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Sample records for calculus of variations

  1. Calculus of variations

    CERN Document Server

    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

  2. Quantum Variational Calculus

    OpenAIRE

    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...

  3. Quantum variational calculus

    CERN Document Server

    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...

  4. Calculus of variations

    CERN Document Server

    Elsgolc, Lev D

    2007-01-01

    This concise text offers both professionals and students an introduction to the fundamentals and standard methods of the calculus of variations. In addition to surveys of problems with fixed and movable boundaries, it explores highly practical direct methods for the solution of variational problems.Topics include the method of variation in problems with fixed boundaries; variational problems with movable boundaries and other problems; sufficiency conditions for an extremum; variational problems of constrained extrema; and direct methods of solving variational problems. Each chapter features nu

  5. 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.

  6. 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

  7. 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.

  8. 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

  9. Introduction to the calculus of variations

    CERN Document Server

    Sagan, Hans

    1992-01-01

    Excellent text provides basis for thorough understanding of the problems, methods and techniques of the calculus of variations and prepares readers for the study of modern optimal control theory. Treatment limited to extensive coverage of single integral problems in one and more unknown functions. Carefully chosen variational problems and over 400 exercises. ""Should find wide acceptance as a text and reference.""-American Mathematical Monthly. 1969 edition. Bibliography.

  10. The early period of the calculus of variations

    CERN Document Server

    Freguglia, Paolo

    2016-01-01

    This monograph explores the early development of the calculus of variations in continental Europe during the Eighteenth Century by illustrating the mathematics of its founders. Closely following the original papers and correspondences of Euler, Lagrange, the Bernoullis, and others, the reader is immersed in the challenge of theory building. We see what the founders were doing, the difficulties they faced, the mistakes they made, and their triumphs. The authors guide the reader through these works with instructive commentaries and complements to the original proofs, as well as offering a modern perspective where useful. The authors begin in 1697 with Johann Bernoulli’s work on the brachystochrone problem and the events leading up to it, marking the dawn of the calculus of variations. From there, they cover key advances in the theory up to the development of Lagrange’s δ-calculus, including: • The isoperimetrical problems • Shortest lines and geodesics • Euler’s Methodus Inveniendi and the two Addi...

  11. A primer on the calculus of variations and optimal control theory

    CERN Document Server

    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...

  12. Fractional variational calculus in terms of Riesz fractional derivatives

    International Nuclear Information System (INIS)

    Agrawal, O P

    2007-01-01

    This paper presents extensions of traditional calculus of variations for systems containing Riesz fractional derivatives (RFDs). Specifically, we present generalized Euler-Lagrange equations and the transversality conditions for fractional variational problems (FVPs) defined in terms of RFDs. We consider two problems, a simple FVP and an FVP of Lagrange. Results of the first problem are extended to problems containing multiple fractional derivatives, functions and parameters, and to unspecified boundary conditions. For the second problem, we present Lagrange-type multiplier rules. For both problems, we develop the Euler-Lagrange-type necessary conditions which must be satisfied for the given functional to be extremum. Problems are considered to demonstrate applications of the formulations. Explicitly, we introduce fractional momenta, fractional Hamiltonian, fractional Hamilton equations of motion, fractional field theory and fractional optimal control. The formulations presented and the resulting equations are similar to the formulations for FVPs given in Agrawal (2002 J. Math. Anal. Appl. 272 368, 2006 J. Phys. A: Math. Gen. 39 10375) and to those that appear in the field of classical calculus of variations. These formulations are simple and can be extended to other problems in the field of fractional calculus of variations

  13. Calculus of variations and optimal control theory a concise introduction

    CERN Document Server

    Liberzon, Daniel

    2011-01-01

    This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the h...

  14. Partial differential equations and calculus of variations

    CERN Document Server

    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.

  15. Optimal control and the calculus of variations

    CERN Document Server

    Pinch, Enid R

    1993-01-01

    This introduction to optimal control theory is intended for undergraduate mathematicians and for engineers and scientists with some knowledge of classical analysis. It includes sections on classical optimization and the calculus of variations. All the important theorems are carefully proved. There are many worked examples and exercises for the reader to attempt.

  16. Presymplectic current and the inverse problem of the calculus of variations

    NARCIS (Netherlands)

    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

  17. 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.

  18. A formalism for the calculus of variations with spinors

    Energy Technology Data Exchange (ETDEWEB)

    Bäckdahl, Thomas, E-mail: thobac@chalmers.se [The School of Mathematics, University of Edinburgh, JCMB 6228, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom and Mathematical Sciences - Chalmers University of Technology and University of Gothenburg - SE-412 96 Gothenburg (Sweden); Valiente Kroon, Juan A., E-mail: j.a.valiente-kroon@qmul.ac.uk [School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS (United Kingdom)

    2016-02-15

    We develop a frame and dyad gauge-independent formalism for the calculus of variations of functionals involving spinorial objects. As a part of this formalism, we define a modified variation operator which absorbs frame and spin dyad gauge terms. This formalism is applicable to both the standard spacetime (i.e., SL(2, ℂ)) 2-spinors as well as to space (i.e., SU(2, ℂ)) 2-spinors. We compute expressions for the variations of the connection and the curvature spinors.

  19. A formalism for the calculus of variations with spinors

    International Nuclear Information System (INIS)

    Bäckdahl, Thomas; Valiente Kroon, Juan A.

    2016-01-01

    We develop a frame and dyad gauge-independent formalism for the calculus of variations of functionals involving spinorial objects. As a part of this formalism, we define a modified variation operator which absorbs frame and spin dyad gauge terms. This formalism is applicable to both the standard spacetime (i.e., SL(2, ℂ)) 2-spinors as well as to space (i.e., SU(2, ℂ)) 2-spinors. We compute expressions for the variations of the connection and the curvature spinors

  20. On the minimizers of calculus of variations problems in Hilbert spaces

    KAUST Repository

    Gomes, Diogo A.

    2014-01-19

    The objective of this paper is to discuss existence, uniqueness and regularity issues of minimizers of one dimensional calculus of variations problem in Hilbert spaces. © 2014 Springer-Verlag Berlin Heidelberg.

  1. On the minimizers of calculus of variations problems in Hilbert spaces

    KAUST Repository

    Gomes, Diogo A.; Nurbekyan, Levon

    2014-01-01

    The objective of this paper is to discuss existence, uniqueness and regularity issues of minimizers of one dimensional calculus of variations problem in Hilbert spaces. © 2014 Springer-Verlag Berlin Heidelberg.

  2. A first course in the calculus of variations

    CERN Document Server

    Kot, Mark

    2014-01-01

    This book is intended for a first course in the calculus of variations, at the senior or beginning graduate level. The reader will learn methods for finding functions that maximize or minimize integrals. The text lays out important necessary and sufficient conditions for extrema in historical order, and it illustrates these conditions with numerous worked-out examples from mechanics, optics, geometry, and other fields. The exposition starts with simple integrals containing a single independent variable, a single dependent variable, and a single derivative, subject to weak variations, but stead

  3. An introduction to the calculus of variations

    CERN Document Server

    Pars, LA

    2009-01-01

    This clear, rigorous introduction to the calculus of variations covers applications to geometry, dynamics, and physics. Focusing upon problems with one independent variable, the text connects the abstract theory to its use in concrete problems. It offers a working knowledge of relevant techniques, plus an impetus for further study.Starting with an overview of fundamental problems and theories, the text advances to illustrative examples and examinations of variable end-points and the fundamental sufficiency theorem. Subsequent chapters explore the isoperimetrical problem, curves in space, the p

  4. An experimental trip to the Calculus of Variations

    Science.gov (United States)

    Arroyo, Josu

    2008-04-01

    This paper presents a collection of experiments in the Calculus of Variations. The implementation of the Gradient Descent algorithm built on cubic-splines acting as "numerically friendly" elementary functions, give us ways to solve variational problems by constructing the solution. It wins a pragmatic point of view: one gets solutions sometimes as fast as possible, sometimes as close as possible to the true solutions. The balance speed/precision is not always easy to achieve. Starting from the most well-known, classic or historical formulation of a variational problem, section 2 describes briefly the bridge between theoretical and computational formulations. The next sections show the results of several kind of experiments; from the most basics, as those about geodesics, to the most complex, as those about vesicles.

  5. Solution of problems in calculus of variations via He's variational iteration method

    International Nuclear Information System (INIS)

    Tatari, Mehdi; Dehghan, Mehdi

    2007-01-01

    In the modeling of a large class of problems in science and engineering, the minimization of a functional is appeared. Finding the solution of these problems needs to solve the corresponding ordinary differential equations which are generally nonlinear. In recent years He's variational iteration method has been attracted a lot of attention of the researchers for solving nonlinear problems. This method finds the solution of the problem without any discretization of the equation. Since this method gives a closed form solution of the problem and avoids the round off errors, it can be considered as an efficient method for solving various kinds of problems. In this research He's variational iteration method will be employed for solving some problems in calculus of variations. Some examples are presented to show the efficiency of the proposed technique

  6. The inverse problem of the calculus of variations for discrete systems

    Science.gov (United States)

    Barbero-Liñán, María; Farré Puiggalí, Marta; Ferraro, Sebastián; Martín de Diego, David

    2018-05-01

    We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also provide a transition between the discrete and the continuous problems and propose variationality as an interesting geometric property to take into account in the design and computer simulation of numerical integrators for constrained systems. For instance, nonholonomic mechanics is generally non variational but some special cases admit an alternative variational description. We apply some standard nonholonomic integrators to such an example to study which ones conserve this property.

  7. On the inverse problem of the calculus of variations in field theory

    International Nuclear Information System (INIS)

    Henneaux, M.

    1984-01-01

    The inverse problem of the calculus of variations is investigated in the case of field theory. Uniqueness of the action principle is demonstrated for the vector Laplace equation in a non-decomposable Riemannian space, as well as for the harmonic map equation. (author)

  8. Presymplectic current and the inverse problem of the calculus of variations

    Science.gov (United States)

    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.

  9. 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.

  10. Dynamic optimization the calculus of variations and optimal control in economics and management

    CERN Document Server

    Kamien, Morton I

    2012-01-01

    Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.

  11. Generalized vector calculus on convex domain

    Science.gov (United States)

    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.

  12. A new differential calculus on a complex banach space with application to variational problems of quantum theory

    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)

  13. Generalized Multiparameters Fractional Variational Calculus

    Directory of Open Access Journals (Sweden)

    Om Prakash Agrawal

    2012-01-01

    Full Text Available This paper builds upon our recent paper on generalized fractional variational calculus (FVC. Here, we briefly review some of the fractional derivatives (FDs that we considered in the past to develop FVC. We first introduce new one parameter generalized fractional derivatives (GFDs which depend on two functions, and show that many of the one-parameter FDs considered in the past are special cases of the proposed GFDs. We develop several parts of FVC in terms of one parameter GFDs. We point out how many other parts could be developed using the properties of the one-parameter GFDs. Subsequently, we introduce two new two- and three-parameter GFDs. We introduce some of their properties, and discuss how they can be used to develop FVC. In addition, we indicate how these formulations could be used in various fields, and how the generalizations presented here can be further extended.

  14. Time scales: from Nabla calculus to Delta calculus and vice versa via duality

    OpenAIRE

    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.

  15. Calculus of variations an introduction to the one-dimensional theory with examples and exercises

    CERN Document Server

    Kielhöfer, Hansjörg

    2018-01-01

    This clear and concise textbook provides a rigorous introduction to the calculus of variations, depending on functions of one variable and their first derivatives. It is based on a translation of a German edition of the book Variationsrechnung (Vieweg+Teubner Verlag, 2010), translated and updated by the author himself.  Topics include: the Euler-Lagrange equation for one-dimensional variational problems, with and without constraints, as well as an introduction to the direct methods. The book targets students who have a solid background in calculus and linear algebra, not necessarily in functional analysis. Some advanced mathematical tools, possibly not familiar to the reader, are given along with proofs in the appendix. Numerous figures, advanced problems and proofs, examples, and exercises with solutions accompany the book, making it suitable for self-study. The book will be particularly useful for beginning graduate students from the physical, engineering, and mathematical sciences with a rigorous th...

  16. Example Solar Electric Propulsion System asteroid tours using variational calculus

    Science.gov (United States)

    Burrows, R. R.

    1985-01-01

    Exploration of the asteroid belt with a vehicle utilizing a Solar Electric Propulsion System has been proposed in past studies. Some of those studies illustrated multiple asteroid rendezvous with trajectories obtained using approximate methods. Most of the inadequacies of those approximations are overcome in this paper, which uses the calculus of variations to calculate the trajectories and associated payloads of four asteroid tours. The modeling, equations, and solution techniques are discussed, followed by a presentation of the results.

  17. Classical mechanics with calculus of variations and optimal control an intuitive introduction

    CERN Document Server

    Levi, Mark

    2014-01-01

    This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the "tennis racket paradox"; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this boo...

  18. Geometrical treatment of non-potential interactions: the exterior variational calculus, dynamical systems, physical 1-forms and variational selfadjointness

    International Nuclear Information System (INIS)

    Trostel, R.

    1982-01-01

    A mathematical objective of this paper is to provide geometrical formulation of the integrability conditions for the existence of an action functional, that is, to provide a geometrical counterpart (similar to that by Abraham, Marsden, and Hughes) of the variational and functional approach to self-adjointness. This objective is achieved via the exterior variational calculus, an exterior differential calculus on the vector space of functions depending on time or space time, using from the outset extensively the concept of functional differentiation as its foundation. Variational self-adjointness equals the variational closure of the physical 1-form, the vanishing of a generalized curl-operation applied to the equations of motion. The convenience of this more formal approach is demonstrated, not only when deriving the conditions of variational self-adjointness for materials of differential type of arbitrary order (particles or fields), using roughly no more than Dirac's delta-distributions, but also when treating materials of a broader class (including causal and acausal constitutive functionals, materials of rate type, integral type, etc.). A physical objective of this paper is achieved by pointing out that, as physics is primarily concerned with the solutions of the evolution equations, i.e., with the set of the zero points of the physical 1-form, an equivalence relation among the physical 1-forms on the infinite dimensional vector space of functions is constructed by leaving the set of their zero points unchanged. Using this result, a direct Lagrangian universality is indicated and an almost one presented. Moreover, all physical 1-forms connected by invertible supermatrices (thus mixing the evolution law of different times or space-time) are equivalent. Choosing these supermatrices to be diagonal in time or space-time yields the indirect analytical representation factors

  19. The malliavin calculus and related topics

    CERN Document Server

    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

  20. A new class of problems in the calculus of variations

    Science.gov (United States)

    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.

  1. Tensor Calculus: Unlearning Vector Calculus

    Science.gov (United States)

    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…

  2. On the existence and uniqueness of minima and maxima on spheres of the integral functional of the calculus of variations

    OpenAIRE

    Ricceri, Biagio

    2005-01-01

    We deal with the integral functional of the calculus of variations assuming that the gradient of the integrand is Lipschitzian. We then prove that if this gradient does not vanish at zero, then the functional has a unique minimum and a unique maximum on each sphere, centered at zero, with radius small enough.

  3. Calculus

    CERN Document Server

    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

  4. Malliavin Calculus With Applications to Stochastic Partial Differential Equations

    CERN Document Server

    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

  5. Dynamic Material Removal Rate and Tool Replacement Optimization with Calculus of Variations

    Science.gov (United States)

    Lan, Tian-Syung; Lo, Chih-Yao; Chiu, Min-Chie; Yeh, Long-Jyi

    This study mathematically presents an optimum material removal control model, where the Material Removal Rate (MRR) is comprehensively introduced, to accomplish the dynamic machining control and tool life determination of a cutting tool under an expected machining quantity. To resolve the incessant cutting-rate control problem, Calculus of Variations is implemented for the optimum solution. Additionally, the decision criteria for selecting the dynamic solution are suggested and the sensitivity analyses for key variables in the optimal solution are fully discussed. The versatility of this study is furthermore exemplified through a numerical illustration from the real-world industry with BORLAND C++ BUILDER. It is shown that the theoretical and simulated results are in good agreement. This study absolutely explores the very promising solution to dynamically organize the MRR in minimizing the machining cost of a cutting tool for the contemporary machining industry.

  6. A Tutorial Review on Fractal Spacetime and Fractional Calculus

    Science.gov (United States)

    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.

  7. Fundamentals of calculus

    CERN Document Server

    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

  8. Impact of Calculus Reform in a Liberal Arts Calculus Course.

    Science.gov (United States)

    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…

  9. Studies on the composition of human dental calculus

    International Nuclear Information System (INIS)

    Molokhia, A.; Nixon, G.S.

    1984-01-01

    The concentrations of Ca, Mg, Na, K, Cl, Zn, Sr, Mn, Ba, Br and Au were determined in individual samples of dental calculus collected from patients resident in the Manchester area. The method used was instrumental neutron activation analysis, combined with gamma-spectrometry. The highest and lowest values of Sr were found in calculus from patients of Asian origin. No differences were found in the elements studied with regard to sex or age. Individual variations were highest in Au and lowest in Ca. (author)

  10. Capsule calculus

    CERN Document Server

    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

  11. The compatibility approach in the classical theory of thermoelectricity seen from the perspective of variational calculus

    Energy Technology Data Exchange (ETDEWEB)

    Seifert, Wolfgang [Institute of Physics, Martin Luther University, Halle-Wittenberg (Germany); Zabrocki, Knud; Mueller, Eckhard [Institute of Materials Research, German Aerospace Center (DLR), 51170 Koeln (Germany); Snyder, G.J. [California Institute of Technology, Pasadena, California 91125 (United States)

    2010-03-15

    The compatibility approach introduced by Snyder and Ursell opens a new pathway for the improvement of thermoelectric (TE) device performance. It has been shown that sufficient compatibility is - besides an increase of the averaged figure of merit Z - essential for efficient operation of a TE device, and that compatibility will facilitate rational materials selection, device design, and the engineering of functionally graded materials (FGMs). In this paper, the authors give an overview of the fundamental results and present a new approach from the perspective of variational calculus. A particular focus is on the role of ideal self-compatibility, i.e., adjusting compatibility locally at any position along a TE leg. (Abstract Copyright [2010], Wiley Periodicals, Inc.)

  12. Fast free-form deformable registration via calculus of variations

    International Nuclear Information System (INIS)

    Lu Weiguo; Chen Mingli; Olivera, Gustavo H; Ruchala, Kenneth J; Mackie, Thomas R

    2004-01-01

    In this paper, we present a fully automatic, fast and accurate deformable registration technique. This technique deals with free-form deformation. It minimizes an energy functional that combines both similarity and smoothness measures. By using calculus of variations, the minimization problem was represented as a set of nonlinear elliptic partial differential equations (PDEs). A Gauss-Seidel finite difference scheme is used to iteratively solve the PDE. The registration is refined by a multi-resolution approach. The whole process is fully automatic. It takes less than 3 min to register two three-dimensional (3D) image sets of size 256 x 256 x 61 using a single 933 MHz personal computer. Extensive experiments are presented. These experiments include simulations, phantom studies and clinical image studies. Experimental results show that our model and algorithm are suited for registration of temporal images of a deformable body. The registration of inspiration and expiration phases of the lung images shows that the method is able to deal with large deformations. When applied to the daily CT images of a prostate patient, the results show that registration based on iterative refinement of displacement field is appropriate to describe the local deformations in the prostate and the rectum. Similarity measures improved significantly after the registration. The target application of this paper is for radiotherapy treatment planning and evaluation that incorporates internal organ deformation throughout the course of radiation therapy. The registration method could also be equally applied in diagnostic radiology

  13. Fractional Vector Calculus and Fractional Special Function

    OpenAIRE

    Li, Ming-Fan; Ren, Ji-Rong; Zhu, Tao

    2010-01-01

    Fractional vector calculus is discussed in the spherical coordinate framework. A variation of the Legendre equation and fractional Bessel equation are solved by series expansion and numerically. Finally, we generalize the hypergeometric functions.

  14. The impact of taking a college pre-calculus course on students' college calculus performance

    Science.gov (United States)

    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.

  15. Calculus light

    CERN Document Server

    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

  16. Study on bioactive compounds of in vitro cultured Calculus Suis and natural Calculus Bovis.

    Science.gov (United States)

    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.

  17. Calculus

    CERN Document Server

    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.

  18. Continuation calculus

    NARCIS (Netherlands)

    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

  19. Discrete Calculus as a Bridge between Scales

    Science.gov (United States)

    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

  20. Calculus

    CERN Document Server

    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

  1. Operational calculus

    CERN Document Server

    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

  2. Calculus of one variable

    CERN Document Server

    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.

  3. Dogs Don't Need Calculus

    Science.gov (United States)

    Bolt, Mike

    2010-01-01

    Many optimization problems can be solved without resorting to calculus. This article develops a new variational method for optimization that relies on inequalities. The method is illustrated by four examples, the last of which provides a completely algebraic solution to the problem of minimizing the time it takes a dog to retrieve a thrown ball,…

  4. Calculus refresher

    CERN Document Server

    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

  5. Steady-state groundwater recharge in trapezoidal-shaped aquifers: A semi-analytical approach based on variational calculus

    Science.gov (United States)

    Mahdavi, Ali; Seyyedian, Hamid

    2014-05-01

    This study presents a semi-analytical solution for steady groundwater flow in trapezoidal-shaped aquifers in response to an areal diffusive recharge. The aquifer is homogeneous, anisotropic and interacts with four surrounding streams of constant-head. Flow field in this laterally bounded aquifer-system is efficiently constructed by means of variational calculus. This is accomplished by minimizing a properly defined penalty function for the associated boundary value problem. Simple yet demonstrative scenarios are defined to investigate anisotropy effects on the water table variation. Qualitative examination of the resulting equipotential contour maps and velocity vector field illustrates the validity of the method, especially in the vicinity of boundary lines. Extension to the case of triangular-shaped aquifer with or without an impervious boundary line is also demonstrated through a hypothetical example problem. The present solution benefits from an extremely simple mathematical expression and exhibits strictly close agreement with the numerical results obtained from Modflow. Overall, the solution may be used to conduct sensitivity analysis on various hydrogeological parameters that affect water table variation in aquifers defined in trapezoidal or triangular-shaped domains.

  6. Parametric identification of the Nomoto generalized model using the apparatus of variational calculus

    Directory of Open Access Journals (Sweden)

    Agarkov S.A.

    2015-03-01

    Full Text Available A new approach to the identification of parameters of the Nomoto generalized vessel model has been proposed. The apparatus of classical calculus and the method of least squares have been used

  7. Vector Differential Calculus

    OpenAIRE

    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...

  8. 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.

  9. Noncausal stochastic calculus

    CERN Document Server

    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 ...

  10. Propositional Calculus in Coq

    OpenAIRE

    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.

  11. Continuation calculus

    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.

  12. The Impact of Taking a College Pre-Calculus Course on Students' College Calculus Performance

    Science.gov (United States)

    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…

  13. Tuplix Calculus

    OpenAIRE

    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...

  14. Polynomial Calculus: Rethinking the Role of Calculus in High Schools

    Science.gov (United States)

    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…

  15. [Fluorescence control of dental calculus removal].

    Science.gov (United States)

    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).

  16. Calculus II For Dummies

    CERN Document Server

    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

  17. Early Vector Calculus: A Path through Multivariable Calculus

    Science.gov (United States)

    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.)

  18. Calculus

    CERN Document Server

    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.

  19. Dental Calculus Arrest of Dental Caries.

    Science.gov (United States)

    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.

  20. Dental Calculus Arrest of Dental Caries

    Science.gov (United States)

    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

  1. The efficacy of selective calculus ablation at 400 nm: comparison to conventional calculus removal methods

    Science.gov (United States)

    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.

  2. Discrete fractional calculus

    CERN Document Server

    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...

  3. Calculus with applications

    CERN Document Server

    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...

  4. Motivation and Study Habits of College Calculus Students: Does Studying Calculus in High School Make a Difference?

    Science.gov (United States)

    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…

  5. SRXRF analysis with spatial resolution of dental calculus

    International Nuclear Information System (INIS)

    Sanchez, Hector Jorge; Perez, Carlos Alberto; Grenon, Miriam

    2000-01-01

    This work presents elemental-composition studies of dental calculus by X-ray fluorescence analysis using synchrotron radiation. The intrinsic characteristics of synchrotron light allow for a semi-quantitative analysis with spatial resolution. The experiments were carried out in the high-vacuum station of the XRF beamline at the Synchrotron Light National Laboratory (Campinas, Brazil). All the measurements were performed in conventional geometry (45 deg. + 45 deg.) and the micro-collimation was attained via a pair of orthogonal slits mounted in the beamline. In this way, pixels of 50 μmx50 μm were obtained keeping a high flux of photons on the sample. Samples of human dental calculus were measured in different positions along their growing axis, in order to determine variations of the compositions in the pattern of deposit. Intensity ratios of minor elements and traces were obtained, and linear profiles and surface distributions were determined. As a general summary, we can conclude that μXRF experiments with spatial resolution on dental calculus are feasible with simple collimation and adequate positioning systems, keeping a high flux of photon. These results open interesting perspectives for the future station of the line, devoted to μXRF, which will reach resolutions of the order of 10 μm

  6. SRXRF analysis with spatial resolution of dental calculus

    Science.gov (United States)

    Sánchez, Héctor Jorge; Pérez, Carlos Alberto; Grenón, Miriam

    2000-09-01

    This work presents elemental-composition studies of dental calculus by X-ray fluorescence analysis using synchrotron radiation. The intrinsic characteristics of synchrotron light allow for a semi-quantitative analysis with spatial resolution. The experiments were carried out in the high-vacuum station of the XRF beamline at the Synchrotron Light National Laboratory (Campinas, Brazil). All the measurements were performed in conventional geometry (45°+45°) and the micro-collimation was attained via a pair of orthogonal slits mounted in the beamline. In this way, pixels of 50 μm×50 μm were obtained keeping a high flux of photons on the sample. Samples of human dental calculus were measured in different positions along their growing axis, in order to determine variations of the compositions in the pattern of deposit. Intensity ratios of minor elements and traces were obtained, and linear profiles and surface distributions were determined. As a general summary, we can conclude that μXRF experiments with spatial resolution on dental calculus are feasible with simple collimation and adequate positioning systems, keeping a high flux of photon. These results open interesting perspectives for the future station of the line, devoted to μXRF, which will reach resolutions of the order of 10 μm.

  7. Correlation between chemical composition of dental calculus and bone samples in ancient human burials: perspectives in paleonutritional studies

    International Nuclear Information System (INIS)

    Capasso, L.; Di Tota, G.; Bondioli, L.

    1997-01-01

    Full text: The authors describe the results of an assay based on the comparison between chemical composition of dental calculus and bone respectively obtained from teeth and bones of ancient skeletons. The chemical analysis has been performed by synchrotron light. The concentrations of the following oligoelements having paleonutritional correlations were analysed: Fe, Cu, Zn, Pb, Sr and Ca. The authors demonstrate that- in a given individual the concentration of such elements in the bone sample were in the range of those obtained for the same elements in the sample of dental calculus. Such correspondence suggests that the chemical analysis of dental calculus may give paleonutritional indications analogous to those deriving from the analysis of bone samples. The authors underline also that the use of dental calculus has a distinct advantage over the use of bone samples, since it may allow a diachronic investigation. In fact, dental calculus typically presents a concentric pattern of growth, and the chemical composition of each layer may vary in accordance with temporal dietary variations. This is not the case for bone. This fact is the theoretical basis for the possible future development of techniques directed to the reconstruction of variations in the dietary habits of ancient individuals, possibly in relation to environmental seasonal changes

  8. Tuplix calculus

    NARCIS (Netherlands)

    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

  9. A robust interpretation of duration calculus

    DEFF Research Database (Denmark)

    Franzle, M.; Hansen, Michael Reichhardt

    2005-01-01

    We transfer the concept of robust interpretation from arithmetic first-order theories to metric-time temporal logics. The idea is that the interpretation of a formula is robust iff its truth value does not change under small variation of the constants in the formula. Exemplifying this on Duration...... Calculus (DC), our findings are that the robust interpretation of DC is equivalent to a multi-valued interpretation that uses the real numbers as semantic domain and assigns Lipschitz-continuous interpretations to all operators of DC. Furthermore, this continuity permits approximation between discrete...

  10. The calculus lifesaver all the tools you need to excel at calculus

    CERN Document Server

    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

  11. On the refinement calculus

    CERN Document Server

    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.

  12. 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...

  13. A generalized nonlocal vector calculus

    Science.gov (United States)

    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.

  14. Calculus

    CERN Document Server

    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

  15. Multivariable calculus with applications

    CERN Document Server

    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...

  16. On the Presentation of Pre-Calculus and Calculus Topics: An Alternate View

    Science.gov (United States)

    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…

  17. Comparative study on major bioactive components in natural, artificial and in-vitro cultured Calculus Bovis.

    Science.gov (United States)

    Yan, Shi-Kai; Wu, Yan-Wen; Liu, Run-Hui; Zhang, Wei-Dong

    2007-01-01

    Major bioactive components in various Calculus Bovis, including natural, artificial and in-vitro cultured Calculus Bovis, were comparatively studied. An approach of high-performance liquid chromatography coupled with ultraviolet and evaporative light scattering detections (HPLC/UV/ELSD) was established to simultaneously determinate six bioactive components thereof, including five bile acids (cholic acid, deoxycholic acid, ursodeoxycholic, chenodeoxycholic acid, hyodeoxycholic acid) and bilirubin. ELSD and UV detector were applied to detect bile acids and bilirubin respectively. The assay was performed on a C(18) column with water-acetonitrile gradient elution and the investigated constituents were authenticated by comparing retention times and mass spectra with those of reference compounds. The proposed method was applied to analyze twenty-one Calculus Bovis extraction samples, and produced data with acceptable linearity, precision, repeatability and accuracy. The result indicated the variations among Calculus Bovis samples under different developmental conditions. Artificial and in-vitro cultured Calculus Bovis, especially in-vitro cultured ones, which contain total bioactive constituents no less than natural products and have the best batch-to-batch uniformity, suffice to be used as substitutes of natural Calculus Bovis.

  18. Bacterial Viability within Dental Calculus: An Untrodden, Inquisitive Clinico-Patho- Microbiological Research.

    Science.gov (United States)

    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

  19. Calculus for dummies

    CERN Document Server

    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

  20. Advanced calculus a transition to analysis

    CERN Document Server

    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

  1. Tensors, differential forms, and variational principles

    CERN Document Server

    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.

  2. Giant calculus: review and report of a case.

    Science.gov (United States)

    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.

  3. Maxima and Minima Without Calculus.

    Science.gov (United States)

    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)

  4. 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

  5. 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)

  6. A Logical Process Calculus

    Science.gov (United States)

    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.

  7. Dental Calculus Arrest of Dental Caries

    OpenAIRE

    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...

  8. ASSESSING STUDENTS' UNDERSTANDING OF PRE-CALCULUS CONCEPTS

    OpenAIRE

    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.

  9. Introduction to global variational geometry

    CERN Document Server

    Krupka, Demeter

    2015-01-01

    The book is devoted to recent research in the global variational theory on smooth manifolds. Its main objective is an extension of the classical variational calculus on Euclidean spaces to (topologically nontrivial) finite-dimensional smooth manifolds; to this purpose the methods of global analysis of differential forms are used. Emphasis is placed on the foundations of the theory of variational functionals on fibered manifolds - relevant geometric structures for variational principles in geometry, physical field theory and higher-order fibered mechanics. The book chapters include: - foundations of jet bundles and analysis of differential forms and vector fields on jet bundles, - the theory of higher-order integral variational functionals for sections of a fibred space, the (global) first variational formula in infinitesimal and integral forms- extremal conditions and the discussion of Noether symmetries and generalizations,- the inverse problems of the calculus of variations of Helmholtz type- variational se...

  10. 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...

  11. Hands-On Calculus

    Science.gov (United States)

    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…

  12. Teaching the Calculus

    Science.gov (United States)

    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…

  13. The Vectorial $\\lambda$-Calculus

    OpenAIRE

    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...

  14. On Some Syntactic Properties of the Modalized Heyting Calculus

    OpenAIRE

    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.

  15. The Calculus of a Vase

    Science.gov (United States)

    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…

  16. Calculus of bivariant function

    OpenAIRE

    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...

  17. Calculus migration characterization during Ho:YAG laser lithotripsy by high-speed camera using suspended pendulum method.

    Science.gov (United States)

    Zhang, Jian James; Rajabhandharaks, Danop; Xuan, Jason Rongwei; Chia, Ray W J; Hasenberg, Thomas

    2017-07-01

    Calculus migration is a common problem during ureteroscopic laser lithotripsy procedure to treat urolithiasis. A conventional experimental method to characterize calculus migration utilized a hosting container (e.g., a "V" grove or a test tube). These methods, however, demonstrated large variation and poor detectability, possibly attributed to the friction between the calculus and the container on which the calculus was situated. In this study, calculus migration was investigated using a pendulum model suspended underwater to eliminate the aforementioned friction. A high-speed camera was used to study the movement of the calculus which covered zero order (displacement), first order (speed), and second order (acceleration). A commercialized, pulsed Ho:YAG laser at 2.1 μm, a 365-μm core diameter fiber, and a calculus phantom (Plaster of Paris, 10 × 10 × 10 mm 3 ) was utilized to mimic laser lithotripsy procedure. The phantom was hung on a stainless steel bar and irradiated by the laser at 0.5, 1.0, and 1.5 J energy per pulse at 10 Hz for 1 s (i.e., 5, 10, and 15 W). Movement of the phantom was recorded by a high-speed camera with a frame rate of 10,000 FPS. The video data files are analyzed by MATLAB program by processing each image frame and obtaining position data of the calculus. With a sample size of 10, the maximum displacement was 1.25 ± 0.10, 3.01 ± 0.52, and 4.37 ± 0.58 mm for 0.5, 1, and 1.5 J energy per pulse, respectively. Using the same laser power, the conventional method showed <0.5 mm total displacement. When reducing the phantom size to 5 × 5 × 5 mm 3 (one eighth in volume), the displacement was very inconsistent. The results suggested that using the pendulum model to eliminate the friction improved sensitivity and repeatability of the experiment. A detailed investigation on calculus movement and other causes of experimental variation will be conducted as a future study.

  18. Non-commuting variations in mathematics and physics a survey

    CERN Document Server

    Preston, Serge

    2016-01-01

    This text presents and studies the method of so –called noncommuting variations in Variational Calculus. This method was pioneered by Vito Volterra who noticed that the conventional Euler-Lagrange (EL-) equations are not applicable in Non-Holonomic Mechanics and suggested to modify the basic rule used in Variational Calculus. This book presents a survey of Variational Calculus with non-commutative variations and shows that most basic properties of conventional Euler-Lagrange Equations are, with some modifications, preserved for EL-equations with K-twisted (defined by K)-variations. Most of the book can be understood by readers without strong mathematical preparation (some knowledge of Differential Geometry is necessary). In order to make the text more accessible the definitions and several necessary results in Geometry are presented separately in Appendices I and II Furthermore in Appendix III a short presentation of the Noether Theorem describing the relation between the symmetries of the differential equa...

  19. Pre-calculus workbook for dummies

    CERN Document Server

    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

  20. 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.

  1. Applications of fractional calculus in physics

    CERN Document Server

    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

  2. Initialized Fractional Calculus

    Science.gov (United States)

    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.

  3. 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

  4. Heuristics as an alternative to variational calculus for optimization of a class of thermal insulation systems

    Energy Technology Data Exchange (ETDEWEB)

    Pramanick, A.K.; Das, P.K. [Indian Inst. of Technology, Kharagpur (India). Dept. of Mechanical Engineering

    2005-04-01

    This article reports an alternative treatment in lieu of the principle of variational calculus for a certain class of optimization problems. In particular, the optimum distribution of insulating material on one side of a flat plate for minimum heat transfer is sought when the other side is exposed to a laminar forced convection. Both conjugate and non-conjugate formulations of the problem are conceived and closed form solutions are presented. Interestingly, optimized insulation profile exhibits a category of equipartition principle in some macroscopic domain. Expression for minimum heat transfer is a function of Biot number in non-conjugate analysis of the model. Contrastingly, the non-dimensional group Jh{sub L} is the characteristic parameter for conjugate formulation. Finally, Bejan's method of intersecting asymptotes is employed to find an order of magnitude for a ceiling value of the wall material. With some scale factor, a range 0 < J{sub max} {<=} 1.506Pr {sup -} {sup 1/3} for the representative material volume can be ascertained, beyond which the optimization exercise reduces to a trivial one and traditional constant thickness profile becomes a recognized design. (author)

  5. 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

  6. Fluorescence detection of dental calculus

    Science.gov (United States)

    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.

  7. 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.

  8. Advanced calculus

    CERN Document Server

    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,

  9. Existence of evolutionary variational solutions via the calculus of variations

    Science.gov (United States)

    Bögelein, Verena; Duzaar, Frank; Marcellini, Paolo

    In this paper we introduce a purely variational approach to time dependent problems, yielding the existence of global parabolic minimizers, that is ∫0T ∫Ω [uṡ∂tφ+f(x,Du)] dx dt⩽∫0T ∫Ω f(x,Du+Dφ) dx dt, whenever T>0 and φ∈C0∞(Ω×(0,T),RN). For the integrand f:Ω×R→[0,∞] we merely assume convexity with respect to the gradient variable and coercivity. These evolutionary variational solutions are obtained as limits of maps depending on space and time minimizing certain convex variational functionals. In the simplest situation, with some growth conditions on f, the method provides the existence of global weak solutions to Cauchy-Dirichlet problems of parabolic systems of the type ∂tu-divDξf(x,Du)=0 in Ω×(0,∞).

  10. Differential Calculus on Quantum Spheres

    OpenAIRE

    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.

  11. 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.

  12. 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...

  13. 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...

  14. 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

  15. Fluorescence spectroscopy of dental calculus

    Science.gov (United States)

    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.

  16. Disappearing renal calculus.

    Science.gov (United States)

    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.

  17. Essential calculus with applications

    CERN Document Server

    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.

  18. Contributions regarding calculus and design of an ultrasonic system used in plasma metallization

    Science.gov (United States)

    Amza, G.

    2015-11-01

    Paper presents the calculus elements and construction for the ultrasonic system used in reconditioning process by metallization. A series of necessary elements used in ultrasonic system dimensioning are given and an ultrasonic system used in reconditioning process by plasma and grain metallization are presented. Also, a calculated ultrasonic system is modelled to work in resonance regime at the frequency f = 22Khz. Stress map inside material, internal energy variation, lost energy variation on length and volume unit are presented.

  19. Leveraging Prior Calculus Study with Embedded Review

    Science.gov (United States)

    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…

  20. Generalized Gaussian Error Calculus

    CERN Document Server

    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...

  1. Pre-Calculus For Dummies

    CERN Document Server

    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

  2. The Effects of Two Semesters of Secondary School Calculus on Students' First and Second Quarter Calculus Grades at the University of Utah

    Science.gov (United States)

    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)

  3. Characteristics of subgingival calculus detection by multiphoton fluorescence microscopy

    Science.gov (United States)

    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.

  4. 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.

  5. 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....

  6. Advanced calculus of a single variable

    CERN Document Server

    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...

  7. Schaum's outline of calculus

    CERN Document Server

    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.

  8. 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.)

  9. 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.

  10. Discounted Duration Calculus

    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....

  11. A Snapshot of the Calculus Classroom

    Science.gov (United States)

    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.

  12. Success in Introductory Calculus: The Role of High School and Pre-calculus Preparation

    OpenAIRE

    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...

  13. 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.

  14. Factors Associated with Success in College Calculus II

    Science.gov (United States)

    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…

  15. 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...

  16. Restricted diversity of dental calculus methanogens over five centuries, France

    OpenAIRE

    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...

  17. RAMAN-SPECTRA OF HUMAN DENTAL CALCULUS

    NARCIS (Netherlands)

    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

  18. Introduction to the operational calculus

    CERN Document Server

    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

  19. 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....

  20. Ancient DNA analysis of dental calculus.

    Science.gov (United States)

    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.

  1. Lacroix and the calculus

    CERN Document Server

    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...

  2. Reliability of recordings of subgingival calculus detected using an ultrasonic device.

    Science.gov (United States)

    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.

  3. Testicular calculus: A rare case.

    Science.gov (United States)

    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.

  4. Improving student learning in calculus through applications

    Science.gov (United States)

    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.

  5. Thematization of the Calculus Graphing Schema

    Science.gov (United States)

    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,…

  6. The stack calculus

    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.

  7. Renal vein thrombosis mimicking urinary calculus: a dilemma of diagnosis.

    Science.gov (United States)

    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.

  8. An AP Calculus Classroom Amusement Park

    Science.gov (United States)

    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.…

  9. A Cross-National Study of Calculus

    Science.gov (United States)

    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…

  10. 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

  11. 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....

  12. Putting Differentials Back into Calculus

    Science.gov (United States)

    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.

  13. The calculus primer

    CERN Document Server

    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

  14. Restricted diversity of dental calculus methanogens over five centuries, France.

    Science.gov (United States)

    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.

  15. Endoscopic vs. tactile evaluation of subgingival calculus.

    Science.gov (United States)

    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.

  16. Noninvasive control of dental calculus removal: qualification of two fluorescence methods

    Science.gov (United States)

    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.

  17. 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.

  18. CLEP calculus

    CERN Document Server

    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

  19. Introductory analysis a deeper view of calculus

    CERN Document Server

    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

  20. Computing for calculus

    CERN Document Server

    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

  1. Calculus of tensors and differential forms

    CERN Document Server

    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.

  2. Calculus with vectors

    CERN Document Server

    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...

  3. Calculus and analysis in Euclidean space

    CERN Document Server

    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...

  4. Two-dimensional calculus

    CERN Document Server

    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

  5. Dental calculus detection using the VistaCam.

    Science.gov (United States)

    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.

  6. Improving Student Success in Calculus: A Comparison of Four College Calculus Classes

    Science.gov (United States)

    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

  7. The calculus a genetic approach

    CERN Document Server

    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

  8. LOOP CALCULUS AND BELIEF PROPAGATION FOR Q-ARY ALPHABET: LOOP TOWER

    Energy Technology Data Exchange (ETDEWEB)

    CHERTKOV, MICHAEL [Los Alamos National Laboratory; CHERNYAK, VLADIMIR [Los Alamos National Laboratory

    2007-01-10

    Loop calculus introduced in [1], [2] constitutes a new theoretical tool that explicitly expresses symbol Maximum-A-Posteriori (MAP) solution of a general statistical inference problem via a solution of the Belief Propagation (BP) equations. This finding brought a new significance to the BP concept, which in the past was thought of as just a loop-free approximation. In this paper they continue a discussion of the Loop Calculus, partitioning the results into three Sections. In Section 1 they introduce a new formulation of the Loop Calculus in terms of a set of transformations (gauges) that keeping the partition function of the problem invariant. The full expression contains two terms referred to as the 'ground state' and 'excited states' contributions. The BP equations are interpreted as a special (BP) gauge fixing condition that emerges as a special orthogonality constraint between the ground state and excited states, which also selects loop contributions as the only surviving ones among the excited states. In Section 2 they demonstrate how the invariant interpretation of the Loop Calculus, introduced in Section 1, allows a natural extension to the case of a general q-ary alphabet, this is achieved via a loop tower sequential construction. The ground level in the tower is exactly equivalent to assigning one color (out of q available) to the 'ground state' and considering all 'excited' states colored in the remaining (q-1) colors, according to the loop calculus rule. Sequentially, the second level in the tower corresponds to selecting a loop from the previous step, colored in (q-1) colors, and repeating the same ground vs excited states splitting procedure into one and (q-2) colors respectively. The construction proceeds till the full (q-1)-levels deep loop tower (and the corresponding contributions to the partition function) are established. In Section 3 they discuss an ultimate relation between the loop calculus and the Bethe

  9. Pre-calculus workbook for dummies

    CERN Document Server

    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

  10. Mathematics for physics with calculus

    CERN Document Server

    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.

  11. 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

  12. 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.

  13. 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....

  14. 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. .

  15. College Readiness: The Evaluation of Students Participating in the Historically Black College and University Program in Pre-Calculus and the Calculus Sequence

    Science.gov (United States)

    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…

  16. Functional Fractional Calculus

    CERN Document Server

    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

  17. Proof Nets for Lambek Calculus

    NARCIS (Netherlands)

    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;

  18. 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 ...

  19. 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...

  20. Miniature endoscopic optical coherence tomography for calculus detection.

    Science.gov (United States)

    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.

  1. 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...

  2. Łukasiewicz mu-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.

  3. The impacts of gingivitis and calculus on Thai children's quality of life.

    Science.gov (United States)

    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.

  4. 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

  5. On the formalism of local variational differential operators

    NARCIS (Netherlands)

    Igonin, S.; Verbovetsky, A.V.; Vitolo, R.

    2002-01-01

    The calculus of local variational differential operators introduced by B. L. Voronov, I. V. Tyutin, and Sh. S. Shakhverdiev is studied in the context of jet super space geometry. In a coordinate-free way, we relate these operators to variational multivectors, for which we introduce and compute the

  6. Understanding Calculus beyond Computations: A Descriptive Study of the Parallel Meanings and Expectations of Teachers and Users of Calculus

    Science.gov (United States)

    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…

  7. Variational Integrals of a Class of Nonhomogeneous -Harmonic Equations

    Directory of Open Access Journals (Sweden)

    Guanfeng Li

    2014-01-01

    Full Text Available We introduce a class of variational integrals whose Euler equations are nonhomogeneous -harmonic equations. We investigate the relationship between the minimization problem and the Euler equation and give a simple proof of the existence of some nonhomogeneous -harmonic equations by applying direct methods of the calculus of variations. Besides, we establish some interesting results on variational integrals.

  8. Topology, calculus and approximation

    CERN Document Server

    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...

  9. Recursive sequences in first-year calculus

    Science.gov (United States)

    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.

  10. Essential AOP: The A 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....

  11. Calculus detection technologies: where do we stand now?

    Science.gov (United States)

    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.

  12. Calculus detection technologies: where do we stand now?

    Science.gov (United States)

    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

  13. 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...

  14. Dental calculus image based on optical coherence tomography

    Science.gov (United States)

    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.

  15. 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

  16. On quadratic variation of martingales

    Indian Academy of Sciences (India)

    On quadratic variation of martingales. 459. The proof relied on the theory of stochastic integration. Subsequently, in Karandikar. [4], the formula was derived using only Doob's maximal inequality. Thus this could be the starting point for the development of stochastic calculus for continuous semimartingales without bringing in ...

  17. Brownian motion, martingales, and stochastic calculus

    CERN Document Server

    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...

  18. The absolute differential calculus calculus of tensors

    CERN Document Server

    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

  19. Dental calculus formation in children and adolescents undergoing hemodialysis.

    Science.gov (United States)

    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.

  20. 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.

  1. Quantum stochastic calculus and representations of Lie superalgebras

    CERN Document Server

    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.

  2. 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...

  3. 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

  4. Multiplicative calculus in biomedical image analysis

    NARCIS (Netherlands)

    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,

  5. Improving Calculus II and III through the Redistribution of Topics

    Science.gov (United States)

    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…

  6. Series expansion in fractional calculus and fractional differential equations

    OpenAIRE

    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...

  7. Introduction to stochastic calculus

    CERN Document Server

    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...

  8. On inverse problem of calculus of variations

    Energy Technology Data Exchange (ETDEWEB)

    Tao, Z-L [College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044 (China)], E-mail: zaolingt@nuist.edu.cn

    2008-02-15

    Using the semi-inverse method proposed by Ji-Huan He, variational principles are established for some nonlinear equations arising in physics, including the (p, 2p)-mZK equation, Klein-Gordon equation, sine-Gordon equation, Liouville equation, Dodd- Bullough-Mikhailov equation, and Tzitzeica-Dodd-Bullough equation.

  9. Computer Managed Instruction Homework Modules for Calculus I.

    Science.gov (United States)

    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.…

  10. Finite-dimensional calculus

    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'.

  11. A Giant Urethral Calculus.

    Science.gov (United States)

    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.

  12. Discrete Calculus by Analogy

    CERN Document Server

    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

  13. Multiple integrals in the calculus of variations

    CERN Document Server

    Morrey, Charles B

    1966-01-01

    From the reviews: "…the book contains a wealth of material essential to the researcher concerned with multiple integral variational problems and with elliptic partial differential equations. The book not only reports the researches of the author but also the contributions of his contemporaries in the same and related fields. The book undoubtedly will become a standard reference for researchers in these areas. …The book is addressed mainly to mature mathematical analysts. However, any student of analysis will be greatly rewarded by a careful study of this book." M. R. Hestenes in Journal of Optimization Theory and Applications "The work intertwines in masterly fashion results of classical analysis, topology, and the theory of manifolds and thus presents a comprehensive treatise of the theory of multiple integral variational problems." L. Schmetterer in Monatshefte für Mathematik "The book is very clearly exposed and contains the last modern theory in this domain. A comprehensive bibliography ends the book...

  14. A calculus for quality

    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...

  15. Investigation of In vitro Mineral forming bacterial isolates from supragingival calculus.

    Science.gov (United States)

    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.

  16. Variational regularization of 3D data experiments with Matlab

    CERN Document Server

    Montegranario, Hebert

    2014-01-01

    Variational Regularization of 3D Data provides an introduction to variational methods for data modelling and its application in computer vision. In this book, the authors identify interpolation as an inverse problem that can be solved by Tikhonov regularization. The proposed solutions are generalizations of one-dimensional splines, applicable to n-dimensional data and the central idea is that these splines can be obtained by regularization theory using a trade-off between the fidelity of the data and smoothness properties.As a foundation, the authors present a comprehensive guide to the necessary fundamentals of functional analysis and variational calculus, as well as splines. The implementation and numerical experiments are illustrated using MATLAB®. The book also includes the necessary theoretical background for approximation methods and some details of the computer implementation of the algorithms. A working knowledge of multivariable calculus and basic vector and matrix methods should serve as an adequat...

  17. A type system for continuation calculus

    NARCIS (Netherlands)

    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

  18. 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.

  19. 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)

  20. AP calculus AB & BC crash course

    CERN Document Server

    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

  1. A phenomenological calculus of Wiener description space.

    Science.gov (United States)

    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.

  2. 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...

  3. 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.

  4. The development and nature of problem-solving among first-semester calculus students

    Science.gov (United States)

    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

  5. Preservation of the metaproteome: variability of protein preservation in ancient dental calculus.

    Science.gov (United States)

    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.

  6. Neutrosophic Precalculus and Neutrosophic Calculus

    OpenAIRE

    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...

  7. 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 ...

  8. Feynman's operational calculus and beyond noncommutativity and time-ordering

    CERN Document Server

    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...

  9. 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.

  10. Pre-calculus 1,001 practice problems for dummies

    CERN Document Server

    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

  11. Effect of non-functional teeth on accumulation of supra-gingival calculus in children.

    Science.gov (United States)

    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.

  12. Imagine Yourself in This Calculus Classroom

    Science.gov (United States)

    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…

  13. Educating about Sustainability while Enhancing Calculus

    Science.gov (United States)

    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…

  14. 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

  15. 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

  16. The dagger lambda 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.

  17. Dental hygiene faculty calibration in the evaluation of calculus detection.

    Science.gov (United States)

    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.

  18. An Introductory Calculus-Based Mechanics Investigation

    Science.gov (United States)

    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…

  19. Using Dynamic Software to Address Common College Calculus Stumbling Blocks

    Science.gov (United States)

    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…

  20. Site specific mineral composition and microstructure of human supra-gingival dental calculus.

    Science.gov (United States)

    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.

  1. Effect of Ramadan fasting on urinary risk factors for calculus formation.

    Science.gov (United States)

    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.

  2. 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)

  3. The Complex Gradient Operator and the CR-Calculus

    OpenAIRE

    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-...

  4. Areas and Volumes in Pre-Calculus

    Science.gov (United States)

    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…

  5. 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.

  6. White noise calculus and Fock space

    CERN Document Server

    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.

  7. 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)

  8. A Transition Course from Advanced Placement to College Calculus

    Science.gov (United States)

    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…

  9. Programming Language Concepts - The Lambda Calculus Approach

    NARCIS (Netherlands)

    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:

  10. Solitary main pancreatic ductal calculus of possible biliary origin causing acute pancreatitis.

    Science.gov (United States)

    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.

  11. 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

  12. Everyday calculus discovering the hidden math all around us

    CERN Document Server

    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

  13. 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

  14. On flipping first-semester calculus: a case study

    Science.gov (United States)

    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.

  15. 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.

  16. Selective ablation of dental calculus with a frequency-doubled Alexandrite laser

    Science.gov (United States)

    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.

  17. 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....

  18. Elementary calculus an infinitesimal approach

    CERN Document Server

    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

  19. Introduction to Differential Calculus Systematic Studies with Engineering Applications for Beginners

    CERN Document Server

    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

  20. [Percentage of uric acid calculus and its metabolic character in Dongjiang River valley].

    Science.gov (United States)

    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.

  1. Fluorescence-based calculus detection using a 405-nm excitation wavelength

    Science.gov (United States)

    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.

  2. Renal calculus

    CERN Document Server

    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...

  3. Science 101: How Do We Use Calculus in Science?

    Science.gov (United States)

    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…

  4. Intitialization, Conceptualization, and Application in the Generalized Fractional Calculus

    Science.gov (United States)

    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.

  5. Initialization, conceptualization, and application in the generalized (fractional) calculus.

    Science.gov (United States)

    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.

  6. The Development and Nature of Problem-Solving among First-Semester Calculus Students

    Science.gov (United States)

    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…

  7. Calculus in High School--At What Cost?

    Science.gov (United States)

    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)

  8. Extended finite operator calculus as an example of algebraization of analysis

    OpenAIRE

    Kwasniewski, A. K.; Borak, E.

    2004-01-01

    A wardian calculus of sequences started almost seventy years ago constitutes the general scheme for extensions of the classical umbral operator calculus considered by many afterwards . At the same time this calculus is an example of the algebraization of the analysis here restricted to the algebra of formal series. This is a review article based on the recent first author contributions. As the survey article it is supplemented by the short indicatory glossaries of notation and terms used by p...

  9. Calculator calculus

    CERN Document Server

    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...

  10. The Path to College Calculus: The Impact of High School Mathematics Coursework

    Science.gov (United States)

    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…

  11. 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.

  12. Descartes' Calculus of Subnormals: What Might Have Been

    Science.gov (United States)

    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…

  13. Provability Calculus of Constructions

    DEFF Research Database (Denmark)

    Nyblad, Kasten

    This thesis presents a type system, Provability Calculus of Constructions (PCoC) that can be used for the formalization of logic. In a theorem prover based on the system, the user can extend the prover with new inference rules in a logically consistent manner. This is done by representing PCo...

  14. 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...

  15. 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...

  16. Generalized Cartan Calculus in general dimension

    Science.gov (United States)

    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.

  17. Subgingival calculus imaging based on swept-source optical coherence tomography

    Science.gov (United States)

    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.

  18. 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

  19. 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)

  20. Towards Model Checking a Spi-Calculus Dialect

    NARCIS (Netherlands)

    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

  1. Backpropagation and ordered derivatives in the time scales calculus.

    Science.gov (United States)

    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.

  2. Regularization of positive definite matrix fields based on multiplicative calculus

    NARCIS (Netherlands)

    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

  3. Unfolding Semantics of the Untyped λ-Calculus with lectrec-Calculus with letrec

    NARCIS (Netherlands)

    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

  4. 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...

  5. Projects for calculus the language of change

    CERN Document Server

    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

  6. Water content contribution in calculus phantom ablation during Q-switched Tm:YAG laser lithotripsy.

    Science.gov (United States)

    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.

  7. Crystalline structure of pulverized dental calculus induces cell death in oral epithelial cells.

    Science.gov (United States)

    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

  8. Calculus of variations involving Caputo-Fabrizio fractional differentiation

    Directory of Open Access Journals (Sweden)

    Nuno R. O. Bastos

    2018-02-01

    Full Text Available This paper is devoted to study some variational problems with functionals containing the Caputo-Fabrizio fractional derivative, that is a fractional derivative with a non-singular kernel.

  9. Effects of Clicker Use on Calculus Students' Mathematics Anxiety

    Science.gov (United States)

    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…

  10. 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....

  11. 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

  12. 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)

  13. [Single and combining effects of Calculus Bovis and zolpidem on inhibitive neurotransmitter of rat striatum corpora].

    Science.gov (United States)

    Liu, Ping; He, Xinrong; Guo, Mei

    2010-04-01

    To investigate the correlation effects between single or combined administration of Calculus Bovis or zolpidem and changes of inhibitive neurotransmitter in rat striatum corpora. Sampling from rat striatum corpora was carried out through microdialysis. The content of two inhibitive neurotransmitters in rat corpus striatum- glycine (Gly) and gama aminobutyric acid (GABA), was determined by HPLC, which involved pre-column derivation with orthophthaladehyde, reversed-phase gradient elution and fluorescence detection. GABA content of rat striatum corpora in Calculus Bovis group was significantly increased compared with saline group (P Calculus Boris plus zolpidem group were increased largely compared with saline group as well (P Calculus Bovis group was higher than combination group (P Calculus Bovis or zolpidem group was markedly increased compared with saline group or combination group (P Calculus Bovis group, zolpidem group and combination group. The magnitude of increase was lower in combination group than in Calculus Bovis group and Zolpidem group, suggesting that Calculus Bovis promoted encephalon inhibition is more powerful than zolpidem. The increase in two inhibitive neurotransmitters did not show reinforcing effect in combination group, suggesting that Calculus Bovis and zolpidem may compete the same receptors. Therefore, combination of Calculus Bovis containing drugs and zolpidem has no clinical significance. Calculus Bovis shouldn't as an aperture-opening drugs be used for resuscitation therapy.

  14. Calculus and Success in a Business School

    Science.gov (United States)

    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…

  15. Fractional calculus in bioengineering, part 3.

    Science.gov (United States)

    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

  16. A comparison of dental ultrasonic technologies on subgingival calculus removal: a pilot study.

    Science.gov (United States)

    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.

  17. Variational Approach in the Theory of Liquid-Crystal State

    Science.gov (United States)

    Gevorkyan, E. V.

    2018-03-01

    The variational calculus by Leonhard Euler is the basis for modern mathematics and theoretical physics. The efficiency of variational approach in statistical theory of liquid-crystal state and in general case in condensed state theory is shown. The developed approach in particular allows us to introduce correctly effective pair interactions and optimize the simple models of liquid crystals with help of realistic intermolecular potentials.

  18. On the Expressive Power of Polyadic Synchronisation in π- calculus

    DEFF Research Database (Denmark)

    Carbone, Marco; Maffeis, Sergio

    2002-01-01

    We extend the pi-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 pi-calculus, we suggest that it permits divergence-free encodings of distributed calculi, ...

  19. Partial Fractions in Calculus, Number Theory, and Algebra

    Science.gov (United States)

    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.

  20. 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.

  1. Thunks and the λ-calculus

    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...

  2. 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...

  3. Computer-Aided Transformation of PDE Models: Languages, Representations, and a Calculus of Operations

    Science.gov (United States)

    2016-01-05

    Computer-aided transformation of PDE models: languages, representations, and a calculus of operations A domain-specific embedded language called...languages, representations, and a calculus of operations Report Title A domain-specific embedded language called ibvp was developed to model initial...Computer-aided transformation of PDE models: languages, representations, and a calculus of operations 1 Vision and background Physical and engineered systems

  4. 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

  5. A MATLAB companion for multivariable calculus

    CERN Document Server

    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...

  6. Hybrid Logical Analyses of the Ambient Calculus

    DEFF Research Database (Denmark)

    Bolander, Thomas; Hansen, René Rydhof

    2007-01-01

    In this paper, hybrid logic is used to formulate a rational reconstruction of a previously published control flow analysis for the mobile ambients calculus and we further show how a more precise flow-sensitive analysis, that takes the ordering of action sequences into account, can be formulated...... in a natural way. 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 be exploited to reduce the "administrative overhead" of the analysis specification and thus simplify it. Finally, we use HyLoTab, a fully automated...

  7. 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

  8. 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)

  9. The giant calculus within the prostatic urethra.

    Science.gov (United States)

    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.

  10. 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

  11. 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.

  12. 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....

  13. 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.

  14. 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.)

  15. Composition and distribution of elements and ultrastructural topography of a human cardiac calculus.

    Science.gov (United States)

    Cheng, Ching-Li; Chang, Hsiao-Huang; Huang, Pei-Jung; Chu, Yu-Ting; Lin, Shan-Yang

    2013-04-01

    Trace elements (TEs) may contribute to the formation of calculi or stones or be involved in the aetiopathogenesis of stone diseases. The compositions and spatial distribution of elements from the inner nucleus to outer crust of the cardiac calculus were investigated by energy-dispersive X-ray fluorescence (EDXRF) spectrometer. The surface topograph, distribution map of elements, elemental and chemical compositions were also determined by environmental scanning electron microscope (ESEM)-energy-dispersive X-ray (EDX) analysis. Twenty-five elements were identifiable from 18 positions on the cardiac calculus by EDXRF spectrometer, in which the highest concentrations of toxic TEs (Ni, Pt, Hg, Sn, Pb, W, Au, Al, Si) and higher levels of essential TEs (Ca, Sr, Cr, P) were detected. A moderate positive Pearson's correlation between TEs concentrations of Mg, Ca or P and location differences from centre to periphery in the cardiac calculus was observed. A positive correlation was also found for Ca/Zn and Ca/Cu, indicating the gradual increase of calcium concentration from inner nucleus to outer crust of cardiac calculus. The drop-like nodules/crystals on the surface of petrous part of cardiac calculus were observed from ESEM analysis. ESEM-EDX analysis determined the calculus to be predominantly composed of calcium hydroxyapatite and cholesterol, as indicated by the petrous surface and drop-like nodules/crystals, respectively. This composition was confirmed using a portable Raman analyser. The spatial distribution analysis indicated a gradual increase in Mg, P and Ca concentrations from the inner nucleus to the outer crust of the cardiac calculus. The major chemical compositions of calcium hydroxyapatite and cholesterol were detected on this cardiac calculus.

  16. 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.

  17. Quantifying calculus: a suggested new approach for recording an important indicator of diet and dental health.

    Science.gov (United States)

    Greene, T R; Kuba, C L; Irish, J D

    2005-01-01

    This paper describes a quantitative approach to the assessment of dental calculus in human archaeological skeletal samples. The approach combines the ranked calculus scoring method described by Buikstra and Ubelaker [1994. Arkansas Archeological Survey Research Series, Arkansas Archeological Survey, Fayetteville, Arkansas] and a modified Simplified Calculus Index, utilized by dental clinicians. We recorded amounts of calculus on the buccal, lingual, and interproximal surface of all extant teeth, and generated an index for the maxillary posterior dentition, maxillary anterior dentition, mandibular posterior dentition, and mandibular anterior dentition for three skeletal samples. They include 145 Egyptian Predynastic individuals from the site of Hierakonpolis, 104 Predynastic individuals from Naqada, Egypt, and 101 Meroitic Nubians from Semna South, present-day Sudan. Mann-Whitney U tests were used to analyze differences between the sexes and among age groups at each site. The results demonstrate that the calculus indices more effectively reveal trends and differences in calculus severity than frequency data can alone. For example, at Hierakonpolis, males (18-35 years) had significantly more calculus in the maxillary posterior dentition than females, while females (50+ years) had significantly more calculus in the maxillary posterior teeth. Frequency data merely showed that 94% of both males and females had calculus. The use of calculus indices can reveal how quickly calculus accumulates with age within the dental arcade and within a sample. Moreover, better understanding of the severity and location of calculus can improve a researcher's knowledge regarding the effect of calculus on dental pathologies, such as carious lesions and periodontal disease.

  18. Two cosmological solutions of Regge calculus

    International Nuclear Information System (INIS)

    Lewis, S.M.

    1982-01-01

    Two cosmological solutions of Regge calculus are presented which correspond to the flat Friedmann-Robertson-Walker and the Kasner solutions of general relativity. By taking advantage of the symmetries that are present, I am able to show explicitly that a limit of Regge calculus does yield Einstein's equations for these cases. The method of averaging these equations when taking limits is important, especially for the Kasner model. I display the leading error term that arises from keeping the Regge equations in discrete form rather than using their continuum limit. In particular, this work shows that for the ''Reggeized'' Friedmann model the minimum volume is a velocity-dominated singularity as in the continuum Friedmann model. However, unlike the latter, the Regge version has a nonzero minimum volume

  19. Enabling quaternion derivatives: the generalized HR calculus

    Science.gov (United States)

    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

  20. Introduction to Integral Calculus Systematic Studies with Engineering Applications for Beginners

    CERN Document Server

    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

  1. 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

  2. Investigation of in vitro Mineral Forming Bacterial Isolates from Subgingival Calculus

    Directory of Open Access Journals (Sweden)

    Turgut Demir

    2014-06-01

    This is the first report to identify and show that bacteria from subgingival calculus under anaerobic conditions are involved in the formation of dental calculus. [Arch Clin Exp Surg 2014; 3(3.000: 153-160

  3. Calculus Instructors' and Students' Discourses on the Derivative

    Science.gov (United States)

    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…

  4. Reflections on Our First Calculus Undergraduate Teaching Assistant

    Science.gov (United States)

    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.

  5. Utilizing Microsoft Mathematics in Teaching and Learning Calculus

    Science.gov (United States)

    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…

  6. Rethinking the Privacy Calculus: On the Role of Dispositional Factors and Affect

    OpenAIRE

    Kehr, Flavius; Wentzel, Daniel; Mayer, Peter

    2013-01-01

    Existing research on information privacy has mostly relied on the privacy calculus model which views privacy-related decision making as a rational process where individuals weigh the anticipated risks of disclosing personal data against the potential benefits. However, scholars have recently challenged two basic propositions of the privacy calculus model. First, some authors have distinguished between general and situational factors in the context of privacy calculus and have argued that ...

  7. Generalizing Automath by means of a lambda-typed lambda calculus

    NARCIS (Netherlands)

    Bruijn, de N.G.; Nederpelt, R.P.; Geuvers, J.H.; Vrijer, de R.C.

    1994-01-01

    The calculus delta conjunction developed in this paper is claimed to be able to embrace all the essential aspects of Automath, apart from the feature of type inclusion which will not be considered in this paper. The calculus deal with a correctness notion for lambda-typed lambda formulas (which are

  8. Variational principles are a powerful tool also for formulating field theories

    OpenAIRE

    Dell'Isola , Francesco; Placidi , Luca

    2012-01-01

    Variational principles and calculus of variations have always been an important tool for formulating mathematical models for physical phenomena. Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest for scientists and engineers and are the main tool for the axiomatization of physical theories

  9. Advances in fractional calculus theoretical developments and applications in physics and engineering

    CERN Document Server

    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.

  10. Successful enrichment and recovery of whole mitochondrial genomes from ancient human dental calculus.

    Science.gov (United States)

    Ozga, Andrew T; Nieves-Colón, Maria A; Honap, Tanvi P; Sankaranarayanan, Krithivasan; Hofman, Courtney A; Milner, George R; Lewis, Cecil M; Stone, Anne C; Warinner, Christina

    2016-06-01

    Archaeological dental calculus is a rich source of host-associated biomolecules. Importantly, however, dental calculus is more accurately described as a calcified microbial biofilm than a host tissue. As such, concerns regarding destructive analysis of human remains may not apply as strongly to dental calculus, opening the possibility of obtaining human health and ancestry information from dental calculus in cases where destructive analysis of conventional skeletal remains is not permitted. Here we investigate the preservation of human mitochondrial DNA (mtDNA) in archaeological dental calculus and its potential for full mitochondrial genome (mitogenome) reconstruction in maternal lineage ancestry analysis. Extracted DNA from six individuals at the 700-year-old Norris Farms #36 cemetery in Illinois was enriched for mtDNA using in-solution capture techniques, followed by Illumina high-throughput sequencing. Full mitogenomes (7-34×) were successfully reconstructed from dental calculus for all six individuals, including three individuals who had previously tested negative for DNA preservation in bone using conventional PCR techniques. Mitochondrial haplogroup assignments were consistent with previously published findings, and additional comparative analysis of paired dental calculus and dentine from two individuals yielded equivalent haplotype results. All dental calculus samples exhibited damage patterns consistent with ancient DNA, and mitochondrial sequences were estimated to be 92-100% endogenous. DNA polymerase choice was found to impact error rates in downstream sequence analysis, but these effects can be mitigated by greater sequencing depth. Dental calculus is a viable alternative source of human DNA that can be used to reconstruct full mitogenomes from archaeological remains. Am J Phys Anthropol 160:220-228, 2016. © 2016 The Authors American Journal of Physical Anthropology Published by Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

  11. Multivariate calculus and geometry

    CERN Document Server

    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.

  12. Representing and reasoning about program in situation calculus

    Science.gov (United States)

    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.

  13. 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.

  14. Evaluating the Use of Learning Objects for Improving Calculus Readiness

    Science.gov (United States)

    Kay, Robin; Kletskin, Ilona

    2010-01-01

    Pre-calculus concepts such as working with functions and solving equations are essential for students to explore limits, rates of change, and integrals. Yet many students have a weak understanding of these key concepts which impedes performance in their first year university Calculus course. A series of online learning objects was developed to…

  15. Advanced Placement Mathematics Calculus, Grade 12 Curriculum Guide.

    Science.gov (United States)

    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…

  16. Splines and variational methods

    CERN Document Server

    Prenter, P M

    2008-01-01

    One of the clearest available introductions to variational methods, this text requires only a minimal background in calculus and linear algebra. Its self-contained treatment explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. The text's first half concerns approximation theoretic notions, exploring the theory and computation of one- and two-dimensional polynomial and other spline functions. Later chapters examine variational methods in the solution of operator equations, focusing on boundary value problems in one and two dimension

  17. 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.)

  18. Catwalk: First-Semester Calculus.

    Science.gov (United States)

    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)

  19. Modelling the Landing of a Plane in a Calculus Lab

    Science.gov (United States)

    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.)

  20. 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)

  1. 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)

  2. DIFFERENTIAL AND INTEGRAL CALCULUS. A TENTATIVE CURRICULUM GUIDE.

    Science.gov (United States)

    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…

  3. Coordinating Multiple Representations in a Reform Calculus Textbook

    Science.gov (United States)

    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…

  4. On certain fractional calculus operators involving generalized Mittag-Leffler function

    OpenAIRE

    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...

  5. Fractional and multivariable calculus model building and optimization problems

    CERN Document Server

    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 ...

  6. Advanced calculus of several variables

    CERN Document Server

    Edwards, C H

    1995-01-01

    Modern conceptual treatment of multivariable calculus, emphasizing the interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. At the same time, ample attention is paid to the classical applications and computational methods. Hundreds of examples, problems and figures. 1973 edition.

  7. A many-sorted calculus based on resolution and paramodulation

    CERN Document Server

    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

  8. Electron microscopy of octacalcium phosphate in the dental calculus.

    Science.gov (United States)

    Kakei, Mitsuo; Sakae, Toshiro; Yoshikawa, Masayoshi

    2009-12-01

    The purpose of this study was to morphologically demonstrate the presence of octacalcium phosphate in the dental calculus by judging from the crystal lattice image and its rapid transformation into apatite crystal, as part of our serial studies on biomineral products. We also aimed to confirm whether the physical properties of octacalcium phosphate are identical with those of the central dark lines observed in crystals of ordinary calcifying hard tissues. Electron micrographs showed that crystals of various sizes form in the dental calculus. The formation of each crystal seemed to be closely associated with the organic substance, possibly originating from degenerated microorganisms at the calcification front. Many crystals had an 8.2-A lattice interval, similar to that of an apatite crystal. Furthermore, some crystals clearly revealed an 18.7-A lattice interval and were vulnerable to electron bombardment. After electron beam exposure, this lattice interval was quickly altered to about half (i.e. 8.2 A), indicating structural conversion. Consequently, a number of apatite crystals in the dental calculus are possibly created by a conversion mechanism involving an octacalcium phosphate intermediate. However, we also concluded that the calcification process in the dental calculus is not similar to that of ordinary calcifying hard tissues.

  9. Class dependency of fuzzy relational database using relational calculus and conditional probability

    Science.gov (United States)

    Deni Akbar, Mohammad; Mizoguchi, Yoshihiro; Adiwijaya

    2018-03-01

    In this paper, we propose a design of fuzzy relational database to deal with a conditional probability relation using fuzzy relational calculus. In the previous, there are several researches about equivalence class in fuzzy database using similarity or approximate relation. It is an interesting topic to investigate the fuzzy dependency using equivalence classes. Our goal is to introduce a formulation of a fuzzy relational database model using the relational calculus on the category of fuzzy relations. We also introduce general formulas of the relational calculus for the notion of database operations such as ’projection’, ’selection’, ’injection’ and ’natural join’. Using the fuzzy relational calculus and conditional probabilities, we introduce notions of equivalence class, redundant, and dependency in the theory fuzzy relational database.

  10. Calculus and Geometry

    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.

  11. Multivariable dynamic calculus on time scales

    CERN Document Server

    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.

  12. 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

  13. Estimation and quantification of human DNA in dental calculus: A pilot study.

    Science.gov (United States)

    Singh, Udita; Goel, Saurabh

    2017-01-01

    Identification using DNA has proved its accuracy multiple times in the field of forensic investigations. Investigators usually rely on either teeth or bone as the DNA reservoirs. However, there are instances where the skeletal or dental remains are not available or not preserved properly. Moreover, due to religious beliefs, the family members of the dead do not allow the investigating team to damage the remains for the sole purpose of identification. To investigate the presence of human DNA in dental calculus and to quantify the amount, if present. This prospective single-blinded pilot study included twenty subjects selected from the patients visiting a dental college. The samples of dental calculus were collected from the thickest portion of calculus deposited on the lingual surfaces of mandibular incisors. These samples were decontaminated and subjected to gel electrophoresis for DNA extraction. DNA was found in 85% cases. The amount of DNA varied from 21 to 37 μg/ml of dental calculus. Dental calculus is a rich reservoir of human DNA.

  14. Hermeneutics of differential calculus in eighteenth-century northern Germany.

    Science.gov (United States)

    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.

  15. A logical approach to security in the context of Ambient Calculus

    DEFF Research Database (Denmark)

    Mardare, Radu Iulian; Priami, Corrado

    2004-01-01

    A logical approach to security in the context of Ambient Calculus. Electronic Notes in Theoretical Computer Science, N 99:3-29, 2004......A logical approach to security in the context of Ambient Calculus. Electronic Notes in Theoretical Computer Science, N 99:3-29, 2004...

  16. 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

  17. 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

  18. The origins of Cauchy's rigorous calculus

    CERN Document Server

    Grabiner, Judith V

    2005-01-01

    This text examines the reinterpretation of calculus by Augustin-Louis Cauchy and his peers in the 19th century. These intellectuals created a collection of well-defined theorems about limits, continuity, series, derivatives, and integrals. 1981 edition.

  19. Stochastic Model Checking of the Stochastic Quality Calculus

    DEFF Research Database (Denmark)

    Nielson, Flemming; Nielson, Hanne Riis; Zeng, Kebin

    2015-01-01

    The Quality Calculus uses quality binders for input to express strategies for continuing the computation even when the desired input has not been received. The Stochastic Quality Calculus adds generally distributed delays for output actions and real-time constraints on the quality binders for input....... This gives rise to Generalised Semi-Markov Decision Processes for which few analytical techniques are available. We restrict delays on output actions to be exponentially distributed while still admitting real-time constraints on the quality binders. This facilitates developing analytical techniques based...

  20. The dental calculus metabolome in modern and historic samples.

    Science.gov (United States)

    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.

  1. Success in Introductory Calculus: The Role of High School and Pre-Calculus Preparation

    Science.gov (United States)

    Ayebo, Abraham; Ukkelberg, Sarah; Assuah, Charles

    2017-01-01

    Calculus at the college level has significant potential to serve as a pump for increasing the number of students majoring in STEM fields. It is a foundation course for all STEM majors and, if mastered well, should provide students with a positive and successful first-year experience and gateway into more advanced courses. Studies have shown that a…

  2. A SAT-Based Analysis of a Calculus for Wireless Sensor Networks

    DEFF Research Database (Denmark)

    Wu, Xi; Nielson, Hanne Riis; Zhu, Huibiao

    2015-01-01

    In viewing the common unreliability problem in wireless communications, the CWQ calculus (a Calculus for Wireless sensor networks from Quality perspective) was recently proposed for modeling and reasoning about WSNs(Wireless Sensor Networks) and their applications from a quality perspective...

  3. 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...

  4. Visual Thinking and Gender Differences in High School Calculus

    Science.gov (United States)

    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…

  5. On the interpretation of Stratonovich calculus

    International Nuclear Information System (INIS)

    Moon, W; Wettlaufer, J S

    2014-01-01

    The Itô–Stratonovich dilemma is revisited from the perspective of the interpretation of Stratonovich calculus using shot noise. Over the long time scales of the displacement of an observable, the principal issue is how to deal with finite/zero autocorrelation of the stochastic noise. The former (non-zero) noise autocorrelation structure preserves the normal chain rule using a mid-point selection scheme, which is the basis Stratonovich calculus, whereas the instantaneous autocorrelation structure of Itô's approach does not. By considering the finite decay of the noise correlations on time scales very short relative to the overall displacement times of the observable, we suggest a generalization of the integral Taylor expansion criterion of Wong and Zakai (1965 Ann. Math. Stat. 36 1560–4) for the validity of the Stratonovich approach. (paper)

  6. Fisher information, Borges operators, and q-calculus

    Science.gov (United States)

    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].

  7. Giant vesical calculus

    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.

  8. Correlation of Salivary Statherin and Calcium Levels with Dental Calculus Formation: A Preliminary Study.

    Science.gov (United States)

    Pateel, Deepak Gowda Sadashivappa; Gunjal, Shilpa; Math, Swarna Y; Murugeshappa, Devarasa Giriyapura; Nair, Sreejith Muraleedharan

    2017-01-01

    Salivary constituents have a wide range of functions including oral calcium homeostasis. Salivary proteins such as statherin inhibit crystal growth of calcium phosphate in supersaturated solutions and interact with several oral bacteria to adsorb on hydroxyapatite. Concurrently, saliva, which is supersaturated with respect to calcium phosphates, is the driving force for plaque mineralization and formation of calculus. Thus, the aim of the present study was to estimate and correlate salivary statherin and calcium concentration to the dental calculus formation. A cross-sectional study was conducted to assess the relationship between salivary statherin, calcium, and dental calculus among 70 subjects, aged 20-55 years. Subjects were divided into 3 groups based on the calculus scores as interpreted by Calculus Index which was followed by collection of whole saliva using Super•SAL™. Salivary calcium levels were assessed by calorimetric method using Calcium Assay kit (Cayman Chemical, Michigan, USA) and statherin levels by using ELISA Kit (Cusabio Biotech). Statherin levels showed a weak negative correlation with the calcium levels and with calculus formation. The mean salivary statherin and calcium concentration were found to be 0.96  μ g/ml and 3.87 mg/ml, respectively. Salivary statherin levels differed significantly among the three groups ( p dental calculus.

  9. Fuzzy relational calculus theory, applications and software

    CERN Document Server

    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...

  10. Quantum calculus new concepts, impulsive IVPs and BVPs, inequalities

    CERN Document Server

    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...

  11. 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 ...

  12. A flow calculus of mwp-bounds for complexity analysis

    DEFF Research Database (Denmark)

    Jones, Neil; Kristiansen, Lars

    2010-01-01

    straightforwardly from our definitions that there exists M such that ⊧ C : M holds iff every value computed by C is bounded by a polynomial in the inputs. Furthermore, we provide a syntactical proof calculus and define the relation ⊢ C : M to hold iff there exists a derivation in the calculus where C...

  13. Calculus Problem Solution And Simulation Using GUI Of Matlab

    Directory of Open Access Journals (Sweden)

    Syaharuddin

    2017-09-01

    Full Text Available This research aims to develop the project application in teaching and learning Calculus using Grapichal User Interface GUI of Matlab. The scope of the development result includes 1 PreCalculus 2 Function Limit 3 Derivative and its application and 4 Integral and its application. Every aspect of development is presented according to the standards of material competence learning achievement indicators and solutions or settlement steps on each issue presented. This project application can be used by lecturers and students in universities to improve motivation mastery of material and student learning outcomes in the Calculus course. Development of this project application is done through 4 stages called 4-D namely Define Design Development and Dissemination. Based on the data analysis the results obtained at the validation stage of expert validity level average of 3.575 which means quite valid. Then on a limited trial the average student gave a response of 92.00 which means very good. While in the first field trial the average student gave a response of 89.30 which means very good and in the second field trial the average student gave a responded of 90.15 which means very good. Besides that we also solve computational calculus problems in Edwin J. Purcell Dale Varbergs Book of Volume 1 of Edition 5 of 48 questions that are divided into 64 cases.

  14. Stochastic integration by parts and functional Itô calculus

    CERN Document Server

    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...

  15. Metaphor Clusters: Characterizing Instructor Metaphorical Reasoning on Limit Concepts in College Calculus

    Science.gov (United States)

    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…

  16. 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 ...

  17. Equivariance, Variational Principles, and the Feynman Integral

    Directory of Open Access Journals (Sweden)

    George Svetlichny

    2008-03-01

    Full Text Available We argue that the variational calculus leading to Euler's equations and Noether's theorem can be replaced by equivariance and invariance conditions avoiding the action integral. We also speculate about the origin of Lagrangian theories in physics and their connection to Feynman's integral.

  18. Presentation of an ingested foreign body as a vesical calculus: a ...

    African Journals Online (AJOL)

    Presentation of an ingested foreign body as a vesical calculus: a common condition, but uncommon presentation. Shailendra Pal Singh a. , Anand Pandey a. , Vipin Gupta a. , Jigyasa Pandey b and. Rajesh Verma a. Vesical calculus is a common entity in children of developing countries. Foreign body ingestion is a common.

  19. A Generalized Nonlocal Calculus with Application to the Peridynamics Model for Solid Mechanics

    OpenAIRE

    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...

  20. In vitro and clinical evaluation of optical coherence tomography for the detection of subgingival calculus and root cementum.

    Science.gov (United States)

    Tsubokawa, Masaki; Aoki, Akira; Kakizaki, Sho; Taniguchi, Yoichi; Ejiri, Kenichiro; Mizutani, Koji; Koshy, Geena; Akizuki, Tatsuya; Oda, Shigeru; Sumi, Yasunori; Izumi, Yuichi

    2018-05-24

    This study evaluated the effectiveness of swept-source optical coherence tomography (ss-OCT) for detecting calculus and root cementum during periodontal therapy. Optical coherence tomography (OCT) images were taken before and after removal of subgingival calculus from extracted teeth and compared with non-decalcified histological sections. Porcine gingival sheets of various thicknesses were applied to the root surfaces of extracted teeth with calculus and OCT images were taken. OCT images were also taken before and after scaling and root planing (SRP) in human patients. In vitro, calculus was clearly detected as a white-gray amorphous structure on the root surface, which disappeared after removal. Cementum was identified as a thin, dark-gray layer. The calculus could not be clearly observed when soft tissues were present on the root surface. Clinically, supragingival calculus and cementum could be detected clearly with OCT, and subgingival calculus in the buccal cervical area of the anterior and premolar teeth was identified, which disappeared after SRP. Digital processing of the original OCT images was useful for clarifying the calculus. In conclusion, ss-OCT showed potential as a periodontal diagnostic tool for detecting cementum and subgingival calculus, although the practical applications of subgingival imaging remain limited.

  1. Complete staghorn calculus in polycystic kidney disease: infection is still the cause.

    Science.gov (United States)

    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.

  2. Laser ablation of dental calculus at 400 nm using a Ti:sapphire laser

    Science.gov (United States)

    Schoenly, Joshua E.; Seka, Wolf; Rechmann, Peter

    2009-02-01

    A Nd:YAG laser-pumped, frequency-doubled Ti:sapphire laser is used for selective ablation of calculus. The laser provides calculus removal. This is in stark contrast with tightly focused Gaussian beams that are energetically inefficient and lead to irreproducible results. Calculus is well ablated at high fluences >=2J/cm2 stalling occurs below this fluence because of photobleaching. Healthy hard tissue is not removed at fluences <=3 J/cm2.

  3. 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

  4. Recalling Prerequisite Material in a Calculus II Course to Improve Student Success

    Science.gov (United States)

    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,…

  5. Presentation of an ingested foreign body as a vesical calculus: a ...

    African Journals Online (AJOL)

    Vesical calculus is a common entity in children of developing countries. Foreign body ingestion is a common occurrence in the pediatric population. An ingested foreign body eroding into the urinary bladder and leading to the formation of a vesical calculus is an extremely rare condition. We encountered a 14-year-old girl ...

  6. 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)

  7. ARTIFICIAL NEURAL-NETWORK PREDICTIONS OF URINARY CALCULUS COMPOSITIONS ANALYZED WITH INFRARED-SPECTROSCOPY

    NARCIS (Netherlands)

    VOLMER, M; WOLTHERS, BG; METTING, HJ; DEHAAN, THY; COENEGRACHT, PMJ; VANDERSLIK, W

    Infrared (IR) spectroscopy is used to analyze urinary calculus (renal stone) constituents. However, interpretation of IR spectra for quantifying urinary calculus constituents in mixtures is difficult, requiring expert knowledge by trained technicians. In our laboratory IR spectra of unknown calculi

  8. 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....

  9. Correlation of Salivary Statherin and Calcium Levels with Dental Calculus Formation: A Preliminary Study

    Directory of Open Access Journals (Sweden)

    Deepak Gowda Sadashivappa Pateel

    2017-01-01

    Full Text Available Background. Salivary constituents have a wide range of functions including oral calcium homeostasis. Salivary proteins such as statherin inhibit crystal growth of calcium phosphate in supersaturated solutions and interact with several oral bacteria to adsorb on hydroxyapatite. Concurrently, saliva, which is supersaturated with respect to calcium phosphates, is the driving force for plaque mineralization and formation of calculus. Thus, the aim of the present study was to estimate and correlate salivary statherin and calcium concentration to the dental calculus formation. Methods. A cross-sectional study was conducted to assess the relationship between salivary statherin, calcium, and dental calculus among 70 subjects, aged 20–55 years. Subjects were divided into 3 groups based on the calculus scores as interpreted by Calculus Index which was followed by collection of whole saliva using Super•SAL™. Salivary calcium levels were assessed by calorimetric method using Calcium Assay kit (Cayman Chemical, Michigan, USA and statherin levels by using ELISA Kit (Cusabio Biotech. Results. Statherin levels showed a weak negative correlation with the calcium levels and with calculus formation. The mean salivary statherin and calcium concentration were found to be 0.96 μg/ml and 3.87 mg/ml, respectively. Salivary statherin levels differed significantly among the three groups (p<0.05. Conclusions. Our preliminary data indicates that statherin could possibly play a role in the formation of dental calculus.

  10. Calculus

    CERN Document Server

    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.

  11. 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

  12. Means and Variances without Calculus

    Science.gov (United States)

    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.

  13. [Does carbonate originate from carbonate-calcium crystal component of the human urinary calculus?].

    Science.gov (United States)

    Yuzawa, Masayuki; Nakano, Kazuhiko; Kumamaru, Takatoshi; Nukui, Akinori; Ikeda, Hitoshi; Suzuki, Kazumi; Kobayashi, Minoru; Sugaya, Yasuhiro; Morita, Tatsuo

    2008-09-01

    It gives important information in selecting the appropriate treatment for urolithiasis to confirm the component of urinary calculus. Presently component analysis of the urinary calculus is generally performed by infrared spectroscopy which is employed by companies providing laboratory testing services in Japan. The infrared spectroscopy determines the molecular components from the absorption spectra in consequence of atomic vibrations. It has the drawback that an accurate crystal structure cannot be analyzed compared with the X-ray diffraction method which analyzes the crystal constituent based on the diffraction of X-rays on crystal lattice. The components of the urinary calculus including carbonate are carbonate apatite and calcium carbonate such as calcite. Although the latter is reported to be very rare component in human urinary calculus, the results by infrared spectroscopy often show that calcium carbonate is included in calculus. The infrared spectroscopy can confirm the existence of carbonate but cannot determine whether carbonate is originated from carbonate apatite or calcium carbonate. Thus, it is not clear whether calcium carbonate is included in human urinary calculus component in Japan. In this study, we examined human urinary calculus including carbonate by use of X-ray structural analysis in order to elucidate the origin of carbonate in human urinary calculus. We examined 17 human calculi which were reported to contain calcium carbonate by infrared spectroscopy performed in the clinical laboratory. Fifteen calculi were obtained from urinary tract, and two were from gall bladder. The stones were analyzed by X-ray powder method after crushed finely. The reports from the clinical laboratory showed that all urinary culculi consisted of calcium carbonate and calcium phosphate, while the gallstones consisted of calcium carbonate. But the components of all urinary calculi were revealed to be carbonate apatite by X-ray diffraction. The components of

  14. 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.

  15. Particular case of operator calculus for generalized functions with supports in cone

    Directory of Open Access Journals (Sweden)

    A. V. Solomko

    2009-06-01

    Full Text Available In this work the construction of functional calculus for strongly continuous semigroups of operators in Schwartz distribution algebra on some cone is generalized. The partial case of vector valued calculus on the base of modification operator Fourier transformation is researched.

  16. Formalization of the Resolution Calculus for First-Order Logic

    DEFF Research Database (Denmark)

    Schlichtkrull, Anders

    2016-01-01

    A formalization in Isabelle/HOL of the resolution calculus for first-order logic is presented. Its soundness and completeness are formally proven using the substitution lemma, semantic trees, Herbrand’s theorem, and the lifting lemma. In contrast to previous formalizations of resolution, it consi......A formalization in Isabelle/HOL of the resolution calculus for first-order logic is presented. Its soundness and completeness are formally proven using the substitution lemma, semantic trees, Herbrand’s theorem, and the lifting lemma. In contrast to previous formalizations of resolution...

  17. 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....

  18. Variational method for integrating radial gradient field

    Science.gov (United States)

    Legarda-Saenz, Ricardo; Brito-Loeza, Carlos; Rivera, Mariano; Espinosa-Romero, Arturo

    2014-12-01

    We propose a variational method for integrating information obtained from circular fringe pattern. The proposed method is a suitable choice for objects with radial symmetry. First, we analyze the information contained in the fringe pattern captured by the experimental setup and then move to formulate the problem of recovering the wavefront using techniques from calculus of variations. The performance of the method is demonstrated by numerical experiments with both synthetic and real data.

  19. 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)

  20. Formalization of the Integral Calculus in the PVS Theorem Prover

    Science.gov (United States)

    Butler, Ricky W.

    2004-01-01

    The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.

  1. A Useful Demonstration of Calculus in a Physics High School Laboratory

    Science.gov (United States)

    Alvarez, Gustavo; Schulte, Jurgen; Stockton, Geoffrey; Wheeler, David

    2018-01-01

    The real power of calculus is revealed when it is applied to actual physical problems. In this paper, we present a calculus inspired physics experiment suitable for high school and undergraduate programs. A model for the theory of the terminal velocity of a falling body subject to a resistive force is developed and its validity tested in an…

  2. 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.

  3. 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

  4. Differential calculus and its applications

    CERN Document Server

    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.

  5. 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...

  6. 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.)

  7. 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.)

  8. Surface area and volume determination of subgingival calculus using laser fluorescence.

    Science.gov (United States)

    Shakibaie, Fardad; Walsh, Laurence J

    2014-03-01

    Visible red (655 nm) laser fluorescence (LF) devices are currently used for identifying deposits of subgingival calculus on the root surfaces of teeth during dental examination and treatment; however, it is not known how the fluorescence readings produced by commercially available LF systems correlate to the nature of the deposits. This laboratory study explored the correlation between LF digital readings and the surface area and volume of subgingival calculus deposits on teeth. A collection of 30 extracted human posterior teeth with various levels of subgingival deposits of calculus across 240 sites were used in a clinical simulation, with silicone impression material used to replicate periodontal soft tissues. The teeth were scored by two examiners by using three commercial LF systems (DIAGNOdent, DIAGNOdent Pen and KEY3). The silicone was removed, and the teeth were removed for photography at × 20 magnification under white or ultraviolet light. The surface area, thickness, and volume were calculated, and both linear least squares regression and nonlinear (Spearman's rank method) correlation coefficients were determined. Visible red LF digital readings showed better correlation to calculus volume than to surface area. Overall, the best performance was found for the KEY3 system (Spearman coefficient 0.59), compared to the Classic DIAGNOdent (0.56) and the DIAGNOdent Pen (0.49). These results indicate that while visible red LF systems vary somewhat in performance, their LF readings provide a useful estimation of the volume of subgingival calculus deposits present on teeth.

  9. Dental calculus is associated with death from heart infarction.

    Science.gov (United States)

    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.

  10. 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...

  11. Dental Calculus and the Evolution of the Human Oral Microbiome.

    Science.gov (United States)

    Warinner, Christina

    2016-07-01

    Characterizing the evolution of the oral microbiome is a challenging, but increasingly feasible, task. Recently, dental calculus has been shown to preserve ancient biomolecules from the oral microbiota, host tissues and diet for tens of thousands of years. As such, it provides a unique window into the ancestral oral microbiome. This article reviews recent advancements in ancient dental calculus research and emerging insights into the evolution and ecology of the human oral microbiome.

  12. On Functional Calculus Estimates

    NARCIS (Netherlands)

    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

  13. Bipower variation for Gaussian processes with stationary increments

    DEFF Research Database (Denmark)

    Barndorff-Nielsen, Ole Eiler; Corcuera, José Manuel; Podolskij, Mark

    2009-01-01

    Convergence in probability and central limit laws of bipower variation for Gaussian processes with stationary increments and for integrals with respect to such processes are derived. The main tools of the proofs are some recent powerful techniques of Wiener/Itô/Malliavin calculus for establishing...

  14. Advanced calculus

    CERN Document Server

    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

  15. Matrix calculus

    CERN Document Server

    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

  16. A calculus of quality for robustness against unreliable communication

    DEFF Research Database (Denmark)

    Nielson, Hanne Riis; Nielson, Flemming; Vigo, Roberto

    2015-01-01

    A main challenge in the development of distributed systems 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...... for default behaviour in case the ideal behaviour fails due to unreliable communication and thereby to increase the quality of service offered by the system. The development is facilitated by a SAT-based robustness analysis to determine whether or not the code is vulnerable to unreliable communication...

  17. An evaluation of a pre-scaling gel (SofScale) on the ease of supragingival calculus removal.

    Science.gov (United States)

    Smith, S R; Foyle, D M; Daniels, J

    1994-09-01

    SofScale is a pre-scaling gel, containing disodium EDTA and sodium lauryl sulphate, which is claimed to soften calculus and therefore facilitate its removal. 31 subjects were treated in a double blind randomised placebo controlled split mouth study to evaluate this product. Test or placebo gels were applied to the lingual surfaces of the mandibular teeth for 4 min and the time taken to complete the removal of supragingival calculus recorded. The operator recorded on which side the calculus was considered easier to remove and the patient indicated how comfortable the scaling had been. The mean calculus index was 1.99 for the SofScale group and 1.97 for the placebo. The mean time taken to complete scaling was 5.31 min for both groups. Using the Student t-test, there were no statistically significant differences (p > 0.7) between either the calculus index or time taken to complete the scaling between the groups. The operator did not consider SofScale to facilitate calculus removal and patients did not find calculus removal more comfortable when SofScale had been used. There was no increased sensitivity in the SofScale group following scaling. The results of this study do not support the use of SofScale as an adjunct to scaling.

  18. Variational methods and effective actions in string models

    International Nuclear Information System (INIS)

    Dereli, T.; Tucker, R.W.

    1987-01-01

    Effective actions motivated by zero-order and first-order actions are examined. Particular attention is devoted to a variational procedure that is consistent with the structure equations involving the Lorentz connection. Attention is drawn to subtleties that can arise in varying higher-order actions and an efficient procedure developed to handle these cases using the calculus of forms. The effect of constrained variations on the field equations is discussed. (author)

  19. 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.

  20. SOq(N) covariant differential calculus on quantum space and quantum deformation of Schroedinger equation

    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.)

  1. 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 ...

  2. Duration Calculus: Logical Foundations

    DEFF Research Database (Denmark)

    Hansen, Michael Reichhardt; Chaochen, Zhou

    1997-01-01

    The Duration Calculus (abbreviated DC) represents a logical approach to formal design of real-time systems, where real numbers are used to model time and Boolean valued functions over time are used to model states and events of real-time systems. Since it introduction, DC has been applied to many...

  3. Continuous fragment of the mu-calculus

    NARCIS (Netherlands)

    Fontaine, G.

    2008-01-01

    In this paper we investigate the Scott continuous fragment of the modal μ-calculus. We discuss its relation with constructivity, where we call a formula constructive if its least fixpoint is always reached in at most ω steps. Our main result is a syntactic characterization of this continuous

  4. Student Achievement in College Calculus, Louisiana State University 1967-1968.

    Science.gov (United States)

    Scannicchio, Thomas Henry

    An investigation of freshmen achievement in an introductory calculus course was performed on the basis of high school mathematics background to find predictors of college calculus grades. Overall high school academic achievement, overall high school mathematics achievement, number of high school mathematics units, pattern of college preparatory…

  5. Advanced calculus

    CERN Document Server

    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

  6. A visual description of 2-component spinor calculus

    International Nuclear Information System (INIS)

    Hellsten, H.

    1975-07-01

    Spinors and algebraic operations on them are given a visual description. This structural interpretation of spinors is to be contrasted with the well known quadratic relation between spinors and visual objects (vectors,flagpoles). The interpretation in the present paper is founded on the observation that the product between two successive rotations half a turn along the legs of an angle will be a rotation through twice that angle. This observation makes it possible to explain visually the doubling of angles, which occurs when vectors are constructed out of spinors. It is seen that, using this explanation, spinor calculus can, in close analogy to 3-dimensional Euclidean vector calculus, be given a purely visual meaning. (Auth.)

  7. Making an Interactive Calculus Textbook.

    Science.gov (United States)

    Larson, Timothy R.

    1995-01-01

    Presents a case study of the design and production of "Interactive Calculus," an interactive multimedia textbook. Discusses reasons for using multimedia textbooks; what an interactive textbook is; content, organization, graphic design, authoring and composition; and work flow. (AEF)

  8. Formalization of the Integral Calculus in the PVS Theorem Prover

    Directory of Open Access Journals (Sweden)

    Ricky Wayne Butler

    2009-04-01

    Full Text Available The PVS Theorem prover is a widely used formal verification tool used for the analysis of safetycritical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht’s classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.

  9. Application of laser peening with a composite-type optical fiberscope for pancreatic calculus fracture

    International Nuclear Information System (INIS)

    Takei, Norio; Ishikawa, Noriko; Ito, Fuyumi; Nishimura, Akihiko; Oka, Kiyoshi

    2010-01-01

    For low infestation treatment on pancreatolithiasis, we propose that laser peening phenomena by use of a composite-type optical fiberscope are useful to crush pancreatic a calculus into fragments, Nanosecond laser pulses go through the composite-type optical fiberscope and are focused on the surface of the pancreatic calculus. Laser processed fracture shapes on the calculus were observed and the pulse energy dependence were measured. The essential points for system integration were discussed. (author)

  10. Generalized calculus with applications to matter and forces

    CERN Document Server

    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 ...

  11. Stochastic calculus an introduction through theory and exercises

    CERN Document Server

    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 ...

  12. Unification and matching in Church's Original Lambda Calculus

    OpenAIRE

    Hustadt, U.

    1992-01-01

    In current implementations of higher-order logics higher-orderunification is used to lift the resolution principle from the first-order case to the higher-order case. Higher-order matching is the core of implementations of higher-order rewriting systems and some systems for program transformation. In this paper I argue that Church's original lambda calculus, called non-forgetful lambda calculus, is an appropriate basis for higher-order matching. I provide two correct and complete algorithms f...

  13. Experimental Design: Utilizing Microsoft Mathematics in Teaching and Learning Calculus

    Science.gov (United States)

    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…

  14. Cartooning in Algebra and Calculus

    Science.gov (United States)

    Moseley, L. Jeneva

    2014-01-01

    This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.

  15. An Excel-Aided Method for Teaching Calculus-Based Business Mathematics

    Science.gov (United States)

    Liang, Jiajuan; Martin, Linda

    2008-01-01

    Calculus-based business mathematics is a required quantitative course for undergraduate business students in most AACSB accredited schools or colleges of business. Many business students, however, have relatively weak mathematical background or even display math-phobia when presented with calculus problems. Because of the popularity of Excel, its…

  16. 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....

  17. 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.

  18. Confluence via strong normalisation in an algebraic λ-calculus with rewriting

    Directory of Open Access Journals (Sweden)

    Pablo Buiras

    2012-03-01

    Full Text Available The linear-algebraic lambda-calculus and the algebraic lambda-calculus are untyped lambda-calculi extended with arbitrary linear combinations of terms. The former presents the axioms of linear algebra in the form of a rewrite system, while the latter uses equalities. When given by rewrites, algebraic lambda-calculi are not confluent unless further restrictions are added. We provide a type system for the linear-algebraic lambda-calculus enforcing strong normalisation, which gives back confluence. The type system allows an abstract interpretation in System F.

  19. A Calculus for Control Flow Analysis of Security Protocols

    DEFF Research Database (Denmark)

    Buchholtz, Mikael; Nielson, Hanne Riis; Nielson, Flemming

    2004-01-01

    The design of a process calculus for anaysing security protocols is governed by three factors: how to express the security protocol in a precise and faithful manner, how to accommodate the variety of attack scenarios, and how to utilise the strengths (and limit the weaknesses) of the underlying...... analysis methodology. We pursue an analysis methodology based on control flow analysis in flow logic style and we have previously shown its ability to analyse a variety of security protocols. This paper develops a calculus, LysaNS that allows for much greater control and clarity in the description...

  20. The Association of Precollege Use of Calculators with Student Performance in College Calculus

    Science.gov (United States)

    Mao, Yi; White, Tyreke; Sadler, Philip M.; Sonnert, Gerhard

    2017-01-01

    This study investigates how the use of calculators during high school mathematics courses is associated with student performance in introductory college calculus courses in the USA. Data were drawn from a nationally representative sample of 7087 students enrolled in college calculus at 134 colleges and universities. They included information about…

  1. Large bladder calculus masking a stone in single-system ureterocele.

    Science.gov (United States)

    Bhaskar, Ved; Sinha, Rahul Janak; Purkait, Bimalesh; Singh, Vishwajeet

    2017-06-14

    Ureterocele in an elderly is a rare entity. The presence of stone within ureterocele along with a large bladder calculus is an even rarer presentation. This phenomenon has not been reported so far to the best of our knowledge. We present an unusual case of a large bladder calculus with a concomitant stone in the associated ureterocele. The diagnosis was missed in the first instance due to the masking effect by the larger bladder calculus. Herein, we discuss this case and its management. © BMJ Publishing Group Ltd (unless otherwise stated in the text of the article) 2017. All rights reserved. No commercial use is permitted unless otherwise expressly granted.

  2. Calculus domains modelled using an original bool algebra based on polygons

    Science.gov (United States)

    Oanta, E.; Panait, C.; Raicu, A.; Barhalescu, M.; Axinte, T.

    2016-08-01

    Analytical and numerical computer based models require analytical definitions of the calculus domains. The paper presents a method to model a calculus domain based on a bool algebra which uses solid and hollow polygons. The general calculus relations of the geometrical characteristics that are widely used in mechanical engineering are tested using several shapes of the calculus domain in order to draw conclusions regarding the most effective methods to discretize the domain. The paper also tests the results of several CAD commercial software applications which are able to compute the geometrical characteristics, being drawn interesting conclusions. The tests were also targeting the accuracy of the results vs. the number of nodes on the curved boundary of the cross section. The study required the development of an original software consisting of more than 1700 computer code lines. In comparison with other calculus methods, the discretization using convex polygons is a simpler approach. Moreover, this method doesn't lead to large numbers as the spline approximation did, in that case being required special software packages in order to offer multiple, arbitrary precision. The knowledge resulted from this study may be used to develop complex computer based models in engineering.

  3. Selective near-UV ablation of subgingival dental calculus: measurement of removal rates

    Science.gov (United States)

    Schoenly, J. E.; Seka, W.; Rechmann, P.

    2010-02-01

    A noncontact profilometer (laser triangulation) was used to measure the removal rates of subgingival dental calculus irradiated with a frequency-doubled Ti:sapphire laser (60-ns pulse duration, 400-nm wavelength, 10-Hz repetition rate, 7-mJ pulse energy). Profilometer traces before and after irradiation were used to create a removal map with 4-μm axial and 15-μm transverse resolution. Twenty-three teeth (15 with calculus and 8 pristine) were irradiated at 90° and 45° under a cooling water spray with a super-Gaussian beam (~300-μm diameter). Subgingival calculus was selectively removed at 5.6 and 4.0 J/cm2 for 90° and 45°, respecetively, within a range of rates, between 2 to 9 μm/pulse. These ablation rates were constant during these exposures. For comparison, pristine cementum irradiated for 10 min at the same peak fluence and pulse repetition rate showed only craters, 15 to 50 μm deep, corresponding to an equivalent removal rate three orders of magnitude smaller than that obtained for calculus. Pristine enamel was not removed under the same irradiation conditions.

  4. Dental calculus: the calcified biofilm and its role in disease development.

    Science.gov (United States)

    Akcalı, Aliye; Lang, Niklaus P

    2018-02-01

    Dental calculus represents the first fossilized record of bacterial communities as a testimony of evolutionary biology. The development of dental calculus is a dynamic process that starts with a nonmineralized biofilm which eventually calcifies. Nonmineralized dental biofilm entraps particles from the oral cavity, including large amounts of oral bacteria, human proteins, viruses and food remnants, and preserves their DNA. The process of mineralization involves metabolic activities of the bacterial colonies and strengthens the attachment of nonmineralized biofilms to the tooth surface. From a clinical point of view, dental calculus always harbors a living, nonmineralized biofilm, jeopardizing the integrity of the dento-gingival or implanto-mucosal unit. This narrative review presents a brief historical overview of dental calculus formation and its clinical relevance in modern periodontal practice. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

  5. Rare calcium oxalate monohydrate calculus attached to the wall of the renal pelvis.

    Science.gov (United States)

    Grases, Felix; Costa-Bauza, Antonia; Prieto, Rafael M; Saus, Carlos; Servera, Antonio; García-Miralles, Reyes; Benejam, Joan

    2011-04-01

    Most renal calculi can be classified using well-established criteria in a manner that reflects both composition and fine structure under specific pathophysiological conditions. However, when a large patient population is considered, rare renal calculi invariably appear, some of which have never been classified; careful study is required to establish stone etiology in such cases. The patient in the present case report formed two types of calculi. One was attached on the wall of the renal pelvis near the ureter and part of the calculus was embedded inside pelvic renal tissue. The calculus developed on an ossified calcification located in the pelvis tissue. Current knowledge on the development of calcification in soft tissues suggests a pre-existing injury as an inducer of its development. A mechanism of calculus formation is proposed. The second stone was a typical jack-stone calculus. © 2011 The Japanese Urological Association.

  6. Raw beef bones as chewing items to reduce dental calculus in Beagle dogs.

    Science.gov (United States)

    Marx, F R; Machado, G S; Pezzali, J G; Marcolla, C S; Kessler, A M; Ahlstrøm, Ø; Trevizan, L

    2016-01-01

    Evaluate the effect of raw bovine cortical bone (CB) (medullary bone cross-sectioned) and marrow or epiphyseal 'spongy' bone (SB) as chew items to reduce dental calculus in adult dogs. Eight 3-year-old Beagle dogs were observed in two study periods. In the first study, the dogs each received a piece of bovine femur CB (122 ± 17 g) daily and in the second study, a piece of bovine femur SB (235 ± 27 g). The first study lasted 12 days and the second 20 days. Dental calculus was evaluated using image integration software. At the start of the studies, dental calculus covered 42.0% and 38.6% of the dental arcade areas, respectively. In study one, the chewing reduced the established dental calculus area to 27.1% (35.5% reduction) after 3 days and after 12 days the dental calculus covering was reduced to 12.3% (70.6% reduction). In study two, the dental calculus covered 16.8% (56.5% reduction) after 3 days, 7.1% (81.6% reduction) after 12 days and 4.7% (87.8% reduction) after 20 days. The CB remained largely intact after 24 h, but SB was reduced to smaller pieces and in some cases totally consumed after 24 h. No complications such as tooth fractures, pieces of bone stuck between teeth or intestinal obstructions were observed during the studies. Chewing raw bovine bones was an effective method of removing dental calculus in dogs. The SB bones removed dental calculus more efficiently in the short term. © 2016 Australian Veterinary Association.

  7. Bacteria and archaea paleomicrobiology of the dental calculus: a review.

    Science.gov (United States)

    Huynh, H T T; Verneau, J; Levasseur, A; Drancourt, M; Aboudharam, G

    2016-06-01

    Dental calculus, a material observed in the majority of adults worldwide, emerged as a source for correlating paleomicrobiology with human health and diet. This mini review of 48 articles on the paleomicrobiology of dental calculus over 7550 years discloses a secular core microbiota comprising nine bacterial phyla - Firmicutes, Actinobacteria, Proteobacteria, Bacteroidetes, TM7, Synergistetes, Chloroflexi, Fusobacteria, Spirochetes - and one archaeal phylum Euryarchaeota; and some accessory microbiota that appear and disappear according to time frame. The diet residues and oral microbes, including bacteria, archaea, viruses and fungi, consisting of harmless organisms and pathogens associated with local and systemic infections have been found trapped in ancient dental calculus by morphological approaches, immunolabeling techniques, isotope analyses, fluorescent in situ hybridization, DNA-based approaches, and protein-based approaches. These observations led to correlation of paleomicrobiology, particularly Streptococcus mutans and archaea, with past human health and diet. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

  8. Pre- and Post-Conditions Expressed in Variants of the Modal µ-Calculus

    Science.gov (United States)

    Tanabe, Yoshinori; Sekizawa, Toshifusa; Yuasa, Yoshifumi; Takahashi, Koichi

    Properties of Kripke structures can be expressed by formulas of the modal µ-calculus. Despite its strong expressive power, the validity problem of the modal µ-calculus is decidable, and so are some of its variants enriched by inverse programs, graded modalities, and nominals. In this study, we show that the pre- and post-conditions of transformations of Kripke structures, such as addition/deletion of states and edges, can be expressed using variants of the modal µ-calculus. Combined with decision procedures we have developed for those variants, the properties of sequences of transformations on Kripke structures can be deduced. We show that these techniques can be used to verify the properties of pointer-manipulating programs.

  9. Calculus Student Descending a Staircase.

    Science.gov (United States)

    Mueller, William

    1999-01-01

    Common student attitudes toward reform methods are conveyed through the thoughts of a student leaving a multivariable calculus exam and musings range over textbooks, homework, workload, group work, writing, noncomputational problems, instructional problems, instructional styles, and classroom activities. (Author/ASK)

  10. Using Dynamic Tools to Develop an Understanding of the Fundamental Ideas of Calculus

    Science.gov (United States)

    Verzosa, Debbie; Guzon, Angela Fatima; De Las Peñas, Ma. Louise Antonette N.

    2014-01-01

    Although dynamic geometry software has been extensively used for teaching calculus concepts, few studies have documented how these dynamic tools may be used for teaching the rigorous foundations of the calculus. In this paper, we describe lesson sequences utilizing dynamic tools for teaching the epsilon-delta definition of the limit and the…

  11. Study Modules for Calculus-Based General Physics. [Includes Modules 1 and 2: Dimensions and Vector Addition; Rectilinear Motion; plus a Trigonometry and Calculus Review].

    Science.gov (United States)

    Fuller, Robert G., Ed.; And Others

    This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

  12. Understanding the calculus

    OpenAIRE

    Tall, David

    1985-01-01

    A number of significant changes have have occurred recently that give us a golden opportunity to review the teaching of calculus. The most obvious is the arrival of the microcomputer in the mathematics classroom, allowing graphic demonstrations and individual investigations into the mathematical ideas. But equally potent are new\\ud insights into mathematics and mathematics education that suggest new ways of approaching the subject.\\ud In this article I shall consider some of the difficulties ...

  13. Calculus Courses' Assessment Data

    Science.gov (United States)

    Pauna, Matti

    2017-01-01

    In this paper we describe computer-aided assessment methods used in online Calculus courses and the data they produce. The online learning environment collects a lot of time-stamped data about every action a student makes. Assessment data can be harnessed into use as a feedback, predictor, and recommendation facility for students and instructors.…

  14. Boolean integral calculus

    Science.gov (United States)

    Tucker, Jerry H.; Tapia, Moiez A.; Bennett, A. Wayne

    1988-01-01

    The concept of Boolean integration is developed, and different Boolean integral operators are introduced. Given the changes in a desired function in terms of the changes in its arguments, the ways of 'integrating' (i.e. realizing) such a function, if it exists, are presented. The necessary and sufficient conditions for integrating, in different senses, the expression specifying the changes are obtained. Boolean calculus has applications in the design of logic circuits and in fault analysis.

  15. 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

  16. A Fixpoint-Based Calculus for Graph-Shaped Computational Fields

    DEFF Research Database (Denmark)

    Lluch Lafuente, Alberto; Loreti, Michele; Montanari, Ugo

    2015-01-01

    topology is represented by a graph-shaped field, namely a network with attributes on both nodes and arcs, where arcs represent interaction capabilities between nodes. We propose a calculus where computation is strictly synchronous and corresponds to sequential computations of fixpoints in the graph......-shaped field. Under some conditions, those fixpoints can be computed by synchronised iterations, where in each iteration the attributes of a node is updated based on the attributes of the neighbours in the previous iteration. Basic constructs are reminiscent of the semiring μ-calculus, a semiring......-valued generalisation of the modal μ-calculus, which provides a flexible mechanism to specify the neighbourhood range (according to path formulae) and the way attributes should be combined (through semiring operators). Additional control-How constructs allow one to conveniently structure the fixpoint computations. We...

  17. On Flipping the Classroom in Large First Year Calculus Courses

    Science.gov (United States)

    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…

  18. Beyond food: The multiple pathways for inclusion of materials into ancient dental calculus.

    Science.gov (United States)

    Radini, Anita; Nikita, Efthymia; Buckley, Stephen; Copeland, Les; Hardy, Karen

    2017-01-01

    Dental calculus (mineralized dental plaque) was first recognised as a potentially useful archaeological deposit in the 1970s, though interest in human dental calculus as a resource material has increased sharply in the past few years. The majority of recent research has focused on the retrieval of plant microfossils embedded in its matrix and interpretation of these finds as largely the result of deliberate consumption of plant-derived food. However, while most of the material described in published works does represent food, dental calculus is in fact a "depositional environment" as material can enter the mouth from a range of sources. In this respect, it therefore represents an archaeological deposit that can also contain extensive non-dietary debris. This can comprise a wide variety of cultural and environmental material which reaches the mouth and can become embedded in dental calculus through alternative pathways. Here, we explore the human behaviors and activities besides eating that can generate a flux of particles into the human mouth, the broad range of additional cultural and environmental information that can be obtained through the analysis and contextualisation of this material, and the implications of the additional pathways by which material can become embedded in dental calculus. © 2017 American Association of Physical Anthropologists.

  19. 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

  20. Dental wax decreases calculus accumulation in small dogs.

    Science.gov (United States)

    Smith, Mark M; Smithson, Christopher W

    2014-01-01

    A dental wax was evaluated after unilateral application in 20 client-owned, mixed and purebred small dogs using a clean, split-mouth study model. All dogs had clinical signs of periodontal disease including plaque, calculus, and/or gingivitis. The wax was randomly applied to the teeth of one side of the mouth daily for 30-days while the contralateral side received no treatment. Owner parameters evaluated included compliance and a subjective assessment of ease of wax application. Gingivitis, plaque and calculus accumulation were scored at the end of the study period. Owners considered the wax easy to apply in all dogs. Compliance with no missed application days was achieved in 8 dogs. The number of missed application days had no effect on wax efficacy. There was no significant difference in gingivitis or plaque accumulation scores when comparing treated and untreated sides. Calculus accumulation scores were significantly less (22.1 %) for teeth receiving the dental wax.

  1. A huge bladder calculus causing acute renal failure.

    Science.gov (United States)

    Komeya, Mitsuru; Sahoda, Tamami; Sugiura, Shinpei; Sawada, Takuto; Kitami, Kazuo

    2013-02-01

    A 81-year-old male was referred to our emergency outpatient unit due to acute renal failure. The level of serum creatinine was 276 μmol/l. A CT scan showed bilateral hydronephroureter, large bladder stone (7 cm × 6 cm × 6 cm) and bladder wall thickness. He was diagnosed as post renal failure due to bilateral hydronephroureter. Large bladder stone is thought to be the cause of bilateral hydronephroureter and renal failure. To improve renal failure, we performed open cystolithotomy and urethral catheterization. Three days after the surgery, the level of serum creatinine decreased to 224 μmol/l. He was discharged from our hospital with uneventful course. Bladder calculus is thought to be a rare cause of renal failure. We summarize the characteristics of bladder calculus causing renal failure. We should keep that long-term pyuria and urinary symptom, and repeated urinary tract infection can cause huge bladder calculus and renal failure in mind.

  2. Improving Student Success in Calculus I Using a Co-Requisite Calculus I Lab

    Science.gov (United States)

    Vestal, Sharon Schaffer; Brandenburger, Thomas; Furth, Alfred

    2015-01-01

    This paper describes how one university mathematics department was able to improve student success in Calculus I by requiring a co-requisite lab for certain groups of students. The groups of students required to take the co-requisite lab were identified by analyzing student data, including Math ACT scores, ACT Compass Trigonometry scores, and…

  3. In vitro performance of DIAGNOdent laser fluorescence device for dental calculus detection on human tooth root surfaces.

    Science.gov (United States)

    Rams, Thomas E; Alwaqyan, Abdulaziz Y

    2017-10-01

    This study assessed the reproducibility of a red diode laser device, and its capability to detect dental calculus in vitro on human tooth root surfaces. On each of 50 extracted teeth, a calculus-positive and calculus-free root surface was evaluated by two independent examiners with a low-power indium gallium arsenide phosphide diode laser (DIAGNOdent) fitted with a periodontal probe-like sapphire tip and emitting visible red light at 655 nm wavelength. Laser autofluorescence intensity readings of examined root surfaces were scored on a 0-99 scale, with duplicate assessments performed using the laser probe tip directed both perpendicular and parallel to evaluated tooth root surfaces. Pearson correlation coefficients of untransformed measurements, and kappa analysis of data dichotomized with a >40 autofluorescence intensity threshold, were calculated to assess intra- and inter-examiner reproducibility of the laser device. Mean autofluorescence intensity scores of calculus-positive and calculus-free root surfaces were evaluated with the Student's t -test. Excellent intra- and inter-examiner reproducibility was found for DIAGNOdent laser autofluorescence intensity measurements, with Pearson correlation coefficients above 94%, and kappa values ranging between 0.96 and 1.0, for duplicate readings taken with both laser probe tip orientations. Significantly higher autofluorescence intensity values were measured when the laser probe tip was directed perpendicular, rather than parallel, to tooth root surfaces. However, calculus-positive roots, particularly with calculus in markedly-raised ledges, yielded significantly greater mean DIAGNOdent laser autofluorescence intensity scores than calculus-free surfaces, regardless of probe tip orientation. DIAGNOdent autofluorescence intensity values >40 exhibited a stronger association with calculus (36.6 odds ratio) then measurements of ≥5 (20.1 odds ratio) when the laser probe tip was advanced parallel to root surfaces. Excellent

  4. Fluorescence properties of human teeth and dental calculus for clinical applications

    Science.gov (United States)

    Lee, Yong-Keun

    2015-04-01

    Fluorescent emission of human teeth and dental calculus is important for the esthetic rehabilitation of teeth, diagnosis of dental caries, and detection of dental calculus. The purposes of this review were to summarize the fluorescence and phosphorescence of human teeth by ambient ultraviolet (UV) light, to investigate the clinically relevant fluorescence measurement methods in dentistry, and to review the fluorescence of teeth and dental calculus by specific wavelength light. Dentine was three times more phosphorescent than enamel. When exposed to light sources containing UV components, the fluorescence of human teeth gives them the quality of vitality, and fluorescent emission with a peak of 440 nm is observed. Esthetic restorative materials should have fluorescence properties similar to those of natural teeth. Based on the fluorescence of teeth and restorative materials as determined with a spectrophotometer, a fluorescence parameter was defined. As to the fluorescence spectra by a specific wavelength, varied wavelengths were investigated for clinical applications, and several methods for the diagnosis of dental caries and the detection of dental calculus were developed. Since fluorescent properties of dental hard tissues have been used and would be expanded in diverse fields of clinical practice, these properties should be investigated further, embracing newly developed optical techniques.

  5. A Simplified Stabilizer ZX-calculus

    Directory of Open Access Journals (Sweden)

    Miriam Backens

    2017-01-01

    Full Text Available The stabilizer ZX-calculus is a rigorous graphical language for reasoning about quantum mechanics.The language is sound and complete: a stabilizer ZX-diagram can be transformed into another one if and only if these two diagrams represent the same quantum evolution or quantum state. We show that the stabilizer ZX-calculus can be simplified, removing unnecessary equations while keeping only the essential axioms which potentially capture fundamental structures of quantum mechanics. We thus give a significantly smaller set of axioms and prove that meta-rules like 'colour symmetry' and 'upside-down symmetry', which were considered as axioms in previous versions of the language, can in fact be derived. In particular, we show that the additional symbol and one of the rules which had been recently introduced to keep track of scalars (diagrams with no inputs or outputs are not necessary.

  6. A giant dumbbell shaped vesico-prostatic urethral calculus: a case report and review of literature.

    Science.gov (United States)

    Prabhuswamy, Vinod Kumar; Tiwari, Rahul; Krishnamoorthy, Ramakrishnan

    2013-01-01

    Calculi in the urethra are an uncommon entity. Giant calculi in prostatic urethra are extremely rare. The decision about treatment strategy of calculi depends upon the size, shape, and position of the calculus and 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 of the previous reported cases, giant calculi were extracted via the transvesical approach and external urethrotomy. A 38-year-old male patient presented with complaints of lower urinary tract symptoms. Further investigations showed a giant urethral calculus secondary to stricture of bulbo-membranous part of the urethra. Surgical removal of calculus was done via transvesical approach. Two calculi were found and extracted. One was a huge dumbbell calculus and the other was a smaller round calculus. This case was reported because of the rare size and the dumbbell nature of the stone. Giant urethral calculi are better managed by open surgery.

  7. A Giant Dumbbell Shaped Vesico-Prostatic Urethral Calculus: A Case Report and Review of Literature

    Science.gov (United States)

    Prabhuswamy, Vinod Kumar; Tiwari, Rahul; Krishnamoorthy, Ramakrishnan

    2013-01-01

    Calculi in the urethra are an uncommon entity. Giant calculi in prostatic urethra are extremely rare. The decision about treatment strategy of calculi depends upon the size, shape, and position of the calculus and 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 of the previous reported cases, giant calculi were extracted via the transvesical approach and external urethrotomy. A 38-year-old male patient presented with complaints of lower urinary tract symptoms. Further investigations showed a giant urethral calculus secondary to stricture of bulbo-membranous part of the urethra. Surgical removal of calculus was done via transvesical approach. Two calculi were found and extracted. One was a huge dumbbell calculus and the other was a smaller round calculus. This case was reported because of the rare size and the dumbbell nature of the stone. Giant urethral calculi are better managed by open surgery. PMID:23762742

  8. Newton Binomial Formulas in Schubert Calculus

    OpenAIRE

    Cordovez, Jorge; Gatto, Letterio; Santiago, Taise

    2008-01-01

    We prove Newton's binomial formulas for Schubert Calculus to determine numbers of base point free linear series on the projective line with prescribed ramification divisor supported at given distinct points.

  9. Treatment of calculus of upper urinary tract with mini-percutaneous nephrolithotomy under ultrasound guidance

    International Nuclear Information System (INIS)

    Gao Feng; Ye Chunhua; Wang Kanger; Sun Yan

    2009-01-01

    Objective: To evaluate the feasibility and availability of minimally invasive percutaneous nephrolithotomy (MPCNL) under ultrasound guidance for treatment of calculus of upper urinary tract. Methods: The clinical data of 48 cases with calculus of upper urinary tract undergoing MPCNL were reviewed. Results: In 48 cases, cutaneous-nephric passages were successfully constructed by ultrasound guidance, stone-free rate was 90%. The average operation time was 90 minutes, the average hospitalization was 8 days. No major complications were noted. Conclusion: Under ultrasound guidance, MPCNL with holmium laser is a simply, safe and effective method for treating calculus of upper urinary tract. (authors)

  10. Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus

    Science.gov (United States)

    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.

  11. A Calculus of Located Entities

    Directory of Open Access Journals (Sweden)

    Adriana Compagnoni

    2014-03-01

    Full Text Available We define BioScapeL, a stochastic pi-calculus in 3D-space. A novel aspect of BioScapeL is that entities have programmable locations. The programmer can specify a particular location where to place an entity, or a location relative to the current location of the entity. The motivation for the extension comes from the need to describe the evolution of populations of biochemical species in space, while keeping a sufficiently high level description, so that phenomena like diffusion, collision, and confinement can remain part of the semantics of the calculus. Combined with the random diffusion movement inherited from BioScape, programmable locations allow us to capture the assemblies of configurations of polymers, oligomers, and complexes such as microtubules or actin filaments. Further new aspects of BioScapeL include random translation and scaling. Random translation is instrumental in describing the location of new entities relative to the old ones. For example, when a cell secretes a hydronium ion, the ion should be placed at a given distance from the originating cell, but in a random direction. Additionally, scaling allows us to capture at a high level events such as division and growth; for example, daughter cells after mitosis have half the size of the mother cell.

  12. Fractional-Order Variational Calculus with Generalized Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Baleanu Dumitru

    2011-01-01

    Full Text Available This paper presents the necessary and sufficient optimality conditions for fractional variational problems involving the right and the left fractional integrals and fractional derivatives defined in the sense of Riemman-Liouville with a Lagrangian depending on the free end-points. To illustrate our approach, two examples are discussed in detail.

  13. 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.)

  14. Calculus: A Computer Oriented Presentation, Part 1 [and] Part 2.

    Science.gov (United States)

    Stenberg, Warren; Walker, Robert J.

    Parts one and two of a one-year computer-oriented calculus course (without analytic geometry) are presented. The ideas of calculus are introduced and motivated through computer (i.e., algorithmic) concepts. An introduction to computing via algorithms and a simple flow chart language allows the book to be self-contained, except that material on…

  15. Functional calculus for C0-semigroups using infinite-dimensional systems theory

    NARCIS (Netherlands)

    Schwenninger, F.L.; Zwart, Hans; Arendt, Wolfgang; Chill, Ralph; Tomilov, Yuri

    2015-01-01

    In this short note we use ideas from systems theory to define a functional calculus for infinitesimal generators of strongly continuous semigroups on a Hilbert space. Among others, we show how this leads to new proofs of (known) results in functional calculus.

  16. One Answer to "What Is Calculus?"

    Science.gov (United States)

    Shilgalis, Thomas W.

    1979-01-01

    A number of questions are posed that can be answered with the aid of calculus. These include best value problems, best shape problems, problems involving integration, and growth and decay problems. (MP)

  17. On flipping the classroom in large first year calculus courses

    Science.gov (United States)

    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.

  18. 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)

  19. Calculus diaries

    CERN Document Server

    Ouellette,, Jennifer

    2011-01-01

    Jennifer Ouellette never took maths in the sixth form, mostly because she – like most of us – assumed she wouldn't need it much in real life. But then the English graduate, now an award-winning science-writer, had a change of heart and decided to revisit the equations and formulas that had haunted her youth. The Calculus Diaries is the fun and fascinating account of a year spent confronting her numbers-phobia head on. With wit and verve, Ouellette explains how she discovered that maths could apply to everything from petrol mileages to dieting, rollercoaster rides to winning in Las Vegas.

  20. Differentiated Instruction in a Calculus Curriculum for College Students in Taiwan

    Science.gov (United States)

    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…