requires little more than familiarity with calculus and linear algebra. The first half presents an introduction to general relativity that describes
The calculus a genetic approach
Toeplitz, Otto
2007-01-01
When first published posthumously in 1963, this book presented a radically different approach to the teaching of calculus. In sharp contrast to the methods of his time, Otto Toeplitz did not teach calculus as a static system of techniques and facts to be memorized. Instead, he drew on his knowledge of the history of mathematics and presented calculus as an organic evolution of ideas beginning with the discoveries of Greek scholars, such as Archimedes, Pythagoras, and Euclid, and developing through the centuries in the work of Kepler, Galileo, Fermat, Newton, and Leibniz. Through this unique a
Pre-calculus workbook for dummies
Gilman, Michelle Rose; Neal, Karina
2009-01-01
Get the confidence and the math skills you need to get started with calculus! Are you preparing for calculus? This easy-to-follow, hands-on workbook helps you master basic pre-calculus concepts and practice the types of problems you'll encounter in your cour sework. You get valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every problem. You'll also memorize the most frequently used equations, see how to avoid common mistakes, understand tricky trig proofs, and much more. 100s of Problems! Detailed, fully worked-out solutions to problem
Mathematics for physics with calculus
Das, Biman
2005-01-01
Designed for students who plan to take or who are presently taking calculus-based physics courses. This book will develop necessary mathematical skills and help students gain the competence to use precalculus, calculus, vector algebra, vector calculus, and the statistical analysis of experimental data. Students taking intermediate physics, engineering, and other science courses will also find the book useful-and will be able to use the book as a mathematical resource for these intermediate level courses. The book emphasizes primarily the use of mathematical techniques and mathematical concepts in Physics and does not go into their rigorous developments.
On exterior variational calculus
International Nuclear Information System (INIS)
Aldrovandi, R.; Kraenkel, R.A.
1987-01-01
Exterior variational calculus is introduced through examples in field theory. It provides a very simple technique to decide on the existence of Lagrangians for given equations of motions and, in the case, to find them. Only local aspects are discussed but the analogy to exterior calculus on finite dimensional manifolds is complete, strongly suggesting its suitability to the study of topological aspects. (Author) [pt
ASSESSING STUDENTS' UNDERSTANDING OF PRE-CALCULUS CONCEPTS
Dr. Jyoti Sharma
2017-01-01
Calculus is one of the most momentous achievements of the human intellect (Boyer, 1949). It has given a new direction to the work of mathematicians and scientists. Calculus has exponentially expanded the scope and use of mathematics in other fields. Learning calculus is important to pursue career in applied mathematics.
Dental Calculus Arrest of Dental Caries
Keyes, Paul H.; Rams, Thomas E.
2016-01-01
Background An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human t...
Jet-calculus approach including coherence effects
International Nuclear Information System (INIS)
Jones, L.M.; Migneron, R.; Narayanan, K.S.S.
1987-01-01
We show how integrodifferential equations typical of jet calculus can be combined with an averaging procedure to obtain jet-calculus-based results including the Mueller interference graphs. Results in longitudinal-momentum fraction x for physical quantities are higher at intermediate x and lower at large x than with the conventional ''incoherent'' jet calculus. These results resemble those of Marchesini and Webber, who used a Monte Carlo approach based on the same dynamics
A Case Study of Student and Instructor Reactions to a Calculus E-Book
Bode, Martina; Khorami, Mehdi; Visscher, Daniel
2014-01-01
This article details the results of testing an e-book in two differential calculus classes. Although we, as math instructors, were drawn to the components of the e-book that promote conceptual understanding--such as the interactive figures--the students reported liking the assessment support most. We found that students were initially excited…
Presymplectic current and the inverse problem of the calculus of variations
Khavkine, Igor
2013-11-01
The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when horizontally closed on solutions, allows us to construct a variational formulation for a subsystem of the given PDE. No constraints on the differential order or number of dependent or independent variables are assumed. The proof follows a recent observation of Bridges, Hydon, and Lawson [Math. Proc. Cambridge Philos. Soc. 148(01), 159-178 (2010)] and generalizes an older result of Henneaux [Ann. Phys. 140(1), 45-64 (1982)] from ordinary differential equations (ODEs) to PDEs. Uniqueness of the variational formulation is also discussed.
Model-checking dense-time Duration Calculus
DEFF Research Database (Denmark)
Fränzle, Martin
2004-01-01
Since the seminal work of Zhou Chaochen, M. R. Hansen, and P. Sestoft on decidability of dense-time Duration Calculus [Zhou, Hansen, Sestoft, 1993] it is well-known that decidable fragments of Duration Calculus can only be obtained through withdrawal of much of the interesting vocabulary...... of this logic. While this was formerly taken as an indication that key-press verification of implementations with respect to elaborate Duration Calculus specifications were also impossible, we show that the model property is well decidable for realistic designs which feature natural constraints...... suitably sparser model classes we obtain model-checking procedures for rich subsets of Duration Calculus. Together with undecidability results also obtained, this sheds light upon the exact borderline between decidability and undecidability of Duration Calculi and related logics....
Proof Nets for Lambek Calculus
Roorda, Dirk
1992-01-01
The proof nets of linear logic are adapted to the non-commutative Lambek calculus. A different criterion for soundness of proof nets is given, which gives rise to new algorithms for proof search. The order sensitiveness of the Lambek calculus is reflected by the planarity condition on proof nets;
Numerical Simulation of Antennae by Discrete Exterior Calculus
International Nuclear Information System (INIS)
Xie Zheng; Ye Zheng; Ma Yujie
2009-01-01
Numerical simulation of antennae is a topic in computational electromagnetism, which is concerned with the numerical study of Maxwell equations. By discrete exterior calculus and the lattice gauge theory with coefficient R, we obtain the Bianchi identity on prism lattice. By defining an inner product of discrete differential forms, we derive the source equation and continuity equation. Those equations compose the discrete Maxwell equations in vacuum case on discrete manifold, which are implemented on Java development platform to simulate the Gaussian pulse radiation on antennaes. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
On the fractional calculus of Besicovitch function
International Nuclear Information System (INIS)
Liang Yongshun
2009-01-01
Relationship between fractional calculus and fractal functions has been explored. Based on prior investigations dealing with certain fractal functions, fractal dimensions including Hausdorff dimension, Box dimension, K-dimension and Packing dimension is shown to be a linear function of order of fractional calculus. Both Riemann-Liouville fractional calculus and Weyl-Marchaud fractional derivative of Besicovitch function have been discussed.
Generalized Functions for the Fractional Calculus
Lorenzo, Carl F.; Hartley, Tom T.
1999-01-01
Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q)[at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q)[a,t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles.
Weak differentiability of product measures
Heidergott, B.F.; Leahu, H.
2010-01-01
In this paper, we study cost functions over a finite collection of random variables. For these types of models, a calculus of differentiation is developed that allows us to obtain a closed-form expression for derivatives where "differentiation" has to be understood in the weak sense. The technique
Scherger, Nicole
2012-01-01
Of the most universal applications in integral calculus are those involved with finding volumes of solids of revolution. These profound problems are typically taught with traditional approaches of the disk and shell methods, after which most calculus curriculums will additionally cover arc length and surfaces of revolution. Even in these visibly…
Differential form representation of stochastic electromagnetic fields
Directory of Open Access Journals (Sweden)
M. Haider
2017-09-01
Full Text Available In this work, we revisit the theory of stochastic electromagnetic fields using exterior differential forms. We present a short overview as well as a brief introduction to the application of differential forms in electromagnetic theory. Within the framework of exterior calculus we derive equations for the second order moments, describing stochastic electromagnetic fields. Since the resulting objects are continuous quantities in space, a discretization scheme based on the Method of Moments (MoM is introduced for numerical treatment. The MoM is applied in such a way, that the notation of exterior calculus is maintained while we still arrive at the same set of algebraic equations as obtained for the case of formulating the theory using the traditional notation of vector calculus. We conclude with an analytic calculation of the radiated electric field of two Hertzian dipole, excited by uncorrelated random currents.
Area Regge calculus and continuum limit
International Nuclear Information System (INIS)
Khatsymovsky, V.M.
2002-01-01
Encountered in the literature generalisations of general relativity to independent area variables are considered, the discrete (generalised Regge calculus) and continuum ones. The generalised Regge calculus can be either with purely area variables or, as we suggest, with area tensor-connection variables. Just for the latter, in particular, we prove that in analogy with corresponding statement in ordinary Regge calculus (by Feinberg, Friedberg, Lee and Ren), passing to the (appropriately defined) continuum limit yields the generalised continuum area tensor-connection general relativity
Enriching an effect calculus with linear types
DEFF Research Database (Denmark)
Egger, Jeff; Møgelberg, Rasmus Ejlers; Simpson, Alex
2009-01-01
We define an ``enriched effect calculus'' by conservatively extending a type theory for computational effects with primitives from linear logic. By doing so, we obtain a generalisation of linear type theory, intended as a formalism for expressing linear aspects of effects. As a worked example, we...... formulate linearly-used continuations in the enriched effect calculus. These are captured by a fundamental translation of the enriched effect calculus into itself, which extends existing call-by-value and call-by-name linearly-used CPS translations. We show that our translation is involutive. Full...... completeness results for the various linearly-used CPS translations follow. Our main results, the conservativity of enriching the effect calculus with linear primitives, and the involution property of the fundamental translation, are proved using a category-theoretic semantics for the enriched effect calculus...
Detection, removal and prevention of calculus: Literature Review
Directory of Open Access Journals (Sweden)
Deepa G. Kamath
2014-01-01
Full Text Available Dental plaque is considered to be a major etiological factor in the development of periodontal disease. Accordingly, the elimination of supra- and sub-gingival plaque and calculus is the cornerstone of periodontal therapy. Dental calculus is mineralized plaque; because it is porous, it can absorb various toxic products that can damage the periodontal tissues. Hence, calculus should be accurately detected and thoroughly removed for adequate periodontal therapy. Many techniques have been used to identify and remove calculus deposits present on the root surface. The purpose of this review was to compile the various methods and their advantages for the detection and removal of calculus.
The use of concept maps as an indicator of significant learning in Calculus
Directory of Open Access Journals (Sweden)
Naíma Soltau Ferrão
2014-03-01
Full Text Available This paper contains reflections and results of a research that aimed to apply and analyze the use of concept maps in Higher Education as an indicator of significant learning concerning derivative as mathematical object with students that finished Differential and Integral Calculus. This is a qualitative approach, situated in the area of mathematics education, based on Ausubel's Theory of Meaningful Learning and on technique of Novak's Concept Mapping. As data acquisition instruments, use of classroom observations, questionnaire, brainstorming and digital conceptual mapping, made by an undergraduate physics course. To analyze we defined four aspects to be observed in the maps constructed by students: (i validity of propositions formed with concepts, (ii hierarchization, (iii cross-links between the propositions, and (vi the presence of applications. The identification of these elements, taken as reference to analyze the maps, allowed the collection of information about how each student has structured and correlated the set of concepts learned on the derivative of a function along their course. Based on the results, we have identified in the digital conceptual maps effective tools to evaluate the students in terms of meaningful learning about specific contents of Differential and Integral Calculus by the hierarchy of concepts, progressive differentiation and integrative reconciliation as defined in the Theory of Meaningful Learning.
General quantum variational calculus
Directory of Open Access Journals (Sweden)
Artur M. C. Brito da Cruz
2018-02-01
Full Text Available We develop a new variational calculus based in the general quantum difference operator recently introduced by Hamza et al. In particular, we obtain optimality conditions for generalized variational problems where the Lagrangian may depend on the endpoints conditions and a real parameter, for the basic and isoperimetric problems, with and without fixed boundary conditions. Our results provide a generalization to previous results obtained for the $q$- and Hahn-calculus.
Directory of Open Access Journals (Sweden)
Matteo Mio
2013-08-01
Full Text Available The paper explores properties of Łukasiewicz mu-calculus, a version of the quantitative/probabilistic modal mu-calculus containing both weak and strong conjunctions and disjunctions from Łukasiewicz (fuzzy logic. We show that this logic encodes the well-known probabilistic temporal logic PCTL. And we give a model-checking algorithm for computing the rational denotational value of a formula at any state in a finite rational probabilistic nondeterministic transition system.
Vector 33: A reduce program for vector algebra and calculus in orthogonal curvilinear coordinates
Harper, David
1989-06-01
This paper describes a package with enables REDUCE 3.3 to perform algebra and calculus operations upon vectors. Basic algebraic operations between vectors and between scalars and vectors are provided, including scalar (dot) product and vector (cross) product. The vector differential operators curl, divergence, gradient and Laplacian are also defined, and are valid in any orthogonal curvilinear coordinate system. The package is written in RLISP to allow algebra and calculus to be performed using notation identical to that for operations. Scalars and vectors can be mixed quite freely in the same expression. The package will be of interest to mathematicians, engineers and scientists who need to perform vector calculations in orthogonal curvilinear coordinates.
Geometric calculus: a new computational tool for Riemannian geometry
International Nuclear Information System (INIS)
Moussiaux, A.; Tombal, P.
1988-01-01
We compare geometric calculus applied to Riemannian geometry with Cartan's exterior calculus method. The correspondence between the two methods is clearly established. The results obtained by a package written in an algebraic language and doing general manipulations on multivectors are compared. We see that the geometric calculus is as powerful as exterior calculus
DEFF Research Database (Denmark)
De Fraine, Bruno; Ernst, Erik; Südholt, Mario
2012-01-01
Aspect-oriented programming (AOP) has produced interesting language designs, but also ad hoc semantics that needs clarification. We contribute to this clarification with a calculus that models essential AOP, both simpler and more general than existing formalizations. In AOP, advice may intercept......-oriented code. Two well-known pointcut categories, call and execution, are commonly considered similar.We formally expose their differences, and resolve the associated soundness problem. Our calculus includes type ranges, an intuitive and concise alternative to explicit type variables that allows advice...... to be polymorphic over intercepted methods. We use calculus parameters to cover type safety for a wide design space of other features. Type soundness is verified in Coq....
Jumarie, Guy
2013-04-01
By using fractional differences, one recently proposed an alternative to the formulation of fractional differential calculus, of which the main characteristics is a new fractional Taylor series and its companion Rolle's formula which apply to non-differentiable functions. The key is that now we have at hand a differential increment of fractional order which can be manipulated exactly like in the standard Leibniz differential calculus. Briefly the fractional derivative is the quotient of fractional increments. It has been proposed that this calculus can be used to construct a differential geometry on manifold of fractional order. The present paper, on the one hand, refines the framework, and on the other hand, contributes some new results related to arc length of fractional curves, area on fractional differentiable manifold, covariant fractal derivative, Riemann-Christoffel tensor of fractional order, fractional differential equations of fractional geodesic, strip modeling of fractal space time and its relation with Lorentz transformation. The relation with Nottale's fractal space-time theory then appears in quite a natural way.
Recursive sequences in first-year calculus
Krainer, Thomas
2016-02-01
This article provides ready-to-use supplementary material on recursive sequences for a second-semester calculus class. It equips first-year calculus students with a basic methodical procedure based on which they can conduct a rigorous convergence or divergence analysis of many simple recursive sequences on their own without the need to invoke inductive arguments as is typically required in calculus textbooks. The sequences that are accessible to this kind of analysis are predominantly (eventually) monotonic, but also certain recursive sequences that alternate around their limit point as they converge can be considered.
Presymplectic current and the inverse problem of the calculus of variations
Energy Technology Data Exchange (ETDEWEB)
Khavkine, Igor, E-mail: i.khavkine@uu.nl [Institute for Theoretical Physics, Utrecht, Leuvenlaan 4, NL-3584 CE Utrecht (Netherlands)
2013-11-15
The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when horizontally closed on solutions, allows us to construct a variational formulation for a subsystem of the given PDE. No constraints on the differential order or number of dependent or independent variables are assumed. The proof follows a recent observation of Bridges, Hydon, and Lawson [Math. Proc. Cambridge Philos. Soc. 148(01), 159–178 (2010)] and generalizes an older result of Henneaux [Ann. Phys. 140(1), 45–64 (1982)] from ordinary differential equations (ODEs) to PDEs. Uniqueness of the variational formulation is also discussed.
Introduction to stochastic calculus
Karandikar, Rajeeva L
2018-01-01
This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly address continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier–Pellumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- and beginning graduate-level stud...
Success in Introductory Calculus: The Role of High School and Pre-calculus Preparation
Ayebo, Abraham; Ukkelberg, Sarah; Assuah, Charles
2017-01-01
Calculus at the college level has significantpotential to serve as a pump for increasing the number of students majoring inSTEM fields. It is a foundation course for all STEM majors and, if mastered well,should provide students with a positive and successful first-year experienceand gateway into more advanced courses. Studies have shown that a high percentage of studentsfailing college calculus has caused a shortage of individuals entering fieldsthat are heavily dependent on mathematics. Many...
Dental calculus image based on optical coherence tomography
Hsieh, Yao-Sheng; Ho, Yi-Ching; Lee, Shyh-Yuan; Chuang, Ching-Cheng; Wang, Chun-Yang; Sun, Chia-Wei
2011-03-01
In this study, the dental calculus was characterized and imaged by means of swept-source optical coherence tomography (SSOCT). The refractive indices of enamel, dentin, cementum and calculus were measured as 1.625+/-0.024, 1.534+/-0.029, 1.570+/-0.021 and 1.896+/-0.085, respectively. The dental calculus lead strong scattering property and thus the region can be identified under enamel with SSOCT imaging. An extracted human tooth with calculus was covered by gingiva tissue as in vitro sample for SSOCT imaging.
Calculus detection technologies: where do we stand now?
Archana, V
2014-01-01
Epidemiological studies have implicated dental calculus as an ideal substrate for subgingival microbial colonization. Therefore, the main objective of periodontal therapy is to eliminate the microbial biofilm along with the calculus deposits from the root surface by root surface debridement. Over the past years, a large number of clinical and laboratory studies have been conducted to evaluate the efficacy of calculus removal by various methods. None of these conventional methods or devices was effective in completely eliminating all the calculus from the diseased root surfaces. In this context, a number of newer technologies have been developed to identify and selectively remove the dental calculus. Regarding this fact, the present article highlights a critical review of these devices based on published clinical and experimental data.
Calculus detection technologies: where do we stand now?
Archana, V
2014-01-01
Epidemiological studies have implicated dental calculus as an ideal substrate for subgingival microbial colonization. Therefore, the main objective of periodontal therapy is to eliminate the microbial biofilm along with the calculus deposits from the root surface by root surface debridement. Over the past years, a large number of clinical and laboratory studies have been conducted to evaluate the efficacy of calculus removal by various methods. None of these conventional methods or devices was effective in completely eliminating all the calculus from the diseased root surfaces. In this context, a number of newer technologies have been developed to identify and selectively remove the dental calculus. Regarding this fact, the present article highlights a critical review of these devices based on published clinical and experimental data. PMID:25870667
Characteristics of subgingival calculus detection by multiphoton fluorescence microscopy
Tung, Oi-Hong; Lee, Shyh-Yuan; Lai, Yu-Lin; Chen, How-Foo
2011-06-01
Subgingival calculus has been recognized as a major cause of periodontitis, which is one of the main chronic infectious diseases of oral cavities and a principal cause of tooth loss in humans. Bacteria deposited in subgingival calculus or plaque cause gingival inflammation, function deterioration, and then periodontitis. However, subgingival calculus within the periodontal pocket is a complicated and potentially delicate structure to be detected with current dental armamentaria, namely dental x-rays and dental probes. Consequently, complete removal of subgingival calculus remains a challenge to periodontal therapies. In this study, the detection of subgingival calculus employing a multiphoton autofluorescence imaging method was characterized in comparison with a one-photon confocal fluorescence imaging technique. Feasibility of such a system was studied based on fluorescence response of gingiva, healthy teeth, and calculus with and without gingiva covered. The multiphoton fluorescence technology perceived the tissue-covered subgingival calculus that cannot be observed by the one-photon confocal fluorescence method.
Dental calculus formation in children and adolescents undergoing hemodialysis.
Martins, Carla; Siqueira, Walter Luiz; Oliveira, Elizabeth; Nicolau, José; Primo, Laura Guimarães
2012-10-01
This study aimed to determine whether dental calculus formation is really higher among patients with chronic kidney disease undergoing hemodialysis than among controls. Furthermore, the study evaluated correlations between dental calculus formation and dental plaque, variables that are related to renal disease and/or saliva composition. The Renal Group was composed of 30 patients undergoing hemodialysis, whereas the Healthy Group had 30 clinically healthy patients. Stimulated whole saliva and parotid saliva were collected. Salivary flow rate and calcium and phosphate concentrations were determined. In the Renal Group the saliva collection was carried out before and after a hemodialysis session. Patients from both groups received intraoral exams, oral hygiene instructions, and dental scaling. Three months later, the dental calculus was measured by the Volpe-Manhold method to determine the rate of dental calculus formation. The Renal Group presented a higher rate of dental calculus formation (p dental calculus formation and whole saliva flow rate in the Renal Group after a hemodialysis session (r = 0.44, p dental calculus was associated with phosphate concentration in whole saliva from the Renal Group (p dental calculus formation, probably due to salivary variables.
Fluorescence spectroscopy of dental calculus
International Nuclear Information System (INIS)
Bakhmutov, D; Gonchukov, S; Sukhinina, A
2010-01-01
The aim of the present study was to investigate the fluorescence properties of dental calculus in comparison with the properties of adjacent unaffected tooth structure using both lasers and LEDs in the UV-visible range for fluorescence excitation. The influence of calculus color on the informative signal is demonstrated. The optimal spectral bands of excitation and registration of the fluorescence are determined
Fluorescence spectroscopy of dental calculus
Bakhmutov, D.; Gonchukov, S.; Sukhinina, A.
2010-05-01
The aim of the present study was to investigate the fluorescence properties of dental calculus in comparison with the properties of adjacent unaffected tooth structure using both lasers and LEDs in the UV-visible range for fluorescence excitation. The influence of calculus color on the informative signal is demonstrated. The optimal spectral bands of excitation and registration of the fluorescence are determined.
Directory of Open Access Journals (Sweden)
Amanda Huminicki
2010-01-01
Full Text Available Optical coherence tomography (OCT and polarized Raman spectroscopy (PRS have been shown as useful methods for distinguishing sound enamel from carious lesions ex vivo. However, factors in the oral environment such as calculus, hypocalcification, and stain could lead to false-positive results. OCT and PRS were used to investigate extracted human teeth clinically examined for sound enamel, white spot lesion (WSL, calculus, hypocalcification, and stain to determine whether these factors would confound WSL detection with these optical methods. Results indicate that OCT allowed differentiating caries from sound enamel, hypocalcification, and stain, with calculus deposits recognizable on OCT images. ANOVA and post-hoc unequal N HSD analyses to compare the mean Raman depolarization ratios from the various groups showed that the mean values were statistically significant at P<.05, except for several comparison pairs. With the current PRS analysis method, the mean depolarization ratios of stained enamel and caries are not significantly different due to the sloping background in the stained enamel spectra. Overall, calculus and hypocalcification are not confounding factors affecting WSL detection using OCT and PRS. Stain does not influence WSL detection with OCT. Improved PRS analysis methods are needed to differentiate carious from stained enamel.
A Calculus of Communicating Systems with Label Passing
DEFF Research Database (Denmark)
Engberg, Uffe Henrik; Nielsen, Mogens
Milner's Calculus of Communicating Systems (CCS) is extended with a mechanism for label passing - as an attempt to remedy some of the shortcomings of CCS w.r.t. dynamic change of agent interconnections. In the extended calculus, restriction is viewed formally as a binder, and the calculus allows...... dynamic change of scope (of label) in connection with communication. It is proved that algebraic properties of strong (and observational) equivalence for CCS are preserved by the extension. Examples illustrating the expressive power of the calculus and its methods for reasoning are given....
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Multiplicative calculus in biomedical image analysis
Florack, L.M.J.; Assen, van H.C.
2011-01-01
We advocate the use of an alternative calculus in biomedical image analysis, known as multiplicative (a.k.a. non-Newtonian) calculus. It provides a natural framework in problems in which positive images or positive definite matrix fields and positivity preserving operators are of interest. Indeed,
A type system for continuation calculus
Geuvers, J.H.; Geraedts, W.; Geron, B.; Stegeren, van J.; Oliva, P.
2014-01-01
Continuation Calculus (CC), introduced by Geron and Geuvers, is a simple foundational model for functional computation. It is closely related to lambda calculus and term rewriting, but it has no variable binding and no pattern matching. It is Turing complete and evaluation is deterministic. Notions
Restricted diversity of dental calculus methanogens over five centuries, France
Hong T. T. Huynh; Vanessa D. Nkamga; Michel Signoli; Stéfan Tzortzis; Romuald Pinguet; Gilles Audoly; Gérard Aboudharam; Michel Drancourt
2016-01-01
Methanogens are acknowledged archaeal members of modern dental calculus microbiota and dental pathogen complexes. Their repertoire in ancient dental calculus is poorly known. We therefore investigated archaea in one hundred dental calculus specimens collected from individuals recovered from six archaeological sites in France dated from the 14th to 19th centuries AD. Dental calculus was demonstrated by macroscopic and cone-beam observations. In 56 calculus specimens free of PCR inhibition, PCR...
A direct extension of Meller's calculus
Directory of Open Access Journals (Sweden)
E. L. Koh
1982-01-01
Full Text Available This paper extends the operational calculus of Meller for the operator Bα=t−αddttα+1ddt to the case where α∈(0,∞. The development is àla Mikusinski calculus and uses Meller's convolution process with a fractional derivative operator.
Advanced calculus of a single variable
Geveci, Tunc
2016-01-01
This advanced undergraduate textbook is based on a one-semester course on single variable calculus that the author has been teaching at San Diego State University for many years. The aim of this classroom-tested book is to deliver a rigorous discussion of the concepts and theorems that are dealt with informally in the first two semesters of a beginning calculus course. As such, students are expected to gain a deeper understanding of the fundamental concepts of calculus, such as limits (with an emphasis on ε-δ definitions), continuity (including an appreciation of the difference between mere pointwise and uniform continuity), the derivative (with rigorous proofs of various versions of L’Hôpital’s rule) and the Riemann integral (discussing improper integrals in-depth, including the comparison and Dirichlet tests). Success in this course is expected to prepare students for more advanced courses in real and complex analysis and this book will help to accomplish this. The first semester of advanced calculus...
Robinson, William Baker
1970-01-01
The predicted and actual achievement in college calculus is compared for students who had studied two semesters of calculus in high school. The regression equation used for prediction was calculated from the performance data of similar students who had not had high school calculus. (CT)
Computer Managed Instruction Homework Modules for Calculus I.
Goodman-Petrushka, Sharon; Roitberg, Yael
This booklet contains 11 modules (290 multiple-choice items) designed for use in the first course of a three-course calculus sequence using the textbook "Calculus with Analytic Geometry" (Dennis G. Zill). In each module, relevant sections of the textbook are identified for users. It can, however, be used in conjunction with any calculus textbook.…
An accessible four-dimensional treatment of Maxwell's equations in terms of differential forms
Sá, Lucas
2017-03-01
Maxwell’s equations are derived in terms of differential forms in the four-dimensional Minkowski representation, starting from the three-dimensional vector calculus differential version of these equations. Introducing all the mathematical and physical concepts needed (including the tool of differential forms), using only knowledge of elementary vector calculus and the local vector version of Maxwell’s equations, the equations are reduced to a simple and elegant set of two equations for a unified quantity, the electromagnetic field. The treatment should be accessible for students taking a first course on electromagnetism.
The theory of pseudo-differential operators on the noncommutative n-torus
Tao, J.
2018-02-01
The methods of spectral geometry are useful for investigating the metric aspects of noncommutative geometry and in these contexts require extensive use of pseudo-differential operators. In a foundational paper, Connes showed that, by direct analogy with the theory of pseudo-differential operators on finite-dimensional real vector spaces, one may derive a similar pseudo-differential calculus on noncommutative n-tori, and with the development of this calculus came many results concerning the local differential geometry of noncommutative tori for n=2,4, as shown in the groundbreaking paper in which the Gauss-Bonnet theorem on the noncommutative two-torus is proved and later papers. Certain details of the proofs in the original derivation of the calculus were omitted, such as the evaluation of oscillatory integrals, so we make it the objective of this paper to fill in all the details. After reproving in more detail the formula for the symbol of the adjoint of a pseudo-differential operator and the formula for the symbol of a product of two pseudo-differential operators, we extend these results to finitely generated projective right modules over the noncommutative n-torus. Then we define the corresponding analog of Sobolev spaces and prove equivalents of the Sobolev and Rellich lemmas.
Pre-calculus 1,001 practice problems for dummies
Sterling, Mary Jane; Sterling
2014-01-01
Prepare for calculus the smart way, with customizable pre-calculus practice 1,001 Pre-Calculus Practice Problems For Dummies offers 1,001 opportunities to gain confidence in your math skills. Much more than a workbook, this study aid provides pre-calculus problems ranked from easy to advanced, with detailed explanations and step-by-step solutions for each one. The companion website gives you free online access to all 1,001 practice problems and solutions, and you can track your progress and ID where you should focus your study time. Accessible on the go by smart phone, tablet, o
A Snapshot of the Calculus Classroom
Weathers, Tony D.; Latterell, Carmen M.
2003-01-01
Essentially a focus group to discuss textbook related issues, a meeting of calculus instructors from a wide variety of environments was convened and sponsored by McGraw Hill to provide feedback on the current state of the calculus classroom. This paper provides a description of the group's discussions.
Imagine Yourself in This Calculus Classroom
Bryan, Luajean
2007-01-01
The efforts to attract students to precalculus, trigonometry, and calculus classes became more successful at the author's school when projects-based classes were offered. Data collection from an untethered hot air balloon flight for calculus students was planned to maximize enrollment. The data were analyzed numerically, graphically, and…
International Nuclear Information System (INIS)
Feinsilver, Philip; Schott, Rene
2009-01-01
We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement infinite terms Rota's 'finite operator calculus'.
DEFF Research Database (Denmark)
Nielson, Hanne Riis; Nielson, Flemming; Vigo, Roberto
2013-01-01
for default behaviour in case the ideal behaviour fails due to unreliable communication and thereby to increase the quality of service offered by the systems. The development is facilitated by a SAT-based robustness analysis to determine whether or not the code is vulnerable to unreliable communication......A main challenge of programming component-based software is to ensure that the components continue to behave in a reasonable manner even when communication becomes unreliable. We propose a process calculus, the Quality Calculus, for programming software components where it becomes natural to plan...
Sigdel, G; Agarwal, A; Keshaw, B W
2014-01-01
Urethral calculi are rare forms of urolithiasis. Majority of the calculi are migratory from urinary bladder or upper urinary tract. Primary urethral calculi usually occur in presence of urethral stricture or diverticulum. In this article we report a case of a giant posterior urethral calculus measuring 7x3x2 cm in a 47 years old male. Patient presented with acute retention of urine which was preceded by burning micturition and dribbling of urine for one week. The calculus was pushed in to the bladder through the cystoscope and was removed by suprapubic cystolithotomy.
Directory of Open Access Journals (Sweden)
Cesar Augusto Hernandez-Suarez
2017-07-01
Full Text Available Many investigations have been carried out with the objective of identifying the difficulties that students have in the learning process of the different mathematical concepts. Some studies have highlighted that the process of teaching mathematical knowledge by teachers in secondary and secondary education in Colombia, has been limited to a minimalist expression of algebraic processes that in no way contribute to the understanding and appropriation of these concepts of origin abstract. Students who enter the various engineering programs in the university must immediately face a Differential Calculus course, which will demand from the student a whole series of competences around the numerical, variational and spatial thoughts. It is in this scenario where we seek to identify the epistemological obstacles presented by the students of the Faculty of Engineering programs at the beginning of the academic training process at the UFPS. An instrument was designed that incorporates a series of activities that use diverse registers of semiotic representation tending to determine the level of appropriation that the students have around the concepts of limit and continuity. From the findings it is highlighted that students assume the concepts of limit and continuity as equals.
AP calculus AB & BC crash course
Rosebush, J
2012-01-01
AP Calculus AB & BC Crash Course - Gets You a Higher Advanced Placement Score in Less Time Crash Course is perfect for the time-crunched student, the last-minute studier, or anyone who wants a refresher on the subject. AP Calculus AB & BC Crash Course gives you: Targeted, Focused Review - Study Only What You Need to Know Crash Course is based on an in-depth analysis of the AP Calculus AB & BC course description outline and actual AP test questions. It covers only the information tested on the exams, so you can make the most of your valuable study time. Written by experienced math teachers, our
RAMAN-SPECTRA OF HUMAN DENTAL CALCULUS
TSUDA, H; ARENDS, J
1993-01-01
Raman spectra of human dental calculus have been observed for the first time by use of micro-Raman spectroscopy. The spectral features of calculus were influenced easily by heating caused by laser irradiation. Therefore, the measurements were carried out at relatively low power (5 mW, 1-mu m spot
An Introductory Calculus-Based Mechanics Investigation
Allen, Bradley
2017-01-01
One challenge for the introductory physics teacher is incorporating calculus techniques into the laboratory setting. It can be difficult to strike a balance between presenting an experimental task for which calculus is essential and making the mathematics accessible to learners who may be apprehensive about applying it. One-dimensional kinematics…
Using Dynamic Software to Address Common College Calculus Stumbling Blocks
Seneres, Alice W.; Kerrigan, John A.
2014-01-01
There are specific topics in college calculus that can be major stumbling blocks for students. Having taught college calculus for four years to over a thousand students, we observed that even the students who have already taken pre-calculus or calculus during their high school careers had common misunderstandings. Students may remember a technique…
Extending Stochastic Network Calculus to Loss Analysis
Directory of Open Access Journals (Sweden)
Chao Luo
2013-01-01
Full Text Available Loss is an important parameter of Quality of Service (QoS. Though stochastic network calculus is a very useful tool for performance evaluation of computer networks, existing studies on stochastic service guarantees mainly focused on the delay and backlog. Some efforts have been made to analyse loss by deterministic network calculus, but there are few results to extend stochastic network calculus for loss analysis. In this paper, we introduce a new parameter named loss factor into stochastic network calculus and then derive the loss bound through the existing arrival curve and service curve via this parameter. We then prove that our result is suitable for the networks with multiple input flows. Simulations show the impact of buffer size, arrival traffic, and service on the loss factor.
Restricted diversity of dental calculus methanogens over five centuries, France.
Huynh, Hong T T; Nkamga, Vanessa D; Signoli, Michel; Tzortzis, Stéfan; Pinguet, Romuald; Audoly, Gilles; Aboudharam, Gérard; Drancourt, Michel
2016-05-11
Methanogens are acknowledged archaeal members of modern dental calculus microbiota and dental pathogen complexes. Their repertoire in ancient dental calculus is poorly known. We therefore investigated archaea in one hundred dental calculus specimens collected from individuals recovered from six archaeological sites in France dated from the 14(th) to 19(th) centuries AD. Dental calculus was demonstrated by macroscopic and cone-beam observations. In 56 calculus specimens free of PCR inhibition, PCR sequencing identified Candidatus Methanobrevibacter sp. N13 in 44.6%, Methanobrevibacter oralis in 19.6%, a new Methanomassiliicoccus luminyensis-like methanogen in 12.5%, a Candidatus Nitrososphaera evergladensis-like in one and Methanoculleus bourgensis in one specimen, respectively. One Candidatus Methanobrevibacter sp. N13 dental calculus was further documented by fluorescent in situ hybridization. The prevalence of dental calculus M. oralis was significantly lower in past populations than in modern populations (P = 0.03, Chi-square test). This investigation revealed a previously unknown repertoire of archaea found in the oral cavity of past French populations as reflected in preserved dental calculus.
Linear algebra a first course with applications to differential equations
Apostol, Tom M
2014-01-01
Developed from the author's successful two-volume Calculus text this book presents Linear Algebra without emphasis on abstraction or formalization. To accommodate a variety of backgrounds, the text begins with a review of prerequisites divided into precalculus and calculus prerequisites. It continues to cover vector algebra, analytic geometry, linear spaces, determinants, linear differential equations and more.
Ancient DNA analysis of dental calculus.
Weyrich, Laura S; Dobney, Keith; Cooper, Alan
2015-02-01
Dental calculus (calcified tartar or plaque) is today widespread on modern human teeth around the world. A combination of soft starchy foods, changing acidity of the oral environment, genetic pre-disposition, and the absence of dental hygiene all lead to the build-up of microorganisms and food debris on the tooth crown, which eventually calcifies through a complex process of mineralisation. Millions of oral microbes are trapped and preserved within this mineralised matrix, including pathogens associated with the oral cavity and airways, masticated food debris, and other types of extraneous particles that enter the mouth. As a result, archaeologists and anthropologists are increasingly using ancient human dental calculus to explore broad aspects of past human diet and health. Most recently, high-throughput DNA sequencing of ancient dental calculus has provided valuable insights into the evolution of the oral microbiome and shed new light on the impacts of some of the major biocultural transitions on human health throughout history and prehistory. Here, we provide a brief historical overview of archaeological dental calculus research, and discuss the current approaches to ancient DNA sampling and sequencing. Novel applications of ancient DNA from dental calculus are discussed, highlighting the considerable scope of this new research field for evolutionary biology and modern medicine. Copyright © 2014 Elsevier Ltd. All rights reserved.
Hall, Angela Renee
2011-01-01
This investigative research focuses on the level of readiness of Science, Technology, Engineering, and Mathematics (STEM) students entering Historically Black Colleges and Universities (HBCU) in the college Calculus sequence. Calculus is a fundamental course for STEM courses. The level of readiness of the students for Calculus can very well play a…
The ZX-calculus is complete for stabilizer quantum mechanics
International Nuclear Information System (INIS)
Backens, Miriam
2014-01-01
The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics (QM), meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound, i.e. any equality that can be derived graphically can also be derived using matrix mechanics. Here, we show that the ZX-calculus is complete for pure qubit stabilizer QM, meaning any equality that can be derived using matrices can also be derived pictorially. The proof relies on bringing diagrams into a normal form based on graph states and local Clifford operations. (paper)
Thematization of the Calculus Graphing Schema
Cooley, Laurel; Baker, Bernadette; Trigueros, Maria
2003-01-01
This article is the result of an investigation of students' conceptualizations of calculus graphing techniques after they had completed at least two semesters of calculus. The work and responses of 27 students to a series of questions that solicit information about the graphical implications of the first derivative, second derivative, continuity,…
A Cross-National Study of Calculus
Chai, Jun; Friedler, Louis M.; Wolff, Edward F.; Li, Jun; Rhea, Karen
2015-01-01
The results from a cross-national study comparing calculus performance of students at East China Normal University (ECNU) in Shanghai and students at the University of Michigan before and after their first university calculus course are presented. Overall, ECNU significantly outperformed Michigan on both the pre- and post-tests, but the Michigan…
Command injection attacks, continuations, and the Lambek calculus
Directory of Open Access Journals (Sweden)
Hayo Thielecke
2016-06-01
Full Text Available This paper shows connections between command injection attacks, continuations, and the Lambek calculus: certain command injections, such as the tautology attack on SQL, are shown to be a form of control effect that can be typed using the Lambek calculus, generalizing the double-negation typing of continuations. Lambek's syntactic calculus is a logic with two implicational connectives taking their arguments from the left and right, respectively. These connectives describe how strings interact with their left and right contexts when building up syntactic structures. The calculus is a form of propositional logic without structural rules, and so a forerunner of substructural logics like Linear Logic and Separation Logic.
Maximum range of a projectile launched from a height h: a non-calculus treatment
International Nuclear Information System (INIS)
Ganci, S; Lagomarsino, D
2014-01-01
The classical example of problem solving, maximizing the range of a projectile launched from height h with velocity v over the ground level, has received various solutions. In some of these, one can find the maximization of the range R by differentiating R as a function of an independent variable or through the implicit differentiation in Cartesian or polar coordinates. In other papers, various elegant non-calculus solutions can be found. In this paper, this problem is revisited on the basis of the elementary analytical geometry and the trigonometry only. (papers)
Maximum range of a projectile launched from a height h: a non-calculus treatment
Ganci, S.; Lagomarsino, D.
2014-07-01
The classical example of problem solving, maximizing the range of a projectile launched from height h with velocity v over the ground level, has received various solutions. In some of these, one can find the maximization of the range R by differentiating R as a function of an independent variable or through the implicit differentiation in Cartesian or polar coordinates. In other papers, various elegant non-calculus solutions can be found. In this paper, this problem is revisited on the basis of the elementary analytical geometry and the trigonometry only.
Improving Student Success in Calculus: A Comparison of Four College Calculus Classes
Bagley, Spencer Franklin
The quality of education in science, technology, engineering, and mathematics (STEM) fields is an issue of particular educational and economic importance, and Calculus I is a linchpin course in STEM major tracks. A national study is currently being conducted examining the characteristics of successful programs in college calculus (CSPCC, 2012). In work related to the CSPCC program, this study examines the effects on student outcomes of four different teaching strategies used at a single institution. The four classes were a traditional lecture, a lecture with discussion, a lecture incorporating both discussion and technology, and an inverted model. This dissertation was guided by three questions: (1) What impact do these four instructional approaches have on students' persistence, beliefs about mathematics, and conceptual and procedural achievement in calculus? (2) How do students at the local institution compare to students in the national database? And (3) How do the similarities and differences in opportunities for learning presented in the four classes contribute to the similarities and differences in student outcomes? Quantitative analysis of surveys and exams revealed few statistically significant differences in outcomes, and students in the inverted classroom often had poorer outcomes than those in other classes. Students in the technology-enhanced class scored higher on conceptual items on the final exam than those in other classes. Comparing to the national database, local students had similar switching rates but less expert-like attitudes and beliefs about mathematics than the national average. Qualitative analysis of focus group interviews, classroom observations, and student course evaluations showed that several implementation issues, some the result of pragmatic constraints, others the result of design choice, weakened affordances provided by innovative features and shrunk the differences between classes. There were substantial differences between the
Neutrosophic Precalculus and Neutrosophic Calculus
Florentin Smarandache
2015-01-01
Neutrosophic Analysis is a generalization of Set Analysis, which in its turn is a generalization of Interval Analysis. Neutrosophic Precalculus is referred to indeterminate staticity, while Neutrosophic Calculus is the mathematics of indeterminate change. The Neutrosophic Precalculus and Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the methods used to deal with such indeterminacy. In this book, the author presents a few examples o...
Feynman's operational calculus and beyond noncommutativity and time-ordering
Johnson, George W; Nielsen, Lance
2015-01-01
This book is aimed at providing a coherent, essentially self-contained, rigorous and comprehensive abstract theory of Feynman's operational calculus for noncommuting operators. Although it is inspired by Feynman's original heuristic suggestions and time-ordering rules in his seminal 1951 paper An operator calculus having applications in quantum electrodynamics, as will be made abundantly clear in the introduction (Chapter 1) and elsewhere in the text, the theory developed in this book also goes well beyond them in a number of directions which were not anticipated in Feynman's work. Hence, the second part of the main title of this book. The basic properties of the operational calculus are developed and certain algebraic and analytic properties of the operational calculus are explored. Also, the operational calculus will be seen to possess some pleasant stability properties. Furthermore, an evolution equation and a generalized integral equation obeyed by the operational calculus are discussed and connections wi...
Endoscopic vs. tactile evaluation of subgingival calculus.
Osborn, Joy B; Lenton, Patricia A; Lunos, Scott A; Blue, Christine M
2014-08-01
Endoscopic technology has been developed to facilitate imagery for use during diagnostic and therapeutic phases of periodontal care. The purpose of this study was to compare the level of subgingival calculus detection using a periodontal endoscope with that of conventional tactile explorer in periodontitis subjects. A convenience sample of 26 subjects with moderate periodontitis in at least 2 quadrants was recruited from the University of Minnesota School of Dentistry to undergo quadrant scaling and root planing. One quadrant from each subject was randomized for tactile calculus detection alone and the other quadrant for tactile detection plus the Perioscope ™ (Perioscopy Inc., Oakland, Cali). A calculus index on a 0 to 3 score was performed at baseline and at 2 post-scaling and root planing visits. Sites where calculus was detected at visit 1 were retreated. T-tests were used to determine within-subject differences between Perioscope™ and tactile measures, and changes in measures between visits. Significantly more calculus was detected using the Perioscope™ vs. tactile explorer for all 3 subject visits (pcalculus detection from baseline to visit 1 were statistically significant for both the Perioscope™ and tactile quadrants (pcalculus detection from visit 1 to visit 2 was only significant for the Perioscope™ quadrant (pcalculus at this visit. It was concluded that the addition of a visual component to calculus detection via the Perioscope™ was most helpful in the re-evaluation phase of periodontal therapy. Copyright © 2014 The American Dental Hygienists’ Association.
Educating about Sustainability while Enhancing Calculus
Pfaff, Thomas J.
2011-01-01
We give an overview of why it is important to include sustainability in mathematics classes and provide specific examples of how to do this for a calculus class. We illustrate that when students use "Excel" to fit curves to real data, fundamentally important questions about sustainability become calculus questions about those curves. (Contains 5…
Fractional Dynamics Applications of Fractional Calculus to Dynamics of Particles, Fields and Media
Tarasov, Vasily E
2010-01-01
"Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and...
Two-parameter asymptotics in magnetic Weyl calculus
International Nuclear Information System (INIS)
Lein, Max
2010-01-01
This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter ε, the case of small coupling λ to the magnetic vector potential naturally occurs in this context. Magnetic Weyl calculus is adapted to incorporate both parameters, at least one of which needs to be small. Of particular interest is the expansion of the Weyl product which can be used to expand the product of operators in a small parameter, a technique which is prominent to obtain perturbation expansions. Three asymptotic expansions for the magnetic Weyl product of two Hoermander class symbols are proven as (i) ε<< 1 and λ<< 1, (ii) ε<< 1 and λ= 1, as well as (iii) ε= 1 and λ<< 1. Expansions (i) and (iii) are impossible to obtain with ordinary Weyl calculus. Furthermore, I relate the results derived by ordinary Weyl calculus with those obtained with magnetic Weyl calculus by one- and two-parameter expansions. To show the power and versatility of magnetic Weyl calculus, I derive the semirelativistic Pauli equation as a scaling limit from the Dirac equation up to errors of fourth order in 1/c.
Introductory analysis a deeper view of calculus
Bagby, Richard J
2000-01-01
Introductory Analysis addresses the needs of students taking a course in analysis after completing a semester or two of calculus, and offers an alternative to texts that assume that math majors are their only audience. By using a conversational style that does not compromise mathematical precision, the author explains the material in terms that help the reader gain a firmer grasp of calculus concepts.* Written in an engaging, conversational tone and readable style while softening the rigor and theory* Takes a realistic approach to the necessary and accessible level of abstraction for the secondary education students* A thorough concentration of basic topics of calculus* Features a student-friendly introduction to delta-epsilon arguments * Includes a limited use of abstract generalizations for easy use* Covers natural logarithms and exponential functions* Provides the computational techniques often encountered in basic calculus
Quantum geometry in dynamical Regge calculus
International Nuclear Information System (INIS)
Hagura, Hiroyuki
2002-01-01
We study geometric properties of dynamical Regge calculus which is a hybridization of dynamical triangulation and quantum Regge calculus. Lattice diffeomorphisms are generated by certain elementary moves on a simplicial lattice in the hybrid model. At the semiclassical level, we discuss a possibility that the lattice diffeomorphisms give a simple explanation for the Bekenstein-Hawking entropy of a black hole. At the quantum level, numerical calculations of 3D pure gravity show that a fractal structure of the hybrid model is the same as that of dynamical triangulation in the strong-coupling phase. In the weak-coupling phase, on the other hand, space-time becomes a spiky configuration, which often occurs in quantum Regge calculus
Directory of Open Access Journals (Sweden)
Philip Atzemoglou
2014-12-01
Full Text Available We present a novel lambda calculus that casts the categorical approach to the study of quantum protocols into the rich and well established tradition of type theory. Our construction extends the linear typed lambda calculus with a linear negation of "trivialised" De Morgan duality. Reduction is realised through explicit substitution, based on a symmetric notion of binding of global scope, with rules acting on the entire typing judgement instead of on a specific subterm. Proofs of subject reduction, confluence, strong normalisation and consistency are provided, and the language is shown to be an internal language for dagger compact categories.
Reliability of recordings of subgingival calculus detected using an ultrasonic device.
Corraini, Priscila; López, Rodrigo
2015-04-01
To assess the intra-examiner reliability of recordings of subgingival calculus detected using an ultrasonic device, and to investigate the influence of subject-, tooth- and site-level factors on the reliability of these subgingival calculus recordings. On two occasions, within a 1-week interval, 147 adult periodontitis patients received a full-mouth clinical periodontal examination by a single trained examiner. Duplicate subgingival calculus recordings, in six sites per tooth, were obtained using an ultrasonic device for calculus detection and removal. Agreement was observed in 65 % of the 22,584 duplicate subgingival calculus recordings, ranging 45 % to 83 % according to subject. Using hierarchical modeling, disagreements in the subgingival calculus duplicate recordings were more likely in all other sites than the mid-buccal, and in sites harboring supragingival calculus. Disagreements were less likely in sites with PD ≥ 4 mm and with furcation involvement ≥ degree 2. Bleeding on probing or suppuration did not influence the reliability of subgingival calculus. At the subject-level, disagreements were less likely in patients presenting with the highest and lowest extent categories of the covariate subgingival calculus. The reliability of subgingival calculus recordings using the ultrasound technology is reasonable. The results of the present study suggest that the reliability of subgingival calculus recordings is not influenced by the presence of inflammation. Moreover, subgingival calculus can be more reliably detected using the ultrasound device at sites with higher need for periodontal therapy, i.e., sites presenting with deep pockets and premolars and molars with furcation involvement.
Noise Analysis of Single-Ended Input Differential Amplifier using Stochastic Differential Equation
Tarun Kumar Rawat; Abhirup Lahiri; Ashish Gupta
2008-01-01
In this paper, we analyze the effect of noise in a single- ended input differential amplifier working at high frequencies. Both extrinsic and intrinsic noise are analyzed using time domain method employing techniques from stochastic calculus. Stochastic differential equations are used to obtain autocorrelation functions of the output noise voltage and other solution statistics like mean and variance. The analysis leads to important design implications and suggests changes in the device parame...
TWO-PHASE EJECTOR of CARBON DIOXIDE HEAT PUMP CALCULUS
Directory of Open Access Journals (Sweden)
Sit B.M.
2010-12-01
Full Text Available It is presented the calculus of the two-phase ejector for carbon dioxide heat pump. The method of calculus is based on the method elaborated by S.M. Kandil, W.E. Lear, S.A. Sherif, and is modified taking into account entrainment ratio as the input for the calculus.
Antiderivative Series for Differentiable Functions
Howard, Roy M.
2004-01-01
A series defining the antiderivative of an n th order differentiable function is defined. This series provides an explicit expression for the second part of the Fundamental Theorem of Calculus and can facilitate the establishment of new antiderivative functions.
On the differential structure of metric measure spaces and applications
Gigli, Nicola
2015-01-01
The main goals of this paper are: (i) To develop an abstract differential calculus on metric measure spaces by investigating the duality relations between differentials and gradients of Sobolev functions. This will be achieved without calling into play any sort of analysis in charts, our assumptions being: the metric space is complete and separable and the measure is Radon and non-negative. (ii) To employ these notions of calculus to provide, via integration by parts, a general definition of distributional Laplacian, thus giving a meaning to an expression like \\Delta g=\\mu, where g is a functi
The Complex Gradient Operator and the CR-Calculus
Kreutz-Delgado, Ken
2009-01-01
A thorough discussion and development of the calculus of real-valued functions of complex-valued vectors is given using the framework of the Wirtinger Calculus. The presented material is suitable for exposition in an introductory Electrical Engineering graduate level course on the use of complex gradients and complex Hessian matrices, and has been successfully used in teaching at UC San Diego. Going beyond the commonly encountered treatments of the first-order complex vector calculus, second-...
Noninvasive control of dental calculus removal: qualification of two fluorescence methods
Gonchukov, S.; Sukhinina, A.; Bakhmutov, D.; Biryukova, T.
2013-02-01
The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise noninvasive detection of calculus-tooth interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing.
Noninvasive control of dental calculus removal: qualification of two fluorescence methods
International Nuclear Information System (INIS)
Gonchukov, S; Sukhinina, A; Bakhmutov, D; Biryukova, T
2013-01-01
The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise noninvasive detection of calculus-tooth interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing.
Areas and Volumes in Pre-Calculus
Jarrett, Joscelyn A.
2008-01-01
This article suggests the introduction of the concepts of areas bounded by plane curves and the volumes of solids of revolution in Pre-calculus. It builds on the basic knowledge that students bring to a pre-calculus class, derives a few more formulas, and gives examples of some problems on plane areas and the volumes of solids of revolution that…
An accessible four-dimensional treatment of Maxwell's equations in terms of differential forms
International Nuclear Information System (INIS)
Sá, Lucas
2017-01-01
Maxwell’s equations are derived in terms of differential forms in the four-dimensional Minkowski representation, starting from the three-dimensional vector calculus differential version of these equations. Introducing all the mathematical and physical concepts needed (including the tool of differential forms), using only knowledge of elementary vector calculus and the local vector version of Maxwell’s equations, the equations are reduced to a simple and elegant set of two equations for a unified quantity, the electromagnetic field. The treatment should be accessible for students taking a first course on electromagnetism. (paper)
Programming Language Concepts - The Lambda Calculus Approach
Fokkinga, M.M.; Asveld, P.R.J.; Nijholt, Antinus
1987-01-01
The Lambda Calculus is a formal system, originally intended as a tool in the foundation of mathematics, but mainly used to study the concepts of algorithm and effective computability. Recently, the Lambda Calculus and related systems acquire attention from Computer Science for another reason too:
Relativistic collapse using Regge calculus: Pt. 1
International Nuclear Information System (INIS)
Dubal, M.R.; Leicester Univ.
1989-01-01
Regge calculus is used to simulate the dynamical collapse of model stars. In this paper we describe the general methodology of including a perfect fluid in dynamical Regge calculus spacetimes. The Regge-Einstein equations for spherical collapse are obtained and are then specialised to mimic a particular continuum gauge. The equivalent continuum problem is also set up. This is to be solved using standard numerical techniques (i.e. the method of finite difference). A subsequent paper will consider the solution of the equations presented here and will use the continuum problem for comparison purposes in order to check the Regge calculus results. (author)
A Transition Course from Advanced Placement to College Calculus
Lucas, Timothy A.; Spivey, Joseph
2011-01-01
In the Spring of 2007, a group of highly motivated mathematics graduate students conducted a review of Duke's Calculus curriculum. They focused on two main problems. The first problem is the result of a very positive trend: a growing number of students are earning AP credit for Calculus I in high school. However, this results in Calculus II…
Everyday calculus discovering the hidden math all around us
Fernandez, Oscar E
2014-01-01
Calculus. For some of us, the word conjures up memories of ten-pound textbooks and visions of tedious abstract equations. And yet, in reality, calculus is fun, accessible, and surrounds us everywhere we go. In Everyday Calculus, Oscar Fernandez shows us how to see the math in our coffee, on the highway, and even in the night sky. Fernandez uses our everyday experiences to skillfully reveal the hidden calculus behind a typical day's events. He guides us through how math naturally emerges from simple observations-how hot coffee cools down, for example-and in discussions of over fifty familia
Towards Model Checking a Spi-Calculus Dialect
Gnesi, S.; Latella, D.; Lenzini, Gabriele
We present a model checking framework for a spi-calculus dialect which uses a linear time temporal logic for expressing security properties. We have provided our spi-calculus dialect, called SPID, with a semantics based on labeled transition systems (LTS), where the intruder is modeled in the
A large primary vaginal calculus in a woman with paraplegia.
Avsar, Ayse Filiz; Keskin, Huseyin Levent; Catma, Tuba; Kaya, Basak; Sivaslioglu, Ahmet Akın
2013-01-01
The study aimed to report a primary vaginal stone, an extremely rare entity, without vesicovaginal fistula in a woman with disability. We describe the case of a large primary vaginal calculus in a 22-year-old woman with paraplegia, which, surprisingly, was not diagnosed until she was examined under general anesthesia during a preparation for laparoscopy for an adnexal mass. The stone had not been identified by physical examination with the patient in a recumbent position or by transabdominal ultrasonography and pelvic tomography during the preoperative preparation. Vaginoscopy was not performed because the vagina was completely filled with the mass. As a result of its size and hard consistency, a right-sided episiotomy was performed and a 136-g stone was removed using ring forceps. A vesicovaginal fistula was excluded. There was no evidence of a foreign body or other nidus on the cut section of the stone, and it was determined to be composed of 100% struvite (ammonium magnesium phosphate). Culture of urine obtained via catheter showed Escherichia coli. After the surgical removal of the calculus without complications, a program of intermittent catheterization was started. The follow-up period was uneventful, and the patient was symptom free at 6 months after the operation. We postulate that the calculus formed as a consequence of urinary contamination of the vagina in association with incontinence and prolonged maintenance in a recumbent posture. This report is important because it highlights that, although vaginal stones are very rare, their possibility should be considered in the differential diagnosis of individuals with long-term paraplegia.
On flipping first-semester calculus: a case study
Petrillo, Joseph
2016-05-01
High failure rates in calculus have plagued students, teachers, and administrators for decades, while science, technology, engineering, and mathematics programmes continue to suffer from low enrollments and high attrition. In an effort to affect this reality, some educators are 'flipping' (or inverting) their classrooms. By flipping, we mean administering course content outside of the classroom and replacing the traditional in-class lectures with discussion, practice, group work, and other elements of active learning. This paper presents the major results from a three-year study of a flipped, first-semester calculus course at a small, comprehensive, American university with a well-known engineering programme. The data we have collected help quantify the positive and substantial effects of our flipped calculus course on failure rates, scores on the common final exam, student opinion of calculus, teacher impact on measurable outcomes, and success in second-semester calculus. While flipping may not be suitable for every teacher, every student, and in every situation, this report provides some evidence that it may be a viable option for those seeking an alternative to the traditional lecture model.
Elementary excitations of biomembranes: Differential geometry of undulations in elastic surfaces
Energy Technology Data Exchange (ETDEWEB)
Hemmen, J. Leo van [Physik Department, Technical University of Munich, 85747 Garching (Germany)]. E-mail: lvh@tum.de; Leibold, Christian [Physik Department, Technical University of Munich, 85747 Garching (Germany)
2007-06-15
Biomembrane undulations are elementary excitations in the elastic surfaces of cells and vesicles. As such they can provide surprising insights into the mechanical processes that shape and stabilize biomembranes. We explain how naturally these undulations can be described by classical differential geometry. In particular, we apply the analytical formalism of differential-geometric calculus to the surfaces generated by a cell membrane and underlying cytoskeleton. After a short derivation of the energy due to a membrane's elasticity, we show how undulations arise as elementary excitations originating from the second derivative of an energy functional. Furthermore, we expound the efficiency of classical differential-geometric formalism to understand the effect of differential operators that characterize processes involved in membrane physics. As an introduction to concepts the paper is self-contained and rarely exceeds calculus level.
Elementary excitations of biomembranes: Differential geometry of undulations in elastic surfaces
International Nuclear Information System (INIS)
Hemmen, J. Leo van; Leibold, Christian
2007-01-01
Biomembrane undulations are elementary excitations in the elastic surfaces of cells and vesicles. As such they can provide surprising insights into the mechanical processes that shape and stabilize biomembranes. We explain how naturally these undulations can be described by classical differential geometry. In particular, we apply the analytical formalism of differential-geometric calculus to the surfaces generated by a cell membrane and underlying cytoskeleton. After a short derivation of the energy due to a membrane's elasticity, we show how undulations arise as elementary excitations originating from the second derivative of an energy functional. Furthermore, we expound the efficiency of classical differential-geometric formalism to understand the effect of differential operators that characterize processes involved in membrane physics. As an introduction to concepts the paper is self-contained and rarely exceeds calculus level
On Lipschitzian quantum stochastic differential inclusions
International Nuclear Information System (INIS)
Ekhaguere, G.O.S.
1990-12-01
Quantum stochastic differential inclusions are introduced and studied within the framework of the Hudson-Parthasarathy formulation of quantum stochastic calculus. Results concerning the existence of solutions of a Lipschitzian quantum stochastic differential inclusion and the relationship between the solutions of such an inclusion and those of its convexification are presented. These generalize the Filippov existence theorem and the Filippov-Wazewski Relaxation Theorem for classical differential inclusions to the present noncommutative setting. (author). 9 refs
Science 101: How Do We Use Calculus in Science?
Robertson, Bill
2014-01-01
How is calculus used in science? That might seem like an odd question to answer in a magazine intended primarily for elementary school teachers. After all, how much calculus gets used in elementary science? Here the author guesses that quite a few readers of this column do not know a whole lot about calculus and have not taken a course in…
Elementary calculus an infinitesimal approach
Keisler, H Jerome
2012-01-01
This first-year calculus book is centered around the use of infinitesimals, an approach largely neglected until recently for reasons of mathematical rigor. It exposes students to the intuition that originally led to the calculus, simplifying their grasp of the central concepts of derivatives and integrals. The author also teaches the traditional approach, giving students the benefits of both methods.Chapters 1 through 4 employ infinitesimals to quickly develop the basic concepts of derivatives, continuity, and integrals. Chapter 5 introduces the traditional limit concept, using approximation p
Hybrid Logical Analyses of the Ambient Calculus
DEFF Research Database (Denmark)
Bolander, Thomas; Hansen, Rene Rydhof
2010-01-01
In this paper, hybrid logic is used to formulate three control flow analyses for Mobile Ambients, a process calculus designed for modelling mobility. We show that hybrid logic is very well-suited to express the semantic structure of the ambient calculus and how features of hybrid logic can...
Continuous strong Markov processes in dimension one a stochastic calculus approach
Assing, Sigurd
1998-01-01
The book presents an in-depth study of arbitrary one-dimensional continuous strong Markov processes using methods of stochastic calculus. Departing from the classical approaches, a unified investigation of regular as well as arbitrary non-regular diffusions is provided. A general construction method for such processes, based on a generalization of the concept of a perfect additive functional, is developed. The intrinsic decomposition of a continuous strong Markov semimartingale is discovered. The book also investigates relations to stochastic differential equations and fundamental examples of irregular diffusions.
Subgingival calculus imaging based on swept-source optical coherence tomography
Hsieh, Yao-Sheng; Ho, Yi-Ching; Lee, Shyh-Yuan; Lu, Chih-Wei; Jiang, Cho-Pei; Chuang, Ching-Cheng; Wang, Chun-Yang; Sun, Chia-Wei
2011-07-01
We characterized and imaged dental calculus using swept-source optical coherence tomography (SS-OCT). The refractive indices of enamel, dentin, cementum, and calculus were measured as 1.625 +/- 0.024, 1.534 +/- 0.029, 1.570 +/- 0.021, and 2.097 +/- 0.094, respectively. Dental calculus leads strong scattering properties, and thus, the region can be identified from enamel with SS-OCT imaging. An extracted human tooth with calculus is covered with gingiva tissue as an in vitro sample for tomographic imaging.
McCarty, George
1982-01-01
How THIS BOOK DIFFERS This book is about the calculus. What distinguishes it, however, from other books is that it uses the pocket calculator to illustrate the theory. A computation that requires hours of labor when done by hand with tables is quite inappropriate as an example or exercise in a beginning calculus course. But that same computation can become a delicate illustration of the theory when the student does it in seconds on his calculator. t Furthermore, the student's own personal involvement and easy accomplishment give hi~ reassurance and en couragement. The machine is like a microscope, and its magnification is a hundred millionfold. We shall be interested in limits, and no stage of numerical approximation proves anything about the limit. However, the derivative of fex) = 67.SgX, for instance, acquires real meaning when a student first appreciates its values as numbers, as limits of 10 100 1000 t A quick example is 1.1 , 1.01 , 1.001 , •••• Another example is t = 0.1, 0.01, in the functio...
Pyrah, Leslie N
1979-01-01
Stone in the urinary tract has fascinated the medical profession from the earliest times and has played an important part in the development of surgery. The earliest major planned operations were for the removal of vesical calculus; renal and ureteric calculi provided the first stimulus for the radiological investigation of the viscera, and the biochemical investigation of the causes of calculus formation has been the training ground for surgeons interested in metabolic disorders. It is therefore no surprise that stone has been the subject of a number of monographs by eminent urologists, but the rapid development of knowledge has made it possible for each one of these authors to produce something new. There is still a technical challenge to the surgeon in the removal of renal calculi, and on this topic we are always glad to have the advice of a master craftsman; but inevitably much of the interest centres on the elucidation of the causes of stone formation and its prevention. Professor Pyrah has had a long an...
Intitialization, Conceptualization, and Application in the Generalized Fractional Calculus
Lorenzo, Carl F.; Hartley, Tom T.
1998-01-01
This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions.
Initialization, conceptualization, and application in the generalized (fractional) calculus.
Lorenzo, Carl F; Hartley, Tom T
2007-01-01
This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions.
Calculus in High School--At What Cost?
Sorge, D. H.; Wheatley, G. H.
1977-01-01
Evidence on the decline in preparation of entering calculus students and the relationship to high school preparation is presented, focusing on the trend toward the de-emphasis of trigonometry and analytic geometry in favor of calculus. Data on students' perception of the adequacy of their preparation are also presented. (Author/MN)
Calculus and Success in a Business School
Kim, Dong-gook; Garcia, Fernando; Dey, Ishita
2012-01-01
Many business schools or colleges require calculus as a prerequisite for certain classes or for continuing to upper division courses. While there are many studies investigating the relationship between performance in calculus and performance in a single course, such as economics, statistics, and finance, there are very few studies investigating…
Superconformal tensor calculus in five dimensions
International Nuclear Information System (INIS)
Fujita, Tomoyuki; Ohashi, Keisuke
2001-01-01
We present a full superconformal tensor calculus in five spacetime dimensions in which the Weyl multiplet has 32 Bose plus 32 Fermi degrees of freedom. It is derived using dimensional reduction from the 6D superconformal tensor calculus. We present two types of 32+32 Weyl multiplets, a vector multiplet, linear multiplet, hypermultiplet and nonlinear multiplet. Their superconformal transformation laws and the embedding and invariant action formulas are given. (author)
Null-strut calculus. I. Kinematics
International Nuclear Information System (INIS)
Kheyfets, A.; LaFave, N.J.; Miller, W.A.
1990-01-01
This paper describes the kinematics of null-strut calculus---a 3+1 Regge calculus approach to general relativity. We show how to model the geometry of spacetime with simplicial spacelike three-geometries (TET's) linked to ''earlier'' and ''later'' momentumlike lattice surfaces (TET * ) entirely by light rays or ''null struts.'' These three-layered lattice spacetime geometries are defined and analyzed using combinatorial formulas for the structure of polytopes. The following paper in this series describes how these three-layered spacetime lattices are used to model spacetimes in full conformity with Einstein's theory of gravity
Comparison between two differential graded algebras in ...
Indian Academy of Sciences (India)
76
A differential calculus on a “space” means the specification of a differential graded algebra (dga), often interpreted as space of forms. In classical geometry the “space” is a manifold and we have the de-Rham dga, whereas in noncommutative geometry a “space” is described by a triple called spectral triple. A spectral triple is ...
Teaching and learning of pre-calculus: an insights of educators ...
African Journals Online (AJOL)
The high-failure of Calculus courses has bring dilemma to the educators worldwide. This study has focus on teaching and learning of Pre-Calculus, a fundamental course for higher level Calculus courses. A well-designed questionnaire was distributed to all respondents to find the difficulties faced by both lecturers and ...
Backpropagation and ordered derivatives in the time scales calculus.
Seiffertt, John; Wunsch, Donald C
2010-08-01
Backpropagation is the most widely used neural network learning technique. It is based on the mathematical notion of an ordered derivative. In this paper, we present a formulation of ordered derivatives and the backpropagation training algorithm using the important emerging area of mathematics known as the time scales calculus. This calculus, with its potential for application to a wide variety of inter-disciplinary problems, is becoming a key area of mathematics. It is capable of unifying continuous and discrete analysis within one coherent theoretical framework. Using this calculus, we present here a generalization of backpropagation which is appropriate for cases beyond the specifically continuous or discrete. We develop a new multivariate chain rule of this calculus, define ordered derivatives on time scales, prove a key theorem about them, and derive the backpropagation weight update equations for a feedforward multilayer neural network architecture. By drawing together the time scales calculus and the area of neural network learning, we present the first connection of two major fields of research.
Water content contribution in calculus phantom ablation during Q-switched Tm:YAG laser lithotripsy.
Zhang, Jian J; Rajabhandharaks, Danop; Xuan, Jason Rongwei; Wang, Hui; Chia, Ray W J; Hasenberg, Tom; Kang, Hyun Wook
2015-01-01
Q-switched (QS) Tm:YAG laser ablation mechanisms on urinary calculi are still unclear to researchers. Here, dependence of water content in calculus phantom on calculus ablation performance was investigated. White gypsum cement was used as a calculus phantom model. The calculus phantoms were ablated by a total 3-J laser pulse exposure (20 mJ, 100 Hz, 1.5 s) and contact mode with N=15 sample size. Ablation volume was obtained on average 0.079, 0.122, and 0.391 mm3 in dry calculus in air, wet calculus in air, and wet calculus in-water groups, respectively. There were three proposed ablation mechanisms that could explain the effect of water content in calculus phantom on calculus ablation performance, including shock wave due to laser pulse injection and bubble collapse, spallation, and microexplosion. Increased absorption coefficient of wet calculus can cause stronger spallation process compared with that caused by dry calculus; as a result, higher calculus ablation was observed in both wet calculus in air and wet calculus in water. The test result also indicates that the shock waves generated by short laser pulse under the in-water condition have great impact on the ablation volume by Tm:YAG QS laser.
Supergravity tensor calculus in 5D from 6D
International Nuclear Information System (INIS)
Kugo, Taichiro; Ohashi, Keisuke
2000-01-01
Supergravity tensor calculus in five spacetime dimensions is derived by dimensional reduction from the d=6 superconformal tensor calculus. In particular, we obtain an off-shell hypermultiplet in 5D from the on-shell hypermultiplet in 6D. Our tensor calculus retains the dilatation gauge symmetry, so that it is a trivial gauge fixing to make the Einstein term canonical in a general matter-Yang-Mills-supergravity coupled system. (author)
The Enriched Eﬀect Calculus: Syntax and Semantics
DEFF Research Database (Denmark)
Møgelberg, Rasmus Ejlers; Simpson, Alex; Egger, Jeff
2014-01-01
This article introduces the enriched effect calculus, which extends established type theories for computational effects with primitives from linear logic. The new calculus provides a formalism for expressing linear aspects of computational effects; e.g. the linear usage of imperative features....... The second half of the article investigates models for the enriched effect calculus, based on enriched category theory. We give several examples of such models, relating them to models of standard effect calculi (such as those based on monads), and to models of intuitionistic linear logic. We also prove...
On the Expressive Power of Polyadic Synchronisation in Pi-Calculus
DEFF Research Database (Denmark)
Carbone, Marco; Maffeis, Sergio
2003-01-01
We extend the π-calculus with polyadic synchronisation, a generalisation of the communication mechanism which allows channel names to be composite. We show that this operator embeds nicely in the theory of π-calculus, we suggest that it permits divergence-free encodings of distributed calculi......, and we show that a limited form of polyadic synchronisation can be encoded weakly in π-calculus. After showing that matching cannot be derived in π-calculus, we compare the expressivity of polyadic synchronisation, mixed choice and matching. In particular we show that the degree of synchronisation...
Discrete Calculus as a Bridge between Scales
Degiuli, Eric; McElwaine, Jim
2012-02-01
Understanding how continuum descriptions of disordered media emerge from the microscopic scale is a fundamental challenge in condensed matter physics. In many systems, it is necessary to coarse-grain balance equations at the microscopic scale to obtain macroscopic equations. We report development of an exact, discrete calculus, which allows identification of discrete microscopic equations with their continuum equivalent [1]. This allows the application of powerful techniques of calculus, such as the Helmholtz decomposition, the Divergence Theorem, and Stokes' Theorem. We illustrate our results with granular materials. In particular, we show how Newton's laws for a single grain reproduce their continuum equivalent in the calculus. This allows introduction of a discrete Airy stress function, exactly as in the continuum. As an application of the formalism, we show how these results give the natural mean-field variation of discrete quantities, in agreement with numerical simulations. The discrete calculus thus acts as a bridge between discrete microscale quantities and continuous macroscale quantities. [4pt] [1] E. DeGiuli & J. McElwaine, PRE 2011. doi: 10.1103/PhysRevE.84.041310
Numerical convergence of discrete exterior calculus on arbitrary surface meshes
Mohamed, Mamdouh S.
2018-02-13
Discrete exterior calculus (DEC) is a structure-preserving numerical framework for partial differential equations solution, particularly suitable for simplicial meshes. A longstanding and widespread assumption has been that DEC requires special (Delaunay) triangulations, which complicated the mesh generation process especially for curved surfaces. This paper presents numerical evidence demonstrating that this restriction is unnecessary. Convergence experiments are carried out for various physical problems using both Delaunay and non-Delaunay triangulations. Signed diagonal definition for the key DEC operator (Hodge star) is adopted. The errors converge as expected for all considered meshes and experiments. This relieves the DEC paradigm from unnecessary triangulation limitation.
A calculus for attribute-based communication
DEFF Research Database (Denmark)
Alrahman, Yehia Abd; De Nicola, Rocco; Loreti, Michele
2015-01-01
The notion of attribute-based communication seems promising to model and analyse systems with huge numbers of interacting components that dynamically adjust and combine their behaviour to achieve specific goals. A basic process calculus, named AbC, is introduced that has as primitive construct...... of how well-established process calculi could be encoded into AbC is given by considering the translation into AbC of a proto-typical π-calculus process....
Differential equations for dummies
Holzner, Steven
2008-01-01
The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.
Regge calculus from discontinuous metrics
International Nuclear Information System (INIS)
Khatsymovsky, V.M.
2003-01-01
Regge calculus is considered as a particular case of the more general system where the linklengths of any two neighbouring 4-tetrahedra do not necessarily coincide on their common face. This system is treated as that one described by metric discontinuous on the faces. In the superspace of all discontinuous metrics the Regge calculus metrics form some hypersurface defined by continuity conditions. Quantum theory of the discontinuous metric system is assumed to be fixed somehow in the form of quantum measure on (the space of functionals on) the superspace. The problem of reducing this measure to the Regge hypersurface is addressed. The quantum Regge calculus measure is defined from a discontinuous metric measure by inserting the δ-function-like phase factor. The requirement that continuity conditions be imposed in a 'face-independent' way fixes this factor uniquely. The term 'face-independent' means that this factor depends only on the (hyper)plane spanned by the face, not on it's form and size. This requirement seems to be natural from the viewpoint of existence of the well-defined continuum limit maximally free of lattice artefacts
Nonlinear elliptic partial differential equations an introduction
Le Dret, Hervé
2018-01-01
This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite dimensional fixed point methods, the Galerkin method, the maximum principle, elliptic regularity, and the calculus of variations. Aimed at graduate students and researchers, this textbook contains numerous examples and exercises and provides several comments and suggestions for further study.
The impacts of gingivitis and calculus on Thai children's quality of life.
Krisdapong, Sudaduang; Prasertsom, Piyada; Rattanarangsima, Khanit; Sheiham, Aubrey; Tsakos, Georgios
2012-09-01
To assess associations of socio-demographic, behavioural and the extent of gingivitis and calculus with oral health-related quality of life (OHRQoL) in nationally representative samples of 12- and 15-year-old Thai children. In the Thailand National Oral Health Survey, 1,063 twelve-year olds and 811 fifteen-year olds were clinically examined and interviewed for OHRQoL using the Child-OIDP and OIDP indices, respectively, and completed a behavioural questionnaire. We assessed associations of condition-specific impacts (CS-impacts) with gingivitis and calculus, adjusted for socio-demographic and behavioural factors. Gingivitis and calculus were highly prevalent: 79.3% in 12-year and 81.5% in 15-year olds. CS-impacts relating to calculus and/or gingivitis were reported by 26.0% of 12-year and 29.6% of 15-year olds. Except for calculus without gingivitis, calculus and/or gingivitis in any form was significantly related to any level of CS-impacts. At a moderate or higher level of CS-impacts, there were significant relationships with extensive calculus and/or gingivitis in 12-year olds and for extensive gingivitis and gingivitis without calculus in 15-year olds. Gingivitis was generally associated with any level of CS-impacts attributed to calculus and/or gingivitis. CS-impacts were related more to gingivitis than to calculus. © 2012 John Wiley & Sons A/S.
A new class of problems in the calculus of variations
Ekeland, Ivar; Long, Yiming; Zhou, Qinglong
2013-11-01
This paper investigates an infinite-horizon problem in the one-dimensional calculus of variations, arising from the Ramsey model of endogeneous economic growth. Following Chichilnisky, we introduce an additional term, which models concern for the well-being of future generations. We show that there are no optimal solutions, but that there are equilibrium strateges, i.e. Nash equilibria of the leader-follower game between successive generations. To solve the problem, we approximate the Chichilnisky criterion by a biexponential criterion, we characterize its equilibria by a pair of coupled differential equations of HJB type, and we go to the limit. We find all the equilibrium strategies for the Chichilnisky criterion. The mathematical analysis is difficult because one has to solve an implicit differential equation in the sense of Thom. Our analysis extends earlier work by Ekeland and Lazrak.
Giant Calculus In The Mouth Of Partially Edentulous Woman, (Case ...
African Journals Online (AJOL)
Objective: This case report is to create awareness of the presence of giant calculus in the mouth, the possible causes and its prevention. Report: This describes the oral condition of a partially edentulous woman with a giant calculus in the mouth. It highlights the effect of such an enormous calculus in the oral cavity.
Improving Calculus II and III through the Redistribution of Topics
George, C. Yousuf; Koetz, Matt; Lewis, Heather A.
2016-01-01
Three years ago our mathematics department rearranged the topics in second and third semester calculus, moving multivariable calculus to the second semester and series to the third semester. This paper describes the new arrangement of topics, and how it could be adapted to calculus curricula at different schools. It also explains the benefits we…
Partial Fractions in Calculus, Number Theory, and Algebra
Yackel, C. A.; Denny, J. K.
2007-01-01
This paper explores the development of the method of partial fraction decomposition from elementary number theory through calculus to its abstraction in modern algebra. This unusual perspective makes the topic accessible and relevant to readers from high school through seasoned calculus instructors.
Differential geometry and mathematical physics
Rudolph, Gerd
Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous d...
Ferguson, Leann J.
2012-01-01
Calculus is an important tool for building mathematical models of the world around us and is thus used in a variety of disciplines, such as physics and engineering. These disciplines rely on calculus courses to provide the mathematical foundation needed for success in their courses. Unfortunately, due to the basal conceptions of what it means to…
DEFF Research Database (Denmark)
Hatcliff, John; Danvy, Olivier
1997-01-01
Thirty-five years ago, thunks were used to simulate call-by-name under call-by-value in Algol 60. Twenty years ago, Plotkin presented continuation-based simulations of call-by-name under call-by-value and vice versa in the λ-calculus. We connect all three of these classical simulations by factori......Thirty-five years ago, thunks were used to simulate call-by-name under call-by-value in Algol 60. Twenty years ago, Plotkin presented continuation-based simulations of call-by-name under call-by-value and vice versa in the λ-calculus. We connect all three of these classical simulations...
Quantum mechanics and umbral calculus
International Nuclear Information System (INIS)
Lopez-Sendino, J E; Negro, J; Olmo, M A del; Salgado, E
2008-01-01
In this paper we present the first steps for obtaining a discrete Quantum Mechanics making use of the Umbral Calculus. The idea is to discretize the continuous Schroedinger equation substituting the continuous derivatives by discrete ones and the space-time continuous variables by well determined operators that verify some Umbral Calculus conditions. In this way we assure that some properties of integrability and symmetries of the continuous equation are preserved and also the solutions of the continuous case can be recovered discretized in a simple way. The case of the Schroedinger equation with a potential depending only in the space variable is discussed.
Area Regge calculus and discontinuous metrics
International Nuclear Information System (INIS)
Wainwright, Chris; Williams, Ruth M
2004-01-01
Taking the triangle areas as independent variables in the theory of Regge calculus can lead to ambiguities in the edge lengths, which can be interpreted as discontinuities in the metric. We construct solutions to area Regge calculus using a triangulated lattice and find that on a spacelike or timelike hypersurface no such discontinuity can arise. On a null hypersurface however, we can have such a situation and the resulting metric can be interpreted as a so-called refractive wave
A Graph Calculus for Predicate Logic
Directory of Open Access Journals (Sweden)
Paulo A. S. Veloso
2013-03-01
Full Text Available We introduce a refutation graph calculus for classical first-order predicate logic, which is an extension of previous ones for binary relations. One reduces logical consequence to establishing that a constructed graph has empty extension, i. e. it represents bottom. Our calculus establishes that a graph has empty extension by converting it to a normal form, which is expanded to other graphs until we can recognize conflicting situations (equivalent to a formula and its negation.
Sandboxing in a Distributed Pi-Calculus
DEFF Research Database (Denmark)
Hüttel, Hans; Kühnrich, Morten
2006-01-01
This paper presents an extension of the Dpi-calculus due to Hennessy and Riely with constructs for signing and authenticating code and for sandboxing. A sort system, built on Milner's sort systems for the polyadic pi-calculus, is presented and proven sound with respect to an error predicate which...... ensures that errors do not occur outside sandboxes and that authentication and migration only happen when allowed. Futhermore a weak subject reduction result involving partial well sortedness is presented....
The dental calculus metabolome in modern and historic samples
DEFF Research Database (Denmark)
Velsko, Irina M.; Overmyer, Katherine A.; Speller, Camilla
2017-01-01
Introduction: Dental calculus is a mineralized microbial dental plaque biofilm that forms throughout life by precipitation of salivary calcium salts. Successive cycles of dental plaque growth and calcification make it an unusually well-preserved, long-term record of host-microbial interaction...... in the archaeological record. Recent studies have confirmed the survival of authentic ancient DNA and proteins within historic and prehistoric dental calculus, making it a promising substrate for investigating oral microbiome evolution via direct measurement and comparison of modern and ancient specimens. Objective: We...... present the first comprehensive characterization of the human dental calculus metabolome using a multi-platform approach. Methods: Ultra performance liquid chromatography-tandem mass spectrometry (UPLC–MS/MS) quantified 285 metabolites in modern and historic (200 years old) dental calculus, including...
Equality and fixpoints in the calculus of structures
DEFF Research Database (Denmark)
Chaudhuri, Kaustuv; Guenot, Nicolas
2014-01-01
The standard proof theory for logics with equality and fixpoints suffers from limitations of the sequent calculus, where reasoning is separated from computational tasks such as unification or rewriting. We propose in this paper an extension of the calculus of structures, a deep inference formalism...
Quantum stochastic calculus and representations of Lie superalgebras
Eyre, Timothy M W
1998-01-01
This book describes the representations of Lie superalgebras that are yielded by a graded version of Hudson-Parthasarathy quantum stochastic calculus. Quantum stochastic calculus and grading theory are given concise introductions, extending readership to mathematicians and physicists with a basic knowledge of algebra and infinite-dimensional Hilbert spaces. The develpment of an explicit formula for the chaotic expansion of a polynomial of quantum stochastic integrals is particularly interesting. The book aims to provide a self-contained exposition of what is known about Z_2-graded quantum stochastic calculus and to provide a framework for future research into this new and fertile area.
Discrete Quantum Gravity in the Regge Calculus Formalism
International Nuclear Information System (INIS)
Khatsymovsky, V.M.
2005-01-01
We discuss an approach to the discrete quantum gravity in the Regge calculus formalism that was developed in a number of our papers. The Regge calculus is general relativity for a subclass of general Riemannian manifolds called piecewise flat manifolds. The Regge calculus deals with a discrete set of variables, triangulation lengths, and contains continuous general relativity as a special limiting case where the lengths tend to zero. In our approach, the quantum length expectations are nonzero and of the order of the Plank scale, 10 -33 cm, implying a discrete spacetime structure on these scales
Discrete quantum gravitation in formalism of Regge calculus
International Nuclear Information System (INIS)
Khatsimovskij, V.M.
2005-01-01
One deals with approach to the discrete quantum gravitation in terms of the Regge calculus formalism. The Regge calculus represents the general relativity theory for the Riemann varieties - the piecewise planar varieties. The Regge calculus makes use of the discrete set of variables, triangulation lengths, and contains the continuous general relativity theory serving as a limiting special case when lengths tend to zero. In terms of our approach the quantum mean values of the mentioned lengths differ from zero and 10 -33 cm Planck length and it implies the discrete structure of space-time at the mentioned scales [ru
Nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.
Nonlinear differential equations
International Nuclear Information System (INIS)
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics
The giant calculus within the prostatic urethra.
Demir, Omer; Kefi, Aykut; Cahangirov, Asif; Cihan, Ahmet; Obuz, Funda; Esen, Adil Ahmet; Celebi, Ilhan
2011-08-01
The giant calculus within the prostatic urethra is a rare clinical entity in the young population. Most of the calculi within the urethra migrate from the urinary bladder and obliterate the urethra. These stones are often composed of calcium phosphate or calcium oxalate. The decision of treatment strategy is affected by the size, shape and position of the calculus and by the status of the urethra. If the stone is large and immovable, it may be extracted via the perineal or the suprapubic approach. In most cases, the giant calculi were extracted via the transvesical approach and external urethrotomy. Our case is the biggest prostatic calculus, known in the literature so far, which was treated endoscopically by the combination of laser and the pneumatic lithotriptor.
Elements of stochastic calculus and analysis
Stroock, Daniel W
2018-01-01
This book gives a somewhat unconventional introduction to stochastic analysis. Although most of the material covered here has appeared in other places, this book attempts to explain the core ideas on which that material is based. As a consequence, the presentation is more an extended mathematical essay than a ``definition, lemma, theorem'' text. In addition, it includes several topics that are not usually treated elsewhere. For example, Wiener's theory of homogeneous chaos is discussed, Stratovich integration is given a novel development and applied to derive Wong and Zakai's approximation theorem, and examples are given of the application of Malliavin's calculus to partial differential equations. Each chapter concludes with several exercises, some of which are quite challenging. The book is intended for use by advanced graduate students and research mathematicians who may be familiar with many of the topics but want to broaden their understanding of them.
Calculus Instructors' and Students' Discourses on the Derivative
Park, Jungeun
2011-01-01
Recently, there has been an increasing interest in collegiate mathematics education, especially teaching and learning calculus (e.g., Oehrtman, Carlson, & Thompson, 2008; Speer, Smith, & Horvath, 2010). Of many calculus concepts, the derivative is known as a difficult concept for students to understand because it involves various concepts…
Reflections on Our First Calculus Undergraduate Teaching Assistant
Deshler, Jessica M.
2016-01-01
This article describes some reflections from the first Calculus I undergraduate teaching assistant in our department as she explored the various ways in which she was able to support both novice and experienced Calculus teachers and the effect of her experience on her academic and career plans.
Executable Behaviour and the π-Calculus (extended abstract
Directory of Open Access Journals (Sweden)
Bas Luttik
2015-08-01
Full Text Available Reactive Turing machines extend classical Turing machines with a facility to model observable interactive behaviour. We call a behaviour executable if, and only if, it is behaviourally equivalent to the behaviour of a reactive Turing machine. In this paper, we study the relationship between executable behaviour and behaviour that can be specified in the pi-calculus. We establish that all executable behaviour can be specified in the pi-calculus up to divergence-preserving branching bisimilarity. The converse, however, is not true due to (intended limitations of the model of reactive Turing machines. That is, the pi-calculus allows the specification of behaviour that is not executable up to divergence-preserving branching bisimilarity. Motivated by an intuitive understanding of executability, we then consider a restriction on the operational semantics of the pi-calculus that does associate with every pi-term executable behaviour, at least up to the version of branching bisimilarity that does not require the preservation of divergence.
Investigation of In vitro Mineral forming bacterial isolates from supragingival calculus.
Baris, O; Demir, T; Gulluce, M
2017-12-01
Although it is known that bacterial mechanisms are involved in dental calculus formation, which is a predisposing factor in periodontal diseases, there have been few studies of such associations, and therefore, information available is limited. The purpose of this study was to isolate and identify aerobic bacteria responsible for direct calcification from supragingival calculus samples. The study was conducted using supragingival calculus samples from patients with periodontal disease, which was required as part of conventional treatment. Isolations were performed by sampling the supragingival calculus with buffer and inoculating the samples on media on which crystallization could be observed. The 16S recombinant DNA of the obtained pure cultures was then amplified and sequenced. A few bacterial species that have not previously been associated with mineralization or identified on bacterial plaque or calculus were detected. The bacteria that caused mineralization an aerobic environment are identified as Neisseria flava, Aggregatibacter segnis, Streptococcus tigurinus, and Morococcus cerebrosus. These findings proved that bacteria potentially play a role in the etiopathology of supragingival calculus. The association between the effects of the identified bacteria on periodontal diseases and calculus formation requires further studies.
Mahalingam, Harshavardhan; Lal, Anupam; Mandal, Arup K; Singh, Shrawan Kumar; Bhattacharyya, Shalmoli; Khandelwal, Niranjan
2015-08-01
This study aimed to assess the accuracy of low-dose dual-energy computed tomography (DECT) in predicting the composition of urinary calculi. A total of 52 patients with urinary calculi were scanned with a 128-slice dual-source DECT scanner by use of a low-dose protocol. Dual-energy (DE) ratio, weighted average Hounsfield unit (HU) of calculi, radiation dose, and image noise levels were recorded. Two radiologists independently rated study quality. Stone composition was assessed after extraction by Fourier transform infrared spectroscopy (FTIRS). Analysis of variance was used to determine if the differences in HU values and DE ratios between the various calculus groups were significant. Threshold cutoff values to classify the calculi into separate groups were identified by receiver operating characteristic curve analysis. A total of 137 calculi were detected. FTIRS analysis differentiated the calculi into five groups: uric acid (n=17), struvite (n=3), calcium oxalate monohydrate and dihydrate (COM-COD, n=84), calcium oxalate monohydrate (COM, n=28), and carbonate apatite (n=5). The HU value could differentiate only uric acid calculi from calcified calculi (p80% sensitivity and specificity to differentiate them. The DE ratio could not differentiate COM from COM-COD calculi. No study was rated poor in quality by either of the observers. The mean radiation dose was 1.8 mSv. Low-dose DECT accurately predicts urinary calculus composition in vivo while simultaneously reducing radiation exposure without compromising study quality.
Length expectation values in quantum Regge calculus
International Nuclear Information System (INIS)
Khatsymovsky, V.M.
2004-01-01
Regge calculus configuration superspace can be embedded into a more general superspace where the length of any edge is defined ambiguously depending on the 4-tetrahedron containing the edge. Moreover, the latter superspace can be extended further so that even edge lengths in each the 4-tetrahedron are not defined, only area tensors of the 2-faces in it are. We make use of our previous result concerning quantization of the area tensor Regge calculus which gives finite expectation values for areas. Also our result is used showing that quantum measure in the Regge calculus can be uniquely fixed once we know quantum measure on (the space of the functionals on) the superspace of the theory with ambiguously defined edge lengths. We find that in this framework quantization of the usual Regge calculus is defined up to a parameter. The theory may possess nonzero (of the order of Planck scale) or zero length expectation values depending on whether this parameter is larger or smaller than a certain value. Vanishing length expectation values means that the theory is becoming continuous, here dynamically in the originally discrete framework
Enabling quaternion derivatives: the generalized HR calculus
Xu, Dongpo; Jahanchahi, Cyrus; Took, Clive C.; Mandic, Danilo P.
2015-01-01
Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutativity of quaternion algebra. To address this issue, we introduce the generalized HR (GHR) derivatives which employ quaternion rotations in a general orthogonal system and provide the left- and right-hand versions of the quaternion derivative of general functions. The GHR calculus also solves the long-standing problems of product and chain rules, mean-value theorem and Taylor's theorem in the quaternion field. At the core of the proposed GHR calculus is quaternion rotation, which makes it possible to extend the principle to other functional calculi in non-commutative settings. Examples in statistical learning theory and adaptive signal processing support the analysis. PMID:26361555
Model-order reduction of lumped parameter systems via fractional calculus
Hollkamp, John P.; Sen, Mihir; Semperlotti, Fabio
2018-04-01
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach to the simulation of non-homogeneous systems dictates the use of numerical solutions and often imposes stringent compromises between accuracy and computational performance. Fractional calculus provides an alternative approach where complex dynamical systems can be modeled with compact fractional equations that not only can still guarantee analytical solutions, but can also enable high levels of order reduction without compromising on accuracy. Different approaches are explored in order to transform the integer order model into a reduced order fractional model able to match the dynamic response of the initial system. Analytical and numerical results show that, under certain conditions, an exact match is possible and the resulting fractional differential models have both a complex and frequency-dependent order of the differential operator. The implications of this type of approach for both model order reduction and model synthesis are discussed.
Utilizing Microsoft Mathematics in Teaching and Learning Calculus
Oktaviyanthi, Rina; Supriani, Yani
2015-01-01
The experimental design was conducted to investigate the use of Microsoft Mathematics, free software made by Microsoft Corporation, in teaching and learning Calculus. This paper reports results from experimental study details on implementation of Microsoft Mathematics in Calculus, students' achievement and the effects of the use of Microsoft…
The development and nature of problem-solving among first-semester calculus students
Dawkins, Paul Christian; Mendoza Epperson, James A.
2014-08-01
This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate this blended instruction as a local representative of the US calculus reform movements that helped foster it. These reform movements tended to emphasize problem-solving as well as multiple mathematical registers and quantitative modelling. Our statistical analysis reveals the influence of the blended traditional/reform calculus instruction on students' ability to solve calculus-related, non-routine problems through repeated measures over the semester. The calculus instruction in this study significantly improved students' performance on non-routine problems, though performance improved more regarding strategies and accuracy than it did for drawing conclusions and providing justifications. We identified problem-solving behaviours that characterized top performance or attrition in the course. Top-performing students displayed greater algebraic proficiency, calculus skills, and more general heuristics than their peers, but overused algebraic techniques even when they proved cumbersome or inappropriate. Students who subsequently withdrew from calculus often lacked algebraic fluency and understanding of the graphical register. The majority of participants, when given a choice, relied upon less sophisticated trial-and-error approaches in the numerical register and rarely used the graphical register, contrary to the goals of US calculus reform. We provide explanations for these patterns in students' problem-solving performance in view of both their preparation for university calculus and the courses' assessment structure, which preferentially rewarded algebraic reasoning. While instruction improved students' problem
Advances in fractional calculus theoretical developments and applications in physics and engineering
Sabatier, J; Machado, J A Teneiro
2007-01-01
Fractional Calculus is a new growing field. Up to this point, researchers, scientists, and engineers have been reluctant to accept the fact that Fractional Calculus can be used in the analysis and design of many systems of practical interests, whereas in similar applications the traditional calculus either fails or provides poor solutionsMany engineers, scientists, and applied mathematicians are looking for books that can provide many applications of Fractional Calculus. This book will provide a partial solution to this problem. Since it covers recent applications of Fractional Calculus, it will be attractive to many engineers, scientists, and applied mathematicians.
Multivariate calculus and geometry
Dineen, Seán
2014-01-01
Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.
Representing and reasoning about program in situation calculus
Yang, Bo; Zhang, Ming-yi; Wu, Mao-nian; Xie, Gang
2011-12-01
Situation calculus is an expressive tool for modeling dynamical system in artificial intelligence, changes in a dynamical world is represented naturally by the notions of action, situation and fluent in situation calculus. Program can be viewed as a discrete dynamical system, so it is possible to model program with situation calculus. To model program written in a smaller core programming language CL, notion of fluent is expanded for representing value of expression. Together with some functions returning concerned objects from expressions, a basic action theory of CL programming is constructed. Under such a theory, some properties of program, such as correctness and termination can be reasoned about.
Reggeon calculus at collider energies
International Nuclear Information System (INIS)
Pajares, C.; Varias, A.; Yepes, P.
1983-01-01
The phenomenology of the perturbative reggeon calculus at collider energies is studied. It is found that the graphs which were neglected at ISR energies are still negligeable at √s=540 GeV. The perturbative series for the total cross section still converges reasonably fast. The values of the different parameters which describe rightly the data up to ISR energies give rise to a total cross section of around 60 mb at √s=540 GeV. For these values, the corresponding low mass and high mass eikonal series converges much more slowly. The non perturbative reggeon calculus gives rise to a total cross section less than 60 mb. (orig.)
Sequent Calculus and Equational Programming
Directory of Open Access Journals (Sweden)
Nicolas Guenot
2015-07-01
Full Text Available Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus. A typed functional language is presented, based on a sequent calculus, that we relate to the syntax and internal language of Agda. In particular, we discuss the use of patterns and case splittings, as well as rules implementing inductive reasoning and dependent products and sums.
Golden quantum oscillator and Binet–Fibonacci calculus
International Nuclear Information System (INIS)
Pashaev, Oktay K; Nalci, Sengul
2012-01-01
The Binet formula for Fibonacci numbers is treated as a q-number and a q-operator with Golden ratio bases q = φ and Q = −1/φ, and the corresponding Fibonacci or Golden calculus is developed. A quantum harmonic oscillator for this Golden calculus is derived so that its spectrum is given only by Fibonacci numbers. The ratio of successive energy levels is found to be the Golden sequence, and for asymptotic states in the limit n → ∞ it appears as the Golden ratio. We call this oscillator the Golden oscillator. Using double Golden bosons, the Golden angular momentum and its representation in terms of Fibonacci numbers and the Golden ratio are derived. Relations of Fibonacci calculus with a q-deformed fermion oscillator and entangled N-qubit states are indicated. (paper)
Golden quantum oscillator and Binet-Fibonacci calculus
Energy Technology Data Exchange (ETDEWEB)
Pashaev, Oktay K; Nalci, Sengul, E-mail: oktaypashaev@iyte.edu.tr [Department of Mathematics, Izmir Institute of Technology, Urla-Izmir 35430 (Turkey)
2012-01-13
The Binet formula for Fibonacci numbers is treated as a q-number and a q-operator with Golden ratio bases q = {phi} and Q = -1/{phi}, and the corresponding Fibonacci or Golden calculus is developed. A quantum harmonic oscillator for this Golden calculus is derived so that its spectrum is given only by Fibonacci numbers. The ratio of successive energy levels is found to be the Golden sequence, and for asymptotic states in the limit n {yields} {infinity} it appears as the Golden ratio. We call this oscillator the Golden oscillator. Using double Golden bosons, the Golden angular momentum and its representation in terms of Fibonacci numbers and the Golden ratio are derived. Relations of Fibonacci calculus with a q-deformed fermion oscillator and entangled N-qubit states are indicated. (paper)
Catwalk: First-Semester Calculus.
Speiser, Bob; Walter, Chuck
1994-01-01
Describes the use of time-lapse photographs of a running cat as a model to investigate the concepts of function and derivative in a college calculus course. Discusses student difficulties and implications for teachers. (MKR)
A study of ∇-discrete fractional calculus operator on the radial ...
African Journals Online (AJOL)
The fractional calculus includes concepts of integrals and derivatives of any complex or real order. The fractional calculus is as old as the usual calculus. Recently, many scientists have been studying on this eld to provide the development and applicability to various areas of mathematics, physics, engineering and other ...
Coordinating Multiple Representations in a Reform Calculus Textbook
Chang, Briana L.; Cromley, Jennifer G.; Tran, Nhi
2016-01-01
Coordination of multiple representations (CMR) is widely recognized as a critical skill in mathematics and is frequently demanded in reform calculus textbooks. However, little is known about the prevalence of coordination tasks in such textbooks. We coded 707 instances of CMR in a widely used reform calculus textbook and analyzed the distributions…
A phenomenological calculus of Wiener description space.
Richardson, I W; Louie, A H
2007-10-01
The phenomenological calculus is a categorical example of Robert Rosen's modeling relation. This paper is an alligation of the phenomenological calculus and generalized harmonic analysis, another categorical example. Our epistemological exploration continues into the realm of Wiener description space, in which constitutive parameters are extended from vectors to vector-valued functions of a real variable. Inherent in the phenomenology are fundamental representations of time and nearness to equilibrium.
Site specific mineral composition and microstructure of human supra-gingival dental calculus.
Hayashizaki, Junko; Ban, Seiji; Nakagaki, Haruo; Okumura, Akihiko; Yoshii, Saori; Robinson, Colin
2008-02-01
Dental calculus has been implicated in the aetiology of several periodontal conditions. Its prevention and removal are therefore desirable clinical goals. While it is known that calculus is very variable in chemical composition, crystallinity and crystallite size little is known about site specific variability within a dentition and between individuals. With this in mind, a study was undertaken to investigate the comparative site specific nature and composition of human dental supra-gingival dental calculus obtained from 66 male patients visiting for their dental check-up using fluorescent X-ray spectroscopy, X-ray diffractometry and Fourier transform infrared spectroscopy. The supra-gingival dental calculus formed on the lingual surfaces of lower anterior teeth and the buccal surfaces of upper molar teeth were classified into four types based on calcium phosphate phases present. There was significant difference in composition of the crystal phase types between lower and upper teeth (pdental calculus on anterior or molar teeth of all samples. The degree of crystallinity of dental calculus formed on the upper molar teeth was higher than that formed on the lower anterior teeth (pdental calculus formed on the lower anterior teeth were higher than on upper molar teeth (pdental supra-gingival dental calculus is related to its location in the mouth.
A many-sorted calculus based on resolution and paramodulation
Walther, Christoph
1987-01-01
A Many-Sorted Calculus Based on Resolution and Paramodulation emphasizes the utilization of advantages and concepts of many-sorted logic for resolution and paramodulation based automated theorem proving.This book considers some first-order calculus that defines how theorems from given hypotheses by pure syntactic reasoning are obtained, shifting all the semantic and implicit argumentation to the syntactic and explicit level of formal first-order reasoning. This text discusses the efficiency of many-sorted reasoning, formal preliminaries for the RP- and ?RP-calculus, and many-sorted term rewrit
Dental hygiene faculty calibration in the evaluation of calculus detection.
Garland, Kandis V; Newell, Kathleen J
2009-03-01
The purpose of this pilot study was to explore the impact of faculty calibration training on intra- and interrater reliability regarding calculus detection. After IRB approval, twelve dental hygiene faculty members were recruited from a pool of twenty-two for voluntary participation and randomized into two groups. All subjects provided two pre- and two posttest scorings of calculus deposits on each of three typodonts by recording yes or no indicating if they detected calculus. Accuracy and consistency of calculus detection were evaluated using an answer key. The experimental group received three two-hour training sessions to practice a prescribed exploring sequence and technique for calculus detection. Participants immediately corrected their answers, received feedback from the trainer, and reconciled missed areas. Intra- and interrater reliability (pre- and posttest) was determined using Cohen's Kappa and compared between groups using repeated measures (split-plot) ANOVA. The groups did not differ from pre- to posttraining (intrarater reliability p=0.64; interrater reliability p=0.20). Training had no effect on reliability levels for simulated calculus detection in this study. Recommendations for future studies of faculty calibration when evaluating students include using patients for assessing rater reliability, employing larger samples at multiple sites, and assessing the impact on students' attitudes and learning outcomes.
Indian Academy of Sciences (India)
IAS Admin
Sphere–Cylinder Theorem, vol- ume and surface area of the torus, volume and surface area of a slice of a solid sphere. The author earned his PhD degree in mathematics. (topology), in 2000, from. Panjab University,. Chandigarh and since then he has been teaching analysis, algebra, calculus and discrete mathematics at.
Effect of Ramadan fasting on urinary risk factors for calculus formation.
Miladipour, Amir Hossein; Shakhssalim, Nasser; Parvin, Mahmoud; Azadvari, Mohaddeseh
2012-01-01
Even though dehydration could aggravate formation of urinary calculi, the effects of fluid and food restriction on calculus formation is not thoroughly defined. The purpose of this study is to evaluate the effects of fluid and food restriction in Ramadan fasting on urinary factors in kidney and urinary calculus formation. Fifty-seven men aged 30 to 55 years old, including 37 recurrent calcium calculus formers and 20 with no history of kidney calculi were evaluated for blood tests, ultrasonography investigations, urinalysis, urine culture, and also 24-hour urine collection test. Metabolites including calcium, oxalate, citrate, uric acid, magnesium, phosphate, potassium, sodium, and creatinine were measured before and during Ramadan fasting. The values of calculus-precipitating solutes as well as inhibitory factors were documented thoroughly. Total excretion of calcium, phosphate, and magnesium in 24-hour urine and also urine volume during fasting were significantly lower than those in the nonfasting period. Urine concentration of calcium during fasting was significantly lower than nonfasting (P calculus formation. We did not find enough evidence in favor of increased risks of calculus formation during Ramadan fasting.
Probabilistic Analysis of the Quality Calculus
DEFF Research Database (Denmark)
Nielson, Hanne Riis; Nielson, Flemming
2013-01-01
We consider a fragment of the Quality Calculus, previously introduced for defensive programming of software components such that it becomes natural to plan for default behaviour in case the ideal behaviour fails due to unreliable communication. This paper develops a probabilistically based trust...... analysis supporting the Quality Calculus. It uses information about the probabilities that expected input will be absent in order to determine the trustworthiness of the data used for controlling the distributed system; the main challenge is to take accord of the stochastic dependency between some...
More on differential calculi on bicrossproducts
International Nuclear Information System (INIS)
Ngakeu, F.
2005-09-01
We extend a previous classification of differentials and Cartan calculus on the bicrossproduct quantum group k(M)-blacktriangleright triangleleft-kG to its dual Hopf algebra H = kM-triangleright blacktriangleleft-k(G). It turns out that the usual bicovariant differential calculi on kM and on k(G) extend naturally to H. We explicitly work out the examples of kZ 2 -triangleright blacktriangleleft (Z 3 ) and kZ 6 -triangleright 3 ). (author)
Regge calculus: applications to classical and quantum gravity
International Nuclear Information System (INIS)
Lewis, S.M.
1983-01-01
Regge calculus is a simplicial approximation to general relativity which preserves many topological and geometrical properties of the exact theory. After discussing the foundations of this technique and deriving some basic identities, specific solutions to Regge calculus are analyzed. In particular, the flat Friedmann-Robertson-Walker (FRW) model is shown. This particular model is used in the discussion of the initial value problem for Regge calculus. An Arnowitt-Deser-Misner type of 3 + 1 decomposition is possible only under very special circumstances; solutions with a non-spatially constant lapse can not generally be decomposed. The flat FRW model is also used to compute the accuracy of this approximation method developed by Regge. A three-dimensional toy model of quantum gravity is discussed that was originally formulated by Ponzano and Regge. A more thorough calculation is performed that takes into account additional terms. The renormalization properties of this model are shown. Finally, speculations are made on the interaction of the geometry, topology and quantum effects using Regge calculus, which, because of its simplicial nature, makes these effects more amenable to calculation and intuition
Three-plus-one formulation of Regge calculus
International Nuclear Information System (INIS)
Piran, T.; Williams, R.M.
1986-01-01
Following the work of Lund and Regge for homogeneous spaces, we construct the action for Regge calculus in its three-plus-one form for general space-times. This is achieved in two ways: a first-order formalism and a second-order formalism. We describe the Regge-calculus analogue of solving the initial-value equations using conformal transformations. The second-order formalism is used to study the time development of two simple model universes
Fisher information, Borges operators, and q-calculus
Pennini, F.; Plastino, A.; Ferri, G. L.
2008-10-01
We discuss applying the increasingly popular q-calculus, or deformed calculus, so as to suitably generalize Fisher’s information measure and the Cramer-Rao inequality. A q-deformation can be attained in multiple ways, and we show that most of them do not constitute legitimate procedures. Within such a context, the only completely acceptable q-deformation is that ensuing from using the so-called Borges derivative [E.P. Borges, Physica A 340 (2004) 95].
Reggeon calculus as a low-order perturbation theory for the Pomeron
International Nuclear Information System (INIS)
DeTar, C.
1975-01-01
We review the foundations of the Gribov Reggeon calculus with an emphasis on the relationship between the energy-plane and J-plane descriptions of the diagrams of the calculus. The question of the ''large-rapidity-gap cutoff'' for the Pomeron and the problem of signature are treated in more detail than in the traditional approach to the calculus. Except for some slight differences, the main results agree with Gribov's original formulation. We advocate the use of the Reggeon calculus as a refinement on the contemporary ''two-component'' model for the Pomeron and collect some formulas useful for phenomenological applications
Secure Data Flow in a Calculus for Context Awareness
DEFF Research Database (Denmark)
Bucur, Doina; Nielsen, Mogens
2008-01-01
We present a Mobile-Ambients-based process calculus to describe context-aware computing in an infrastructure-based Ubiquitous Computing setting. In our calculus, computing agents can provide and discover contextual information and are owners of security policies. Simple access control to contextual...
Visual Thinking and Gender Differences in High School Calculus
Haciomeroglu, Erhan Selcuk; Chicken, Eric
2012-01-01
This study sought to examine calculus students' mathematical performances and preferences for visual or analytic thinking regarding derivative and antiderivative tasks presented graphically. It extends previous studies by investigating factors mediating calculus students' mathematical performances and their preferred modes of thinking. Data were…
Metric regularity and subdifferential calculus
International Nuclear Information System (INIS)
Ioffe, A D
2000-01-01
The theory of metric regularity is an extension of two classical results: the Lyusternik tangent space theorem and the Graves surjection theorem. Developments in non-smooth analysis in the 1980s and 1990s paved the way for a number of far-reaching extensions of these results. It was also well understood that the phenomena behind the results are of metric origin, not connected with any linear structure. At the same time it became clear that some basic hypotheses of the subdifferential calculus are closely connected with the metric regularity of certain set-valued maps. The survey is devoted to the metric theory of metric regularity and its connection with subdifferential calculus in Banach spaces
The dental calculus metabolome in modern and historic samples.
Velsko, Irina M; Overmyer, Katherine A; Speller, Camilla; Klaus, Lauren; Collins, Matthew J; Loe, Louise; Frantz, Laurent A F; Sankaranarayanan, Krithivasan; Lewis, Cecil M; Martinez, Juan Bautista Rodriguez; Chaves, Eros; Coon, Joshua J; Larson, Greger; Warinner, Christina
2017-01-01
Dental calculus is a mineralized microbial dental plaque biofilm that forms throughout life by precipitation of salivary calcium salts. Successive cycles of dental plaque growth and calcification make it an unusually well-preserved, long-term record of host-microbial interaction in the archaeological record. Recent studies have confirmed the survival of authentic ancient DNA and proteins within historic and prehistoric dental calculus, making it a promising substrate for investigating oral microbiome evolution via direct measurement and comparison of modern and ancient specimens. We present the first comprehensive characterization of the human dental calculus metabolome using a multi-platform approach. Ultra performance liquid chromatography-tandem mass spectrometry (UPLC-MS/MS) quantified 285 metabolites in modern and historic (200 years old) dental calculus, including metabolites of drug and dietary origin. A subset of historic samples was additionally analyzed by high-resolution gas chromatography-MS (GC-MS) and UPLC-MS/MS for further characterization of metabolites and lipids. Metabolite profiles of modern and historic calculus were compared to identify patterns of persistence and loss. Dipeptides, free amino acids, free nucleotides, and carbohydrates substantially decrease in abundance and ubiquity in archaeological samples, with some exceptions. Lipids generally persist, and saturated and mono-unsaturated medium and long chain fatty acids appear to be well-preserved, while metabolic derivatives related to oxidation and chemical degradation are found at higher levels in archaeological dental calculus than fresh samples. The results of this study indicate that certain metabolite classes have higher potential for recovery over long time scales and may serve as appropriate targets for oral microbiome evolutionary studies.
Solitary main pancreatic ductal calculus of possible biliary origin causing acute pancreatitis.
Chaparala, Ramakrishna Prasad Chowdary; Patel, Rafiuddin; Guthrie, James Ahsley; Davies, Mervyn Huw; Guillou, Pierre J; Menon, Krishna V
2005-09-10
Pancreatic ductal calculi are most often associated with chronic pancreatitis. Radiological features of chronic pancreatitis are readily evident in the presence of these calculi. However, acute pancreatitis due to a solitary main pancreatic ductal calculus of biliary origin is rare. A 59-year-old man presented with a first episode of acute pancreatitis. Contrast enhanced computerized tomography (CT) scan and endoscopic retrograde cholangiopancreatography (ERCP) revealed a calculus in the main pancreatic duct in the head of the pancreas causing acute pancreatitis. There were no features suggestive of chronic pancreatitis on CT scanning. The episode acute pancreatitis was managed conservatively. ERCP extraction of the calculus failed as the stone was impacted in the main pancreatic duct resulting in severe acute pancreatitis. Once this resolved, a transduodenal exploration and extraction of the pancreatic ductal calculus was performed successfully. Crystallographic analysis revealed the composition of the calculus was different to that seen in chronic pancreatitis, but more in keeping with a calculus of biliary origin. This could be explained by migration of the biliary calculus via the common channel into the main pancreatic duct. Following the operation the patient made an uneventful recovery and was well at two-year follow up. Acute pancreatitis due to a solitary main pancreatic ductal calculus of biliary origin is rare. Failing endoscopic extraction, transduodenal exploration and extraction is a safe option after resolution of acute pancreatitis.
Duality and calculus of convex objects (theory and applications)
International Nuclear Information System (INIS)
Brinkhuis, Ya; Tikhomirov, V M
2007-01-01
A new approach to convex calculus is presented, which allows one to treat from a single point of view duality and calculus for various convex objects. This approach is based on the possibility of associating with each convex object (a convex set or a convex function) a certain convex cone without loss of information about the object. From the duality theorem for cones duality theorems for other convex objects are deduced as consequences. The theme 'Duality formulae and the calculus of convex objects' is exhausted (from a certain precisely formulated point of view). Bibliography: 5 titles.
African Journals Online (AJOL)
Giant vesical calculus. A case report. H. H. LAUBSCHER. Summary. An exceptional case of bladder stone is presented. The case is unusual as regards the size of the stone and the fact that the patient did··not seek medical assistance much earlier, as this was readily avail- able. Furthermore, recovery after removal of the.
Preservation of the metaproteome: variability of protein preservation in ancient dental calculus.
Mackie, Meaghan; Hendy, Jessica; Lowe, Abigail D; Sperduti, Alessandra; Holst, Malin; Collins, Matthew J; Speller, Camilla F
2017-01-01
Proteomic analysis of dental calculus is emerging as a powerful tool for disease and dietary characterisation of archaeological populations. To better understand the variability in protein results from dental calculus, we analysed 21 samples from three Roman-period populations to compare: 1) the quantity of extracted protein; 2) the number of mass spectral queries; and 3) the number of peptide spectral matches and protein identifications. We found little correlation between the quantity of calculus analysed and total protein identifications, as well as no systematic trends between site location and protein preservation. We identified a wide range of individual variability, which may be associated with the mechanisms of calculus formation and/or post-depositional contamination, in addition to taphonomic factors. Our results suggest dental calculus is indeed a stable, long-term reservoir of proteins as previously reported, but further systematic studies are needed to identify mechanisms associated with protein entrapment and survival in dental calculus.
Effect of non-functional teeth on accumulation of supra-gingival calculus in children.
Ashkenazi, M; Miller, R; Levin, L
2012-10-01
To evaluate the occurrence of supra-gingival calculus in children aged 6-9 years with disuse conditions such as: presence of dental pain, open-bite or erupting teeth. A cohort of 327 children aged 7.64±2.12 (range: 6-9) years (45% girls) were screened for presence of supra-gingival calculus in relation to open bite, erupting teeth and dental pain. Presence of dental calculus was evaluated dichotomically in the buccal, palatinal/lingual and occlusal surfaces. Plaque index (PI) and gingival index (GI) were also evaluated. Supra-gingival calculus was found in 15.9% of the children mainly in the mandibular incisors. Children aged 6-7 years had a higher prevalence of calculus as compared to children aged 7-8 years (23% vs. 13.5%, p=0.057) or 8-9 years (23% vs. 12.4%, p=0.078), respectively. No statistical relation was found between plaque and gingival indices and presence of calculus. The prevalence of calculus among children with openbite was significantly higher than that of children without open-bite (29.4% vs. 10.7%, p=0.0006, OR=3.489). The prevalence of calculus among children with erupting teeth in their oral cavity was higher than that of children without erupting teeth (17.7% vs. 9%, respectively, p=0.119). No statistical correlation was found between presence of dental pain and calculus (15.4% vs. 15.9%; p=0.738). Accumulation of calculus in children aged 6-10 years was found mainly in the mandibular incisors, decreased with age and was correlated with open-bite.
[Percentage of uric acid calculus and its metabolic character in Dongjiang River valley].
Chong, Hong-Heng; An, Geng
2009-02-15
To study the percentage of uric acid calculus in uroliths and its metabolic character in Dongjiang River valley. To analyze the chemical composition of 290 urinary stones by infrared (IR) spectroscopy and study the ratio changes of uric acid calculus. Uric acid calculus patients and healthy people were studied. Personal characteristics, dietary habits were collected. Conditional logistic regression was used for data analysis and studied the dietary risk factors of uric acid calculus. Patients with uric acid calculus, calcium oxalate and those without urinary calculus were undergone metabolic evaluation analysis. The results of uric acid calculus patients compared to another two groups to analysis the relations between the formation of uric acid calculus and metabolism factors. Uric acid calculi were found in 53 cases (18.3%). The multiple logistic regression analysis suggested that low daily water intake, eating more salted and animal food, less vegetable were very closely associated with uric acid calculus. Comparing to calcium oxalate patients, the urine volume, the value of pH, urine calcium, urine oxalic acid were lower, but uric acid was higher than it. The value of pH, urine oxalic acid and citric acid were lower than them, but uric acid and urine calcium were higher than none urinary calculus peoples. Blood potassium and magnesium were lower than them. The percentage of uric acid stones had obvious advanced. Less daily water intake, eating salted food, eating more animal food, less vegetables and daily orange juice intake, eating sea food are the mainly dietary risk factors to the formation of uric acid calculus. Urine volume, the value of pH, citric acid, urine calcium, urine uric acid and the blood natrium, potassium, magnesium, calcium, uric acid have significant influence to the information of uric acid stones.
Fuzzy relational calculus theory, applications and software
Peeva, Ketty
2004-01-01
This book examines fuzzy relational calculus theory with applications in various engineering subjects. The scope of the text covers unified and exact methods with algorithms for direct and inverse problem resolution in fuzzy relational calculus. Extensive engineering applications of fuzzy relation compositions and fuzzy linear systems (linear, relational and intuitionistic) are discussed. Some examples of such applications include solutions of equivalence, reduction and minimization problems in fuzzy machines, pattern recognition in fuzzy languages, optimization and inference engines in textile and chemical engineering, etc. A comprehensive overview of the authors' original work in fuzzy relational calculus is also provided in each chapter. The attached CD-Rom contains a toolbox with many functions for fuzzy calculations, together with an original algorithm for inverse problem resolution in MATLAB. This book is also suitable for use as a textbook in related courses at advanced undergraduate and graduate level...
Selective ablation of dental calculus with a frequency-doubled Alexandrite laser
Rechmann, Peter; Hennig, Thomas
1996-01-01
The aim of the study was the selective removal of dental calculus by means of pulsed lasers. In a first approach the optical characteristics of subgingival calculus were calculated using fluorescence emission spectroscopy (excitation laser: N2-laser, wavelength 337 nm, pulse duration 4 ns). Subgingival calculus seems to absorb highly in the ultraviolet spectral region up to 420 nm. According to these measurements a frequency doubled Alexandrite-laser (wavelength 377 nm, pulse duration 100 ns, repetition rate 110 Hz) was used to irradiate calculus located on enamel, at the cementum enamel junction and on the root surface (located on dentin or on cementum). Irradiation was performed perpendicular to the root surface with a laser fluence of 1 Jcm-2. During the irradiation procedure an effective water cooling-system was engaged. Histological investigations were done on undecalcified sections. As a result, engaging low fluences allows a fast and strictly selective removal of subgingival calculus. Even more the investigations revealed that supragingival calculus can be removed in a strictly selective manner engaging a frequency doubled Alexandrite-laser. No adverse side effects to the surrounding tissues could be found.
Modified Regge calculus as an explanation of dark energy
International Nuclear Information System (INIS)
Stuckey, W M; McDevitt, T J; Silberstein, M
2012-01-01
Using the Regge calculus, we construct a Regge differential equation for the time evolution of the scale factor a(t) in the Einstein-de Sitter cosmology model (EdS). We propose two modifications to the Regge calculus approach: (1) we allow the graphical links on spatial hypersurfaces to be large, as in direct particle interaction when the interacting particles reside in different galaxies, and (2) we assume that luminosity distance D L is related to graphical proper distance D p by the equation D L = (1+z)√D p ·D p , where the inner product can differ from its usual trivial form. The modified Regge calculus model (MORC), EdS and ΛCDM are compared using the data from the Union2 Compilation, i.e. distance moduli and redshifts for type Ia supernovae. We find that a best fit line through logD L versus logz gives a correlation of 0.9955 and a sum of squares error (SSE) of 1.95. By comparison, the best fit ΛCDM gives SSE = 1.79 using H o = 69.2 kms -1 Mpc, Ω M = 0.29 and Ω Λ = 0.71. The best fit EdS gives SSE = 2.68 using H o 60.9 km s -1 Mpc. The best-fit MORC gives SSE = 1.77 and H o = 73.9 km s -1 Mpc using R = A -1 = 8.38 Gcy and m = 1.71 x 10 52 kg, where R is the current graphical proper distance between nodes, A -1 is the scaling factor from our non-trivial inner product, and m is the nodal mass. Thus, the MORC improves the EdS as well as ΛCDM in accounting for distance moduli and redshifts for type Ia supernovae without having to invoke accelerated expansion, i.e. there is no dark energy and the universe is always decelerating. (paper)
Prostatic fossa calculus | El Abiad | Pan African Medical Journal
African Journals Online (AJOL)
As part of the evaluation, a plain radiograph was performed and incidentally showed a radiopaque prostatic calculus (Red arrows). A retrograde urethrocystography, performed after a 10-days course of antibiotics, confirmed the presence of an approximately 35 mm non-obstructive calculus occupying almost the whole ...
A compositional proof system for the modal μ-calculus
DEFF Research Database (Denmark)
Andersen, Henrik Reif; Stirling, C.; Winskel,, G.
1994-01-01
We present a proof system for determining satisfaction between processes in a fairly general process algebra and assertions of the modal μ-calculus. The proof system is compositional in the structure of processes. It extends earlier work on compositional reasoning within the modal μ-calculus and ...
Non-commutative residue of projections in Boutet de Monvel's calculus
DEFF Research Database (Denmark)
Gaarde, Anders
2007-01-01
Using results by Melo, Nest, Schick, and Schrohe on the K-theory of Boutet de Monvel's calculus of boundary value problems, we show that the non-commutative residue introduced by Fedosov, Golse, Leichtnam, and Schrohe vanishes on projections in the calculus. This partially answers a question raised...... in a recent collaboration with Grubb, namely whether the residue is zero on sectorial projections for boundary value problems: This is confirmed to be true when the sectorial projections is in the calculus....
Application of Quantum Process Calculus to Higher Dimensional Quantum Protocols
Directory of Open Access Journals (Sweden)
Simon J. Gay
2014-07-01
Full Text Available We describe the use of quantum process calculus to describe and analyze quantum communication protocols, following the successful field of formal methods from classical computer science. We have extended the quantum process calculus to describe d-dimensional quantum systems, which has not been done before. We summarise the necessary theory in the generalisation of quantum gates and Bell states and use the theory to apply the quantum process calculus CQP to quantum protocols, namely qudit teleportation and superdense coding.
The perturbative Regge-calculus regime of loop quantum gravity
International Nuclear Information System (INIS)
Bianchi, Eugenio; Modesto, Leonardo
2008-01-01
The relation between loop quantum gravity and Regge calculus has been pointed out many times in the literature. In particular the large spin asymptotics of the Barrett-Crane vertex amplitude is known to be related to the Regge action. In this paper we study a semiclassical regime of loop quantum gravity and show that it admits an effective description in terms of perturbative area-Regge-calculus. The regime of interest is identified by a class of states given by superpositions of four-valent spin networks, peaked on large spins. As a probe of the dynamics in this regime, we compute explicitly two- and three-area correlation functions at the vertex amplitude level. We find that they match with the ones computed perturbatively in area-Regge-calculus with a single 4-simplex, once a specific perturbative action and measure have been chosen in the Regge-calculus path integral. Correlations of other geometric operators and the existence of this regime for other models for the dynamics are briefly discussed
Quantum calculus new concepts, impulsive IVPs and BVPs, inequalities
Ahmad, Bashir; Tariboon, Jessada
2016-01-01
The main objective of this book is to extend the scope of the q-calculus based on the definition of q-derivative [Jackson (1910)] to make it applicable to dense domains. As a matter of fact, Jackson's definition of q-derivative fails to work for impulse points while this situation does not arise for impulsive equations on q-time scales as the domains consist of isolated points covering the case of consecutive points. In precise terms, we study quantum calculus on finite intervals.In the first part, we discuss the concepts of qk-derivative and qk-integral, and establish their basic properties. As applications, we study initial and boundary value problems of impulsive qk-difference equations and inclusions equipped with different kinds of boundary conditions. We also transform some classical integral inequalities and develop some new integral inequalities for convex functions in the context of qk-calculus. In the second part, we develop fractional quantum calculus in relation to a new qk-shifting operator and e...
Patel, Rita Manubhai; McCombs, Paul; Zollman, Alan
2014-01-01
Novice students have difficulty with the topic of limits in calculus. We believe this is in part because of the multiple perspectives and shifting metaphors available to solve items correctly. We investigated college calculus instructors' personal concepts of limits. Based upon previous research investigating introductory calculus student…
The Development and Nature of Problem-Solving among First-Semester Calculus Students
Dawkins, Paul Christian; Epperson, James A. Mendoza
2014-01-01
This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate…
Calculus, Biology and Medicine: A Case Study in Quantitative Literacy for Science Students
Directory of Open Access Journals (Sweden)
Kim Rheinlander
2011-01-01
Full Text Available This paper describes a course designed to enhance the numeracy of biology and pre-medical students. The course introduces students with the background of one semester of calculus to systems of nonlinear ordinary differential equations as they appear in the mathematical biology literature. Evaluation of the course showed increased enjoyment and confidence in doing mathematics, and an increased appreciation of the utility of mathematics to science. Students who complete this course are better able to read the research literature in mathematical biology and carry out research problems of their own.
Recalling Prerequisite Material in a Calculus II Course to Improve Student Success
Mokry, Jeanette
2016-01-01
This article discusses preparation assignments used in a Calculus II course that cover material from prerequisite courses. Prior to learning new material, students work on problems outside of class involving concepts from algebra, trigonometry, and Calculus I. These problems are directly built upon in order to answer Calculus II questions,…
The Path to College Calculus: The Impact of High School Mathematics Coursework
Sadler, Philip; Sonnert, Gerhard
2018-01-01
This study addresses a longstanding question among high school mathematics teachers and college mathematics professors: Which is the best preparation for college calculus-- (a) a high level of mastery of mathematics considered preparatory for calculus (algebra, geometry, precalculus) or (b) taking calculus itself in high school? We used a data set…
A Generalized Nonlocal Calculus with Application to the Peridynamics Model for Solid Mechanics
Alali, Bacim; Liu, Kuo; Gunzburger, Max
2014-01-01
A nonlocal vector calculus was introduced in [2] that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A generalization is developed that provides a more general setting for the nonlocal vector calculus that is independent of particular nonlocal models. It is shown that general nonlocal calculus operators are integral operators with specific integral kernels. General nonlocal calculus properties are developed, including nonlocal...
Type Inference for Session Types in the Pi-Calculus
DEFF Research Database (Denmark)
Graversen, Eva Fajstrup; Harbo, Jacob Buchreitz; Huttel, Hans
2014-01-01
In this paper we present a direct algorithm for session type inference for the π-calculus. Type inference for session types has previously been achieved by either imposing limitations and restriction on the π-calculus, or by reducing the type inference problem to that for linear types. Our approach...
ANALYTICAL MODEL FOR LATHE TOOL DISPLACEMENTS CALCULUS IN THE MANUFACTURING P ROCESS
Directory of Open Access Journals (Sweden)
Catălin ROŞU
2014-01-01
Full Text Available In this paper, we present an analytical model for lathe tools displacements calculus in the manufacturing process. We will present step by step the methodology for the displacements calculus and in the end we will insert these relations in a program for automatic calculus and we extract the conclusions. There is taken into account only the effects of the bending moments (because these insert the highest displacements. The simplifying assumptions and the calculus relations for the displacements (linea r and angular ones are presented in an original way.
Distributed mean curvature on a discrete manifold for Regge calculus
International Nuclear Information System (INIS)
Conboye, Rory; Miller, Warner A; Ray, Shannon
2015-01-01
The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of the volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as the fractional rate of change of the normal vector. (paper)
Distributed mean curvature on a discrete manifold for Regge calculus
Conboye, Rory; Miller, Warner A.; Ray, Shannon
2015-09-01
The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of the volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as the fractional rate of change of the normal vector.
Feynman path integral in area tensor Regge calculus and positivity
International Nuclear Information System (INIS)
Khatsymovsky, V.M.
2004-01-01
The versions of quantum measure in the area tensor Regge calculus constructed in the previous paper are studied on the simplest configurations of the system. These are found to be positively defined in the Euclidean case on physical surface corresponding to the ordinary Regge calculus (but not outside this surface), that is, adopt probabilistic interpretation. (Since Euclidean measure is defined via analytical continuation, positivity is not evident property.) An argument for positivity on physical surface on general configurations of area tensor Regge calculus is given
Complete staghorn calculus in polycystic kidney disease: infection is still the cause.
Mao, Zhiguo; Xu, Jing; Ye, Chaoyang; Chen, Dongping; Mei, Changlin
2013-08-01
Kidney stones in patients with autosomal dominant polycystic kidney disease are common, regarded as the consequence of the combination of anatomic abnormality and metabolic risk factors. However, complete staghorn calculus is rare in polycystic kidney disease and predicts a gloomy prognosis of kidney. For general population, recent data showed metabolic factors were the dominant causes for staghorn calculus, but for polycystic kidney disease patients, the cause for staghorn calculus remained elusive. We report a case of complete staghorm calculus in a polycystic kidney disease patient induced by repeatedly urinary tract infections. This 37-year-old autosomal dominant polycystic kidney disease female with positive family history was admitted in this hospital for repeatedly upper urinary tract infection for 3 years. CT scan revealed the existence of a complete staghorn calculus in her right kidney, while there was no kidney stone 3 years before, and the urinary stone component analysis showed the composition of calculus was magnesium ammonium phosphate. UTI is an important complication for polycystic kidney disease and will facilitate the formation of staghorn calculi. As staghorn calculi are associated with kidney fibrosis and high long-term renal deterioration rate, prompt control of urinary tract infection in polycystic kidney disease patient will be beneficial in preventing staghorn calculus formation.
Model checking biological systems described using ambient calculus
DEFF Research Database (Denmark)
Mardare, Radu Iulian; Priami, Corrado; Qualia, Paola
2005-01-01
Model checking biological systems described using ambient calculus. In Proc. of the second International Workshop on Computational Methods in Systems Biology (CMSB04), Lecture Notes in Bioinformatics 3082:85-103, Springer, 2005.......Model checking biological systems described using ambient calculus. In Proc. of the second International Workshop on Computational Methods in Systems Biology (CMSB04), Lecture Notes in Bioinformatics 3082:85-103, Springer, 2005....
Eye Irritation Test of Bovis Calculus Pharmacopuncture Solutions for Eye Drop
Directory of Open Access Journals (Sweden)
Hyeong-sik Seo
2008-06-01
Full Text Available Objective : This study was done to investigate the safety of Bovis Calculus pharmacopuncture solution manufactured with freezing dryness method to use eye drop. Methods : The eye irritation test of this material was performed according to the Regulation of Korea Food & Drug Administration (2005. 10. 21, KFDA 2005-60. After Bovis Calculus pharmacopuncture solution was medicated in the left eye of the rabbits, the auther observed eye irritation of the cornea, iris, conjunctiva at 1, 2, 3, 4 & 7day. Results : 1. After Bovis Calculus pharmacopuncture solution was medicated in the left eye of the rabbits, there wasn’t physical problem at 9 rabbits. 2. After Bovis Calculus pharmacopuncture solutionwas medicated in the left eye of the rabbits, there wasn’t eye irritation of the cornea, iris, conjunctiva at 1, 2, 3, 4 & 7day. Conclusions : I suggested that Bovis Calculus pharmacopuncture solution didn’t induced eye irritation in rabbits.
Gupta, Swati; Jain, P K; Kumra, Madhumani; Rehani, Shweta; Mathias, Yulia; Gupta, Ramakant; Mehendiratta, Monica; Chander, Anil
2016-07-01
Chronic inflammatory periodontal diseases i.e. gingivitis and periodontitis are one of the most common afflictions faced by human beings. Dental plaque, which is a pool of pathogenic microorganisms, remains to be current mainstay in etiopathogenesis. Dental calculus, which is a mineralized product of this plaque remains ignored and is considered merely as an ash heap of minor significance. However, the intriguing array in disease etiopathogenesis bulldozed researchers to suspect the role of calculus in disease chrysalis but still the viability of bacteria inside calculus and thus its pathogenicity remains an intricacy; the answer to which lies in the Pandora's Box. The present study was undertaken to investigate the viability of bacteria within dental calculus along with their identification. Also, to classify dental calculus on the basis of mineralization and to observe the variation of viable microflora found in dental calculus with the extent of mineralization and disease severity. A total of 60 samples were obtained, by harvesting two samples of supragingival calculus from each patient having chronic inflammatory periodontal disease. These samples were divided into two groups (Group A and Group B). Samples of Group A were kept non-irradiated and samples of Group B were exposed to UV radiation. The samples were categorized into less, moderately and highly mineralized according to the force required for crushing them. All the crushed calculus samples were then divided into three parts. These were used for dark-field microscopy, gram staining and bacterial cultures. Bacterial identification of the cultures obtained was also carried out by performing various biochemical assays. The present study revealed the presence of motile spirochaetes within the samples under dark-field microscope. Gram staining revealed presence of numerous gram positive cocci and gram negative bacilli. Bacterial cultures showed growth of variety of aerobic and capnophilic microorganisms. The
Initial data for time-symmetric gravitational radiation using Regge calculus
International Nuclear Information System (INIS)
Dubal, M.R.
1989-01-01
We apply Regge calculus to the construction of initial data for Brill waves: axisymmetric non-rotating vacuum solutions of Einstein's equation. The Regge calculus solutions are compared with those of the continuum theory, with encouraging results. (author)
Unfolding Semantics of the Untyped λ-Calculus with lectrec-Calculus with letrec
Rochel, J.
2016-01-01
We investigate the relationship between finite terms in lambda-letrec, the lambda calculus with letrec, and the infinite lambda terms they express. We say that a lambda-letrec term expresses a lambda term if the latter can be obtained as an infinite unfolding of the former. Unfolding is the process
Means and Variances without Calculus
Kinney, John J.
2005-01-01
This article gives a method of finding discrete approximations to continuous probability density functions and shows examples of its use, allowing students without calculus access to the calculation of means and variances.
Regularization of positive definite matrix fields based on multiplicative calculus
Florack, L.M.J.; Bruckstein, A.M.; Haar Romeny, ter B.M.; Bronstein, A.M.; Bronstein, M.M.
2012-01-01
Multiplicative calculus provides a natural framework in problems involving positive images and positivity preserving operators. In increasingly important, complex imaging frameworks, such as diffusion tensor imaging, it complements standard calculus in a nontrivial way. The purpose of this article
Crystalline structure of pulverized dental calculus induces cell death in oral epithelial cells.
Ziauddin, S M; Yoshimura, A; Montenegro Raudales, J L; Ozaki, Y; Higuchi, K; Ukai, T; Kaneko, T; Miyazaki, T; Latz, E; Hara, Y
2018-06-01
Dental calculus is a mineralized deposit attached to the tooth surface. We have shown that cellular uptake of dental calculus triggers nucleotide-binding oligomerization domain-like receptor family pyrin domain-containing 3 (NLRP3) inflammasome activation, leading to the processing of the interleukin-1β precursor into its mature form in mouse and human phagocytes. The activation of the NLRP3 inflammasome also induced a lytic form of programmed cell death, pyroptosis, in these cells. However, the effects of dental calculus on other cell types in periodontal tissue have not been investigated. The aim of this study was to determine whether dental calculus can induce cell death in oral epithelial cells. HSC-2 human oral squamous carcinoma cells, HOMK107 human primary oral epithelial cells and immortalized mouse macrophages were exposed to dental calculus or 1 of its components, hydroxyapatite crystals. For inhibition assays, the cells were exposed to dental calculus in the presence or absence of cytochalasin D (endocytosis inhibitor), z-YVAD-fmk (caspase-1 inhibitor) or glyburide (NLRP3 inflammasome inhibitor). Cytotoxicity was determined by measuring lactate dehydrogenase (LDH) release and staining with propidium iodide. Tumor necrosis factor-α production was quantified by enzyme-linked immunosorbent assay. Oral epithelial barrier function was examined by permeability assay. Dental calculus induced cell death in HSC-2 cells, as judged by LDH release and propidium iodide staining. Dental calculus also induced LDH release from HOMK107 cells. Following heat treatment, dental calculus lost its capacity to induce tumor necrosis factor-α in mouse macrophages, but could induce LDH release in HSC-2 cells, indicating a major role of inorganic components in cell death. Hydroxyapatite crystals also induced cell death in both HSC-2 and HOMK107 cells, as judged by LDH release, indicating the capacity of crystal particles to induce cell death. Cell death induced by dental
A Calculus of Circular Proofs and its Categorical Semantics
DEFF Research Database (Denmark)
Santocanale, Luigi
2002-01-01
We present a calculus of "circular proofs": the graph underlying a proof is not a finite tree but instead it is allowed to contain a certain amount of cycles.The main challenge in developing a theory for the calculus is to define the semantics of proofs, since the usual method by induction...
A Calculus of Circular Proofs and its Categorical Semantics
DEFF Research Database (Denmark)
Santocanale, Luigi
2002-01-01
We present a calculus of “circular proofs”: the graph underlying a proof is not a finite tree but instead it is allowed to contain a certain amount of cycles.The main challenge in developing a theory for the calculus is to define the semantics of proofs, since the usual method by induction...
Descartes' Calculus of Subnormals: What Might Have Been
Boudreaux, Gregory Mark; Walls, Jess E.
2013-01-01
Rene Descartes' method for finding tangents (equivalently, subnormals) depends on geometric and algebraic properties of a family of circles intersecting a given curve. It can be generalized to establish a calculus of subnormals, an alternative to the calculus of Newton and Leibniz. Here we prove subnormal counterparts of the well-known…
Variational calculus with constraints on general algebroids
Energy Technology Data Exchange (ETDEWEB)
Grabowska, Katarzyna [Physics Department, Division of Mathematical Methods in Physics, University of Warsaw, Hoza 69, 00-681 Warszawa (Poland); Grabowski, Janusz [Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, PO Box 21, 00-956 Warszawa (Poland)], E-mail: konieczn@fuw.edu.pl, E-mail: jagrab@impan.gov.pl
2008-05-02
Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and geometrical settings. The constrained Euler-Lagrange equations are derived for analogs of holonomic, vakonomic and nonholonomic constraints. This general model covers the majority of first-order Lagrangian systems which are present in the literature and reduces to the standard variational calculus and the Euler-Lagrange equations in classical mechanics for E = TM.
Variational calculus with constraints on general algebroids
International Nuclear Information System (INIS)
Grabowska, Katarzyna; Grabowski, Janusz
2008-01-01
Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and geometrical settings. The constrained Euler-Lagrange equations are derived for analogs of holonomic, vakonomic and nonholonomic constraints. This general model covers the majority of first-order Lagrangian systems which are present in the literature and reduces to the standard variational calculus and the Euler-Lagrange equations in classical mechanics for E = TM
A sequent calculus for signed interval logic
DEFF Research Database (Denmark)
Rasmussen, Thomas Marthedal
2001-01-01
We propose and discuss a complete sequent calculus formulation for Signed Interval Logic (SIL) with the chief purpose of improving proof support for SIL in practice. The main theoretical result is a simple characterization of the limit between decidability and undecidability of quantifier-free SIL....... We present a mechanization of SIL in the generic proof assistant Isabelle and consider techniques for automated reasoning. Many of the results and ideas of this report are also applicable to traditional (non-signed) interval logic and, hence, to Duration Calculus....
Modular invariance and covariant loop calculus
International Nuclear Information System (INIS)
Petersen, J.L.; Roland, K.O.; Sidenius, J.R.
1988-01-01
The covariant loop calculus provides an efficient technique for computing explicit expressions for the density on moduli space corresponding to arbitrary (bosonic string) loop diagrams. Since modular invariance is not manifest, however, we carry out a detailed comparison with known explicit two- and three-loop results derived using analytic geometry (one loop is known to be okay). We establish identity to 'high' order in some moduli and exactly in others. Agreement is found as a result of various nontrivial cancellations, in part related to number theory. We feel our results provide very strong support for the correctness of the covariant loop calculus approach. (orig.)
Modular invariance and covariant loop calculus
International Nuclear Information System (INIS)
Petersen, J.L.; Roland, K.O.; Sidenius, J.R.
1988-01-01
The covariant loop calculus provides and efficient technique for computing explicit expressions for the density on moduli space corresponding to arbitrary (bosonic string) loop diagrams. Since modular invariance is not manifest, however, we carry out a detailed comparison with known explicit 2- and 3- loop results derived using analytic geometry (1 loop is known to be ok). We establish identity to 'high' order in some moduli and exactly in others. Agreement is found as a result of various non-trivial cancellations, in part related to number theory. We feel our results provide very strong support for the correctness of the covariant loop calculus approach. (orig.)
Dynamical Regge calculus as lattice gravity
International Nuclear Information System (INIS)
Hagura, Hiroyuki
2001-01-01
We propose a hybrid approach to lattice quantum gravity by combining simultaneously the dynamical triangulation with the Regge calculus, called the dynamical Regge calculus (DRC). In this approach lattice diffeomorphism is realized as an exact symmetry by some hybrid (k, l) moves on the simplicial lattice. Numerical study of 3D pure gravity shows that an entropy of the DRC is not exponetially bounded if we adopt the uniform measure Π i dl i . On the other hand, using the scale-invariant measure Π i dl i /l i , we can calculate observables and observe a large hysteresis between two phases that indicates the first-order nature of the phase transition
Model Checking Processes Specified In Join-Calculus Algebra
Directory of Open Access Journals (Sweden)
Sławomir Piotr Maludziński
2014-01-01
Full Text Available This article presents a model checking tool used to verify concurrent systems specified in join-calculus algebra. The temporal properties of systems under verification are expressed in CTL logic. Join-calculus algebra with its operational semantics defined by the chemical abstract machine serves as the basic method for the specification of concurrent systems and their synchronization mechanisms, and allows the examination of more complex systems.
A comparison of dental ultrasonic technologies on subgingival calculus removal: a pilot study.
Silva, Lidia Brión; Hodges, Kathleen O; Calley, Kristin Hamman; Seikel, John A
2012-01-01
This pilot study compared the clinical endpoints of the magnetostrictive and piezoelectric ultrasonic instruments on calculus removal. The null hypothesis stated that there is no statistically significant difference in calculus removal between the 2 instruments. A quasi-experimental pre- and post-test design was used. Eighteen participants were included. The magnetostrictive and piezoelectric ultrasonic instruments were used in 2 assigned contra-lateral quadrants on each participant. A data collector, blind to treatment assignment, assessed the calculus on 6 predetermined tooth sites before and after ultrasonic instrumentation. Calculus size was evaluated using ordinal measurements on a 4 point scale (0, 1, 2, 3). Subjects were required to have size 2 or 3 calculus deposit on the 6 predetermined sites. One clinician instrumented the pre-assigned quadrants. A maximum time of 20 minutes of instrumentation was allowed with each technology. Immediately after instrumentation, the data collector then conducted the post-test calculus evaluation. The repeated analysis of variance (ANOVA) was used to analyze the pre- and post-test calculus data (p≤0.05). The null hypothesis was accepted indicating that there is no statistically significant difference in calculus removal when comparing technologies (p≤0.05). Therefore, under similar conditions, both technologies removed the same amount of calculus. This research design could be used as a foundation for continued research in this field. Future studies include implementing this study design with a larger sample size and/or modifying the study design to include multiple clinicians who are data collectors. Also, deposit removal with periodontal maintenance patients could be explored.
Dental calculus is associated with death from heart infarction.
Söder, Birgitta; Meurman, Jukka H; Söder, Per-Östen
2014-01-01
We studied whether the amount of dental calculus is associated with death from heart infarction in the dental infection-atherosclerosis paradigm. Participants were 1676 healthy young Swedes followed up from 1985 to 2011. At the beginning of the study all subjects underwent oral clinical examination including dental calculus registration scored with calculus index (CI). Outcome measure was cause of death classified according to WHO International Classification of Diseases. Unpaired t-test, Chi-square tests, and multiple logistic regressions were used. Of the 1676 participants, 2.8% had died during follow-up. Women died at a mean age of 61.5 years and men at 61.7 years. The difference in the CI index score between the survivors versus deceased patients was significant by the year 2009 (P dental visits, dental plaque, periodontal pockets, education, income, socioeconomic status, and pack-years of smoking, CI score appeared to be associated with 2.3 times the odds ratio for cardiac death. The results confirmed our study hypothesis by showing that dental calculus indeed associated statistically with cardiac death due to infarction.
On Functional Calculus Estimates
Schwenninger, F.L.
2015-01-01
This thesis presents various results within the field of operator theory that are formulated in estimates for functional calculi. Functional calculus is the general concept of defining operators of the form $f(A)$, where f is a function and $A$ is an operator, typically on a Banach space. Norm
Stochastic Pi-calculus Revisited
DEFF Research Database (Denmark)
Cardelli, Luca; Mardare, Radu Iulian
2013-01-01
We develop a version of stochastic Pi-calculus with a semantics based on measure theory. We dene the behaviour of a process in a rate environment using measures over the measurable space of processes induced by structural congruence. We extend the stochastic bisimulation to include the concept of...
Extending the Extensional Lambda Calculus with Surjective Pairing is Conservative
DEFF Research Database (Denmark)
Støvring, Kristian
2006-01-01
We answer Klop and de Vrijer's question whether adding surjective-pairing axioms to the extensional lambda calculus yields a conservative extension. The answer is positive. As a byproduct we obtain a "syntactic" proof that the extensional lambda calculus with surjective pairing is consistent....
Bodewig, E
1959-01-01
Matrix Calculus, Second Revised and Enlarged Edition focuses on systematic calculation with the building blocks of a matrix and rows and columns, shunning the use of individual elements. The publication first offers information on vectors, matrices, further applications, measures of the magnitude of a matrix, and forms. The text then examines eigenvalues and exact solutions, including the characteristic equation, eigenrows, extremum properties of the eigenvalues, bounds for the eigenvalues, elementary divisors, and bounds for the determinant. The text ponders on approximate solutions, as well
Giant urinary bladder calculus: Case report | Otieno | East African ...
African Journals Online (AJOL)
A vertical calculus weighing more than 100 g is categorised as a giant urinary bladder stone. Giant urinary bladder stones are very rare and very few cases have been reported in English literature and only one case from Africa. This is a case report of a patient with a giant urinary bladder calculus presenting as a rectal ...
Effects of Clicker Use on Calculus Students' Mathematics Anxiety
Batchelor, John
2015-01-01
This paper reports the results of a survey study of clicker use and mathematics anxiety among students enrolled in an undergraduate calculus course during the Fall 2013 semester. Students in two large lecture sections of calculus completed surveys at the beginning and end of the course. One class used clickers, whereas the other class was taught…
Projects for calculus the language of change
Stroyan, Keith D
1999-01-01
Projects for Calculus is designed to add depth and meaning to any calculus course. The fifty-two projects presented in this text offer the opportunity to expand the use and understanding of mathematics. The wide range of topics will appeal to both instructors and students. Shorter, less demanding projects can be managed by the independent learner, while more involved, in-depth projects may be used for group learning. Each task draws on special mathematical topics and applications from subjects including medicine, engineering, economics, ecology, physics, and biology.Subjects including:* Medicine* Engineering* Economics* Ecology* Physics* Biology
Data Quality Indicators Composition and Calculus: Engineering and Information Systems Approaches
Directory of Open Access Journals (Sweden)
Leon REZNIK
2015-02-01
Full Text Available Big Data phenomenon is a result of novel technological developments in sensor, computer and communication technologies. Nowadays more and more data are produced by nanoscale photonic, optoelectronic and electronic devices. However, their quality characteristics could be very low. The paper proposes new methods of the data management with huge data amounts that is based on associating of data quality indicators with each data entity. To achieve this goal, one needs to define the composition of the data quality indicators and to develop their integration calculus. As data quality evaluation involves multi-disciplinary research, various metrics have been investigated. The paper describes two major approaches in assigning the data quality indicators and developing their integration calculus. The information systems approach employs traditional high-level metrics like data accuracy, consistency and completeness. The engineering approach utilizes signal characteristics processed with the probability based calculus. The data quality metrics composition and calculus are discussed. The tools developed to automate the metrics selection and calculus procedures are presented. The user- friendly interface examples are provided.