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
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
Weinstock, Robert
1975-01-01
Basic introduction covering isoperimetric problems, theory of elasticity, quantum mechanics, electrostatics, geometrical optics, particle dynamics, more. Exercises throughout. "A very useful book." - J. L. Synge, American Mathematical Monthly.
Partial differential equations and calculus of variations
Leis, Rolf
1988-01-01
This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory.
Optimal control and the calculus of variations
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.
Introduction to the calculus of variations
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.
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...
An introduction to the calculus of variations
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
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
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...
Calculus of variations and optimal control theory a concise introduction
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...
The early period of the calculus of variations
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...
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.
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
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.
Multiple integrals in the calculus of variations
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...
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
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.
A first course in the calculus of variations
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
Differential geometry and the calculus of variations
Hermann, Robert
1968-01-01
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat
The calculus of variations in the large
Morse, M
1934-01-01
Morse theory is a study of deep connections between analysis and topology. In its classical form, it provides a relationship between the critical points of certain smooth functions on a manifold and the topology of the manifold. It has been used by geometers, topologists, physicists, and others as a remarkably effective tool to study manifolds. In the 1980s and 1990s, Morse theory was extended to infinite dimensions with great success. This book is Morse's own exposition of his ideas. It has been called one of the most important and influential mathematical works of the twentieth century. Calc
Lectures on the calculus of variations
Bolza, Oskar
2018-01-01
Pioneering modern treatise studies the development of the subject from Euler to Hilbert, addressing basic problems with sufficient generality and rigor to provide a sound introduction for serious study. 1904 edition.
An experimental trip to the Calculus of Variations
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.
Existence of evolutionary variational solutions via the calculus of variations
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,∞).
A new class of problems in the calculus of variations
Ekeland, Ivar; Long, Yiming; Zhou, Qinglong
2013-11-01
This paper investigates an infinite-horizon problem in the one-dimensional calculus of variations, arising from the Ramsey model of endogeneous economic growth. Following Chichilnisky, we introduce an additional term, which models concern for the well-being of future generations. We show that there are no optimal solutions, but that there are equilibrium strateges, i.e. Nash equilibria of the leader-follower game between successive generations. To solve the problem, we approximate the Chichilnisky criterion by a biexponential criterion, we characterize its equilibria by a pair of coupled differential equations of HJB type, and we go to the limit. We find all the equilibrium strategies for the Chichilnisky criterion. The mathematical analysis is difficult because one has to solve an implicit differential equation in the sense of Thom. Our analysis extends earlier work by Ekeland and Lazrak.
On the minimizers of calculus of variations problems in Hilbert spaces
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.
On the minimizers of calculus of variations problems in Hilbert spaces
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.
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
Dynamic optimization the calculus of variations and optimal control in economics and management
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.
A primer on the calculus of variations and optimal control theory
Mesterton-Gibbons, Mike
2009-01-01
The calculus of variations is used to find functions that optimize quantities expressed in terms of integrals. Optimal control theory seeks to find functions that minimize cost integrals for systems described by differential equations. This book is an introduction to both the classical theory of the calculus of variations and the more modern developments of optimal control theory from the perspective of an applied mathematician. It focuses on understanding concepts and how to apply them. The range of potential applications is broad: the calculus of variations and optimal control theory have been widely used in numerous ways in biology, criminology, economics, engineering, finance, management science, and physics. Applications described in this book include cancer chemotherapy, navigational control, and renewable resource harvesting. The prerequisites for the book are modest: the standard calculus sequence, a first course on ordinary differential equations, and some facility with the use of mathematical softwa...
Presymplectic current and the inverse problem of the calculus of variations
Khavkine, I.
2013-01-01
The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when horizontally closed on solutions, allows us to construct a
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
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.
Variational calculus with constraints on general algebroids
Energy Technology Data Exchange (ETDEWEB)
Grabowska, Katarzyna [Physics Department, Division of Mathematical Methods in Physics, University of Warsaw, Hoza 69, 00-681 Warszawa (Poland); Grabowski, Janusz [Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, PO Box 21, 00-956 Warszawa (Poland)], E-mail: konieczn@fuw.edu.pl, E-mail: jagrab@impan.gov.pl
2008-05-02
Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and geometrical settings. The constrained Euler-Lagrange equations are derived for analogs of holonomic, vakonomic and nonholonomic constraints. This general model covers the majority of first-order Lagrangian systems which are present in the literature and reduces to the standard variational calculus and the Euler-Lagrange equations in classical mechanics for E = TM.
Variational calculus with constraints on general algebroids
International Nuclear Information System (INIS)
Grabowska, Katarzyna; Grabowski, Janusz
2008-01-01
Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and geometrical settings. The constrained Euler-Lagrange equations are derived for analogs of holonomic, vakonomic and nonholonomic constraints. This general model covers the majority of first-order Lagrangian systems which are present in the literature and reduces to the standard variational calculus and the Euler-Lagrange equations in classical mechanics for E = TM
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)
The inverse problem of the calculus of variations for discrete systems
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.
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.
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.
Presymplectic current and the inverse problem of the calculus of variations
Khavkine, Igor
2013-11-01
The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when horizontally closed on solutions, allows us to construct a variational formulation for a subsystem of the given PDE. No constraints on the differential order or number of dependent or independent variables are assumed. The proof follows a recent observation of Bridges, Hydon, and Lawson [Math. Proc. Cambridge Philos. Soc. 148(01), 159-178 (2010)] and generalizes an older result of Henneaux [Ann. Phys. 140(1), 45-64 (1982)] from ordinary differential equations (ODEs) to PDEs. Uniqueness of the variational formulation is also discussed.
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.
Classical mechanics with calculus of variations and optimal control an intuitive introduction
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...
Calculus of variations mechanics, control and other applications
MacCluer, Charles R
2012-01-01
First truly up-to-date treatment offers a simple introduction to optimal control, linear-quadratic control design, and more. Broad perspective features numerous exercises, hints, outlines, and appendixes, including a practical discussion of MATLAB. 2005 edition.
Calculus of variations an introduction to the one-dimensional theory with examples and exercises
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...
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
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.
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
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.)
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
Dynamic Material Removal Rate and Tool Replacement Optimization with Calculus of Variations
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.
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.
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
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)
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)
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
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.
Impact of Calculus Reform in a Liberal Arts Calculus Course.
Brosnan, Patricia A.; Ralley, Thomas G.
This report describes the changes in a freshman-level calculus course that occurred as a consequence of adopting the Harvard Consortium Calculus text. The perspective is that of the lecturer. The course is intended as an introduction to calculus for liberal arts students, that is, students who will not be expected to use calculus as a mathematical…
Calculus of bivariant function
PTÁČNÍK, Jan
2011-01-01
This thesis deals with the introduction of function of two variables and differential calculus of this function. This work should serve as a textbook for students of elementary school's teacher. Each chapter contains a summary of basic concepts and explanations of relationships, then solved model exercises of the topic and finally the exercises, which should solve the student himself. Thesis have transmit to students basic knowledges of differential calculus of functions of two variables, inc...
Example Solar Electric Propulsion System asteroid tours using variational calculus
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.
The absolute differential calculus calculus of tensors
Levi-Cività, Tullio
1926-01-01
Written by a towering figure of twentieth-century mathematics, this classic examines the mathematical background necessary for a grasp of relativity theory. Tullio Levi-Civita provides a thorough treatment of the introductory theories that form the basis for discussions of fundamental quadratic forms and absolute differential calculus, and he further explores physical applications.Part one opens with considerations of functional determinants and matrices, advancing to systems of total differential equations, linear partial differential equations, algebraic foundations, and a geometrical intro
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.
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...
The use of Adomian decomposition method for solving problems in calculus of variations
Directory of Open Access Journals (Sweden)
Mehdi Dehghan
2006-01-01
Full Text Available In this paper, a numerical method is presented for finding the solution of some variational problems. The main objective is to find the solution of an ordinary differential equation which arises from the variational problem. This work is done using Adomian decomposition method which is a powerful tool for solving large amount of problems. In this approach, the solution is found in the form of a convergent power series with easily computed components. To show the efficiency of the method, numerical results are presented.
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.
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
Calculus of variations in rate of reactions tax using the general pertubation theory
International Nuclear Information System (INIS)
Silva, F.C. da.
1981-02-01
A perturbation expression to calculate the variations in the rates of integral parameters (such as reaction rates) of a reactor using a Time-Independent Generalized Perturbation Theory, was developed. This theory makes use of the concepts of neutron generation and neutron importance with respect to a given process occurring in a system. The application of Time-Dependent Generalized Perturbation Theory to the calculation of Burnup, by using the expressions derived by A. Gandini, along with the perturbation expression derived in the Time Independent Generalized Perturbation Theory, is done. (Author) [pt
Muldowney, Patrick
2012-01-01
A Modern Theory of Random Variation is a new and radical re-formulation of the mathematical underpinnings of subjects as diverse as investment, communication engineering, and quantum mechanics. Setting aside the classical theory of probability measure spaces, the book utilizes a mathematically rigorous version of the theory of random variation that bases itself exclusively on finitely additive probability distribution functions. In place of twentieth century Lebesgue integration and measure theory, the author uses the simpler concept of Riemann sums, and the non-absolute Riemann-type integration of Henstock. Readers are supplied with an accessible approach to standard elements of probability theory such as the central limmit theorem and Brownian motion as well as remarkable, new results on Feynman diagrams and stochastic integrals. Throughout the book, detailed numerical demonstrations accompany the discussions of abstract mathematical theory, from the simplest elements of the subject to the most complex. I...
A Duality Theory for Non-convex Problems in the Calculus of Variations
Bouchitté, Guy; Fragalà, Ilaria
2018-02-01
We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no duality gap. Further, we provide necessary and sufficient optimality conditions, and we show that our duality principle can be reformulated as a min-max result which is quite useful for numerical implementations. As an example, we illustrate the application of our method to a celebrated free boundary problem. The results were announced in Bouchitté and Fragalà (C R Math Acad Sci Paris 353(4):375-379, 2015).
Discontinuous gradient differential equations and trajectories in the calculus of variations
International Nuclear Information System (INIS)
Bogaevskii, I A
2006-01-01
The concept of gradient of smooth functions is generalized for their sums with concave functions. An existence, uniqueness, and continuous dependence theorem for increasing time is formulated and proved for solutions of an ordinary differential equation the right-hand side of which is the gradient of the sum of a concave and a smooth function. With the use of this result a physically natural motion of particles, well defined even at discontinuities of the velocity field, is constructed in the variational problem of the minimal mechanical action in a space of arbitrary dimension. For such a motion of particles in the plane all typical cases of the birth and the interaction of point clusters of positive mass are described.
Discontinuous gradient differential equations and trajectories in the calculus of variations
Bogaevskii, I. A.
2006-12-01
The concept of gradient of smooth functions is generalized for their sums with concave functions. An existence, uniqueness, and continuous dependence theorem for increasing time is formulated and proved for solutions of an ordinary differential equation the right-hand side of which is the gradient of the sum of a concave and a smooth function. With the use of this result a physically natural motion of particles, well defined even at discontinuities of the velocity field, is constructed in the variational problem of the minimal mechanical action in a space of arbitrary dimension. For such a motion of particles in the plane all typical cases of the birth and the interaction of point clusters of positive mass are described.
Fluorescence spectroscopy of dental calculus
International Nuclear Information System (INIS)
Bakhmutov, D; Gonchukov, S; Sukhinina, A
2010-01-01
The aim of the present study was to investigate the fluorescence properties of dental calculus in comparison with the properties of adjacent unaffected tooth structure using both lasers and LEDs in the UV-visible range for fluorescence excitation. The influence of calculus color on the informative signal is demonstrated. The optimal spectral bands of excitation and registration of the fluorescence are determined
Fluorescence spectroscopy of dental calculus
Bakhmutov, D.; Gonchukov, S.; Sukhinina, A.
2010-05-01
The aim of the present study was to investigate the fluorescence properties of dental calculus in comparison with the properties of adjacent unaffected tooth structure using both lasers and LEDs in the UV-visible range for fluorescence excitation. The influence of calculus color on the informative signal is demonstrated. The optimal spectral bands of excitation and registration of the fluorescence are determined.
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…
Chernyak, Vladimir Y.; Chertkov, Michael; Bierkens, Joris; Kappen, Hilbert J.
2014-01-01
In stochastic optimal control (SOC) one minimizes the average cost-to-go, that consists of the cost-of-control (amount of efforts), cost-of-space (where one wants the system to be) and the target cost (where one wants the system to arrive), for a system participating in forced and controlled Langevin dynamics. We extend the SOC problem by introducing an additional cost-of-dynamics, characterized by a vector potential. We propose derivation of the generalized gauge-invariant Hamilton-Jacobi-Bellman equation as a variation over density and current, suggest hydrodynamic interpretation and discuss examples, e.g., ergodic control of a particle-within-a-circle, illustrating non-equilibrium space-time complexity.
Directory of Open Access Journals (Sweden)
Musilová Jana
2016-12-01
Full Text Available As widely accepted, justified by the historical developments of physics, the background for standard formulation of postulates of physical theories leading to equations of motion, or even the form of equations of motion themselves, come from empirical experience. Equations of motion are then a starting point for obtaining specific conservation laws, as, for example, the well-known conservation laws of momenta and mechanical energy in mechanics. On the other hand, there are numerous examples of physical laws or equations of motion which can be obtained from a certain variational principle as Euler-Lagrange equations and their solutions, meaning that the \\true trajectories" of the physical systems represent stationary points of the corresponding functionals.
Optimal transport for applied mathematicians calculus of variations, PDEs, and modeling
Santambrogio, Filippo
2015-01-01
This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and appl...
Polynomial Calculus: Rethinking the Role of Calculus in High Schools
Grant, Melva R.; Crombie, William; Enderson, Mary; Cobb, Nell
2016-01-01
Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in…
Fluorescence detection of dental calculus
Gonchukov, S.; Biryukova, T.; Sukhinina, A.; Vdovin, Yu
2010-11-01
This work is devoted to the optimization of fluorescence dental calculus diagnostics in optical spectrum. The optimal wavelengths for fluorescence excitation and registration are determined. Two spectral ranges 620 - 645 nm and 340 - 370 nm are the most convenient for supra- and subgingival calculus determination. The simple implementation of differential method free from the necessity of spectrometer using was investigated. Calculus detection reliability in the case of simple implementation is higher than in the case of spectra analysis at optimal wavelengths. The use of modulated excitation light and narrowband detection of informative signal allows us to decrease essentially its diagnostic intensity even in comparison with intensity of the low level laser dental therapy.
The Shape of a Sausage: A Challenging Problem in the Calculus of Variations
Deakin, Michael A. B.
2010-01-01
Many familiar household objects (such as sausages) involve the maximization of a volume under geometric constraints. A flexible but inextensible membrane bounds a volume which is to be filled to capacity. In the case of the sausage, a full analytic solution is here provided. Other related but more difficult problems seem to demand approximate…
Directory of Open Access Journals (Sweden)
Marcelo Perencin de Arruda Ribeiro
2005-06-01
Full Text Available In this work, optimal control techniques were used to optimize the feed of reactants during the enzymatic synthesis of ampicillin in a semi-batch reactor. Simulation results showed that a semi-batch integrated reactor (with product crystallization might achieve 88% 6-APA (6-aminepenicillanic acid conversion and 92% of PGME (phenylglycine methyl ester yield, with a productivity between 3.5 and 5.5 mM min-1.A síntese enzimática de ampicilina oferece menor impacto ambiental em relação ao processo utilizado atualmente pela indústria farmacêutica. Mas seu rendimento e produtividade devem ser melhorados para tornar essa rota competitiva. Alguns estudos empíricos para otimizar a rota enzimática de síntese de antibióticos beta-lactâmicos vêm sendo realizados. Entretanto, a utilização sistemática de métodos matemáticos de otimização nesse processo não é encontrada na literatura. Neste trabalho, utilizaram-se técnicas de controle ótimo para otimizar a alimentação de reagentes na síntese enzimática de ampicilina em reator operando em batelada alimentada. Resultados simulados mostram que, em reator integrado (com precipitação dos produtos operado em batelada alimentada, conversões de 6-APA e rendimento de EMFG de 88% a 92% são factíveis, assim como produtividades entre 3,5 e 5,5 mM.min-1.
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
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.
Advanced calculus of several variables
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.
Tensor Calculus: Unlearning Vector Calculus
Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita
2018-01-01
Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…
The impact of taking a college pre-calculus course on students' college calculus performance
Sonnert, Gerhard; Sadler, Philip M.
2014-11-01
Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and four-year colleges continues to grow, and these courses are well-populated with students who already took pre-calculus in high school. We examine student performance in college calculus, using regression discontinuity to estimate the effects of taking college pre-calculus or not, in a national US sample of 5507 students at 132 institutions. We find that students who take college pre-calculus do not earn higher calculus grades.
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.
[Fluorescence control of dental calculus removal].
Bakhmutov, D N; Gonchukov, S A; Lonkina, T V; Sukhinina, A V
2012-01-01
The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In the frames of this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise detection of tooth-calculus interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing (as ultrasonic or laser devices).
Dental Calculus Arrest of Dental Caries
Keyes, Paul H.; Rams, Thomas E.
2016-01-01
Background An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human t...
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...
Dental Calculus Arrest of Dental Caries.
Keyes, Paul H; Rams, Thomas E
An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human teeth for the presence and location of dental caries, dental calculus, and dental plaque biofilms. A total of 1,200 teeth were preserved in 10% buffered formal saline, and viewed while moist by a single experienced examiner using a research stereomicroscope at 15-25× magnification. Representative teeth were sectioned and photographed, and their dental plaque biofilms subjected to gram-stain examination with light microscopy at 100× magnification. Dental calculus was observed on 1,140 (95%) of the extracted human teeth, and no dental carious lesions were found underlying dental calculus-covered surfaces on 1,139 of these teeth. However, dental calculus arrest of dental caries was found on one (0.54%) of 187 evaluated teeth that presented with unrestored proximal enamel caries. On the distal surface of a maxillary premolar tooth, dental calculus mineralization filled the outer surface cavitation of an incipient dental caries lesion. The dental calculus-covered carious lesion extended only slightly into enamel, and exhibited a brown pigmentation characteristic of inactive or arrested dental caries. In contrast, the tooth's mesial surface, without a superficial layer of dental calculus, had a large carious lesion going through enamel and deep into dentin. These observations further document the potential protective effects of dental calculus mineralization against dental caries.
Dental Calculus Arrest of Dental Caries
Keyes, Paul H.; Rams, Thomas E.
2016-01-01
Background An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human teeth for the presence and location of dental caries, dental calculus, and dental plaque biofilms. Materials and methods A total of 1,200 teeth were preserved in 10% buffered formal saline, and viewed while moist by a single experienced examiner using a research stereomicroscope at 15-25× magnification. Representative teeth were sectioned and photographed, and their dental plaque biofilms subjected to gram-stain examination with light microscopy at 100× magnification. Results Dental calculus was observed on 1,140 (95%) of the extracted human teeth, and no dental carious lesions were found underlying dental calculus-covered surfaces on 1,139 of these teeth. However, dental calculus arrest of dental caries was found on one (0.54%) of 187 evaluated teeth that presented with unrestored proximal enamel caries. On the distal surface of a maxillary premolar tooth, dental calculus mineralization filled the outer surface cavitation of an incipient dental caries lesion. The dental calculus-covered carious lesion extended only slightly into enamel, and exhibited a brown pigmentation characteristic of inactive or arrested dental caries. In contrast, the tooth's mesial surface, without a superficial layer of dental calculus, had a large carious lesion going through enamel and deep into dentin. Conclusions These observations further document the potential protective effects of dental calculus mineralization against dental caries. PMID:27446993
Thematization of the Calculus Graphing Schema
Cooley, Laurel; Baker, Bernadette; Trigueros, Maria
2003-01-01
This article is the result of an investigation of students' conceptualizations of calculus graphing techniques after they had completed at least two semesters of calculus. The work and responses of 27 students to a series of questions that solicit information about the graphical implications of the first derivative, second derivative, continuity,…
A Snapshot of the Calculus Classroom
Weathers, Tony D.; Latterell, Carmen M.
2003-01-01
Essentially a focus group to discuss textbook related issues, a meeting of calculus instructors from a wide variety of environments was convened and sponsored by McGraw Hill to provide feedback on the current state of the calculus classroom. This paper provides a description of the group's discussions.
RAMAN-SPECTRA OF HUMAN DENTAL CALCULUS
TSUDA, H; ARENDS, J
1993-01-01
Raman spectra of human dental calculus have been observed for the first time by use of micro-Raman spectroscopy. The spectral features of calculus were influenced easily by heating caused by laser irradiation. Therefore, the measurements were carried out at relatively low power (5 mW, 1-mu m spot
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...
A Cross-National Study of Calculus
Chai, Jun; Friedler, Louis M.; Wolff, Edward F.; Li, Jun; Rhea, Karen
2015-01-01
The results from a cross-national study comparing calculus performance of students at East China Normal University (ECNU) in Shanghai and students at the University of Michigan before and after their first university calculus course are presented. Overall, ECNU significantly outperformed Michigan on both the pre- and post-tests, but the Michigan…
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.
Study on bioactive compounds of in vitro cultured Calculus Suis and natural Calculus Bovis.
Wan, Tien-Chun; Cheng, Fu-Yuan; Liu, Yu-Tse; Lin, Liang-Chuan; Sakata, Ryoichi
2009-12-01
The purpose of the study was to investigate bioactive compounds of in vitro cultured Calculus Suis and natural Calculus Bovis obtained as valuable by-products from animals used for meat production. The results showed that the components of natural Calculus Bovis were rich in bilirubin and biliverdin and had higher content of essential amino acids. The major amino acids of in vitro cultured Calculus Suis were identified as glycine, alanine, glutamic acid and aspartic acid, and those for natural Calculus Bovis were found to be glutamic acid, aspartic acid, proline, and arginine. The methionine and cysteine contents of precursors for glutathione in natural Calculus Bovis were significantly higher than those of in vitro cultured Calculus Suis. The mineral contents of zinc, iron and manganese of natural Calculus Bovis were significantly higher than those of in vitro cultured Calculus Suis. The major bile acids in both products were cholic acid and dehydrocholic acid, respectively. The chenodeoxycholic and ursodeoxycholic acid content of in vitro cultured Calculus Suis was significantly higher than that of natural Calculus Bovis.
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.
Strogatz, Steven
2009-01-01
Many academics like to isolate a piece of the world to study: an important social issue, a central philosophical problem, a key moment in history. They know they're oversimplifying but they do it anyway--it's the only way to make progress, and what's more, their little worlds are often more beautiful than the real one. This paper shares a story of…
Giant calculus: review and report of a case.
Woodmansey, Karl; Severine, Anthony; Lembariti, Bakari S
2013-01-01
Dental calculus is a common oral finding. The term giant calculus is used to describe unusually large deposits of dental calculus. Several extreme cases have been reported in the dental literature. The specific etiology of these cases remains uncertain. This paper reviews previously reported cases, and presents another extreme example of giant calculus.
Applications of fractional calculus in physics
2000-01-01
Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus.This volume provides an introduction to fractional calculus for physicists, and co
Restricted diversity of dental calculus methanogens over five centuries, France
Hong T. T. Huynh; Vanessa D. Nkamga; Michel Signoli; Stéfan Tzortzis; Romuald Pinguet; Gilles Audoly; Gérard Aboudharam; Michel Drancourt
2016-01-01
Methanogens are acknowledged archaeal members of modern dental calculus microbiota and dental pathogen complexes. Their repertoire in ancient dental calculus is poorly known. We therefore investigated archaea in one hundred dental calculus specimens collected from individuals recovered from six archaeological sites in France dated from the 14th to 19th centuries AD. Dental calculus was demonstrated by macroscopic and cone-beam observations. In 56 calculus specimens free of PCR inhibition, PCR...
On Some Syntactic Properties of the Modalized Heyting Calculus
Muravitsky, Alexei
2016-01-01
We show that the modalized Heyting calculus introduced by Leo Esakia admits a normal axiomatization. Then, we prove that the inference rules $\\square\\alpha/\\alpha$ and $\\square\\alpha\\rightarrow\\alpha/\\alpha$ are admissible in this calculus. Finally, we show that this calculus and intuitionistic propositional calculus are assertorically equipollent, which leads to a variant of limited separation property for the modalized Heyting calculus.
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)
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…
Ricceri, Biagio
2006-12-01
Given a bounded domain [Omega][subset of]Rn, we prove that if is a C1 function whose gradient is Lipschitzian in Rn+1 and non-zero at 0, then, for each r>0 small enough, the restriction of the integral functional to the sphere has a unique global minimum and a unique global maximum.
The origins of Cauchy's rigorous calculus
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.
Introductory analysis a deeper view of calculus
Bagby, Richard J
2000-01-01
Introductory Analysis addresses the needs of students taking a course in analysis after completing a semester or two of calculus, and offers an alternative to texts that assume that math majors are their only audience. By using a conversational style that does not compromise mathematical precision, the author explains the material in terms that help the reader gain a firmer grasp of calculus concepts.* Written in an engaging, conversational tone and readable style while softening the rigor and theory* Takes a realistic approach to the necessary and accessible level of abstraction for the secondary education students* A thorough concentration of basic topics of calculus* Features a student-friendly introduction to delta-epsilon arguments * Includes a limited use of abstract generalizations for easy use* Covers natural logarithms and exponential functions* Provides the computational techniques often encountered in basic calculus
A phenomenological calculus of Wiener description space.
Richardson, I W; Louie, A H
2007-10-01
The phenomenological calculus is a categorical example of Robert Rosen's modeling relation. This paper is an alligation of the phenomenological calculus and generalized harmonic analysis, another categorical example. Our epistemological exploration continues into the realm of Wiener description space, in which constitutive parameters are extended from vectors to vector-valued functions of a real variable. Inherent in the phenomenology are fundamental representations of time and nearness to equilibrium.
Endoscopic vs. tactile evaluation of subgingival calculus.
Osborn, Joy B; Lenton, Patricia A; Lunos, Scott A; Blue, Christine M
2014-08-01
Endoscopic technology has been developed to facilitate imagery for use during diagnostic and therapeutic phases of periodontal care. The purpose of this study was to compare the level of subgingival calculus detection using a periodontal endoscope with that of conventional tactile explorer in periodontitis subjects. A convenience sample of 26 subjects with moderate periodontitis in at least 2 quadrants was recruited from the University of Minnesota School of Dentistry to undergo quadrant scaling and root planing. One quadrant from each subject was randomized for tactile calculus detection alone and the other quadrant for tactile detection plus the Perioscope ™ (Perioscopy Inc., Oakland, Cali). A calculus index on a 0 to 3 score was performed at baseline and at 2 post-scaling and root planing visits. Sites where calculus was detected at visit 1 were retreated. T-tests were used to determine within-subject differences between Perioscope™ and tactile measures, and changes in measures between visits. Significantly more calculus was detected using the Perioscope™ vs. tactile explorer for all 3 subject visits (pcalculus detection from baseline to visit 1 were statistically significant for both the Perioscope™ and tactile quadrants (pcalculus detection from visit 1 to visit 2 was only significant for the Perioscope™ quadrant (pcalculus at this visit. It was concluded that the addition of a visual component to calculus detection via the Perioscope™ was most helpful in the re-evaluation phase of periodontal therapy. Copyright © 2014 The American Dental Hygienists’ Association.
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
On the Presentation of Pre-Calculus and Calculus Topics: An Alternate View
Davydov, Aleksandr; Sturm-Beiss, Rachel
2008-01-01
The orders of presentation of pre-calculus and calculus topics, and the notation used, deserve careful study as they affect clarity and ultimately students' level of understanding. We introduce an alternate approach to some of the topics included in this sequence. The suggested alternative is based on years of teaching in colleges within and…
International Nuclear Information System (INIS)
Stefanou, G.D.
1975-01-01
The calculation of time-dependent stresses in structural systems operating at elevated temperatures with temperature gradients is discussed. The proposed method described in this report is of a direct formulation technique and
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.
Ancient DNA analysis of dental calculus.
Weyrich, Laura S; Dobney, Keith; Cooper, Alan
2015-02-01
Dental calculus (calcified tartar or plaque) is today widespread on modern human teeth around the world. A combination of soft starchy foods, changing acidity of the oral environment, genetic pre-disposition, and the absence of dental hygiene all lead to the build-up of microorganisms and food debris on the tooth crown, which eventually calcifies through a complex process of mineralisation. Millions of oral microbes are trapped and preserved within this mineralised matrix, including pathogens associated with the oral cavity and airways, masticated food debris, and other types of extraneous particles that enter the mouth. As a result, archaeologists and anthropologists are increasingly using ancient human dental calculus to explore broad aspects of past human diet and health. Most recently, high-throughput DNA sequencing of ancient dental calculus has provided valuable insights into the evolution of the oral microbiome and shed new light on the impacts of some of the major biocultural transitions on human health throughout history and prehistory. Here, we provide a brief historical overview of archaeological dental calculus research, and discuss the current approaches to ancient DNA sampling and sequencing. Novel applications of ancient DNA from dental calculus are discussed, highlighting the considerable scope of this new research field for evolutionary biology and modern medicine. Copyright © 2014 Elsevier Ltd. All rights reserved.
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.
Regularization of positive definite matrix fields based on multiplicative calculus
Florack, L.M.J.; Bruckstein, A.M.; Haar Romeny, ter B.M.; Bronstein, A.M.; Bronstein, M.M.
2012-01-01
Multiplicative calculus provides a natural framework in problems involving positive images and positivity preserving operators. In increasingly important, complex imaging frameworks, such as diffusion tensor imaging, it complements standard calculus in a nontrivial way. The purpose of this article
Calculus of tensors and differential forms
Sinha, Rajnikant
2014-01-01
Calculus of tensors and differential forms is an introductory-level textbook. Through this book, students will familiarize themselves with tools they need in order to use for further study on general relativity and research, such as affine tensors, tensor calculus on manifolds, relative tensors, Lie derivatives, wedge products, differential forms, and Stokes' theorem. The treatment is concrete and in detail, so that abstract concepts do not deter even physics and engineering students. This self contained book requires undergraduate-level calculus of several variables and linear algebra as prerequisite. Fubini's theorem in real analysis, to be used in Stokes' theorem, has been proved earlier than Stokes' theorem so that students don't have to search elsewhere.
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...
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...
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.
ASSESSING STUDENTS' UNDERSTANDING OF PRE-CALCULUS CONCEPTS
Dr. Jyoti Sharma
2017-01-01
Calculus is one of the most momentous achievements of the human intellect (Boyer, 1949). It has given a new direction to the work of mathematicians and scientists. Calculus has exponentially expanded the scope and use of mathematics in other fields. Learning calculus is important to pursue career in applied mathematics.
Projects for calculus the language of change
Stroyan, Keith D
1999-01-01
Projects for Calculus is designed to add depth and meaning to any calculus course. The fifty-two projects presented in this text offer the opportunity to expand the use and understanding of mathematics. The wide range of topics will appeal to both instructors and students. Shorter, less demanding projects can be managed by the independent learner, while more involved, in-depth projects may be used for group learning. Each task draws on special mathematical topics and applications from subjects including medicine, engineering, economics, ecology, physics, and biology.Subjects including:* Medicine* Engineering* Economics* Ecology* Physics* Biology
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.
Improving Calculus II and III through the Redistribution of Topics
George, C. Yousuf; Koetz, Matt; Lewis, Heather A.
2016-01-01
Three years ago our mathematics department rearranged the topics in second and third semester calculus, moving multivariable calculus to the second semester and series to the third semester. This paper describes the new arrangement of topics, and how it could be adapted to calculus curricula at different schools. It also explains the benefits we…
The fundamental theorem of linearised Regge calculus
International Nuclear Information System (INIS)
Barrett, J.W.
1987-01-01
In linearised Regge calculus in a topologically trivial region, the space of linearised deviations of the edge lengths from a flat configuration, divided by the subspace of deformations due to translations of the vertices, is equivalent to the space of the linearised curvatures which satisfy the Bianchi identities. (orig.)
Advanced calculus of a single variable
Geveci, Tunc
2016-01-01
This advanced undergraduate textbook is based on a one-semester course on single variable calculus that the author has been teaching at San Diego State University for many years. The aim of this classroom-tested book is to deliver a rigorous discussion of the concepts and theorems that are dealt with informally in the first two semesters of a beginning calculus course. As such, students are expected to gain a deeper understanding of the fundamental concepts of calculus, such as limits (with an emphasis on ε-δ definitions), continuity (including an appreciation of the difference between mere pointwise and uniform continuity), the derivative (with rigorous proofs of various versions of L’Hôpital’s rule) and the Riemann integral (discussing improper integrals in-depth, including the comparison and Dirichlet tests). Success in this course is expected to prepare students for more advanced courses in real and complex analysis and this book will help to accomplish this. The first semester of advanced calculus...
Continuous fragment of the mu-calculus
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
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...
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.
Characteristics of subgingival calculus detection by multiphoton fluorescence microscopy
Tung, Oi-Hong; Lee, Shyh-Yuan; Lai, Yu-Lin; Chen, How-Foo
2011-06-01
Subgingival calculus has been recognized as a major cause of periodontitis, which is one of the main chronic infectious diseases of oral cavities and a principal cause of tooth loss in humans. Bacteria deposited in subgingival calculus or plaque cause gingival inflammation, function deterioration, and then periodontitis. However, subgingival calculus within the periodontal pocket is a complicated and potentially delicate structure to be detected with current dental armamentaria, namely dental x-rays and dental probes. Consequently, complete removal of subgingival calculus remains a challenge to periodontal therapies. In this study, the detection of subgingival calculus employing a multiphoton autofluorescence imaging method was characterized in comparison with a one-photon confocal fluorescence imaging technique. Feasibility of such a system was studied based on fluorescence response of gingiva, healthy teeth, and calculus with and without gingiva covered. The multiphoton fluorescence technology perceived the tissue-covered subgingival calculus that cannot be observed by the one-photon confocal fluorescence method.
Success in Introductory Calculus: The Role of High School and Pre-calculus Preparation
Ayebo, Abraham; Ukkelberg, Sarah; Assuah, Charles
2017-01-01
Calculus at the college level has significantpotential to serve as a pump for increasing the number of students majoring inSTEM fields. It is a foundation course for all STEM majors and, if mastered well,should provide students with a positive and successful first-year experienceand gateway into more advanced courses. Studies have shown that a high percentage of studentsfailing college calculus has caused a shortage of individuals entering fieldsthat are heavily dependent on mathematics. Many...
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
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)
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
Some aspects of q-boson calculus
International Nuclear Information System (INIS)
Smirnov, Yu.F.; Kibler, M.R.
1992-10-01
The Jordan-Schwinger calculus is discussed, using deformed bosons. This work constitutes a first step toward a complete study of the SU q (2) unit tensor. The objective is to find a realization of the components of this tensor in terms of q-bosons. The q-deformed Schwinger algebra relative to SU q (2) is defined, and an algorithm for producing recurrent relations between Clebsch-Gordan coefficients for SU q (2) is given. (K.A.) 18 refs
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
Geometrical foundations of tensor calculus and relativity
Schuller , Frédéric; Lorent , Vincent
2006-01-01
Manifolds, particularly space curves: basic notions 1 The first groundform, the covariant metric tensor 11 The second groundform, Meusnier's theorem 19 Transformation groups in the plane 28 Co- and contravariant components for a special affine transformation in the plane 29 Surface vectors 32 Elements of tensor calculus 36 Generalization of the first groundform to the space 46 The covariant (absolute) derivation 57 Examples from elasticity theory 61 Geodesic lines 63 Main curvatur...
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
SRXRF analysis with spatial resolution of dental calculus
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.
Time scales: from Nabla calculus to Delta calculus and vice versa via duality
Caputo, M. Cristina
2009-01-01
In this note we show how one can obtain results from the nabla calculus from results on the delta calculus and vice versa via a duality argument. We provide applications of the main results to the calculus of variations on time scales.
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.
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....
Renal vein thrombosis mimicking urinary calculus: a dilemma of diagnosis.
Wang, Yimin; Chen, Shanwen; Wang, Wei; Liu, Jianyong; Jin, Baiye
2015-07-02
Renal vein thrombosis (RVT) with flank pain, and hematuria, is often mistaken with renal colic originating from ureteric or renal calculus. Especially in young and otherwise healthy patients, clinicians are easily misled by clinical presentation and calcified RVT. A 38-year-old woman presented with flank pain and hematuria suggestive of renal calculus on ultrasound. She underwent extracorporeal shock wave lithotripsy that failed, leading to the recommendation that percutaneous lithotomy was necessary to remove the renal calculus. In preoperative view of the unusual shape of the calculus without hydronephrosis, noncontrast computed tomography was taken and demonstrated left ureteric calculus. However computed tomography angiography revealed, to our surprise, a calcified RVT that was initially thought to be a urinary calculus. This case shows that a calcified RVT might mimic a urinary calculus on conventional ultrasonography and ureteric calculus on noncontrast computed tomography. Subsequent computed tomography angiography disclosed that a calcified RVT caused the imaging findings, thus creating a potentially dangerous clinical pitfall. Hence, it is suggested that the possibility of a RVT needs to be considered in the differential diagnosis whenever one detects an uncommon shape for a urinary calculus.
Constrained variational calculus for higher order classical field theories
Energy Technology Data Exchange (ETDEWEB)
Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn, E-mail: cedricmc@icmat.e, E-mail: mdeleon@icmat.e, E-mail: david.martin@icmat.e [Instituto de Ciencias Matematicas, CSIC-UAM-UC3M-UCM, Serrano 123, 28006 Madrid (Spain)
2010-11-12
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.
Constrained variational calculus for higher order classical field theories
International Nuclear Information System (INIS)
Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn
2010-01-01
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.
Descartes' Calculus of Subnormals: What Might Have Been
Boudreaux, Gregory Mark; Walls, Jess E.
2013-01-01
Rene Descartes' method for finding tangents (equivalently, subnormals) depends on geometric and algebraic properties of a family of circles intersecting a given curve. It can be generalized to establish a calculus of subnormals, an alternative to the calculus of Newton and Leibniz. Here we prove subnormal counterparts of the well-known…
Effects of Clicker Use on Calculus Students' Mathematics Anxiety
Batchelor, John
2015-01-01
This paper reports the results of a survey study of clicker use and mathematics anxiety among students enrolled in an undergraduate calculus course during the Fall 2013 semester. Students in two large lecture sections of calculus completed surveys at the beginning and end of the course. One class used clickers, whereas the other class was taught…
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)
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...
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...
Evaluating the Use of Learning Objects for Improving Calculus Readiness
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…
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, ...
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...
Modelling the Landing of a Plane in a Calculus Lab
Morante, Antonio; Vallejo, Jose A.
2012-01-01
We exhibit a simple model of a plane landing that involves only basic concepts of differential calculus, so it is suitable for a first-year calculus lab. We use the computer algebra system Maxima and the interactive geometry software GeoGebra to do the computations and graphics. (Contains 5 figures and 1 note.)
Restricted diversity of dental calculus methanogens over five centuries, France.
Huynh, Hong T T; Nkamga, Vanessa D; Signoli, Michel; Tzortzis, Stéfan; Pinguet, Romuald; Audoly, Gilles; Aboudharam, Gérard; Drancourt, Michel
2016-05-11
Methanogens are acknowledged archaeal members of modern dental calculus microbiota and dental pathogen complexes. Their repertoire in ancient dental calculus is poorly known. We therefore investigated archaea in one hundred dental calculus specimens collected from individuals recovered from six archaeological sites in France dated from the 14(th) to 19(th) centuries AD. Dental calculus was demonstrated by macroscopic and cone-beam observations. In 56 calculus specimens free of PCR inhibition, PCR sequencing identified Candidatus Methanobrevibacter sp. N13 in 44.6%, Methanobrevibacter oralis in 19.6%, a new Methanomassiliicoccus luminyensis-like methanogen in 12.5%, a Candidatus Nitrososphaera evergladensis-like in one and Methanoculleus bourgensis in one specimen, respectively. One Candidatus Methanobrevibacter sp. N13 dental calculus was further documented by fluorescent in situ hybridization. The prevalence of dental calculus M. oralis was significantly lower in past populations than in modern populations (P = 0.03, Chi-square test). This investigation revealed a previously unknown repertoire of archaea found in the oral cavity of past French populations as reflected in preserved dental calculus.
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…
Success in Introductory Calculus: The Role of High School and Pre-Calculus Preparation
Ayebo, Abraham; Ukkelberg, Sarah; Assuah, Charles
2017-01-01
Calculus at the college level has 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…
Unfolding Semantics of the Untyped λ-Calculus with lectrec-Calculus with letrec
Rochel, J.
2016-01-01
We investigate the relationship between finite terms in lambda-letrec, the lambda calculus with letrec, and the infinite lambda terms they express. We say that a lambda-letrec term expresses a lambda term if the latter can be obtained as an infinite unfolding of the former. Unfolding is the process
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
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
The Initial Conditions of Fractional Calculus
International Nuclear Information System (INIS)
Trigeassou, J. C.; Maamri, N.
2011-01-01
During the past fifty years , Fractional Calculus has become an original and renowned mathematical tool for the modelling of diffusion Partial Differential Equations and the design of robust control algorithms. However, in spite of these celebrated results, some theoretical problems have not yet received a satisfying solution. The mastery of initial conditions, either for Fractional Differential Equations (FDEs) or for the Caputo and Riemann-Liouville fractional derivatives, remains an open research domain. The solution of this fundamental problem, also related to the long range memory property, is certainly the necessary prerequisite for a satisfying approach to modelling and control applications. The fractional integrator and its continuously frequency distributed differential model is a valuable tool for the simulation of fractional systems and the solution of initial condition problems. Indeed, the infinite dimensional state vector of fractional integrators allows the direct generalization to fractional calculus of the theoretical results of integer order systems. After a reminder of definitions and properties related to fractional derivatives and systems, this presentation is intended to show, based on the results of two recent publications [1,2], how the fractional integrator provides the solution of the initial condition problem of FDEs and of Caputo and Riemann-Liouville fractional derivatives. Numerical simulation examples illustrate and validate these new theoretical concepts.
Affine connection form of Regge calculus
Khatsymovsky, V. M.
2016-12-01
Regge action is represented analogously to how the Palatini action for general relativity (GR) as some functional of the metric and a general connection as independent variables represents the Einstein-Hilbert action. The piecewise flat (or simplicial) spacetime of Regge calculus is equipped with some world coordinates and some piecewise affine metric which is completely defined by the set of edge lengths and the world coordinates of the vertices. The conjugate variables are the general nondegenerate matrices on the three-simplices which play the role of a general discrete connection. Our previous result on some representation of the Regge calculus action in terms of the local Euclidean (Minkowsky) frame vectors and orthogonal connection matrices as independent variables is somewhat modified for the considered case of the general linear group GL(4, R) of the connection matrices. As a result, we have some action invariant w.r.t. arbitrary change of coordinates of the vertices (and related GL(4, R) transformations in the four-simplices). Excluding GL(4, R) connection from this action via the equations of motion we have exactly the Regge action for the considered spacetime.
The quantization of Regge calculus
International Nuclear Information System (INIS)
Rocek, M.; Williams, R.M.; Cambridge Univ.
1984-01-01
We discuss the quantization of Regge's discrete description of Einstein's theory of gravitation. We show how the continuum theory emerges in the weak field long wavelength limit. We also discuss reparametrizations and conformal transformations. (orig.)
The calculus of committee composition.
Directory of Open Access Journals (Sweden)
Eric Libby
Full Text Available Modern institutions face the recurring dilemma of designing accurate evaluation procedures in settings as diverse as academic selection committees, social policies, elections, and figure skating competitions. In particular, it is essential to determine both the number of evaluators and the method for combining their judgments. Previous work has focused on the latter issue, uncovering paradoxes that underscore the inherent difficulties. Yet the number of judges is an important consideration that is intimately connected with the methodology and the success of the evaluation. We address the question of the number of judges through a cost analysis that incorporates the accuracy of the evaluation method, the cost per judge, and the cost of an error in decision. We associate the optimal number of judges with the lowest cost and determine the optimal number of judges in several different scenarios. Through analytical and numerical studies, we show how the optimal number depends on the evaluation rule, the accuracy of the judges, the (cost per judge/(cost per error ratio. Paradoxically, we find that for a panel of judges of equal accuracy, the optimal panel size may be greater for judges with higher accuracy than for judges with lower accuracy. The development of any evaluation procedure requires knowledge about the accuracy of evaluation methods, the costs of judges, and the costs of errors. By determining the optimal number of judges, we highlight important connections between these quantities and uncover a paradox that we show to be a general feature of evaluation procedures. Ultimately, our work provides policy-makers with a simple and novel method to optimize evaluation procedures.
Generalized vector calculus on convex domain
Agrawal, Om P.; Xu, Yufeng
2015-06-01
In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.
Elements of stochastic calculus and analysis
Stroock, Daniel W
2018-01-01
This book gives a somewhat unconventional introduction to stochastic analysis. Although most of the material covered here has appeared in other places, this book attempts to explain the core ideas on which that material is based. As a consequence, the presentation is more an extended mathematical essay than a ``definition, lemma, theorem'' text. In addition, it includes several topics that are not usually treated elsewhere. For example, Wiener's theory of homogeneous chaos is discussed, Stratovich integration is given a novel development and applied to derive Wong and Zakai's approximation theorem, and examples are given of the application of Malliavin's calculus to partial differential equations. Each chapter concludes with several exercises, some of which are quite challenging. The book is intended for use by advanced graduate students and research mathematicians who may be familiar with many of the topics but want to broaden their understanding of them.
Quantum stochastic calculus and representations of Lie superalgebras
Eyre, Timothy M W
1998-01-01
This book describes the representations of Lie superalgebras that are yielded by a graded version of Hudson-Parthasarathy quantum stochastic calculus. Quantum stochastic calculus and grading theory are given concise introductions, extending readership to mathematicians and physicists with a basic knowledge of algebra and infinite-dimensional Hilbert spaces. The develpment of an explicit formula for the chaotic expansion of a polynomial of quantum stochastic integrals is particularly interesting. The book aims to provide a self-contained exposition of what is known about Z_2-graded quantum stochastic calculus and to provide a framework for future research into this new and fertile area.
Discrete quantum 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
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.
A generalization of tensor calculus and its application to physics
International Nuclear Information System (INIS)
Ashtekar, A.
1982-01-01
Penrose's abstract index notation and axiomatic introduction of covariant derivatives in tensor calculus is generalized to fields with internal degrees of freedom. The result provides, in particular, an intrinsic formulation of gauge theories without the use of bundles. (author)
Forest Carbon Uptake and the Fundamental Theorem of Calculus
Zobitz, John
2013-01-01
Using the fundamental theorem of calculus and numerical integration, we investigate carbon absorption of ecosystems with measurements from a global database. The results illustrate the dynamic nature of ecosystems and their ability to absorb atmospheric carbon.
Present stage evaluation of Furnas calculus methodology qualification
International Nuclear Information System (INIS)
1987-07-01
This technical note is about the present stage evaluation of FURNAS Calculus Methodology Qualification related to reload licensing process and licensing support of operation questions of Angra 1 NPP concerning transient and Core ThermalHydraulic areas. (Author) [pt
Hermeneutics of differential calculus in eighteenth-century northern Germany.
Blanco, Mónica
2008-01-01
This paper applies comparative textbook analysis to studying the mathematical development of differential calculus in northern German states during the eighteenth century. It begins with describing how the four textbooks analyzed presented the foundations of calculus and continues with assessing the influence each of these foundational approaches exerted on the resolution of problems, such as the determination of tangents and extreme values, and even on the choice of coordinates for both algebraic and transcendental curves.
Improving Student Success in Calculus: A Comparison of Four College Calculus Classes
Bagley, Spencer Franklin
The quality of education in science, technology, engineering, and mathematics (STEM) fields is an issue of particular educational and economic importance, and Calculus I is a linchpin course in STEM major tracks. A national study is currently being conducted examining the characteristics of successful programs in college calculus (CSPCC, 2012). In work related to the CSPCC program, this study examines the effects on student outcomes of four different teaching strategies used at a single institution. The four classes were a traditional lecture, a lecture with discussion, a lecture incorporating both discussion and technology, and an inverted model. This dissertation was guided by three questions: (1) What impact do these four instructional approaches have on students' persistence, beliefs about mathematics, and conceptual and procedural achievement in calculus? (2) How do students at the local institution compare to students in the national database? And (3) How do the similarities and differences in opportunities for learning presented in the four classes contribute to the similarities and differences in student outcomes? Quantitative analysis of surveys and exams revealed few statistically significant differences in outcomes, and students in the inverted classroom often had poorer outcomes than those in other classes. Students in the technology-enhanced class scored higher on conceptual items on the final exam than those in other classes. Comparing to the national database, local students had similar switching rates but less expert-like attitudes and beliefs about mathematics than the national average. Qualitative analysis of focus group interviews, classroom observations, and student course evaluations showed that several implementation issues, some the result of pragmatic constraints, others the result of design choice, weakened affordances provided by innovative features and shrunk the differences between classes. There were substantial differences between the
Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi
2017-01-01
A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy
Dental Calculus and the Evolution of the Human Oral Microbiome.
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.
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
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)
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.
Dental hygiene faculty calibration in the evaluation of calculus detection.
Garland, Kandis V; Newell, Kathleen J
2009-03-01
The purpose of this pilot study was to explore the impact of faculty calibration training on intra- and interrater reliability regarding calculus detection. After IRB approval, twelve dental hygiene faculty members were recruited from a pool of twenty-two for voluntary participation and randomized into two groups. All subjects provided two pre- and two posttest scorings of calculus deposits on each of three typodonts by recording yes or no indicating if they detected calculus. Accuracy and consistency of calculus detection were evaluated using an answer key. The experimental group received three two-hour training sessions to practice a prescribed exploring sequence and technique for calculus detection. Participants immediately corrected their answers, received feedback from the trainer, and reconciled missed areas. Intra- and interrater reliability (pre- and posttest) was determined using Cohen's Kappa and compared between groups using repeated measures (split-plot) ANOVA. The groups did not differ from pre- to posttraining (intrarater reliability p=0.64; interrater reliability p=0.20). Training had no effect on reliability levels for simulated calculus detection in this study. Recommendations for future studies of faculty calibration when evaluating students include using patients for assessing rater reliability, employing larger samples at multiple sites, and assessing the impact on students' attitudes and learning outcomes.
Noninvasive control of dental calculus removal: qualification of two fluorescence methods
Gonchukov, S.; Sukhinina, A.; Bakhmutov, D.; Biryukova, T.
2013-02-01
The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise noninvasive detection of calculus-tooth interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing.
Noninvasive control of dental calculus removal: qualification of two fluorescence methods
International Nuclear Information System (INIS)
Gonchukov, S; Sukhinina, A; Bakhmutov, D; Biryukova, T
2013-01-01
The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise noninvasive detection of calculus-tooth interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing.
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…
Contributions regarding calculus and design of an ultrasonic system used in plasma metallization
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.
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.
The malliavin calculus and related topics
Nualart, David
1995-01-01
The Malliavin calculus (or stochastic calculus of variations) is an infinite-dimensional differential calculus on the Wiener space Originally, it was developed to prove a probabilistic proof to Hörmander's "sum of squares" theorem, but more recently it has found application in a variety of stochastic differential equation problems This monograph presents the main features of the Malliavin calculus and discusses in detail its connection with the anticipating stochastic calculus The author begins by developing analysis on the Wiener space, and then uses this to analyze the regularity of probability laws and to prove Hörmander's theorem Subsequent chapters apply the Malliavin calculus to anticipating stochastic differential equations and to studying the Markov property of solutions to stochastic differential equations with boundary conditions
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.
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.
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
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 ...
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
Bacteria and archaea paleomicrobiology of the dental calculus: a review.
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.
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)
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
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...
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...
Direct evidence of milk consumption from ancient human dental calculus
DEFF Research Database (Denmark)
Warinner, C.; Hendy, J.; Speller, C.
2014-01-01
directly to individuals and their dairy livestock. Here we report the first direct evidence of milk consumption, the whey protein β-lactoglobulin (BLG), preserved in human dental calculus from the Bronze Age (ca. 3000 BCE) to the present day. Using protein tandem mass spectrometry, we demonstrate that BLG...... is a species-specific biomarker of dairy consumption, and we identify individuals consuming cattle, sheep, and goat milk products in the archaeological record. We then apply this method to human dental calculus from Greenland's medieval Norse colonies, and report a decline of this biomarker leading up...
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 ...
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...
The Path to College Calculus: The Impact of High School Mathematics Coursework
Sadler, Philip; Sonnert, Gerhard
2018-01-01
This study addresses a longstanding question among high school mathematics teachers and college mathematics professors: Which is the best preparation for college calculus-- (a) a high level of mastery of mathematics considered preparatory for calculus (algebra, geometry, precalculus) or (b) taking calculus itself in high school? We used a data set…
The Development and Nature of Problem-Solving among First-Semester Calculus Students
Dawkins, Paul Christian; Epperson, James A. Mendoza
2014-01-01
This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate…
The convergence of lattice solutions of linearised Regge calculus
International Nuclear Information System (INIS)
Barrett, J.W.; Williams, R.M.
1988-01-01
Sequences of configurations of linearised Regge calculus converging to plane wave solutions are constructed to illustrate an earlier result on convergence. It is shown that, for these examples, the convergence criterion filters out the solutions which do not satisfy Einstein's equations from those which do. (author)
Fractional Vector Calculus and Fractional Special Function
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.
Multivariate Limits and Continuity: A Survey of Calculus Textbooks.
Thompson, Thomas M.; Wiggins, Kenneth L.
There has been much recent discussion concerning the content of the standard calculus course for students majoring in mathematics and the sciences. Some of this discussion has focused on the available textbooks. One weakness noted in some of these books involves the definitions of limit and continuity for functions of several variables. A…
The history of the calculus and its conceptual development
Boyer, Carl B
1959-01-01
Fluent description of the development of both the integral and differential calculus. Early beginnings in antiquity, medieval contributions, and a century of anticipation lead up to a consideration of Newton and Leibniz, the period of indecison that followed them, and the final rigorous formulation that we know today.
A 3 + 1 Regge calculus model of the Taub universe
International Nuclear Information System (INIS)
Tuckey, P.A.
1988-01-01
The Piran and Williams [1986 Phys. Rev. D 33,1622] second-order formulation of 3 + 1 Regge calculus is used to calculate the evolution of a model of the Taub universe. The model displays qualitatively the correct behaviour, thereby giving some verification of the 3 + 1 formulation. (author)
Peer Conferences in Calculus: The Impact of Systematic Training
Reinholz, Daniel
2017-01-01
This paper describes an intervention for improving the quality of peer assessment conferences in calculus. Although a body of work highlights the learning benefits of peer assessment, few papers have described the nature of student conversations during peer conferences/assessment in detail. This paper provides deeper insight into what those…
Calculus of One and More Variables with Maple
Samkova, Libuse
2012-01-01
This is a guide to using Maple in teaching fundamental calculus of one, two and three variables (limits, derivatives, integrals, etc.), also suitable for Maple beginners. It outlines one of the ways to effective use of computers in the teaching process. It scans advantages and disadvantages of using Maple in relation to students and teacher. The…
Stage of GAN (Grupo de Analise do Nucleo) calculus methodology
International Nuclear Information System (INIS)
Silva, C.F. da.
1987-11-01
This Technical Note presents the stage of GAN Calculus Methodology in areas of Neutronics, Fuel Rod Performance and Fission Products Inventory. Proposals of GAN's members are presented and analyzed for each of these areas and a work schedule is established. (author)
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.
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.
Using Origami Boxes to Explore Concepts of Geometry and Calculus
Wares, Arsalan
2011-01-01
The purpose of this classroom note is to provide an example of how a simple origami box can be used to explore important concepts of geometry and calculus. This article describes how an origami box can be folded, then it goes on to describe how its volume and surface area can be calculated. Finally, it describes how the box could be folded to…
An Investigation of Calculus Learning Using Factorial Modeling.
Dick, Thomas P.; Balomenos, Richard H.
Structural covariance models that would explain the correlations observed among mathematics achievement and participation measures and related cognitive and affective variables were developed. A sample of college calculus students (N=268; 124 females and 144 males) was administered a battery of cognitive tests (including measures of spatial-visual…
SOME CONSIDERATIONS REGARDING THE STRENGTH CALCULUS OF A LATHE TOOL
Directory of Open Access Journals (Sweden)
Catălin ROŞU
2013-05-01
Full Text Available In this paper a strength calculus of a lathe tool is made. The main purpose of this study is to determineequivalent stress relations that can be useful for an engineer in the design situation. The simplifying assumptionsand the equivalent stress relations are presented from an original point of view.
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.
Formalization of the Integral Calculus in the PVS Theorem Prover
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.
Methods of calculus for neutron spectrometry in proportional counters
International Nuclear Information System (INIS)
Butragueno, J.L.; Blazquez, J.B.; Barrado, J.M.
1976-01-01
Response functions for cylindrical proportional counters with hidrogenated gases have been determined, taking in account only wall effect, by means of two independent calculus methods. One of them is a Montecarlo application and the other one analytical at all. Results of both methods have been compared. (author) [es
Methods of calculus for neutron spectrometry in proportional counters
International Nuclear Information System (INIS)
Butragueno Casado, J.L.; Blazquez Martinez, J.B.; Barrado Menendez, J.M.
1976-01-01
Response functions for cylindrical proportional counters with hydrogenated gases have been determined, taking in account only wall effect, by means of two independent calculus methods. One of them is a Monte Carlo application and the other one analytica at all. Results of both methods have been compared. (Author)
Electron microscopy of octacalcium phosphate in the dental calculus.
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.
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
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
Decidable Fragments of a Higher Order Calculus with Locations
DEFF Research Database (Denmark)
Bundgaard, Mikkel; Godskesen, Jens Christian; Huttel, Hans
2009-01-01
Homer is a higher order process calculus with locations. In this paper we study Homer in the setting of the semantic finite control property, which is a finite reachability criterion that implies decidability of barbed bisimilarity. We show that strong and weak barbed bisimilarity are undecidable...
Atypical presentation of an enormous vesical calculus: A case report
African Journals Online (AJOL)
A.T. Lawal
2016-05-20
May 20, 2016 ... Abstract. Giant vesical calculi, though rare, are still encountered in contemporary urologic practice despite the increased availability, accessibility, and affordability of modern imaging modalities and urologic care. This is the case report of a middle-aged man with an unusually large vesical calculus.
Bladder calculus resulting from an intravesical translocation of ...
African Journals Online (AJOL)
Although perforation of the uterus by an intrauterine contraceptive device (IUCD) is commonly encountered, intravesical translocation and secondary calculus formation is a very rare complication.We report a case of a 60-year old multiparous woman in whom an intrauterine contraceptive Copper-T device inserted 12 years ...
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...
Unusual giant prostatic urethral calculus | Bello | Journal of Surgical ...
African Journals Online (AJOL)
Giant vesico-prostatic urethral calculus is uncommon. Urethral stones rarely form primarily in the urethra, and they are usually associated with urethral strictures, posterior urethral valve or diverticula. We report a case of a 32-year-old man with giant vesico-prostatic (collar-stud) urethral stone presenting with sepsis and ...
Relation of Spatial Skills to Calculus Proficiency: A Brief Report
Cromley, Jennifer G.; Booth, Julie L.; Wills, Theodore W.; Chang, Briana L.; Tran, Nhi; Madeja, Michael; Shipley, Thomas F.; Zahner, William
2017-01-01
Spatial skills have been shown in various longitudinal studies to be related to multiple science, technology, engineering, and math (STEM) achievement and retention. The specific nature of this relation has been probed in only a few domains, and has rarely been investigated for calculus, a critical topic in preparing students for and in STEM…
Inquiry-Based Learning of Transcendental Functions in Calculus
Ekici, Celil; Gard, Andrew
2017-01-01
In a series of group activities supplemented with independent explorations and assignments, calculus students investigate functions similar to their own derivatives. Graphical, numerical, and algebraic perspectives are suggested, leading students to develop deep intuition into elementary transcendental functions even as they lay the foundation for…
Calculus of Elementary Functions, Part IV. Teacher's Commentary. Preliminary Edition.
Herriot, Sarah T.; And Others
This teacher's guide is designed for use with the SMSG textbook "Calculus of Elementary Functions." It contains solutions to exercises found in Chapter 9, Integration Theory and Technique; Chapter 10, Simple Differential Equations; Appendix 5, Area and Integral; Appendix 6; Appendix 7, Continuity Theory; and Appendix 8, More About…
Case Report: Giant Vesical Calculus | Aliyu | Nigerian Journal of ...
African Journals Online (AJOL)
RESULTS: The calculus weighed 1.6kg and measured 13cm X 9.5cm X 9.2cm in length breadth and height; and contained calcium carbonate, calcium oxalate, magnesium phosphate and uric acid. It was a complex stone, sticking to the hypertrophied bladder wall. A biopsy of the bladder mucosa revealed no malignancy.
A metric model of lambda calculus with guarded recursion
DEFF Research Database (Denmark)
Birkedal, Lars; Schwinghammer, Jan; Støvring, Kristian
2010-01-01
We give a model for Nakano’s typed lambda calculus with guarded recursive definitions in a category of metric spaces. By proving a computational adequacy result that relates the interpretation with the operational semantics, we show that the model can be used to reason about contextual equivalence....
A Technical Approach in Graphical Study of Calculus Using Maple ...
African Journals Online (AJOL)
We immediately saw this as an opportunity to motivate calculus concepts by using graphical representations and animations. Animation provides motivation, reinforcement, and credibility when used properly. The paper therefore describes some of the major challenges that were encountered while introducing this technique ...
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.
Judson, Thomas W.; Nishimori, Toshiyuki
2005-01-01
In this study we investigated above-average high school calculus students from Japan and the United States in order to determine any differences in their conceptual understanding of calculus and their ability to use algebra to solve traditional calculus problems. We examined and interviewed 18 Calculus BC students in the United States and 26…
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,
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
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 ...
The impacts of gingivitis and calculus on Thai children's quality of life.
Krisdapong, Sudaduang; Prasertsom, Piyada; Rattanarangsima, Khanit; Sheiham, Aubrey; Tsakos, Georgios
2012-09-01
To assess associations of socio-demographic, behavioural and the extent of gingivitis and calculus with oral health-related quality of life (OHRQoL) in nationally representative samples of 12- and 15-year-old Thai children. In the Thailand National Oral Health Survey, 1,063 twelve-year olds and 811 fifteen-year olds were clinically examined and interviewed for OHRQoL using the Child-OIDP and OIDP indices, respectively, and completed a behavioural questionnaire. We assessed associations of condition-specific impacts (CS-impacts) with gingivitis and calculus, adjusted for socio-demographic and behavioural factors. Gingivitis and calculus were highly prevalent: 79.3% in 12-year and 81.5% in 15-year olds. CS-impacts relating to calculus and/or gingivitis were reported by 26.0% of 12-year and 29.6% of 15-year olds. Except for calculus without gingivitis, calculus and/or gingivitis in any form was significantly related to any level of CS-impacts. At a moderate or higher level of CS-impacts, there were significant relationships with extensive calculus and/or gingivitis in 12-year olds and for extensive gingivitis and gingivitis without calculus in 15-year olds. Gingivitis was generally associated with any level of CS-impacts attributed to calculus and/or gingivitis. CS-impacts were related more to gingivitis than to calculus. © 2012 John Wiley & Sons A/S.
The Impact of Taking a College Pre-Calculus Course on Students' College Calculus Performance
Sonnert, Gerhard; Sadler, Philip M.
2014-01-01
Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and…
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
Geometric calculus according to the Ausdehnungslehre of H. Grassmann
Peano, Giuseppe
2000-01-01
Calcolo Geometrico, G. Peano's first publication in mathematical logic, is a model of expository writing, with a significant impact on 20th century mathematics. Kannenberg's lucid and crisp translation, Geometric Calculus, will appeal to historians of mathematics, researchers, graduate students, and general readers interested in the foundations of mathematics and the development of a formal logical language. In Chapter IX, with the innocent-sounding title "Transformations of a linear system," one finds the crown jewel of the book: Peano's axiom system for a vector space, the first-ever presentation of a set of such axioms. The very wording of the axioms (which Peano calls "definitions") has a remarkably modern ring, almost like a modern introduction to linear algebra. Peano also presents the basic calculus of set operation, introducing the notation for 'intersection,' 'union,' and 'element of,' many years before it was accepted. Despite its uniqueness, Calcolo Geometrico has been strangely neglected by histor...
On the combinatorial foundations of Regge-calculus
International Nuclear Information System (INIS)
Budach, L.
1989-01-01
Lipschitz-Killing curvatures of piecewise flat spaces are combinatorial analogues of Lipschitz-Killing curvatures of Riemannian manifolds. In the following paper rigorous combinatorial representations and proofs of all basic results for Lipschitz-Killing curvatures not using analytic arguments are given. The principal tools for an elementary representation of Regge calculus can be developed by means of basic properties of dihedral angles. (author)
Preservation of the metaproteome: variability of protein preservation in ancient dental calculus.
Mackie, Meaghan; Hendy, Jessica; Lowe, Abigail D; Sperduti, Alessandra; Holst, Malin; Collins, Matthew J; Speller, Camilla F
2017-01-01
Proteomic analysis of dental calculus is emerging as a powerful tool for disease and dietary characterisation of archaeological populations. To better understand the variability in protein results from dental calculus, we analysed 21 samples from three Roman-period populations to compare: 1) the quantity of extracted protein; 2) the number of mass spectral queries; and 3) the number of peptide spectral matches and protein identifications. We found little correlation between the quantity of calculus analysed and total protein identifications, as well as no systematic trends between site location and protein preservation. We identified a wide range of individual variability, which may be associated with the mechanisms of calculus formation and/or post-depositional contamination, in addition to taphonomic factors. Our results suggest dental calculus is indeed a stable, long-term reservoir of proteins as previously reported, but further systematic studies are needed to identify mechanisms associated with protein entrapment and survival in dental calculus.
Summability calculus a comprehensive theory of fractional finite sums
Alabdulmohsin, Ibrahim M
2018-01-01
This book develops the foundations of "summability calculus", which is a comprehensive theory of fractional finite sums. It fills an important gap in the literature by unifying and extending disparate historical results. It also presents new material that has not been published before. Importantly, it shows how the study of fractional finite sums benefits from and contributes to many areas of mathematics, such as divergent series, numerical integration, approximation theory, asymptotic methods, special functions, series acceleration, Fourier analysis, the calculus of finite differences, and information theory. As such, it appeals to a wide audience of mathematicians whose interests include the study of special functions, summability theory, analytic number theory, series and sequences, approximation theory, asymptotic expansions, or numerical methods. Richly illustrated, it features chapter summaries, and includes numerous examples and exercises. The content is mostly developed from scratch using only undergr...
Semiclassical regime of Regge calculus and spin foams
International Nuclear Information System (INIS)
Bianchi, Eugenio; Satz, Alejandro
2009-01-01
Recent attempts to recover the graviton propagator from spin foam models involve the use of a boundary quantum state peaked on a classical geometry. The question arises whether beyond the case of a single simplex this suffices for peaking the interior geometry in a semiclassical configuration. In this paper we explore this issue in the context of quantum Regge calculus with a general triangulation. Via a stationary phase approximation, we show that the boundary state succeeds in peaking the interior in the appropriate configuration, and that boundary correlations can be computed order by order in an asymptotic expansion. Further, we show that if we replace at each simplex the exponential of the Regge action by its cosine-as expected from the semiclassical limit of spin foam models-then the contribution from the sign-reversed terms is suppressed in the semiclassical regime and the results match those of conventional Regge calculus
Resolution of Localized Chronic Periodontitis Associated with Longstanding Calculus Deposits
Lai, Pin-Chuang; Walters, John D.
2014-01-01
This report, which is based on nonstandardized serial radiographs obtained over a period of 15 years, documents a case of localized chronic periodontitis associated with progressive deposition of calculus on the distal aspect of a mandibular second molar. The site was treated by scaling and root planing, followed by a course of adjunctive systemic azithromycin. Treatment yielded favorable reductions in probing depth and clinical inflammation, leaving only few isolated sites with pockets no de...
Bunny hops: using multiplicities of zeroes in calculus for graphing
Miller, David; Deshler, Jessica M.; Hansen, Ryan
2016-07-01
Students learn a lot of material in each mathematics course they take. However, they are not always able to make meaningful connections between content in successive mathematics courses. This paper reports on a technique to address a common topic in calculus I courses (intervals of increase/decrease and concave up/down) while also making use of students' pre-existing knowledge about the behaviour of functions around zeroes based on multiplicities.
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.)
Extended finite operator calculus as an example of algebraization of analysis
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...
Ideas of Physical Forces and Differential Calculus in Ancient India
Girish, T. E.; Nair, C. Radhakrishnan
2010-01-01
We have studied the context and development of the ideas of physical forces and differential calculus in ancient India by studying relevant literature related to both astrology and astronomy since pre-Greek periods. The concept of Naisargika Bala (natural force) discussed in Hora texts from India is defined to be proportional to planetary size and inversely related to planetary distance. This idea developed several centuries prior to Isaac Newton resembles fundamental physical forces in natur...
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
Reliability of recordings of subgingival calculus detected using an ultrasonic device.
Corraini, Priscila; López, Rodrigo
2015-04-01
To assess the intra-examiner reliability of recordings of subgingival calculus detected using an ultrasonic device, and to investigate the influence of subject-, tooth- and site-level factors on the reliability of these subgingival calculus recordings. On two occasions, within a 1-week interval, 147 adult periodontitis patients received a full-mouth clinical periodontal examination by a single trained examiner. Duplicate subgingival calculus recordings, in six sites per tooth, were obtained using an ultrasonic device for calculus detection and removal. Agreement was observed in 65 % of the 22,584 duplicate subgingival calculus recordings, ranging 45 % to 83 % according to subject. Using hierarchical modeling, disagreements in the subgingival calculus duplicate recordings were more likely in all other sites than the mid-buccal, and in sites harboring supragingival calculus. Disagreements were less likely in sites with PD ≥ 4 mm and with furcation involvement ≥ degree 2. Bleeding on probing or suppuration did not influence the reliability of subgingival calculus. At the subject-level, disagreements were less likely in patients presenting with the highest and lowest extent categories of the covariate subgingival calculus. The reliability of subgingival calculus recordings using the ultrasound technology is reasonable. The results of the present study suggest that the reliability of subgingival calculus recordings is not influenced by the presence of inflammation. Moreover, subgingival calculus can be more reliably detected using the ultrasound device at sites with higher need for periodontal therapy, i.e., sites presenting with deep pockets and premolars and molars with furcation involvement.
Calculation of parton fragmentation functions from jet calculus: gluon applications
International Nuclear Information System (INIS)
Lassila, K.E.; Ng, A.
1985-01-01
A method is presented for calculation of general parton fragmentation functions based on jet calculus plus meson and baryon wave functions. Results for gluon fragmentation into mesons and baryons are discussed and related to recent information on upsilon decay into gluons. The expressions derived can be used directly in e + e - cross section predictions and will need to be folded in with baryon parton distribution functions when used in p-barp collisions. (author)
Calculation of relativistic model stars using Regge calculus
International Nuclear Information System (INIS)
Porter, J.
1987-01-01
A new approach to the Regge calculus, developed in a previous paper, is used in conjunction with the velocity potential version of relativistic fluid dynamics due to Schutz [1970, Phys. Rev., D, 2, 2762] to calculate relativistic model stars. The results are compared with those obtained when the Tolman-Oppenheimer-Volkov equations are solved by other numerical methods. The agreement is found to be excellent. (author)
Malliavin Calculus With Applications to Stochastic Partial Differential Equations
Sanz-Solé, Marta
2005-01-01
Developed in the 1970s to study the existence and smoothness of density for the probability laws of random vectors, Malliavin calculus--a stochastic calculus of variation on the Wiener space--has proven fruitful in many problems in probability theory, particularly in probabilistic numerical methods in financial mathematics.This book presents applications of Malliavin calculus to the analysis of probability laws of solutions to stochastic partial differential equations driven by Gaussian noises that are white in time and coloured in space. The first five chapters introduce the calculus itself
Rethinking the Privacy Calculus: On the Role of Dispositional Factors and Affect
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 ...
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....
Laser ablation of dental calculus at 400 nm using a Ti:sapphire laser
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.
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)
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.)
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...
Analysis of Errors and Misconceptions in the Learning of Calculus by Undergraduate Students
Muzangwa, Jonatan; Chifamba, Peter
2012-01-01
This paper is going to analyse errors and misconceptions in an undergraduate course in Calculus. The study will be based on a group of 10 BEd. Mathematics students at Great Zimbabwe University. Data is gathered through use of two exercises on Calculus 1&2.The analysis of the results from the tests showed that a majority of the errors were due…
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 ...
[Percentage of uric acid calculus and its metabolic character in Dongjiang River valley].
Chong, Hong-Heng; An, Geng
2009-02-15
To study the percentage of uric acid calculus in uroliths and its metabolic character in Dongjiang River valley. To analyze the chemical composition of 290 urinary stones by infrared (IR) spectroscopy and study the ratio changes of uric acid calculus. Uric acid calculus patients and healthy people were studied. Personal characteristics, dietary habits were collected. Conditional logistic regression was used for data analysis and studied the dietary risk factors of uric acid calculus. Patients with uric acid calculus, calcium oxalate and those without urinary calculus were undergone metabolic evaluation analysis. The results of uric acid calculus patients compared to another two groups to analysis the relations between the formation of uric acid calculus and metabolism factors. Uric acid calculi were found in 53 cases (18.3%). The multiple logistic regression analysis suggested that low daily water intake, eating more salted and animal food, less vegetable were very closely associated with uric acid calculus. Comparing to calcium oxalate patients, the urine volume, the value of pH, urine calcium, urine oxalic acid were lower, but uric acid was higher than it. The value of pH, urine oxalic acid and citric acid were lower than them, but uric acid and urine calcium were higher than none urinary calculus peoples. Blood potassium and magnesium were lower than them. The percentage of uric acid stones had obvious advanced. Less daily water intake, eating salted food, eating more animal food, less vegetables and daily orange juice intake, eating sea food are the mainly dietary risk factors to the formation of uric acid calculus. Urine volume, the value of pH, citric acid, urine calcium, urine uric acid and the blood natrium, potassium, magnesium, calcium, uric acid have significant influence to the information of uric acid stones.
Using Dynamic Tools to Develop an Understanding of the Fundamental Ideas of Calculus
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…
The Role of Cognitive Ability and Preferred Mode of Processing in Students' Calculus Performance
Haciomeroglu, Erhan Selcuk
2015-01-01
The present study sought to design calculus tasks to determine students' preference for visual or analytic processing as well as examine the role of preferred mode of processing in calculus performance and its relationship to spatial ability and verbal-logical reasoning ability. Data were collected from 150 high school students who were enrolled…
The Association of Precollege Use of Calculators with Student Performance in College Calculus
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…
The development and nature of problem-solving among first-semester calculus students
Dawkins, Paul Christian; Mendoza Epperson, James A.
2014-08-01
This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate this blended instruction as a local representative of the US calculus reform movements that helped foster it. These reform movements tended to emphasize problem-solving as well as multiple mathematical registers and quantitative modelling. Our statistical analysis reveals the influence of the blended traditional/reform calculus instruction on students' ability to solve calculus-related, non-routine problems through repeated measures over the semester. The calculus instruction in this study significantly improved students' performance on non-routine problems, though performance improved more regarding strategies and accuracy than it did for drawing conclusions and providing justifications. We identified problem-solving behaviours that characterized top performance or attrition in the course. Top-performing students displayed greater algebraic proficiency, calculus skills, and more general heuristics than their peers, but overused algebraic techniques even when they proved cumbersome or inappropriate. Students who subsequently withdrew from calculus often lacked algebraic fluency and understanding of the graphical register. The majority of participants, when given a choice, relied upon less sophisticated trial-and-error approaches in the numerical register and rarely used the graphical register, contrary to the goals of US calculus reform. We provide explanations for these patterns in students' problem-solving performance in view of both their preparation for university calculus and the courses' assessment structure, which preferentially rewarded algebraic reasoning. While instruction improved students' problem
Resolution of Localized Chronic Periodontitis Associated with Longstanding Calculus Deposits
Directory of Open Access Journals (Sweden)
Pin-Chuang Lai
2014-01-01
Full Text Available This report, which is based on nonstandardized serial radiographs obtained over a period of 15 years, documents a case of localized chronic periodontitis associated with progressive deposition of calculus on the distal aspect of a mandibular second molar. The site was treated by scaling and root planing, followed by a course of adjunctive systemic azithromycin. Treatment yielded favorable reductions in probing depth and clinical inflammation, leaving only few isolated sites with pockets no deeper than 4 mm. Two years after completion of active treatment, there was radiographic evidence of increased bone density distal to the second molar.
Resolution of localized chronic periodontitis associated with longstanding calculus deposits.
Lai, Pin-Chuang; Walters, John D
2014-01-01
This report, which is based on nonstandardized serial radiographs obtained over a period of 15 years, documents a case of localized chronic periodontitis associated with progressive deposition of calculus on the distal aspect of a mandibular second molar. The site was treated by scaling and root planing, followed by a course of adjunctive systemic azithromycin. Treatment yielded favorable reductions in probing depth and clinical inflammation, leaving only few isolated sites with pockets no deeper than 4 mm. Two years after completion of active treatment, there was radiographic evidence of increased bone density distal to the second molar.
Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations
Mohamed, Mamdouh S.
2017-05-23
A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.
Comment on “Variational Iteration Method for Fractional Calculus Using He’s Polynomials”
Directory of Open Access Journals (Sweden)
Ji-Huan He
2012-01-01
boundary value problems. This note concludes that the method is a modified variational iteration method using He’s polynomials. A standard variational iteration algorithm for fractional differential equations is suggested.
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)
Numerical Simulation of Antennae by Discrete Exterior Calculus
International Nuclear Information System (INIS)
Xie Zheng; Ye Zheng; Ma Yujie
2009-01-01
Numerical simulation of antennae is a topic in computational electromagnetism, which is concerned with the numerical study of Maxwell equations. By discrete exterior calculus and the lattice gauge theory with coefficient R, we obtain the Bianchi identity on prism lattice. By defining an inner product of discrete differential forms, we derive the source equation and continuity equation. Those equations compose the discrete Maxwell equations in vacuum case on discrete manifold, which are implemented on Java development platform to simulate the Gaussian pulse radiation on antennaes. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Assessment of Peer-Led Team Learning in Calculus I: A Five-Year Study
Merkel, John Conrad; Brania, Abdelkrim
2015-01-01
This five-year study of the peer-led team learning (PLTL) paradigm examined its implementation in a Calculus I course at an all-male HBCU institution. For this study we set up a strong control group and measured the effect of PLTL in the teaching and learning of Calculus I through two points of measure: retention and success rates and learning…
Yaacob, Yuzita; Wester, Michael; Steinberg, Stanly
2010-01-01
This paper presents a prototype of a computer learning assistant ILMEV (Interactive Learning-Mathematica Enhanced Vector calculus) package with the purpose of helping students to understand the theory and applications of integration in vector calculus. The main problem for students using Mathematica is to convert a textbook description of a…
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.
Effect of non-functional teeth on accumulation of supra-gingival calculus in children.
Ashkenazi, M; Miller, R; Levin, L
2012-10-01
To evaluate the occurrence of supra-gingival calculus in children aged 6-9 years with disuse conditions such as: presence of dental pain, open-bite or erupting teeth. A cohort of 327 children aged 7.64±2.12 (range: 6-9) years (45% girls) were screened for presence of supra-gingival calculus in relation to open bite, erupting teeth and dental pain. Presence of dental calculus was evaluated dichotomically in the buccal, palatinal/lingual and occlusal surfaces. Plaque index (PI) and gingival index (GI) were also evaluated. Supra-gingival calculus was found in 15.9% of the children mainly in the mandibular incisors. Children aged 6-7 years had a higher prevalence of calculus as compared to children aged 7-8 years (23% vs. 13.5%, p=0.057) or 8-9 years (23% vs. 12.4%, p=0.078), respectively. No statistical relation was found between plaque and gingival indices and presence of calculus. The prevalence of calculus among children with openbite was significantly higher than that of children without open-bite (29.4% vs. 10.7%, p=0.0006, OR=3.489). The prevalence of calculus among children with erupting teeth in their oral cavity was higher than that of children without erupting teeth (17.7% vs. 9%, respectively, p=0.119). No statistical correlation was found between presence of dental pain and calculus (15.4% vs. 15.9%; p=0.738). Accumulation of calculus in children aged 6-10 years was found mainly in the mandibular incisors, decreased with age and was correlated with open-bite.
Solitary main pancreatic ductal calculus of possible biliary origin causing acute pancreatitis.
Chaparala, Ramakrishna Prasad Chowdary; Patel, Rafiuddin; Guthrie, James Ahsley; Davies, Mervyn Huw; Guillou, Pierre J; Menon, Krishna V
2005-09-10
Pancreatic ductal calculi are most often associated with chronic pancreatitis. Radiological features of chronic pancreatitis are readily evident in the presence of these calculi. However, acute pancreatitis due to a solitary main pancreatic ductal calculus of biliary origin is rare. A 59-year-old man presented with a first episode of acute pancreatitis. Contrast enhanced computerized tomography (CT) scan and endoscopic retrograde cholangiopancreatography (ERCP) revealed a calculus in the main pancreatic duct in the head of the pancreas causing acute pancreatitis. There were no features suggestive of chronic pancreatitis on CT scanning. The episode acute pancreatitis was managed conservatively. ERCP extraction of the calculus failed as the stone was impacted in the main pancreatic duct resulting in severe acute pancreatitis. Once this resolved, a transduodenal exploration and extraction of the pancreatic ductal calculus was performed successfully. Crystallographic analysis revealed the composition of the calculus was different to that seen in chronic pancreatitis, but more in keeping with a calculus of biliary origin. This could be explained by migration of the biliary calculus via the common channel into the main pancreatic duct. Following the operation the patient made an uneventful recovery and was well at two-year follow up. Acute pancreatitis due to a solitary main pancreatic ductal calculus of biliary origin is rare. Failing endoscopic extraction, transduodenal exploration and extraction is a safe option after resolution of acute pancreatitis.
A Useful Demonstration of Calculus in a Physics High School Laboratory
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…
Site specific mineral composition and microstructure of human supra-gingival dental calculus.
Hayashizaki, Junko; Ban, Seiji; Nakagaki, Haruo; Okumura, Akihiko; Yoshii, Saori; Robinson, Colin
2008-02-01
Dental calculus has been implicated in the aetiology of several periodontal conditions. Its prevention and removal are therefore desirable clinical goals. While it is known that calculus is very variable in chemical composition, crystallinity and crystallite size little is known about site specific variability within a dentition and between individuals. With this in mind, a study was undertaken to investigate the comparative site specific nature and composition of human dental supra-gingival dental calculus obtained from 66 male patients visiting for their dental check-up using fluorescent X-ray spectroscopy, X-ray diffractometry and Fourier transform infrared spectroscopy. The supra-gingival dental calculus formed on the lingual surfaces of lower anterior teeth and the buccal surfaces of upper molar teeth were classified into four types based on calcium phosphate phases present. There was significant difference in composition of the crystal phase types between lower and upper teeth (pdental calculus on anterior or molar teeth of all samples. The degree of crystallinity of dental calculus formed on the upper molar teeth was higher than that formed on the lower anterior teeth (pdental calculus formed on the lower anterior teeth were higher than on upper molar teeth (pdental supra-gingival dental calculus is related to its location in the mouth.
Implementing Projects in Calculus on a Large Scale at the University of South Florida
Fox, Gordon A.; Campbell, Scott; Grinshpan, Arcadii; Xu, Xiaoying; Holcomb, John; Bénéteau, Catherine; Lewis, Jennifer E.; Ramachandran, Kandethody
2017-01-01
This paper describes the development of a program of project-based learning in Calculus courses at a large urban research university. In this program, students developed research projects in consultation with a faculty advisor in their major, and supervised by their calculus instructors. Students wrote up their projects in a prescribed format…
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 ...
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.
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...
Generalizing Automath by means of a lambda-typed lambda calculus
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
A giant dumbbell shaped vesico-prostatic urethral calculus: a case report and review of literature.
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.
Factors Associated with Success in a Calculus Course: An Examination of Personal Variables
Ubuz, Behiye
2011-01-01
This study examined relationships between students' personal variables (gender, prior achievements, age and academic major) and their success in the first year undergraduate calculus course. The study sample consisted of 59 first year undergraduate students taking Math 154 Calculus II course. A written test about integral, sequence and series…
Improving Student Learning of Calculus Topics via Modified Just-in-Time Teaching Methods
Natarajan, Rekha; Bennett, Andrew
2014-01-01
Although the use of traditional just-in-time teaching techniques has long been viewed positively by students and instructors in undergraduate calculus courses, past studies in this area have not addressed gains in student achievement with respect to specific calculus topics. This paper investigates the latter by administering modified just-in-time…
Lue, Yuang-Tswong
2015-01-01
This study was to design, develop, and investigate instructional units for freshmen with low academic achievement to learn before they study calculus. Because the concepts, skills, and theories of function are fundamental for the calculus course but the below average students were not familiar with the basic knowledge and ability in function when…
What Does It Mean for a Student to Understand the First-Year Calculus? Perspectives of 24 Experts
Sofronas, Kimberly S.; DeFranco, Thomas C.; Vinsonhaler, Charles; Gorgievski, Nicholas; Schroeder, Larissa; Hamelin, Chris
2011-01-01
This article presents the views of 24 nationally recognized authorities in the field of mathematics, and in particular the calculus, on student understanding of the first-year calculus. A framework emerged that includes four overarching end goals for understanding of the first-year calculus: (a) mastery of the fundamental concepts and-or skills of…
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.
Fractional calculus model of electrical impedance applied to human skin.
Vosika, Zoran B; Lazovic, Goran M; Misevic, Gradimir N; Simic-Krstic, Jovana B
2013-01-01
Fractional calculus is a mathematical approach dealing with derivatives and integrals of arbitrary and complex orders. Therefore, it adds a new dimension to understand and describe basic nature and behavior of complex systems in an improved way. Here we use the fractional calculus for modeling electrical properties of biological systems. We derived a new class of generalized models for electrical impedance and applied them to human skin by experimental data fitting. The primary model introduces new generalizations of: 1) Weyl fractional derivative operator, 2) Cole equation, and 3) Constant Phase Element (CPE). These generalizations were described by the novel equation which presented parameter [Formula: see text] related to remnant memory and corrected four essential parameters [Formula: see text] We further generalized single generalized element by introducing specific partial sum of Maclaurin series determined by parameters [Formula: see text] We defined individual primary model elements and their serial combination models by the appropriate equations and electrical schemes. Cole equation is a special case of our generalized class of models for[Formula: see text] Previous bioimpedance data analyses of living systems using basic Cole and serial Cole models show significant imprecisions. Our new class of models considerably improves the quality of fitting, evaluated by mean square errors, for bioimpedance data obtained from human skin. Our models with new parameters presented in specific partial sum of Maclaurin series also extend representation, understanding and description of complex systems electrical properties in terms of remnant memory effects.
Fractional calculus model of electrical impedance applied to human skin.
Directory of Open Access Journals (Sweden)
Zoran B Vosika
Full Text Available Fractional calculus is a mathematical approach dealing with derivatives and integrals of arbitrary and complex orders. Therefore, it adds a new dimension to understand and describe basic nature and behavior of complex systems in an improved way. Here we use the fractional calculus for modeling electrical properties of biological systems. We derived a new class of generalized models for electrical impedance and applied them to human skin by experimental data fitting. The primary model introduces new generalizations of: 1 Weyl fractional derivative operator, 2 Cole equation, and 3 Constant Phase Element (CPE. These generalizations were described by the novel equation which presented parameter [Formula: see text] related to remnant memory and corrected four essential parameters [Formula: see text] We further generalized single generalized element by introducing specific partial sum of Maclaurin series determined by parameters [Formula: see text] We defined individual primary model elements and their serial combination models by the appropriate equations and electrical schemes. Cole equation is a special case of our generalized class of models for[Formula: see text] Previous bioimpedance data analyses of living systems using basic Cole and serial Cole models show significant imprecisions. Our new class of models considerably improves the quality of fitting, evaluated by mean square errors, for bioimpedance data obtained from human skin. Our models with new parameters presented in specific partial sum of Maclaurin series also extend representation, understanding and description of complex systems electrical properties in terms of remnant memory effects.
Direct evidence of milk consumption from ancient human dental calculus.
Warinner, C; Hendy, J; Speller, C; Cappellini, E; Fischer, R; Trachsel, C; Arneborg, J; Lynnerup, N; Craig, O E; Swallow, D M; Fotakis, A; Christensen, R J; Olsen, J V; Liebert, A; Montalva, N; Fiddyment, S; Charlton, S; Mackie, M; Canci, A; Bouwman, A; Rühli, F; Gilbert, M T P; Collins, M J
2014-11-27
Milk is a major food of global economic importance, and its consumption is regarded as a classic example of gene-culture evolution. Humans have exploited animal milk as a food resource for at least 8500 years, but the origins, spread, and scale of dairying remain poorly understood. Indirect lines of evidence, such as lipid isotopic ratios of pottery residues, faunal mortality profiles, and lactase persistence allele frequencies, provide a partial picture of this process; however, in order to understand how, where, and when humans consumed milk products, it is necessary to link evidence of consumption directly to individuals and their dairy livestock. Here we report the first direct evidence of milk consumption, the whey protein β-lactoglobulin (BLG), preserved in human dental calculus from the Bronze Age (ca. 3000 BCE) to the present day. Using protein tandem mass spectrometry, we demonstrate that BLG is a species-specific biomarker of dairy consumption, and we identify individuals consuming cattle, sheep, and goat milk products in the archaeological record. We then apply this method to human dental calculus from Greenland's medieval Norse colonies, and report a decline of this biomarker leading up to the abandonment of the Norse Greenland colonies in the 15(th) century CE.
Robotic-assisted laparoscopic management of a caliceal diverticular calculus
Torricelli, Fabio Cesar Miranda; Batista, Lucas T; Colombo, Jose Roberto; Coelho, Rafael Ferreira
2014-01-01
Purpose To report the first case of robotic-assisted laparoscopic management of a symptomatic caliceal diverticular calculus and review the literature on laparoscopic treatment for this condition. Case report A 33-year-old obese woman with a 2×1 cm calculus within an anterior caliceal diverticulum located in the middle pole of the left kidney was referred to our service. She had already undergone two flexible ureterorenoscopies without success. We considered that a percutaneous approach would be very challenging due to stone location, thus we elected to perform a robotic-assisted laparoscopic procedure for stone removal and diverticulum fulguration. The procedure was uneventfully performed with no intraoperative or postoperative complications. The patient was discharged from the hospital on the second postoperative day and after 1.5 years of follow-up she is asymptomatic with no recurrence. Conclusions The robotic-assisted laparoscopic approach to caliceal diverticular calculi is feasible and safe, providing one more option for treatment of stones in challenging locations. PMID:25188925
Putting Differentials Back into Calculus
Dray, Tevian; Manogue, Corrine A.
2010-01-01
We argue that the use of differentials in introductory calculus courses is useful and provides a unifying theme, leading to a coherent view of the calculus. Along the way, we meet several interpretations of differentials, some better than others.
On new applications of fractional calculus
Directory of Open Access Journals (Sweden)
Shilpi Jain
2019-07-01
Full Text Available In the present paper author derive a number of integrals concerning various special functions which are applications of the one of Osler result. Osler provided extensions to the familiar Leibniz rule for the nth derivative of product of two functions.
CONSIDERATIONS ABOUT APPLICATION OF GRAPHICAL CALCULUS
Directory of Open Access Journals (Sweden)
Anghel Alina Angelica
2015-06-01
Full Text Available Some typical engineering problems can be solved using graphical methods in an integrated way for knowledge of design, mathematics, mechanics and physics. This paper presents some graphical methods which improve student’s performances on streigth of intuitive interpretation, visualization and understanding solutions of engineering problems. The increased use of graphical methods adds another layer of interpretation to a given task requiring the coordination of different knowledge, in order to produce a correct solution and to improve the product design.
Sequent Calculus in the Topos of Trees
DEFF Research Database (Denmark)
Clouston, Ranald; Goré, Rajeev
2015-01-01
Nakano’s “later” modality, inspired by Gödel-Löb provability logic, has been applied in type systems and program logics to capture guarded recursion. Birkedal et al modelled this modality via the internal logic of the topos of trees. We show that the semantics of the propositional fragment of thi...
Optimization of Cubic Polynomial Functions without Calculus
Taylor, Ronald D., Jr.; Hansen, Ryan
2008-01-01
In algebra and precalculus courses, students are often asked to find extreme values of polynomial functions in the context of solving an applied problem; but without the notion of derivative, something is lost. Either the functions are reduced to quadratics, since students know the formula for the vertex of a parabola, or solutions are…
The geometry of classical Regge calculus
International Nuclear Information System (INIS)
Barrett, J.W.
1987-01-01
Standard notions of Riemannian geometry are applied to the case of piecewise-flat manifolds. Particular care is taken to explain how one may define some particular vectors and tensors in an invariant way at points of a conical singularity. The geometry surrounding the equations of motion and the energy-momentum of the piecewise-flat manifold is developed in detail. The resolution theorem is presented, which states that on certain resolution hypersurfaces there is a clear connection between the energy-momentum of the piecewise-flat manifold and the Regge equations of motion. (author)
The Decision Calculus of Terrorist Leaders
J. Tyson Chatagnier; Alex Mintz; Yair Samban
2012-01-01
This article contributes to the literature on terrorist group decision-making by introducing a new procedure, Applied Decision Analysis, in an attempt to understand how leaders of terrorist organizations make decisions. We examine twenty-three decisions taken by leaders of three terrorist organizations: Al-Qaeda, Hamas, and Hizballah. We also demonstrate the use of the Applied Decision Analysis procedure to uncover the "Decision DNA" or “decision code” of leaders of such organizat...
Theory and calculus of cubical complexes
Perlman, M.
1973-01-01
Combination switching networks with multiple outputs may be represented by Boolean functions. Report has been prepared which describes derivation and use of extraction algorithm that may be adapted to simplification of such simultaneous Boolean functions.
Calculus of the Cryebis 2 supraconductor solenoid
International Nuclear Information System (INIS)
Levy, G.
1985-01-01
This report describes the design of the superconducting solenoid CRYEBIS 2. With the prescribed parameters (5 Teslas central field, 120mm for inner diameter, 1600 mm for length), one determinates the dimensions of coil, its energy, the conductor, the working point of the magnet with its critical limits (intensity, field, temperature). The superconducting switch is calculated in the same manner. The study of a quench shows the good behaviour of the coil which is always safe even the detection system is in failure. In final, the mechanical stresses are verified lower than yield strength [fr
Calculus of the radical integrals in electrons
International Nuclear Information System (INIS)
Soto Vargas, C.W.
1996-01-01
The radial integrals which arise from the distorted wave treatment of photon emission processes in electron and positron scattering, involve products of the electron's (or positron's) in going and outgoing wave functions and the radial part of the electromagnetic Green's function. They can be performed analytically for point Dirac-Coulomb wave functions, but are difficult to evaluate because they involve slowly converging doubly infinite series. We present a discussion and review of the formulation and methods employed to calculate these basic integral at a given value of the energy transferred. (author) [es
Diagnosis and management of gallbladder calculus disease.
Schmidt, Malte; Dumot, John A; Søreide, Odd; Søndenaa, Karl
2012-11-01
The number and rate of cholecystectomy are increasing worldwide, although indications for operative treatment remain empirical, and several issues in the understanding of the condition are not concisely outlined. Our intention is to summarize and interpret current opinion regarding the indications and timing of cholecystectomy in calculous gallbladder disease. Publications concerned with gallstone disease and related topics were searched for in MEDLINE using PubMed and summarized according to clinical scenarios with an emphasis on recent research. Only one randomized controlled trial has investigated the management (conservative vs. surgery) of patients with acute cholecystitis and several have compared early with deferred surgery. Two RCTs have examined treatment of uncomplicated, symptomatic gallstone disease. Apart from these, the overwhelming majority of publications are retrospective case series. Recent literature confirms that cholecystectomy for an asymptomatic or incidental gallstone is not justified. Symptomatic, uncomplicated gallstone disease may be classified into four severity groups based on severity and frequency of pain attacks, which may guide indication for cholecystectomy. Most patients below the age of 70 seem to prefer operative treatment. Acute cholecystitis may be treated with early operation if reduction of hospital days is an issue. Patients older than 70 years with significant comorbidities may forego surgical treatment without undue hazard. Symptoms following cholecystectomy remain in 25% or more and recent evidence suggest these are caused by a functional gastrointestinal disorder.
An Application of Calculus to Cinematography.
Sworder, Steven C.
This paper presents a laboratory exercise in which an integration problem is applied to cinematography, without the need for apparatus. The problem situation is about the oscillation control of a camera platform to attain the contrast angular rate of objects. Wave equations for describing the oscillations are presented and an expression for…
Calculus of a reactor VVER-1000 benchmark
International Nuclear Information System (INIS)
Dourougie, C.
1998-01-01
In the framework of the FMDP (Fissile Materials Disposition Program between the US and Russian, a benchmark was tested. The pin cells contain low enriched uranium (LEU) and mixed oxide fuels (MOX). The calculations are done for a wide range of temperatures and solute boron concentrations, in accidental conditions. (A.L.B.)
Crystalline structure of pulverized dental calculus induces cell death in oral epithelial cells.
Ziauddin, S M; Yoshimura, A; Montenegro Raudales, J L; Ozaki, Y; Higuchi, K; Ukai, T; Kaneko, T; Miyazaki, T; Latz, E; Hara, Y
2018-06-01
Dental calculus is a mineralized deposit attached to the tooth surface. We have shown that cellular uptake of dental calculus triggers nucleotide-binding oligomerization domain-like receptor family pyrin domain-containing 3 (NLRP3) inflammasome activation, leading to the processing of the interleukin-1β precursor into its mature form in mouse and human phagocytes. The activation of the NLRP3 inflammasome also induced a lytic form of programmed cell death, pyroptosis, in these cells. However, the effects of dental calculus on other cell types in periodontal tissue have not been investigated. The aim of this study was to determine whether dental calculus can induce cell death in oral epithelial cells. HSC-2 human oral squamous carcinoma cells, HOMK107 human primary oral epithelial cells and immortalized mouse macrophages were exposed to dental calculus or 1 of its components, hydroxyapatite crystals. For inhibition assays, the cells were exposed to dental calculus in the presence or absence of cytochalasin D (endocytosis inhibitor), z-YVAD-fmk (caspase-1 inhibitor) or glyburide (NLRP3 inflammasome inhibitor). Cytotoxicity was determined by measuring lactate dehydrogenase (LDH) release and staining with propidium iodide. Tumor necrosis factor-α production was quantified by enzyme-linked immunosorbent assay. Oral epithelial barrier function was examined by permeability assay. Dental calculus induced cell death in HSC-2 cells, as judged by LDH release and propidium iodide staining. Dental calculus also induced LDH release from HOMK107 cells. Following heat treatment, dental calculus lost its capacity to induce tumor necrosis factor-α in mouse macrophages, but could induce LDH release in HSC-2 cells, indicating a major role of inorganic components in cell death. Hydroxyapatite crystals also induced cell death in both HSC-2 and HOMK107 cells, as judged by LDH release, indicating the capacity of crystal particles to induce cell death. Cell death induced by dental
A coinductive calculus of binary trees
A.M. Silva (Alexandra); J.J.M.M. Rutten (Jan)
2007-01-01
htmlabstractWe study the set T_A of infinite binary trees with nodes labelled in a semiring A from a coalgebraic perspective. We present coinductive definition and proof principles based on the fact that T_A carries a final coalgebra structure. By viewing trees as formal power series, we develop a
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…
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
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)
Essential calculus with applications
Silverman, Richard A
1989-01-01
Rigorous but accessible text introduces undergraduate-level students to necessary background math, then clear coverage of differential calculus, differentiation as a tool, integral calculus, integration as a tool, and functions of several variables. Numerous problems and a supplementary section of ""Hints and Answers."" 1977 edition.
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
Lindstrom, Peter A.; And Others
This document consists of four units. The first of these views calculus applications to work, area, and distance problems. It is designed to help students gain experience in: 1) computing limits of Riemann sums; 2) computing definite integrals; and 3) solving elementary area, distance, and work problems by integration. The second module views…
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
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.
Initialized Fractional Calculus
Lorenzo, Carl F.; Hartley, Tom T.
2000-01-01
This paper demonstrates the need for a nonconstant initialization for the fractional calculus and establishes a basic definition set for the initialized fractional differintegral. This definition set allows the formalization of an initialized fractional calculus. Two basis calculi are considered; the Riemann-Liouville and the Grunwald fractional calculi. Two forms of initialization, terminal and side are developed.
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
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.
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.
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...
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…
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...
Modified Regge calculus as an explanation of dark energy
International Nuclear Information System (INIS)
Stuckey, W M; McDevitt, T J; Silberstein, M
2012-01-01
Using the Regge calculus, we construct a Regge differential equation for the time evolution of the scale factor a(t) in the Einstein-de Sitter cosmology model (EdS). We propose two modifications to the Regge calculus approach: (1) we allow the graphical links on spatial hypersurfaces to be large, as in direct particle interaction when the interacting particles reside in different galaxies, and (2) we assume that luminosity distance D L is related to graphical proper distance D p by the equation D L = (1+z)√D p ·D p , where the inner product can differ from its usual trivial form. The modified Regge calculus model (MORC), EdS and ΛCDM are compared using the data from the Union2 Compilation, i.e. distance moduli and redshifts for type Ia supernovae. We find that a best fit line through logD L versus logz gives a correlation of 0.9955 and a sum of squares error (SSE) of 1.95. By comparison, the best fit ΛCDM gives SSE = 1.79 using H o = 69.2 kms -1 Mpc, Ω M = 0.29 and Ω Λ = 0.71. The best fit EdS gives SSE = 2.68 using H o 60.9 km s -1 Mpc. The best-fit MORC gives SSE = 1.77 and H o = 73.9 km s -1 Mpc using R = A -1 = 8.38 Gcy and m = 1.71 x 10 52 kg, where R is the current graphical proper distance between nodes, A -1 is the scaling factor from our non-trivial inner product, and m is the nodal mass. Thus, the MORC improves the EdS as well as ΛCDM in accounting for distance moduli and redshifts for type Ia supernovae without having to invoke accelerated expansion, i.e. there is no dark energy and the universe is always decelerating. (paper)
Maxima and Minima Without Calculus.
Birnbaum, Ian
1982-01-01
Approaches to extrema that do not require calculus are presented to help free maxima/minima problems from the confines of calculus. Many students falsely suppose that these types of problems can only be dealt with through calculus, since few, if any, noncalculus examples are usually presented. (MP)
Investigation of In vitro Mineral forming bacterial isolates from supragingival calculus.
Baris, O; Demir, T; Gulluce, M
2017-12-01
Although it is known that bacterial mechanisms are involved in dental calculus formation, which is a predisposing factor in periodontal diseases, there have been few studies of such associations, and therefore, information available is limited. The purpose of this study was to isolate and identify aerobic bacteria responsible for direct calcification from supragingival calculus samples. The study was conducted using supragingival calculus samples from patients with periodontal disease, which was required as part of conventional treatment. Isolations were performed by sampling the supragingival calculus with buffer and inoculating the samples on media on which crystallization could be observed. The 16S recombinant DNA of the obtained pure cultures was then amplified and sequenced. A few bacterial species that have not previously been associated with mineralization or identified on bacterial plaque or calculus were detected. The bacteria that caused mineralization an aerobic environment are identified as Neisseria flava, Aggregatibacter segnis, Streptococcus tigurinus, and Morococcus cerebrosus. These findings proved that bacteria potentially play a role in the etiopathology of supragingival calculus. The association between the effects of the identified bacteria on periodontal diseases and calculus formation requires further studies.
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.
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.
Teacher knowledge of error analysis in differential calculus
Directory of Open Access Journals (Sweden)
Eunice K. Moru
2014-12-01
Full Text Available The study investigated teacher knowledge of error analysis in differential calculus. Two teachers were the sample of the study: one a subject specialist and the other a mathematics education specialist. Questionnaires and interviews were used for data collection. The findings of the study reflect that the teachers’ knowledge of error analysis was characterised by the following assertions, which are backed up with some evidence: (1 teachers identified the errors correctly, (2 the generalised error identification resulted in opaque analysis, (3 some of the identified errors were not interpreted from multiple perspectives, (4 teachers’ evaluation of errors was either local or global and (5 in remedying errors accuracy and efficiency were emphasised more than conceptual understanding. The implications of the findings of the study for teaching include engaging in error analysis continuously as this is one way of improving knowledge for teaching.
Elements of queueing theory palm martingale calculus and stochastic recurrences
Baccelli, François
2003-01-01
The Palm theory and the Loynes theory of stationary systems are the two pillars of the modern approach to queuing. This book, presenting the mathematical foundations of the theory of stationary queuing systems, contains a thorough treatment of both of these. This approach helps to clarify the picture, in that it separates the task of obtaining the key system formulas from that of proving convergence to a stationary state and computing its law. The theory is constantly illustrated by classical results and models: Pollaczek-Khintchin and Tacacs formulas, Jackson and Gordon-Newell networks, multiserver queues, blocking queues, loss systems etc., but it also contains recent and significant examples, where the tools developed turn out to be indispensable. Several other mathematical tools which are useful within this approach are also presented, such as the martingale calculus for point processes, or stochastic ordering for stationary recurrences. This thoroughly revised second edition contains substantial addition...
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...
Multivariable calculus with applications
Lax, Peter D
2017-01-01
This text in multivariable calculus fosters comprehension through meaningful explanations. Written with students in mathematics, the physical sciences, and engineering in mind, it extends concepts from single variable calculus such as derivative, integral, and important theorems to partial derivatives, multiple integrals, Stokes’ and divergence theorems. Students with a background in single variable calculus are guided through a variety of problem solving techniques and practice problems. Examples from the physical sciences are utilized to highlight the essential relationship between calculus and modern science. The symbiotic relationship between science and mathematics is shown by deriving and discussing several conservation laws, and vector calculus is utilized to describe a number of physical theories via partial differential equations. Students will learn that mathematics is the language that enables scientific ideas to be precisely formulated and that science is a source for the development of mathemat...
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.
The n-loop expansion of the Reggeon calculus
International Nuclear Information System (INIS)
Dash, J.W.; Harrington, S.J.
1975-01-01
The technique known in solid state physics as the n-loop expansion is applied to calculate the critical indices of the phi 3 Gribov Reggeon calculus directly in two transverse dimensions. Infrared pathologies of the massless theory require the calculation to be done in the infinite momentum limit of the massive theory. For n = 1 the results are close to those of the epsilon-expansion in O(epsilon). For n = 2 the β function has no zero, analogously to the case in solid state physics. Use of a Pade approximant for β yields sigmasub(tot) approximately (ln s)sup(0.27) at infinity, close to the O(epsilon 2 ) result. (Auth.)
N-loop expansion of the Reggeon calculus
International Nuclear Information System (INIS)
Dash, J.W.; Harrington, S.J.
1975-08-01
The technique known in solid state physics as the n-loop expansion is applied to calculate the critical indices of the phi 3 Gribov Reggeon calculus directly in two transverse dimensions. Infrared pathologies of the massless theory require the calculation to be done in the infinite momentum limit of the massive theory. For n = 1 the results are close to those of the epsilon-expansion in O(epsilon). For n = 2 the β function has no zero, analogously to the case in solid state physics. Use of a Pade approximant for β → sigma/sub tot/ approximately equals(ln s) 0 . 27 at infinity, close to the O(epsilon 2 ) result
Automating sensitivity analysis of computer models using computer calculus
International Nuclear Information System (INIS)
Oblow, E.M.; Pin, F.G.
1986-01-01
An automated procedure for performing sensitivity analysis has been developed. The procedure uses a new FORTRAN compiler with computer calculus capabilities to generate the derivatives needed to set up sensitivity equations. The new compiler is called GRESS - Gradient Enhanced Software System. Application of the automated procedure with direct and adjoint sensitivity theory for the analysis of non-linear, iterative systems of equations is discussed. Calculational efficiency consideration and techniques for adjoint sensitivity analysis are emphasized. The new approach is found to preserve the traditional advantages of adjoint theory while removing the tedious human effort previously needed to apply this theoretical methodology. Conclusions are drawn about the applicability of the automated procedure in numerical analysis and large-scale modelling sensitivity studies
Automating sensitivity analysis of computer models using computer calculus
International Nuclear Information System (INIS)
Oblow, E.M.; Pin, F.G.
1985-01-01
An automated procedure for performing sensitivity analyses has been developed. The procedure uses a new FORTRAN compiler with computer calculus capabilities to generate the derivatives needed to set up sensitivity equations. The new compiler is called GRESS - Gradient Enhanced Software System. Application of the automated procedure with ''direct'' and ''adjoint'' sensitivity theory for the analysis of non-linear, iterative systems of equations is discussed. Calculational efficiency consideration and techniques for adjoint sensitivity analysis are emphasized. The new approach is found to preserve the traditional advantages of adjoint theory while removing the tedious human effort previously needed to apply this theoretical methodology. Conclusions are drawn about the applicability of the automated procedure in numerical analysis and large-scale modelling sensitivity studies. 24 refs., 2 figs
A comparison of dental ultrasonic technologies on subgingival calculus removal: a pilot study.
Silva, Lidia Brión; Hodges, Kathleen O; Calley, Kristin Hamman; Seikel, John A
2012-01-01
This pilot study compared the clinical endpoints of the magnetostrictive and piezoelectric ultrasonic instruments on calculus removal. The null hypothesis stated that there is no statistically significant difference in calculus removal between the 2 instruments. A quasi-experimental pre- and post-test design was used. Eighteen participants were included. The magnetostrictive and piezoelectric ultrasonic instruments were used in 2 assigned contra-lateral quadrants on each participant. A data collector, blind to treatment assignment, assessed the calculus on 6 predetermined tooth sites before and after ultrasonic instrumentation. Calculus size was evaluated using ordinal measurements on a 4 point scale (0, 1, 2, 3). Subjects were required to have size 2 or 3 calculus deposit on the 6 predetermined sites. One clinician instrumented the pre-assigned quadrants. A maximum time of 20 minutes of instrumentation was allowed with each technology. Immediately after instrumentation, the data collector then conducted the post-test calculus evaluation. The repeated analysis of variance (ANOVA) was used to analyze the pre- and post-test calculus data (p≤0.05). The null hypothesis was accepted indicating that there is no statistically significant difference in calculus removal when comparing technologies (p≤0.05). Therefore, under similar conditions, both technologies removed the same amount of calculus. This research design could be used as a foundation for continued research in this field. Future studies include implementing this study design with a larger sample size and/or modifying the study design to include multiple clinicians who are data collectors. Also, deposit removal with periodontal maintenance patients could be explored.
Schubert calculus and threshold polynomials of affine fusion
International Nuclear Information System (INIS)
Irvine, S.E.; Walton, M.A.
2000-01-01
We show how the threshold level of affine fusion, the fusion of Wess-Zumino-Witten (WZW) conformal field theories, fits into the Schubert calculus introduced by Gepner. The Pieri rule can be modified in a simple way to include the threshold level, so that calculations may be done for all (non-negative integer) levels at once. With the usual Giambelli formula, the modified Pieri formula deforms the tensor product coefficients (and the fusion coefficients) into what we call threshold polynomials. We compare them with the q-deformed tensor product coefficients and fusion coefficients that are related to q-deformed weight multiplicities. We also discuss the meaning of the threshold level in the context of paths on graphs
Quantum Regge Calculus of Einstein-Cartan theory
International Nuclear Information System (INIS)
Xue Shesheng
2009-01-01
We study the Quantum Regge Calculus of Einstein-Cartan theory to describe quantum dynamics of Euclidean space-time discretized as a 4-simplices complex. Tetrad field e μ (x) and spin-connection field ω μ (x) are assigned to each 1-simplex. Applying the torsion-free Cartan structure equation to each 2-simplex, we discuss parallel transports and construct a diffeomorphism and local gauge-invariant Einstein-Cartan action. Invariant holonomies of tetrad and spin-connection fields along large loops are also given. Quantization is defined by a bounded partition function with the measure of SO(4)-group valued ω μ (x) fields and Dirac-matrix valued e μ (x) fields over 4-simplices complex.
Exploring the applications of fractional calculus: Hierarchically built semiflexible polymers
International Nuclear Information System (INIS)
Fürstenberg, Florian; Dolgushev, Maxim; Blumen, Alexander
2015-01-01
In this article we study, through extensions of the generalized Gaussian scheme, the dynamics of semiflexible treelike polymers under the influence of external forces acting on particular (say, charged) monomers. Semiflexibility is introduced following our previous work (Dolgushev and Blumen, 2009 [15]), a procedure which allows one to study treelike structures with arbitrary stiffness and branching. Exemplarily, we illustrate the procedure using linear chains and hyperbranched polymers modeled through Vicsek fractals, and obtain in every case the monomer displacement averaged over the structure. Anomalous behavior manifests itself in the intermediate time region, where the different fractal architectures show distinct scaling behaviors. These behaviors are due to the power law behavior of the spectral density and lead, for arbitrary pulling forces, based on causality and the linear superposition principle, to fractional calculus expressions, in accordance to former phenomenological fractional laws in polymer physics.
Enhancing the blended learning experience of Calculus I students
Directory of Open Access Journals (Sweden)
A. Al-Ghassani
2015-08-01
Full Text Available Blended Learning showed in the last two decades to be one of the effective ways in education and training. We illustrate our initiative experience with blended learning in the course Calculus I. The main goals we want to achieve are improving students understanding of the course concepts, increasing the level of uniformity in this multi-sections course and enhancing students blended learning experience online and offline. Consequently, this affects positively students' academic performance. We describe and discuss the results that we achieved and the challenges we encountered in view of the initiative aims and goals. The blended learning delivery methods were through Learning Management System (LMS as the online medium and through new offline activities inside and outside the classroom. The LMS we used is Moodle. We designed the resources and activities to cater for the learners different needs. The offline activities were chosen and designed to strengthen the weakness in students study skills based in our experience.
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...
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...
Numerical convergence of discrete exterior calculus on arbitrary surface meshes
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi
2018-01-01
Discrete exterior calculus (DEC) is a structure-preserving numerical framework for partial differential equations solution, particularly suitable for simplicial meshes. A longstanding and widespread assumption has been that DEC requires special
Composition and distribution of elements and ultrastructural topography of a human cardiac calculus.
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.
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi
2016-01-01
A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a
A few insights into the nature of classical and quantum gravity via null-strut calculus
International Nuclear Information System (INIS)
Kheyfets, Arkady
1989-01-01
Null-strut calculus is a 3 + 1 formulation of standard Regge calculus, wherein the dynamics of 3-geometry is propagated in time along light rays, or 'null struts'. However, just as Regge calculus is a discrete and geometric tool for the description of Einstein's theory of gravitation, so too NSC offers itself as a discrete and geometric tool for the description of Einstein's spacetime as the dynamics of discrete spacelike 3-geometries in time, or discrete geometrodynamics. It has for its objectives to provide a discrete model of a 3 + 1 split of spacetime into space plus time, while in so doing to preserve and illuminate the geometric content of Einstein's theory of gravity. The feature of 'light-cone-produced duality' is central to null-strut calculus. This paper will capitalise on this feature, and will attempt to provide some insights into the nature of classical and quantum gravity. (Author)
Leveraging Prior Calculus Study with Embedded Review
Nikolov, Margaret C.; Withers, Wm. Douglas
2016-01-01
We propose a new course structure to address the needs of college students with previous calculus study but no course validations as an alternative to repeating the first year of calculus. Students are introduced directly to topics from Calculus III unpreceded by a formal review of topics from Calculus I or II, but with additional syllabus time…
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
Smooth vectors and Weyl-Pedersen calculus for representations of nilpotent Lie groups
Beltita, Ingrid; Beltita, Daniel
2009-01-01
We present some recent results on smooth vectors for unitary irreducible representations of nilpotent Lie groups. Applications to the Weyl-Pedersen calculus of pseudo-differential operators with symbols on the coadjoint orbits are also discussed.
Rare calcium oxalate monohydrate calculus attached to the wall of the renal pelvis.
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.
Class dependency of fuzzy relational database using relational calculus and conditional probability
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.
Surgical removal of a large vaginal calculus formed after a tension-free vaginal tape procedure.
Zilberlicht, Ariel; Feiner, Benjamin; Haya, Nir; Auslender, Ron; Abramov, Yoram
2016-11-01
Vaginal calculus is a rare disorder which has been reported in association with urethral diverticulum, urogenital sinus anomaly, bladder exstrophy and the tension-free vaginal tape (TVT) procedure. We report a 42-year-old woman who presented with persistent, intractable urinary tract infection (UTI) following a TVT procedure. Cystoscopy demonstrated an eroded tape with the formation of a bladder calculus, and the patient underwent laser cystolithotripsy and cystoscopic resection of the tape. Following this procedure, her UTI completely resolved and she remained asymptomatic for several years. Seven years later she presented with a solid vaginal mass. Pelvic examination followed by transvaginal ultrasonography and magnetic resonance imaging demonstrated a large vaginal calculus located at the lower third of the anterior vaginal wall adjacent to the bladder neck. This video presents the transvaginal excision and removal of the vaginal calculus.
A numerical study of the Regge calculus and smooth lattice methods on a Kasner cosmology
International Nuclear Information System (INIS)
Brewin, Leo
2015-01-01
Two lattice based methods for numerical relativity, the Regge calculus and the smooth lattice relativity, will be compared with respect to accuracy and computational speed in a full 3+1 evolution of initial data representing a standard Kasner cosmology. It will be shown that both methods provide convergent approximations to the exact Kasner cosmology. It will also be shown that the Regge calculus is of the order of 110 times slower than the smooth lattice method. (paper)
Analysis of football player's motion in view of fractional calculus
Couceiro, Micael S.; Clemente, Filipe M.; Martins, Fernando M. L.
2013-06-01
Accurately retrieving the position of football players over time may lay the foundations for a whole series of possible new performance metrics for coaches and assistants. Despite the recent developments of automatic tracking systems, the misclassification problem ( i.e., misleading a given player by another) still exists and requires human operators as final evaluators. This paper proposes an adaptive fractional calculus (FC) approach to improve the accuracy of tracking methods by estimating the position of players based on their trajectory so far. One half-time of an official football match was used to evaluate the accuracy of the proposed approach under different sampling periods of 250, 500 and 1000 ms. Moreover, the performance of the FC approach was compared with position-based and velocity-based methods. The experimental evaluation shows that the FC method presents a high classification accuracy for small sampling periods. Such results suggest that fractional dynamics may fit the trajectory of football players, thus being useful to increase the autonomy of tracking systems.
Effect of Ramadan fasting on urinary risk factors for calculus formation.
Miladipour, Amir Hossein; Shakhssalim, Nasser; Parvin, Mahmoud; Azadvari, Mohaddeseh
2012-01-01
Even though dehydration could aggravate formation of urinary calculi, the effects of fluid and food restriction on calculus formation is not thoroughly defined. The purpose of this study is to evaluate the effects of fluid and food restriction in Ramadan fasting on urinary factors in kidney and urinary calculus formation. Fifty-seven men aged 30 to 55 years old, including 37 recurrent calcium calculus formers and 20 with no history of kidney calculi were evaluated for blood tests, ultrasonography investigations, urinalysis, urine culture, and also 24-hour urine collection test. Metabolites including calcium, oxalate, citrate, uric acid, magnesium, phosphate, potassium, sodium, and creatinine were measured before and during Ramadan fasting. The values of calculus-precipitating solutes as well as inhibitory factors were documented thoroughly. Total excretion of calcium, phosphate, and magnesium in 24-hour urine and also urine volume during fasting were significantly lower than those in the nonfasting period. Urine concentration of calcium during fasting was significantly lower than nonfasting (P calculus formation. We did not find enough evidence in favor of increased risks of calculus formation during Ramadan fasting.
International Nuclear Information System (INIS)
He, Ji-Huan; Elagan, S.K.; Li, Z.B.
2012-01-01
The fractional complex transform is suggested to convert a fractional differential equation with Jumarie's modification of Riemann–Liouville derivative into its classical differential partner. Understanding the fractional complex transform and the chain rule for fractional calculus are elucidated geometrically. -- Highlights: ► The chain rule for fractional calculus is invalid, a counter example is given. ► The fractional complex transform is explained geometrically. ► Fractional equations can be converted into differential equations.
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,…
Selective ablation of dental calculus with a frequency-doubled Alexandrite laser
Rechmann, Peter; Hennig, Thomas
1996-01-01
The aim of the study was the selective removal of dental calculus by means of pulsed lasers. In a first approach the optical characteristics of subgingival calculus were calculated using fluorescence emission spectroscopy (excitation laser: N2-laser, wavelength 337 nm, pulse duration 4 ns). Subgingival calculus seems to absorb highly in the ultraviolet spectral region up to 420 nm. According to these measurements a frequency doubled Alexandrite-laser (wavelength 377 nm, pulse duration 100 ns, repetition rate 110 Hz) was used to irradiate calculus located on enamel, at the cementum enamel junction and on the root surface (located on dentin or on cementum). Irradiation was performed perpendicular to the root surface with a laser fluence of 1 Jcm-2. During the irradiation procedure an effective water cooling-system was engaged. Histological investigations were done on undecalcified sections. As a result, engaging low fluences allows a fast and strictly selective removal of subgingival calculus. Even more the investigations revealed that supragingival calculus can be removed in a strictly selective manner engaging a frequency doubled Alexandrite-laser. No adverse side effects to the surrounding tissues could be found.
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
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
Baronti, Marco; van der Putten, Robertus; Venturi, Irene
2016-01-01
This book, intended as a practical working guide for students in Engineering, Mathematics, Physics, or any other field where rigorous calculus is needed, includes 450 exercises. Each chapter starts with a summary of the main definitions and results, which is followed by a selection of solved exercises accompanied by brief, illustrative comments. A selection of problems with indicated solutions rounds out each chapter. A final chapter explores problems that are not designed with a single issue in mind but instead call for the combination of a variety of techniques, rounding out the book’s coverage. Though the book’s primary focus is on functions of one real variable, basic ordinary differential equations (separation of variables, linear first order and constant coefficients ODEs) are also discussed. The material is taken from actual written tests that have been delivered at the Engineering School of the University of Genoa. Literally thousands of students have worked on these problems, ensuring their real-...
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.
Advanced calculus a transition to analysis
Dence, Thomas P
2010-01-01
Designed for a one-semester advanced calculus course, Advanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis -- providing a mathematically sophisticated introduction to functional analytical concepts. The text is interesting to read and includes many illustrative worked-out examples and instructive exercises, and precise historical notes to aid in further exploration of calculus. Ancillary list: * Companion website, Ebook- http://www.elsevierdirect.com/product.jsp?isbn=9780123749550 * Student Solutions Manual- To come * Instructor
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...
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...
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.
Non-exponential extinction of radiation by fractional calculus modelling
International Nuclear Information System (INIS)
Casasanta, G.; Ciani, D.; Garra, R.
2012-01-01
Possible deviations from exponential attenuation of radiation in a random medium have been recently studied in several works. These deviations from the classical Beer-Lambert law were justified from a stochastic point of view by Kostinski (2001) . In his model he introduced the spatial correlation among the random variables, i.e. a space memory. In this note we introduce a different approach, including a memory formalism in the classical Beer-Lambert law through fractional calculus modelling. We find a generalized Beer-Lambert law in which the exponential memoryless extinction is only a special case of non-exponential extinction solutions described by Mittag-Leffler functions. We also justify this result from a stochastic point of view, using the space fractional Poisson process. Moreover, we discuss some concrete advantages of this approach from an experimental point of view, giving an estimate of the deviation from exponential extinction law, varying the optical depth. This is also an interesting model to understand the meaning of fractional derivative as an instrument to transmit randomness of microscopic dynamics to the macroscopic scale.
Directory of Open Access Journals (Sweden)
Thomas E. Rams
2017-10-01
Conclusions: Excellent intra- and inter-examiner reproducibility of autofluorescence intensity measurements was obtained with the DIAGNOdent laser fluorescence device on human tooth roots. Calculus-positive root surfaces exhibited significantly greater DIAGNOdent laser autofluorescence than calculus-free tooth roots, even with the laser probe tip directed parallel to root surfaces. These findings provide further in vitro validation of the potential utility of a DIAGNOdent laser fluorescence device for identifying dental calculus on human tooth root surfaces.
Generalized Gaussian Error Calculus
Grabe, Michael
2010-01-01
For the first time in 200 years Generalized Gaussian Error Calculus addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. Since experimentalists realized that measurements in general are burdened by unknown systematic errors, the classical, widespread used evaluation procedures scrutinizing the consequences of random errors alone turned out to be obsolete. As a matter of course, the error calculus to-be, treating random and unknown systematic errors side by side, should ensure the consistency and traceability of physical units, physical constants and physical quantities at large. The generalized Gaussian error calculus considers unknown systematic errors to spawn biased estimators. Beyond, random errors are asked to conform to the idea of what the author calls well-defined measuring conditions. The approach features the properties of a building kit: any overall uncertainty turns out to be the sum of a contribution due to random errors, to be taken from a confidence inter...
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.
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....
Introduction to stochastic calculus
Karandikar, Rajeeva L
2018-01-01
This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly address continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier–Pellumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- and beginning graduate-level stud...
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.
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
Kalanov, Temur Z.
2014-03-01
A critical analysis of the foundations of standard vector calculus is proposed. The methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is proved that the vector calculus is incorrect theory because: (a) it is not based on a correct methodological basis - the unity of formal logic and of rational dialectics; (b) it does not contain the correct definitions of ``movement,'' ``direction'' and ``vector'' (c) it does not take into consideration the dimensions of physical quantities (i.e., number names, denominate numbers, concrete numbers), characterizing the concept of ''physical vector,'' and, therefore, it has no natural-scientific meaning; (d) operations on ``physical vectors'' and the vector calculus propositions relating to the ''physical vectors'' are contrary to formal logic.
Beyond food: The multiple pathways for inclusion of materials into ancient dental calculus.
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.
[Does carbonate originate from carbonate-calcium crystal component of the human urinary calculus?].
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
On the formalism of local variational differential operators
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
Dental calculus evidence of Taï Forest Chimpanzee plant consumption and life history transitions
Power, Robert C.; Salazar-García, Domingo C.; Wittig, Roman M.; Freiberg, Martin; Henry, Amanda G.
2015-10-01
Dental calculus (calcified dental plaque) is a source of multiple types of data on life history. Recent research has targeted the plant microremains preserved in this mineralised deposit as a source of dietary and health information for recent and past populations. However, it is unclear to what extent we can interpret behaviour from microremains. Few studies to date have directly compared the microremain record from dental calculus to dietary records, and none with long-term observation dietary records, thus limiting how we can interpret diet, food acquisition and behaviour. Here we present a high-resolution analysis of calculus microremains from wild chimpanzees (Pan troglodytes verus) of Taï National Park, Côte d’Ivoire. We test microremain assemblages against more than two decades of field behavioural observations to establish the ability of calculus to capture the composition of diet. Our results show that some microremain classes accumulate as long-lived dietary markers. Phytolith abundance in calculus can reflect the proportions of plants in the diet, yet this pattern is not true for starches. We also report microremains can record information about other dietary behaviours, such as the age of weaning and learned food processing techniques like nut-cracking.
Estimation and quantification of human DNA in dental calculus: A pilot study.
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.
A Giant Dumbbell Shaped Vesico-Prostatic Urethral Calculus: A Case Report and Review of Literature
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
Surface area and volume determination of subgingival calculus using laser fluorescence.
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.
Sevimli, Eyup
2016-01-01
This study aims to evaluate the consistency of teaching content with teaching approaches in calculus on the basis of lecturers' views. In this sense, the structures of the examples given in two commonly used calculus textbooks, both in traditional and reform classrooms, are compared. The content analysis findings show that the examples in both…
Differential Calculus on Quantum Spheres
Welk, Martin
1998-01-01
We study covariant differential calculus on the quantum spheres S_q^2N-1. Two classification results for covariant first order differential calculi are proved. As an important step towards a description of the noncommutative geometry of the quantum spheres, a framework of covariant differential calculus is established, including a particular first order calculus obtained by factorization, higher order calculi and a symmetry concept.
On a modification of the spinor calculus of Infeeld and van der Waerden
International Nuclear Information System (INIS)
Buchdahl, H.A.
1990-01-01
A modification of the spinor calculus of Infeeld and van der Waerden is presented in which σ kμν is no longer covariant constant. The structure of spin space is enriched by a spinor f μνρσ defined on it. Flatness of the Riemannian world space no longer necessarily entails the vanishing of the curvature of the spin space. After a brief look at Dirac's equation, the revised calculus is re-interpreted in terms of a Riemann-Cartan space, with σ kμν again covariant constant. (author)
Introduction to the operational calculus
Berg, Lothar
2013-01-01
Introduction to the Operational Calculus is a translation of ""Einfuhrung in die Operatorenrechnung, Second Edition."" This book deals with Heaviside's interpretation, on the Laplace integral, and on Jan Mikusinki's fundamental work ""Operational Calculus."" Throughout the book, basic algebraic concepts appear as aids to understanding some relevant points of the subject. An important field for research in analysis is asymptotic properties. This text also discusses examples to show the potentialities in applying operational calculus that run beyond ordinary differential equations with constant
Pre- and Post-Conditions Expressed in Variants of the Modal µ-Calculus
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.
Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces
Meljanac, Stjepan; Krešić–Jurić, Saša; Martinić, Tea
2017-07-01
This paper investigates bicovariant differential calculus on noncommutative spaces of the Lie algebra type. For a given Lie algebra g0, we construct a Lie superalgebra g =g0⊕g1 containing noncommutative coordinates and one-forms. We show that g can be extended by a set of generators TAB whose action on the enveloping algebra U (g ) gives the commutation relations between monomials in U (g0 ) and one-forms. Realizations of noncommutative coordinates, one-forms, and the generators TAB as formal power series in a semicompleted Weyl superalgebra are found. In the special case dim(g0 ) =dim(g1 ) , we also find a realization of the exterior derivative on U (g0 ) . The realizations of these geometric objects yield a bicovariant differential calculus on U (g0 ) as a deformation of the standard calculus on the Euclidean space.
Mohamed, Mamdouh S.
2016-02-11
A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.
The application of Regge calculus to quantum gravity and quantum field theory in a curved background
International Nuclear Information System (INIS)
Warner, N.P.
1982-01-01
The application of Regge calculus to quantum gravity and quantum field theory in a curved background is discussed. A discrete form of exterior differential calculus is developed, and this is used to obtain Laplacians for p-forms on the Regge manifold. To assess the accuracy of these approximations, the eigenvalues of the discrete Laplacians were calculated for the regular tesselations of S 2 and S 3 . The results indicate that the methods obtained in this paper may be used in curved space-times with an accuracy comparing with that obtained in lattice gauge theories on a flat background. It also becomes evident that Regge calculus provides particularly suitable lattices for Monte-Carlo techniques. (author)
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi
2016-05-01
A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.
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;…
Modelling with Relational Calculus of Object and Component Systems - rCOS
DEFF Research Database (Denmark)
Chen, Zhenbang; Hannousse, Abdel Hakim; Hung, Dang Van
2008-01-01
This chapter presents a formalization of functional and behavioural requirements, and a refinement of requirements to a design for CoCoME using the Relational Calculus of Object and Component Systems (rCOS). We give a model of requirements based on an abstraction of the use cases described...... in Chapter 3.2. Then the refinement calculus of rCOS is used to derive design models corresponding to the top level designs of Chapter 3.4. We demonstrate how rCOS supports modelling different views and their relationships of the system and the separation of concerns in the development....
On the use of functional calculus for phase-type and related distributions
DEFF Research Database (Denmark)
Bladt, Mogens; Navarro, Azucena Campillo; Nielsen, Bo Friis
2016-01-01
of matrices. Functional calculus, which is a branch of operator theory frequently associated with complex analysis, can be applied to phase-type and matrix-exponential distributions in a rather straightforward way. In this article we provide a number of examples of how to execute the formal arguments.......The area of phase-type distributions is renowned for its ability to obtain closed form formulas or algorithmically exact solutions to many complex stochastic models. The method of functional calculus will provide an additional tool along these lines for establishing results in terms of functions...
The calculus of get-out-the-vote in a high turnout setting
DEFF Research Database (Denmark)
Bhatti, Yosef; Dahlgaard, Jens Olav; Hansen, Jonas Hedegaard
Through a get-out-the-vote experiment we study the effect of eight different statements related to ‘the calculus of voting’ and prospect theory on voter turnout in a high salience election with proportional representation of multiple parties. The treatments are randomly assigned to more than 60...... several arguments (ITT: 1.3 percentage points, std.error. 0.62). This supports the idea that citizens are more convinced when receiving multiple arguments. There is no evidence of difference between versions of the letters emphasizing individual elements of the calculus of voting or whether the decision...
On the use of functional calculus for phase-type and related distributions
DEFF Research Database (Denmark)
Bladt, Mogens; Campillo Navarro, Azucena; Nielsen, Bo Friis
of matrices. Functional calculus, which is a branch of operator theory frequently associated with complex analysis, can be applied to phase-type and matrix-exponential distributions in a rather straightforward way. In this paper we provide a number of examples on how to execute the formal arguments.......The area of phase-type distributions is renowned for its ability to obtain closed form formulas or algorithmically exact solutions to many complex stochastic models. The method of functional calculus will provide an additional tool along these lines for establishing results in terms of functions...
A useful demonstration of calculus in a physics high school laboratory
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 experiment of a falling magnet in a column of self-induced eddy currents. The presented method combines multiple physics concepts such as 1D kinematics, classical mechanics, electromagnetism and non-trivial mathematics. It offers the opportunity for lateral as well as project-based learning.
Calabrese, Nicolino; Galgut, Peter; Mordan, Nicola
2007-10-01
Dental calculus is considered to be simply a "plaque-retentive factor", and therefore only a secondary aetiological factor in the pathogenesis of periodontitis. Recent studies have suggested a more active role for calculus. Our objective was to demonstrate the presence of periodontal pathogens in the non-mineralised areas of supra- and subgingival dental calculus. Subjects for the study were derived from patients with substantial amounts of supragingival calculus in the lower anterior region who had moderate periodontal disease, having been referred to the periodontal department at the Eastman Dental Hospital for periodontal care. Calculus was removed in as large pieces as possible by the use of a sickle or a push scaler placed underneath the apical or facial border of the calculus and fracturing it from the tooth surface in a single stroke. The orientation and absence of dental plaque was confirmed using light microscopy for each sample prior to inclusion in this study. Samples were prepared for transmission electron microscopic (TEM) observation after immunogold staining with polyclonal antibodies for the presence of Actinobacillus actinomycetemcomitans (A. a.), Porphyromonas gingivalis (P. g.) and Treponema denticola (T. d.). Most of the samples contained at least one of the bacterial species examined, either in the lacunae or in the covering dental plaque. T. d. was the most frequently identified species and was found in nearly all of the subgingival samples, whilstA. a. was rarely observed. In this limited study, supra- and subgingival dental calculus appears to be capable of maintaining periodontal pathogens within the deep recesses of its structural lacunae and channels. Therefore, calculus could possibly play a relevant role in the aetiology and pathogenesis of periodontitis. The presence of T. d. in the majority of specimens requires further investigation as its pathogenic potential may be underestimated in current published microbiological research, and
Directory of Open Access Journals (Sweden)
Catălin ROŞU
2015-05-01
Full Text Available In this paper, starting from the stress values presented in Roşu (2015 [1], a method for determining direct calculus formulas for the lathe tool equivalent stress values during the manufacturing of steel shafts is established. There is used the regression analysis for the formulas determination. The equivalent stress will be dependant on the cutting depth. The obtained formulas will be verified by using an analytical model from Strength of Materials. The results and the calculus formulas are presented from an original point of view.
A Type System for the Vectorial Aspect of the Linear-Algebraic Lambda-Calculus
Directory of Open Access Journals (Sweden)
Pablo Arrighi
2012-07-01
Full Text Available We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms resulting from the reduction of programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. We show that the resulting typed lambda-calculus is strongly normalizing and features a weak subject-reduction.
Impacted calculus within a urethral stent: A rare cause of urinary retention
Directory of Open Access Journals (Sweden)
Shanmugasundaram Rajaian
2011-01-01
Full Text Available An elderly male presented to the emergency department with acute urinary retention. He had poor flow of urine associated with serosanguinous discharge per urethra for 3 days duration. Earlier he underwent permanent metallic urethral stenting for post TURP bulbar urethral stricture. Plain X-ray of Pelvis showed an impacted calculus within the urethral stent in bulbar urethra. Urethrolitholapaxy was done with semirigid ureteroscope. Urethral stent was patent and well covered. Subsequently he had an uneventful recovery. We describe a unique case of acute urinary retention due to calculus impaction within a urethral stent.
An intrahepatic calculus superimposed over the right renal shadow: a case of mistaken identity.
Learney, Robert M; Shrotri, Nitin
2010-08-01
A 36-year-old Caucasian British woman presented with a classic case of right renal colic. Initial plain abdominal radiography and intravenous urography identified an 8 x 5 mm calculus apparently lying within a right lower pole calyx. Following failed extracorporeal lithotripsy and flexible ureterorenoscopy, cross-sectional imaging revealed a misdiagnosis by superposition of an intrahepatic calculus over the right renal shadow. This case serves to support cross-sectional imaging in the diagnosis of renal calculi. Copyright 2010 Elsevier Inc. All rights reserved.
Go Figure: Calculus Students' Use of Figures and Graphs in Technical Report Writing
Directory of Open Access Journals (Sweden)
Thomas J. Pfaff
2011-01-01
Full Text Available Understanding how to read and use graphs to communicate scientific and mathematical information is critical for STEM majors, as well as an important part of quantitative literacy. Our study suggests that first-semester calculus students do not know how to use graphs in a technical report without explicit instruction. Although not a surprising result, it leaves us wondering about when such skills are developed, and if calculus I is a place to start. Our work is now exploring the potential benefit on students' use of graphs by having them formally evaluate other students' reports.
The Characteristic of the Process of Students' Metacognition in Solving Calculus Problems
Purnomo, Dwi; Nusantara, Toto; Subanji; Rahardjo, Swasono
2017-01-01
This article is the result of research aims to describe the patterns and characteristics of the process of metacognition student of mathematics in solving calculus problems. Description was done by looking at changes in "awareness," "evaluation," and "regulation" as components of metacognition. The changes in…
A Formal Verification of the Alternating Bit Protocol in the Calculus of Constructions
Bezem, M.A.; Groote, J.F.
We report on a formal verification of the Alternating Bit Protocol (ABP) in the Calculus of Constructions. We outline a semi-formal correctness proof of the ABP with sufficient detail to be formalised. Thereafter we show by examples how the formalised proof has been verified by the automated proof
Jukic Matic, Ljerka; Dahl, Bettina
2014-01-01
This paper reports a study on retention of differential and integral calculus concepts of a second-year student of physical chemistry at a Danish university. The focus was on what knowledge the student retained 14 months after the course and on what effect beliefs about mathematics had on the retention. We argue that if a student can quickly…
Salleh, Tuan Salwani; Zakaria, Effandi
2016-01-01
The objective of this research is to investigate the effectiveness of a learning strategy using Maple in integral calculus. This research was conducted using a quasi-experimental nonequivalent control group design. One hundred engineering technology students at a technical university were chosen at random. The effectiveness of the learning…
Building an Understanding of Functions: A Series of Activities for Pre-Calculus
Carducci, Olivia M.
2008-01-01
Building block toys can be used to illustrate various concepts connected with functions including graphs and rates of change of linear and exponential functions, piecewise functions, and composition of functions. Five brief activities suitable for a pre-calculus course are described.
Removal of artificial dental calculus by use of conventional and diamond ultrasound tips.
Directory of Open Access Journals (Sweden)
Roberto Carlos Mourão Pinho
2017-04-01
Full Text Available Introduction: Periodontal disease is considered a public health problem and may lead to serious complications as the general health of patient. The main therapeutic procedure is scaling and root planing, which can be performed by a variety of techniques and instruments Objective:The aim of the present study was to evaluate the removal of calculus, produced artificially, by using a conventional ultrasonic tip and a diamond – CVD tip. Method: The calculus was produced with artificial sawdust and glue-based cyanoacrylate and distributed in twenty areas also standardized on two plates of acrylic resin (chemical activated, holding 10 samples per plate. Standards / samples were divided by lot into two simple groups, being A (treated with conventional tip and B (treated with CVD tip. Results:The treatment in Group A, promoted an average area of 20.48 ± 4.20 mm2 free of artificial calculus which is significantly higher (p <0.05 than the area removed in Group B (15.37 ± 5.29 mm2. Conclusion:The results showed that the conventional tip presented higher results than CVD tip for efficacy in the removal of calculus.
Application of several physical techniques in the total analysis of a canine urinary calculus.
Rodgers, A L; Mezzabotta, M; Mulder, K J; Nassimbeni, L R
1981-06-01
A single calculus from the bladder of a Beagle bitch has been analyzed by a multiple technique approach employing x-ray diffraction, infrared spectroscopy, scanning electron microscopy, x-ray fluorescence spectrometry, atomic absorption spectrophotometry and density gradient fractionation. The qualitative and quantitative data obtained showed excellent agreement, lending confidence to such an approach for the evaluation and understanding of stone disease.
Numerical convergence of discrete exterior calculus on arbitrary surface meshes
Mohamed, Mamdouh S.
2018-02-13
Discrete exterior calculus (DEC) is a structure-preserving numerical framework for partial differential equations solution, particularly suitable for simplicial meshes. A longstanding and widespread assumption has been that DEC requires special (Delaunay) triangulations, which complicated the mesh generation process especially for curved surfaces. This paper presents numerical evidence demonstrating that this restriction is unnecessary. Convergence experiments are carried out for various physical problems using both Delaunay and non-Delaunay triangulations. Signed diagonal definition for the key DEC operator (Hodge star) is adopted. The errors converge as expected for all considered meshes and experiments. This relieves the DEC paradigm from unnecessary triangulation limitation.
Geometrical enhancement of the electric field: Application of fractional calculus in nanoplasmonics
Baskin, E.; Iomin, A.
2011-12-01
We developed an analytical approach, for a wave propagation in metal-dielectric nanostructures in the quasi-static limit. This consideration establishes a link between fractional geometry of the nanostructure and fractional integro-differentiation. The method is based on fractional calculus and permits to obtain analytical expressions for the electric-field enhancement.
Berezowska, A.; Fischer, A.R.H.; Ronteltap, A.; Kuznesof, S.; Macready, A.; Fallaize, R.; Trijp, van J.C.M.
2014-01-01
Background: Personalised nutrition (PN) may provide major health benefits to consumers. A potential barrier to the uptake of PN is consumers' reluctance to disclose sensitive information upon which PN is based. This study adopts the privacy calculus to explore how PN service attributes contribute to
Thomas Berdmore, dentist of His Majesty, George III, and dental calculus.
Andreana, S; Andreana, G; Gonzalez, Y M; Ciancio, S
1996-11-01
Thomas Berdmore's book, Disorders of Deformities of the Teeth and Gums, presents examples of early concepts of preventive dentistry and treatment of periodontal diseases. Various aspects of dental calculus formation and composition are analyzed. Also the effects of periodontal disease as seen by Berdmore are discussed, and ways of treatment in 1770 summarized.
Selective near-UV ablation of subgingival dental calculus: measurement of removal rates
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.
Timing analysis of rate-constrained traffic in TTEthernet using network calculus
DEFF Research Database (Denmark)
Zhao, Luxi; Pop, Paul; Li, Qiao
2017-01-01
calculus (NC) to determine the worst-case end-to-end delays of RC traffic in TTEthernet. The main contribution of this paper is capturing the effects of all the integration policies on the latency bounds of RC traffic using NC, and the consideration of relative frame offsets of TT traffic to reduce...
Early Vector Calculus: A Path through Multivariable Calculus
Robertson, Robert L.
2013-01-01
The divergence theorem, Stokes' theorem, and Green's theorem appear near the end of calculus texts. These are important results, but many instructors struggle to reach them. We describe a pathway through a standard calculus text that allows instructors to emphasize these theorems. (Contains 2 figures.)
Fock space representation of differential calculus on the noncommutative quantum space
International Nuclear Information System (INIS)
Mishra, A.K.; Rajasekaran, G.
1997-01-01
A complete Fock space representation of the covariant differential calculus on quantum space is constructed. The consistency criteria for the ensuing algebraic structure, mapping to the canonical fermions and bosons and the consequences of the new algebra for the statistics of quanta are analyzed and discussed. The concept of statistical transmutation between bosons and fermions is introduced. copyright 1997 American Institute of Physics
Discovering the Art of Mathematics: Using String Art to Investigate Calculus
von Renesse, Christine; Ecke, Volker
2016-01-01
One goal of our Discovering the Art of Mathematics project is to empower students in the liberal arts to become confident creators of art and imaginative creators of mathematics. In this paper, we describe our experience with using string art to guide liberal arts students in exploring ideas of calculus. We provide excerpts from our inquiry-based…
Topology, calculus and approximation
Komornik, Vilmos
2017-01-01
Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...
Fluorescence properties of human teeth and dental calculus for clinical applications
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.
Double dumb-bell calculus in childhood | Joshi | African Journal of ...
African Journals Online (AJOL)
An eight-year old male was admitted with complaints of right scrotal swelling, dysuria and intermittent retention of urine for 10 days. On per-rectal examination, a hard mass was palpable in the posterior urethra. An X-ray (KUB) of the abdomen revealed a double dumb-bell calculus at the base of bladder, extending into the ...
Wei, Zhi-Feng; Xu, Xiao-Feng; Cheng, Wen; Zhou, Wen-Quan; Ge, Jing-Ping; Zhang, Zheng-Yu; Gao, Jian-Ping
2012-05-01
To study the causes, clinical manifestations, treatment and prevention of calculus that develops in the prostatic cavity after transurethral resection of the prostate. We reported 11 cases of calculus that developed in the prostatic cavity after transurethral resection or transurethral plasmakinetic resection of prostate. The patients complained of repeated symptoms of frequent micturition, urgent micturition and urodynia after operation, accompanied with urinary tract infection and some with urinary obstruction, which failed to respond to anti-infective therapies. Cystoscopy revealed calculi in the prostatic cavity, with eschar, sphacelus, uneven wound surface and small diverticula in some cases. After diagnosis, 1 case was treated by holmium laser lithotripsy and a second transurethral resection of the prostate, while the other 10 had the calculi removed under the cystoscope, followed by 1 -2 weeks of anti-infective therapy. After treatment, all the 11 cases showed normal results of routine urinalysis, and no more symptoms of frequent micturition, urgent micturition and urodynia. Three- to six-month follow-up found no bladder irritation symptoms and urinary tract infection. Repeated symptoms of frequent micturition, urgent micturition, urodynia and urinary tract infection after transurethral resection of the prostate should be considered as the indicators of calculus in the prostatic cavity, which can be confirmed by cystoscopy. It can be treated by lithotripsy or removal of the calculus under the cystoscope, or even a second transurethral resection of the prostate. For its prevention, excessive electric coagulation and uneven wound surface should be avoided and anti-infection treatment is needed.
Proof Nets for Lambek Calculus
Roorda, Dirk
1992-01-01
The proof nets of linear logic are adapted to the non-commutative Lambek calculus. A different criterion for soundness of proof nets is given, which gives rise to new algorithms for proof search. The order sensitiveness of the Lambek calculus is reflected by the planarity condition on proof nets;
Barker, Bruce O.; Bannon, James
This paper describes the Hawaii Interactive Television System (HITS) program and provides an evaluation of the first year of broadcasts for the advanced placement (AP) calculus course. HITS allows two-way video-audio interaction among origination sites, but the configuration used by the Department of Education for its Teleschool program is the…
Bismut's way of the Malliavin calculus for large order generators on a Lie group
Léandre, Rémi
2018-01-01
We adapt Bismut's mechanism of the Malliavin Calculus to right invariant big order generator on a Lie group. We use deeply the symmetry in order to avoid the use of the Malliavin matrix. As an application, we deduce logarithmic estimates in small time of the heat kernel.
Wade, Carol; Sonnert, Gerhard; Sadler, Philip M.; Hazari, Zahra; Watson, Charity
2016-01-01
This article compares the views of teachers and professors about the transition from secondary mathematics to tertiary calculus. Quantitative analysis revealed five categories where teachers and professors differed significantly in the relative frequency of addressing them. Using the rite of passage theory, the separation and incorporation phases…
Instructor Use of Tablet PCs in a College Pre-Calculus Course: Implementation & Assessment
Connelly Stockton, Julianna; Gregory, Peter
2012-01-01
A group of six math instructors used tablet PCs to teach their individual sections of a high enrollment gateway Pre-Calculus course in a diverse urban four-year college. Student performance in the experimental sections were compared to those in 31 other sections in terms of student retention, pass rates, and score on the department-wide…
Calculus Limits Involving Infinity: The Role of Students' Informal Dynamic Reasoning
Jones, Steven R.
2015-01-01
Few studies on calculus limits have centred their focus on student understanding of limits at infinity or infinite limits that involve continuous functions (as opposed to discrete sequences). This study examines student understanding of these types of limits using both pure mathematics and applied-science functions and formulas. Seven calculus…
Lee, Ho; Ryan, Robert T; Kim, Jeehyun; Choi, Bernard; Arakeri, Navanit V; Teichman, Joel M H; Welch, A J
2004-08-01
During pulsed laser lithotripsy, the calculus is subject to a strong recoil momentum which moves the calculus away from laser delivery and prolongs the operation. This study was designed to quantify the recoil momentum during Ho:YAG laser lithotripsy. The correlation among crater shape, debris trajectory, laser-induced bubble and recoil momentum was investigated. Calculus phantoms made from plaster of Paris were ablated with free running Ho:YAG lasers. The dynamics of recoil action of a calculus phantom was monitored by a high-speed video camera and the laser ablation craters were examined with Optical Coherent Tomography (OCT). Higher radiant exposure resulted in larger ablation volume (mass) which increased the recoil momentum. Smaller fibers produced narrow craters with a steep contoured geometry and decreased recoil momentum compared to larger fibers. In the presence of water, recoil motion of the phantom deviated from that of phantom in air. Under certain conditions, we observed the phantom rocking towards the fiber after the laser pulse. The shape of the crater is one of the major contributing factors to the diminished recoil momentum of smaller fibers. The re-entrance flow of water induced by the bubble collapse is considered to be the cause of the rocking of the phantom.
An evaluation of a pre-scaling gel (SofScale) on the ease of supragingival calculus removal.
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.
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.
The Effect of Attending Tutoring on Course Grades in Calculus I
Rickard, Brian; Mills, Melissa
2018-01-01
Tutoring centres are common in universities in the United States, but there are few published studies that statistically examine the effects of tutoring on student success. This study utilizes multiple regression analysis to model the effect of tutoring attendance on final course grades in Calculus I. Our model predicted that every three visits to…
On the definition of the partition function in quantum Regge calculus
International Nuclear Information System (INIS)
Nishimura, Jun
1995-01-01
We argue that the definition of the partition function used recently to demonstrate the failure of Regge calculus is wrong. In fact, in the one-dimensional case, we show that there is a more natural definition, with which one can reproduce the correct results. (author)
[Clinical analysis of 41 children's urinary calculus and acute renal failure].
Li, Lu-Ping; Fan, Ying-Zhong; Zhang, Qian; Zhang, Sheng-Li
2013-04-01
To analyze the treatment of acute renal failure caused by irrational drug use. Data of 41 cases of acute renal failure seen from July 2008 to June 2012 in our hospital were reviewed. Bilateral renal parenchymas diffuse echo was found enhanced by ultrasound in all cases. Calculus image was not found by X-ray. All children had medical history of using cephalosporins or others. Alkalinization of urine and antispasmodic treatment were given to all children immediately, 17 children were treated with hemodialysis and 4 children accepted intraureteral cannula placement. In 24 children who accepted alkalinization of urine and antispasmodic treatment micturition could be restored within 24 hours, in 11 children micturition recovered after only one hemodialysis treatment and 2 children gradually restored micturition after hemodialysis twice, 4 children who accepted intraureteral cannula immediately restored micturition. In all children micturition recovered gradually after a week of treatment. Ultrasound examination showed that 39 children's calculus disappeared totally and renal parenchymas echo recovered to normal. The residual calculi with diameter less than 5 mm were found in 2 children, but they had no symptoms. The children received potassium sodium hydrogen citrate granules per os and were discharged from hospital. Ultrasound showed calculus disappeared totally one month later. Irrational drug use can cause children urolithiasis combined with acute renal failure, while renal dysfunction can reverse by drug withdrawal and early alkalinization of urine, antispasmodic treatment, intraureteral cannula or hemodialysis when necessary, most calculus can be expelled after micturition recovered to normal.
Peer-Led Guided in Calculus at University of South Florida
Bénéteau, Catherine; Fox, Gordon; Xu, Xiaoying; Lewis, Jennifer E.; Ramachandran, Kandethody; Campbell, Scott; Holcomb, John
2016-01-01
This paper describes the development of a Peer-Led Guided Inquiry (PLGI) program for teaching calculus at the University of South Florida. This approach uses the POGIL (Process Oriented Guided Inquiry Learning) teaching strategy and the small group learning model PLTL (Peer-Led Team Learning). The developed materials used a learning cycle based on…
On Transitions between Representations: The Role of Contextual Reasoning in Calculus Problem Solving
Zazkis, Dov
2016-01-01
This article argues for a shift in how researchers discuss and examine students' uses and understandings of multiple representations within a calculus context. An extension of Zazkis, Dubinsky, and Dautermann's (1996) visualization/analysis framework to include contextual reasoning is proposed. Several examples that detail transitions between…
Calculus Students' and Instructors' Conceptualizations of Slope: A Comparison across Academic Levels
Nagle, Courtney; Moore-Russo, Deborah; Viglietti, Janine; Martin, Kristi
2013-01-01
This study considers tertiary calculus students' and instructors' conceptualizations of slope. Qualitative techniques were employed to classify responses to 5 items using conceptualizations of slope identified across various research settings. Students' responses suggest that they rely on procedurally based conceptualizations of…
TENSOR CALCULUS with applications to Differential Theory of Surfaces and Dynamics
DEFF Research Database (Denmark)
Nielsen, Søren R. K.
The present outline on tensor calculus with special application to differential theory of surfaces and dynamics represents a modified and extended version of a lecture note written by the author as an introduction to a course on shell theory given together with Ph.D. Jesper Winther Stærdahl...
Transversality of Electromagnetic Waves in the Calculus-Based Introductory Physics Course
Burko, Lior M.
2008-01-01
Introductory calculus-based physics textbooks state that electromagnetic waves are transverse and list many of their properties, but most such textbooks do not bring forth arguments why this is so. Both physical and theoretical arguments are at a level appropriate for students of courses based on such books, and could be readily used by…
A Case Study of Student and Instructor Reactions to a Calculus E-Book
Bode, Martina; Khorami, Mehdi; Visscher, Daniel
2014-01-01
This article details the results of testing an e-book in two differential calculus classes. Although we, as math instructors, were drawn to the components of the e-book that promote conceptual understanding--such as the interactive figures--the students reported liking the assessment support most. We found that students were initially excited…
Covariant differential calculus on quantum Minkowski space and the q-analogue of Dirac equation
International Nuclear Information System (INIS)
Song Xingchang; Academia Sinica, Beijing
1992-01-01
The covariant differential calculus on the quantum Minkowski space is presented with the help of the generalized Wess-Zumino method and the quantum Pauli matrices and quantum Dirac matrices are constructed parallel to those in the classical case. Combining these two aspects a q-analogue of Dirac equation follows directly. (orig.)
Easey, Michael; Gleeson, Jim
2016-01-01
The aim of the larger study, of which this paper is a part, is to investigate the decline in Year 10 male students' participation in senior calculus mathematics courses at an independent boys' school located in metropolitan Queensland. This paper draws on Sealey and Noyes's (2010) relevance framework to conduct document analysis and interviews…
A Step-indexed Semantic Model of Types for the Call-by-Name Lambda Calculus
Meurer, Benedikt
2011-01-01
Step-indexed semantic models of types were proposed as an alternative to purely syntactic safety proofs using subject-reduction. Building upon the work by Appel and others, we introduce a generalized step-indexed model for the call-by-name lambda calculus. We also show how to prove type safety of general recursion in our call-by-name model.
The application of 99mTc-EC renal dynamic imaging in urinary system calculus
International Nuclear Information System (INIS)
Dai Ruqi; Li Shiyun; Liu Xueshu; Huang Wei
2002-01-01
Objective: To evaluate the clinical value of 99m Tc-EC renal dynamic imaging (RDI) for diagnosis of urinary system calculus. Methods: 135 case with confirmed urinary system calculus by ultrasound and IVP were examined by 99m Tc-EC renal dynamic imaging and to analyze the degree of hydronephrosis and the remaining renal function. The quantitative indexes used were effective renal plasma flow (ERPF) and peak uptake rate (PUR). Results: RDI almost accorded with IVP in renal calculus complicated by mild and moderate hydronephrosis cases. On other cases of the severe hydronephrosis and serious renal insufficiency, RDI was more sensitive than IVP which had no excretion in 6 patients with hydronephrosis. ERPF and PUR showed the remaining function of the morbid kidney more accurately than other methods. In severe and mild hydronephrosis the ERPF were 84.3 ± 49 ml/min and 202.2 ± 52.4 ml/min, the PUR were 20.4 ± 11.5% and 48.5 ± 13.6% respectively. Conclusion: RDI can correctly reflect the degree of hydronephrosis and the remaining function of the morbid kidney in urinary system calculus, which would be helpful for the clinical surgical planning
Discrete Calculus as a Bridge between Scales
Degiuli, Eric; McElwaine, Jim
2012-02-01
Understanding how continuum descriptions of disordered media emerge from the microscopic scale is a fundamental challenge in condensed matter physics. In many systems, it is necessary to coarse-grain balance equations at the microscopic scale to obtain macroscopic equations. We report development of an exact, discrete calculus, which allows identification of discrete microscopic equations with their continuum equivalent [1]. This allows the application of powerful techniques of calculus, such as the Helmholtz decomposition, the Divergence Theorem, and Stokes' Theorem. We illustrate our results with granular materials. In particular, we show how Newton's laws for a single grain reproduce their continuum equivalent in the calculus. This allows introduction of a discrete Airy stress function, exactly as in the continuum. As an application of the formalism, we show how these results give the natural mean-field variation of discrete quantities, in agreement with numerical simulations. The discrete calculus thus acts as a bridge between discrete microscale quantities and continuous macroscale quantities. [4pt] [1] E. DeGiuli & J. McElwaine, PRE 2011. doi: 10.1103/PhysRevE.84.041310
Directory of Open Access Journals (Sweden)
Hyeongsik Seo
2009-09-01
Full Text Available Objectives : This experimental study was performed to investigate the safety and efficacy of Bovis Calculus pharmacopuncture solution manufactured with freezing dryness method to use eye drop. To identify the use of it as eye drop, the eye irritation test of rabbits and the antibacterial test of Staphylococcus aureus, Staphylococcus epidermidis, Pseudomonas aeruginosa, Aspergillus niger, Fusarium oxysporum, and Candida albicans were performed. Methods : 1. 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 administered in the left eye of the rabbits, eye irritation of the cornea, iris and conjunctiva was observed at 1, 2, 3, 4 & 7day. 2. After administering Bovis Calculus pharmacopuncture solution on bacterial species(Staphylococcus aureus, Staphylococcus epidermidis, Pseudomonas aeruginosa, Aspergillus niger, Fusarium oxysporum, Candida albicans which cause Keratitis, MIC(Minimum Inhibition Concentration and the size of inhibition zone were measured. Anti-bacterial potency was also measured using the size of inhibition zone. Results : 1. After Bovis Calculus pharmacopuncture solution was administered in the left eye of the rabbits, it was found that none of nine rabbits have abnormal signs and weight changes. 2. After Bovis Calculus pharmacopuncture solution was medicated in the left eye of the rabbits, no eye irritation of the cornea, iris and conjunctiva was observed at 1, 2, 3, 4 & 7day. 3. There was no response to MIC on bacterial species (Staphylococcus aureus, Staphylococcus epidermidis, Pseudomonas aeruginosa, Aspergillus niger, Fusarium oxysporum, Candida albicans after Bovis Calculus pharmacopuncture solution was medicated. Conclusions : The present study suggests that Bovis Calculus pharmacopuncture solution is a nontoxic and non-irritant medicine, which does not cause eye irritation in
Placement Model for First-Time Freshmen in Calculus I (Math 131): University of Northern Colorado
Heiny, Robert L.; Heiny, Erik L.; Raymond, Karen
2017-01-01
Two approaches, Linear Discriminant Analysis, and Logistic Regression are used and compared to predict success or failure for first-time freshmen in the first calculus course at a medium-sized public, 4-year institution prior to Fall registration. The predictor variables are high school GPA, the number, and GPA's of college prep mathematics…
The Use of Geogebra Software as a Calculus Teaching and Learning Tool
Nobre, Cristiane Neri; Meireles, Magali Rezende Gouvêa; Vieira, Niltom, Jr.; de Resende, Mônica Neli; da Costa, Lucivânia Ester; da Rocha, Rejane Corrêa
2016-01-01
Information and Communication Technologies (ICT) in education provide a new learning environment where the student builds his own knowledge, allowing his visualization and experimentation. This study evaluated the Geogebra software in the learning process of Calculus. It was observed that the proposed activities helped in the graphical…
A Study of Creative Reasoning Opportunities in Assessments in Undergraduate Calculus Courses
Mac an Bhaird, Ciarán; Nolan, Brien C.; O'Shea, Ann; Pfeiffer, Kirsten
2017-01-01
In this article we present the findings of a research study which investigated the opportunities for creative reasoning (CR) made available to first year undergraduate students in assessments. We compared three first year calculus courses across two Irish universities using Lithner's framework. This framework sets apart imitative reasoning (IR)…
Cause-Effect Analysis: Improvement of a First Year Engineering Students' Calculus Teaching Model
van der Hoff, Quay; Harding, Ansie
2017-01-01
This study focuses on the mathematics department at a South African university and in particular on teaching of calculus to first year engineering students. The paper reports on a cause-effect analysis, often used for business improvement. The cause-effect analysis indicates that there are many factors that impact on secondary school teaching of…
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.
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
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.
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.
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
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
The release of vitamin C from chewing gum and its effects on supragingival calculus formation.
Lingström, Peter; Fure, Solveig; Dinitzen, Bettina; Fritzne, Christina; Klefbom, Carin; Birkhed, Dowen
2005-02-01
The aims of this study were to evaluate (i): whether vitamin C in chewing gum, alone or in combination with carbamide, influences calculus formation, and (ii) whether carbamide affects the release, stability and uptake of vitamin C in a chewing gum. In two test series (Series I and II), 30 subjects, all calculus formers, participated. They were instructed to chew on five (Series I) or 10 (Series II) pieces of gum per day for a period of 3 months. The chewing gums were: vitamin C (60 mg, Series I), non-vitamin C (Series I) and vitamin C + carbamide (30 mg + 30 mg, Series II). In both series, no gum was used as a negative control. Calculus formation was scored on three lingual sites on the six anterior mandibular teeth according to the Volpe-Manhold index. The effect on plaque and gingivitis was also determined. A significant reduction in the total calculus score was observed after the use of vitamin C (33%) and vitamin C + carbamide (12%) gums compared with no gum use; this reduction was most pronounced in the heavy calculus formers. A reduced amount of visible plaque was also observed after use of vitamin C and non-vitamin C gum, but only the vitamin C gum reduced the number of bleeding sites (37%). In a separate study, the release, stability and uptake of vitamin C were evaluated using the iodine titration method in both saliva and urine after exposure to the following gums: vitamin C + carbamide (30 mg + 30 mg) and vitamin C (30 mg). There was no indication that carbamide affected the release, stability or uptake of vitamin C when used in a chewing gum.
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...
Functional Fractional Calculus
Das, Shantanu
2011-01-01
When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with 'ordinary' differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematic
A Tutorial Review on Fractal Spacetime and Fractional Calculus
He, Ji-Huan
2014-11-01
This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.
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
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...
Misu, La; Ketut Budayasa, I.; Lukito, Agung
2018-03-01
This study describes the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. The metacognition profile is a natural and intact description of a person’s cognition that involves his own thinking in terms of using his knowledge, planning and monitoring his thinking process, and evaluating his thinking results when understanding a concept. The purpose of this study was to produce the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. This research method is explorative method with the qualitative approach. The subjects of this study are mathematics and mathematics education students who have studied integral calculus. The results of this study are as follows: (1) the summarizing category, the mathematics and mathematics education students can use metacognition knowledge and metacognition skills in understanding the concept of indefinite integrals. While the definite integrals, only mathematics education students use metacognition skills; and (2) the explaining category, mathematics students can use knowledge and metacognition skills in understanding the concept of indefinite integrals, while the definite integrals only use metacognition skills. In addition, mathematics education students can use knowledge and metacognition skills in understanding the concept of both indefinite and definite integrals.
Yuliana, Yuliana; Tasari, Tasari; Wijayanti, Septiana
2017-01-01
The objectives of this research are (1) to develop Guided Discovery Learning in integral calculus subject; (2) to identify the effectiveness of Guided Discovery Learning in improving the students' understanding toward integral calculus subject. This research was quasy experimental research with the students of even semester in Mathematics Education Widya Dharma University as the sample. Cluster Random sampling was conducted to determine control group that was taught using Conventional model a...
Fractional Dynamics Applications of Fractional Calculus to Dynamics of Particles, Fields and Media
Tarasov, Vasily E
2010-01-01
"Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and...
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.
On Functional Calculus Estimates
Schwenninger, F.L.
2015-01-01
This thesis presents various results within the field of operator theory that are formulated in estimates for functional calculi. Functional calculus is the general concept of defining operators of the form $f(A)$, where f is a function and $A$ is an operator, typically on a Banach space. Norm
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.
Effect of Frequency of Brushing Teeth on Plaque and Calculus Accumulation, and Gingivitis in Dogs.
Harvey, Colin; Serfilippi, Laurie; Barnvos, Donald
2015-01-01
The efficacy of brushing the teeth of beagle dogs in a randomized, controlled, blinded study design using a clearly-defined brushing technique was evaluated for 4 brushing frequencies: brushing daily, brushing every other day, brushing weekly and brushing every other week, compared with no brushing in a control group of dogs. All dogs were fed a standard dry kibble diet during the study. Standard plaque, calculus, and gingivitis indices were used to score the teeth. A 'clean tooth' model was used. No gingival or non-gingival lacerations or other signs of injury to oral tissues were found at the end of the 28 day trial period. Brushing more frequently had greater effectiveness in retarding accumulation of plaque and calculus, and reducing the severity of pre-existing gingivitis. Brushing daily or every other day produced statistically significant improved results compared with brushing weekly or every other week. Based on the results of this study, daily brushing is recommended.
Wick calculus on spaces of generalized functions of compound poisson white noise
Lytvynov, Eugene W.; Rebenko, Alexei L.; Shchepan'ur, Gennadi V.
1997-04-01
We derive white noise calculus for a compound Poisson process. Namely, we consider, on the Schwartz space of tempered distributions, S', a measure of compound Poisson white noise, μcp, and construct a whole scale of standard nuclear triples ( Scp) - x ⊃ L2cp) ≡ L2( S', dμcp) ⊃( Scpx, x≥ 0, which are obtained as images under some isomorphism of the corresponding triples centred at a Fock space. It turns out that the most interesting case is x = 1, when our triple coincides with the triple that is constructed by using a system of Appell polynomials in the framework of non-Gaussian biorthogonal analysis. Our special attention is paid to the Wick calculus of the Poisson field, or the quantum compound Poisson white noise process in other terms, which is the family of operators acting from ( Scp) 1 into ( Scp) 1 as multiplication by the compound Poisson white noise ω( t).
Complete axiomatization of the stutter-invariant fragment of the linear time µ-calculus
Gheerbrant, A.
2010-01-01
The logic µ(U) is the fixpoint extension of the "Until"-only fragment of linear-time temporal logic. It also happens to be the stutter-invariant fragment of linear-time µ-calculus µ(◊). We provide complete axiomatizations of µ(U) on the class of finite words and on the class of ω-words. We introduce
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...
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...
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...
Vaninsky, Alexander
2015-04-01
Defining the logarithmic function as a definite integral with a variable upper limit, an approach used by some popular calculus textbooks, is problematic. We discuss the disadvantages of such a definition and provide a way to fix the problem. We also consider a definition-based, rigorous derivation of the derivative of the exponential function that is easier, more intuitive, and complies with the standard definitions of the number e, the logarithmic, and the exponential functions.
Ghorbani, Mahboobeh; Bogdan, Paul
2014-01-01
Healthcare costs in the US are among the highest in the world. Chronic diseases such as diabetes significantly contribute to these extensive costs. Despite technological advances to improve sensing and actuation devices, we still lack a coherent theory that facilitates the design and optimization of efficient and robust medical cyber-physical systems for managing chronic diseases. In this paper, we propose a mathematical model for capturing the complex dynamics of blood glucose time series (e.g., time dependent and fractal behavior) observed in real world measurements via fractional calculus concepts. Building upon our time dependent fractal model, we propose a novel model predictive controller for an artificial pancreas that regulates insulin injection. We verify the accuracy of our controller by comparing it to conventional non-fractal models using real world measurements and show how the nonlinear optimal controller based on fractal calculus concepts is superior to non-fractal controllers in terms of average risk index and prediction accuracy.
Yaprak, E; Yolcubal, I; Sinanoğlu, A; Doğrul-Demiray, A; Guzeldemir-Akcakanat, E; Marakoğlu, I
2017-02-01
Various trace elements, including toxic heavy metals, may exist in dental calculus. However, the effect of environmental factors on heavy metal composition of dental calculus is unknown. Smoking is a major environmental source for chronic toxic heavy metal exposition. The aim of this study is to compare toxic heavy metal accumulation levels in supragingival dental calculus of smokers and non-smokers. A total of 29 supragingival dental calculus samples were obtained from non-smoker (n = 14) and smoker (n = 15) individuals. Subjects with a probability of occupational exposure were excluded from the study. Samples were analyzed by inductively coupled plasma mass spectrometry in terms of 26 metals and metalloids, including toxic heavy metals. Toxic heavy metals, arsenic (p 0.05). Within the limitations of this study, it can be concluded that the elementary composition of dental calculus may be affected by environmental factors such as tobacco smoke. Therefore, dental calculus may be utilized as a non-invasive diagnostic biological material for monitoring chronic oral heavy metal exposition. However, further studies are required to evaluate its diagnostic potential. © 2016 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.
International Nuclear Information System (INIS)
Cheng, S-C; Wu, J-N; Tsai, M-R; Hsieh, W-F
2009-01-01
We suggest a better mathematical method, fractional calculus, for studying the behavior of the atom-field interaction in photonic crystals. By studying the spontaneous emission of an atom in a photonic crystal with a one-band isotropic model, we found that the long-time inducing memory of the spontaneous emission is a fractional phenomenon. This behavior could be well described by fractional calculus. The results show no steady photon-atom bound state for the atomic resonant transition frequency lying in the proximity of the allowed band edge which was encountered in a previous study (Woldeyohannes and John 2003 J. Opt. B: Quantum Semiclass. Opt. 5 R43). The correctness of this result is validated by the 'cut-off smoothing' density of photon states (DOS) with fractional calculus. By obtaining a rigorous solution without the multiple-valued problem for the system, we show that the method of fractional calculus has a logically concise property.
Calculus Courses' Assessment Data
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.…
A generalized nonlocal vector calculus
Alali, Bacim; Liu, Kuo; Gunzburger, Max
2015-10-01
A nonlocal vector calculus was introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A formulation is developed that provides a more general setting for the nonlocal vector calculus that is independent of particular nonlocal models. It is shown that general nonlocal calculus operators are integral operators with specific integral kernels. General nonlocal calculus properties are developed, including nonlocal integration by parts formula and Green's identities. The nonlocal vector calculus introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) is shown to be recoverable from the general formulation as a special example. This special nonlocal vector calculus is used to reformulate the peridynamics equation of motion in terms of the nonlocal gradient operator and its adjoint. A new example of nonlocal vector calculus operators is introduced, which shows the potential use of the general formulation for general nonlocal models.
Sir William Osler's perceptions of urolithiasis and the case of the indigo calculus.
Moran, Michael E; Das, Sakti; Rosenberg, Stuart A
2005-12-01
Sir William Osler published his textbook, The Principles and Practice of Medicine, in 1892. It became the definitive treatise on a wide variety of diseases. The section on nephrolithiasis clearly presents the etiology, pathology, symptoms, diagnosis, and treatments. What remains a mystery is the mention, under rare forms of human stones, of a type called "indigo." A search of Index Medicus starting from 1909 backward to its inception in 1879 was performed for key words "indigo," "calculus," "renal" or "bladder stones" and "indicanuria." Twelve textbooks of urology published before 1940 were scrutinized for references to indigo calculi. Only two references to indigo were found, both related to its use for treating constipation (1887 and 1891). Of the 12 textbooks, only 4 make passing reference to "indigo stones." They all mention that such calculi are very rare, but direct references to cases are lacking. One textbook references a study of blue stones from Egyptian mummies. It is unlikely that Osler's reference to an indigo calculus was taken lightly during his writing of The Principles and Practice of Medicine. The case of the indigo calculus is fascinating and perhaps enlightening if only for the source of Osler's intrigue.
Papastavridis, John G
1999-01-01
Tensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints.
The calculus a genetic approach
Toeplitz, Otto
2007-01-01
When first published posthumously in 1963, this book presented a radically different approach to the teaching of calculus. In sharp contrast to the methods of his time, Otto Toeplitz did not teach calculus as a static system of techniques and facts to be memorized. Instead, he drew on his knowledge of the history of mathematics and presented calculus as an organic evolution of ideas beginning with the discoveries of Greek scholars, such as Archimedes, Pythagoras, and Euclid, and developing through the centuries in the work of Kepler, Galileo, Fermat, Newton, and Leibniz. Through this unique a
Effectiveness of MnemoPow (Mnemonics Power Device in Teaching Limit Theorems of Calculus
Directory of Open Access Journals (Sweden)
Aldrin John J. Estonanto
2017-11-01
Full Text Available Calculus is oftentimes avoided by most students due to the common notion of its difficulty as a subject. Likewise, some studies revealed that most students find the topics in this subject very abstract to understand. To address these problems, a mnemonic device called MnemoPow (Mnemonics Power was developed. A quasi- experimental study was conducted in the laboratory high school of one state college in Sorsogon City to evaluate the effectiveness of the proposed mnemonic device. Two classes composed of forty- five (n= 45 students each were involved in this study as controlled and experimental group. The controlled group was introduced to Limit Theorems of Calculus using traditional lecture method while the experimental group was exposed to MnemoPow Device. Results of Pretest and Posttest were tested using t- test at 0. 05 level. Findings revealed that there is a significant difference between the performance of both groups. MnemoPow Device was found to be an effective approach in teaching Limit Theorems in Calculus.
Cristiani, Emanuela; Radini, Anita; Borić, Dušan; Robson, Harry K; Caricola, Isabella; Carra, Marialetizia; Mutri, Giuseppina; Oxilia, Gregorio; Zupancich, Andrea; Šlaus, Mario; Vujević, Dario
2018-05-25
In this contribution we dismantle the perceived role of marine resources and plant foods in the subsistence economy of Holocene foragers of the Central Mediterranean using a combination of dental calculus and stable isotope analyses. The discovery of fish scales and flesh fragments, starch granules and other plant and animal micro-debris in the dental calculus of a Mesolithic forager dated to the end of the 8th millenium BC and buried in the Vlakno Cave on Dugi Otok Island in the Croatian Archipelago demonstrates that marine resources were regularly consumed by the individual together with a variety of plant foods. Since previous stable isotope data in the Eastern Adriatic and the Mediterranean region emphasises that terrestrial-based resources contributed mainly to Mesolithic diets in the Mediterranean Basin, our results provide an alternative view of the dietary habits of Mesolithic foragers in the Mediterranean region based on a combination of novel methodologies and data.
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
Extraction of prostatic lumina and automated recognition for prostatic calculus image using PCA-SVM.
Wang, Zhuocai; Xu, Xiangmin; Ding, Xiaojun; Xiao, Hui; Huang, Yusheng; Liu, Jian; Xing, Xiaofen; Wang, Hua; Liao, D Joshua
2011-01-01
Identification of prostatic calculi is an important basis for determining the tissue origin. Computation-assistant diagnosis of prostatic calculi may have promising potential but is currently still less studied. We studied the extraction of prostatic lumina and automated recognition for calculus images. Extraction of lumina from prostate histology images was based on local entropy and Otsu threshold recognition using PCA-SVM and based on the texture features of prostatic calculus. The SVM classifier showed an average time 0.1432 second, an average training accuracy of 100%, an average test accuracy of 93.12%, a sensitivity of 87.74%, and a specificity of 94.82%. We concluded that the algorithm, based on texture features and PCA-SVM, can recognize the concentric structure and visualized features easily. Therefore, this method is effective for the automated recognition of prostatic calculi.
Extraction of Prostatic Lumina and Automated Recognition for Prostatic Calculus Image Using PCA-SVM
Wang, Zhuocai; Xu, Xiangmin; Ding, Xiaojun; Xiao, Hui; Huang, Yusheng; Liu, Jian; Xing, Xiaofen; Wang, Hua; Liao, D. Joshua
2011-01-01
Identification of prostatic calculi is an important basis for determining the tissue origin. Computation-assistant diagnosis of prostatic calculi may have promising potential but is currently still less studied. We studied the extraction of prostatic lumina and automated recognition for calculus images. Extraction of lumina from prostate histology images was based on local entropy and Otsu threshold recognition using PCA-SVM and based on the texture features of prostatic calculus. The SVM classifier showed an average time 0.1432 second, an average training accuracy of 100%, an average test accuracy of 93.12%, a sensitivity of 87.74%, and a specificity of 94.82%. We concluded that the algorithm, based on texture features and PCA-SVM, can recognize the concentric structure and visualized features easily. Therefore, this method is effective for the automated recognition of prostatic calculi. PMID:21461364
Nephrectomy for infected stag horn calculus confounded by the presence of squamous cell carcinoma.
Kondisetty, Sandeep; Borkar, Pallavi Vijay; Thomas, Appu
2017-09-27
Squamous cell carcinoma of kidney is a rare tumour of the many tumours seen in the kidney. It is usually associated with chronic irritation by a foreign body, which is mostly a stag horn calculus. Diagnosis of carcinoma in the presence of stag horn calculus is bizarre as it is seen in only <1% of patients. After imaging in this patient, the lymph nodes were enlarged and showed necrosis, which favoured the diagnosis of tuberculosis in a country where it is endemic. The pathological examination after surgery has amazed us by the presence of squamous cell carcinoma with lymph nodes positive with metastasis to vertebrae as the patient has presented to us with all symptoms of infection like pain and fever, which never made us think about malignancy preoperatively. © 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.
Analysis of tutoring in Calculus and Physics: a case study in Engineering courses
Directory of Open Access Journals (Sweden)
Jeronimo Becker Flores
2017-05-01
Full Text Available In this article, we analyzed the Calculus and Physics’ tutoring developed by a Higher Education Institution (HEI. The research consists of a qualitative approach of a type of case study. We began from the analytical reading of a theoretical basis which was relevant to the theme and then, we performed interviews with the professors responsible for the monitoring. The material was analyzed in the light of the Discursive Textual Analysis (DTA. As main results, we indicated that, in spite of the commonalities, there is no integrated work between Calculus and Physics subjects. In addition, we aimed the need of a reconciled pedagogical role among teachers, scholarship students and common ones. We also considered the need of future studies that reinforce and increase the discussions developed here.
Schoenly, Joshua E; Seka, Wolf; Rechmann, Peter
2010-01-01
A frequency-doubled Ti:sapphire laser is shown to selectively ablate dental calculus. The optimal transverse shape of the laser beam, including its variability under water-cooling, is determined for selective ablation of dental calculus. Intensity profiles under various water-cooling conditions were optically observed. The 400-nm laser was coupled into a multimode optical fiber using an f = 2.5-cm lens and light-shaping diffuser. Water-cooling was supplied coaxially around the fiber. Five human tooth samples (four with calculus and one pristine) were irradiated perpendicular to the tooth surface while the tooth was moved back and forth at 0.3 mm/second, varying between 20 and 180 iterations. The teeth were imaged before and after irradiation using light microscopy with a flashing blue light-emitting diode (LED). An environmental scanning electron microscope imaged each tooth after irradiation. High-order super-Gaussian intensity profiles are observed at the output of a fiber coiled around a 4-in. diameter drum. Super-Gaussian beams have a more-homogenous fluence distribution than Gaussian beams and have a higher energy efficiency for selective ablation. Coaxial water-cooling does not noticeably distort the intensity distribution within 1 mm from the optical fiber. In contrast, lasers focused to a Gaussian cross section (Calculus is preferentially ablated at high fluences (> or =2 J/cm(2)); below this fluence, stalling occurs because of photo-bleaching of the calculus. Healthy dental hard tissue is not removed at fluences calculus with a frequency-doubled Ti:sapphire laser. Fluences over 2 J/cm(2) are required to remove calculus efficiently since photo-bleaching stalls calculus removal below that value.
An outline of possible pre-course diagnostics for differential calculus
Directory of Open Access Journals (Sweden)
Aneshkumar Maharaj
2014-07-01
Full Text Available There is a view that many first-year students lack the basic knowledge and skills expected of them to study at university level. We examined the expected work habits and pre-course diagnostics for students who choose to take a course on differential calculus. We focused on the lecturer pre-course expectations of a student in the context of work habits, knowledge and technical skills. In particular, we formulated outcomes and then sample diagnostic questions to test whether the identified learning outcomes on expected work habits and learning are in place. If students are made aware of the expected learning outcomes and if they take the diagnostic test, they should be able to achieve greater success in their studies. The validity of this assumption will be the subject of a future paper which will report on the implementation of the learning outcomes and diagnostic questions that we formulated for pre-course diagnostics in differential calculus.