Fisher information, Borges operators, and q-calculus

Science.gov (United States)

Pennini, F.; Plastino, A.; Ferri, G. L.

2008-10-01

We discuss applying the increasingly popular q-calculus, or deformed calculus, so as to suitably generalize Fisher’s information measure and the Cramer-Rao inequality. A q-deformation can be attained in multiple ways, and we show that most of them do not constitute legitimate procedures. Within such a context, the only completely acceptable q-deformation is that ensuing from using the so-called Borges derivative [E.P. Borges, Physica A 340 (2004) 95].

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.

Tensor Calculus: Unlearning Vector Calculus

Science.gov (United States)

Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

2018-01-01

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…

Constructive Representation Theory for the Feynman Operator Calculus

CERN Document Server

Gill, T L

2006-01-01

In this paper, we survey recent progress on the constructive theory of the Feynman operator calculus. We first develop an operator version of the Henstock-Kurzweil integral, and a new Hilbert space that allows us to construct the elementary path integral in the manner originally envisioned by Feynman. After developing our time-ordered operator theory we extend a few of the important theorems of semigroup theory, including the Hille-Yosida theorem. As an application, we unify and extend the theory of time-dependent parabolic and hyperbolic evolution equations. We then develop a general perturbation theory and use it to prove that all theories generated by semigroups are asympotic in the operator-valued sense of Poincar e. This allows us to provide a general theory for the interaction representation of relativistic quantum theory. We then show that our theory can be reformulated as a physically motivated sum over paths, and use this version to extend the Feynman path integral to include more general interaction...

Discrete fractional calculus

CERN Document Server

Goodrich, Christopher

2015-01-01

This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...

Calculus for dummies

CERN Document Server

Ryan, Mark

2014-01-01

Slay the calculus monster with this user-friendly guide Calculus For Dummies, 2nd Edition makes calculus manageable-even if you're one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the ""how"" and ""why"" in plain English instead of math-speak. Through relevant instruction and practical examples, you'll s

Generalized vector calculus on convex domain

Science.gov (United States)

Agrawal, Om P.; Xu, Yufeng

2015-06-01

In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.

White noise calculus and Fock space

CERN Document Server

Obata, Nobuaki

1994-01-01

White Noise Calculus is a distribution theory on Gaussian space, proposed by T. Hida in 1975. This approach enables us to use pointwise defined creation and annihilation operators as well as the well-established theory of nuclear space.This self-contained monograph presents, for the first time, a systematic introduction to operator theory on fock space by means of white noise calculus. The goal is a comprehensive account of general expansion theory of Fock space operators and its applications. In particular,first order differential operators, Laplacians, rotation group, Fourier transform and their interrelations are discussed in detail w.r.t. harmonic analysis on Gaussian space. The mathematical formalism used here is based on distribution theory and functional analysis , prior knowledge of white noise calculus is not required.

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 ...

Symbolic boundary calculus and feedback operators

DEFF Research Database (Denmark)

Pedersen, Michael

1991-01-01

The recent developments in microlocal analysis and pseudodifferential boundary calculus are well suited tools in the investigation of a large number of problems occurring in control theory for partial differential equations. We explain some of the basic ideas of a pseudodifferential model...

Calculus

CERN Document Server

Jones, Patrick

2014-01-01

Practice makes perfect-and helps deepen your understanding of calculus 1001 Calculus Practice Problems For Dummies takes you beyond the instruction and guidance offered in Calculus For Dummies, giving you 1001 opportunities to practice solving problems from the major topics in your calculus course. Plus, an online component provides you with a collection of calculus problems presented in multiple-choice format to further help you test your skills as you go. Gives you a chance to practice and reinforce the skills you learn in your calculus courseHelps you refine your understanding of calculusP

Laparoscopic Cholecystectomy in Chronic Calculus Cholecystitis

Directory of Open Access Journals (Sweden)

Prakash Sapkota

2013-12-01

Full Text Available Introduction: Laparoscopic cholecystectomy has clearly become the choice over open cholecystectomy in the treatment of hepatobiliary disease since its introduction by Mouret in 1987. This study evaluates a series of patients with chronic calculus cholecystitis who were treated with laparoscopic and open cholecystectomy and assesses the outcomes of both techniques. Objective: To evaluate the efficacy of laparoscopic vs open cholecystectomy in chronic calculus cholecystitis and establish the out-comes of this treatment modality at Lumbini Medical College and Teaching Hospital. Methods: This was a retrospective analysis over a one-year period (January 1, 2012 to December 31, 2012, per-formed by single surgeon at Lumbini Medical College and Teaching Hospital located midwest of Nepal. 166 patients underwent surgical treatment for chronic calculus cholecystitis. Patients included were only chronic calculus cholecystitis proven histopathologocally and the rest were excluded. Data was collected which included patients demographics, medical history, presentation, complications, conversion rates from laparoscopic. cholecystectomy to open cholecystectomy, operative and postoperative time. Results: Patients treated with laparoscopic cholecystectomy for chronic calculus cholecystitis had shorter operating times and length of stay compared to patients treated with open cholecystectomy for chronic calculus cholecystitis. Conversion rates were 3.54% in chronic calculus cholecystitis during the study period. Complications were also lower in patients who underwent laparoscopic cholecystectomy versus open cholecystectomy for cholelithiasis. Conclusions: Laparoscopic cholecystectomy appears to be a reliable, safe, and cost-effective treatment modality for chronic calculus cholecystitis.

Pre-Calculus For Dummies

CERN Document Server

Kuang, Yang

2012-01-01

The fun and easy way to learn pre-calculus Getting ready for calculus but still feel a bit confused? Have no fear. Pre-Calculus For Dummies is an un-intimidating, hands-on guide that walks you through all the essential topics, from absolute value and quadratic equations to logarithms and exponential functions to trig identities and matrix operations. With this guide's help you'll quickly and painlessly get a handle on all of the concepts - not just the number crunching - and understand how to perform all pre-calc tasks, from graphing to tackling proofs. You'll also get a new appreciation for

The stack calculus

Directory of Open Access Journals (Sweden)

Alberto Carraro

2013-03-01

Full Text Available We introduce a functional calculus with simple syntax and operational semantics in which the calculi introduced so far in the Curry-Howard correspondence for Classical Logic can be faithfully encoded. Our calculus enjoys confluence without any restriction. Its type system enforces strong normalization of expressions and it is a sound and complete system for full implicational Classical Logic. We give a very simple denotational semantics which allows easy calculations of the interpretation of expressions.

Scale calculus and the Schroedinger equation

International Nuclear Information System (INIS)

Cresson, Jacky

2003-01-01

This paper is twofold. In a first part, we extend the classical differential calculus to continuous nondifferentiable functions by developing the notion of scale calculus. The scale calculus is based on a new approach of continuous nondifferentiable functions by constructing a one parameter family of differentiable functions f(t,ε) such that f(t,ε)→f(t) when ε goes to zero. This led to several new notions as representations: fractal functions and ε-differentiability. The basic objects of the scale calculus are left and right quantum operators and the scale operator which generalizes the classical derivative. We then discuss some algebraic properties of these operators. We define a natural bialgebra, called quantum bialgebra, associated with them. Finally, we discuss a convenient geometric object associated with our study. In a second part, we define a first quantization procedure of classical mechanics following the scale relativity theory developed by Nottale. We obtain a nonlinear Schroedinger equation via the classical Newton's equation of dynamics using the scale operator. Under special assumptions we recover the classical Schroedinger equation and we discuss the relevance of these assumptions

Computational approach to Thornley's problem by bivariate operational calculus

Science.gov (United States)

Bazhlekova, E.; Dimovski, I.

2012-10-01

Thornley's problem is an initial-boundary value problem with a nonlocal boundary condition for linear onedimensional reaction-diffusion equation, used as a mathematical model of spiral phyllotaxis in botany. Applying a bivariate operational calculus we find explicit representation of the solution, containing two convolution products of special solutions and the arbitrary initial and boundary functions. We use a non-classical convolution with respect to the space variable, extending in this way the classical Duhamel principle. The special solutions involved are represented in the form of fast convergent series. Numerical examples are considered to show the application of the present technique and to analyze the character of the solution.

BRST-operator for quantum Lie algebra and differential calculus on quantum groups

International Nuclear Information System (INIS)

Isaev, A.P.; Ogievetskij, O.V.

2001-01-01

For A Hopf algebra one determined structure of differential complex in two dual external Hopf algebras: A external expansion and in A* dual algebra external expansion. The Heisenberg double of these two Hopf algebras governs the differential algebra for the Cartan differential calculus on A algebra. The forst differential complex is the analog of the de Rame complex. The second complex coincide with the standard complex. Differential is realized as (anti)commutator with Q BRST-operator. Paper contains recursion relation that determines unequivocally Q operator. For U q (gl(N)) Lie quantum algebra one constructed BRST- and anti-BRST-operators and formulated the theorem of the Hodge expansion [ru

The ZX-calculus is complete for stabilizer quantum mechanics

International Nuclear Information System (INIS)

Backens, Miriam

2014-01-01

The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics (QM), meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound, i.e. any equality that can be derived graphically can also be derived using matrix mechanics. Here, we show that the ZX-calculus is complete for pure qubit stabilizer QM, meaning any equality that can be derived using matrices can also be derived pictorially. The proof relies on bringing diagrams into a normal form based on graph states and local Clifford operations. (paper)

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...

Multiplicative calculus in biomedical image analysis

NARCIS (Netherlands)

Florack, L.M.J.; Assen, van H.C.

2011-01-01

We advocate the use of an alternative calculus in biomedical image analysis, known as multiplicative (a.k.a. non-Newtonian) calculus. It provides a natural framework in problems in which positive images or positive definite matrix fields and positivity preserving operators are of interest. Indeed,

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.

Synthesizing controllers from duration calculus

DEFF Research Database (Denmark)

Fränzle, Martin

1996-01-01

Duration Calculus is a logic for reasoning about requirements for real-time systems at a high level of abstraction from operational detail, which qualifies it as an interesting starting point for embedded controller design. Such a design activity is generally thought to aim at a control device...... the physical behaviours of which satisfy the requirements formula, i.e. the refinement relation between requirements and implementations is taken to be trajectory inclusion. Due to the abstractness of the vocabulary of Duration Calculus, trajectory inclusion between control requirements and controller designs...... for embedded controller design and exploit this fact for developing an automatic procedure for controller synthesis from specifications formalized in Duration Calculus. As far as we know, this is the first positive result concerning feasibility of automatic synthesis from dense-time Duration Calculus....

On Functional Calculus Estimates

NARCIS (Netherlands)

Schwenninger, F.L.

2015-01-01

This thesis presents various results within the field of operator theory that are formulated in estimates for functional calculi. Functional calculus is the general concept of defining operators of the form $f(A)$, where f is a function and $A$ is an operator, typically on a Banach space. Norm

Quantum variational calculus

CERN Document Server

Malinowska, Agnieszka B

2014-01-01

This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of its results is that they are able to deal with nondifferentiable (even discontinuous) functions, which are important in applications. Possible applications in economics are discussed. Economists model time as continuous or discrete. Although individual economic decisions are generally made at discrete time intervals, they may well be less than perfectly synchronized in ways discrete models postulate. On the other hand, the usual assumption that economic activity takes place continuously, is nothing else than a convenient abstraction that in many applications is far from reality. The Hahn quantum calculus helps to bridge the gap between the two families of models: continuous and discrete. Quantum Variational Calculus is self-contained and unified in presentation. It provides an opportunity for an introduction to the quantum calculus of variations fo...

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

OpenAIRE

Alali, Bacim; Liu, Kuo; Gunzburger, Max

2014-01-01

A nonlocal vector calculus was introduced in [2] that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A generalization is developed that provides a more general setting for the nonlocal vector calculus that is independent of particular nonlocal models. It is shown that general nonlocal calculus operators are integral operators with specific integral kernels. General nonlocal calculus properties are developed, including nonlocal...

Finite-dimensional calculus

International Nuclear Information System (INIS)

Feinsilver, Philip; Schott, Rene

2009-01-01

We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement infinite terms Rota's 'finite operator calculus'.

Calculus light

CERN Document Server

Friedman, Menahem

2011-01-01

Another Calculus book? As long as students find calculus scary, the failure rate in mathematics is higher than in all other subjects, and as long as most people mistakenly believe that only geniuses can learn and understand mathematics, there will always be room for a new book of Calculus. We call it Calculus Light. This book is designed for a one semester course in ""light"" calculus -- mostly single variable, meant to be used by undergraduate students without a wide mathematical background and who do not major in mathematics but study subjects such as engineering, biology or management infor

Fractional calculus in bioengineering, part 3.

Science.gov (United States)

Magin, Richard L

2004-01-01

Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub

Calculus

CERN Document Server

Larson, Ron

2014-01-01

The Larson CALCULUS program has a long history of innovation in the calculus market. It has been widely praised by a generation of students and professors for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.

Impact of Calculus Reform in a Liberal Arts Calculus Course.

Science.gov (United States)

Brosnan, Patricia A.; Ralley, Thomas G.

This report describes the changes in a freshman-level calculus course that occurred as a consequence of adopting the Harvard Consortium Calculus text. The perspective is that of the lecturer. The course is intended as an introduction to calculus for liberal arts students, that is, students who will not be expected to use calculus as a mathematical…

Calculus

CERN Document Server

Grossman, Stanley I

1981-01-01

Calculus, Second Edition discusses the techniques and theorems of calculus. This edition introduces the sine and cosine functions, distributes ?-? material over several chapters, and includes a detailed account of analytic geometry and vector analysis.This book also discusses the equation of a straight line, trigonometric limit, derivative of a power function, mean value theorem, and fundamental theorems of calculus. The exponential and logarithmic functions, inverse trigonometric functions, linear and quadratic denominators, and centroid of a plane region are likewise elaborated. Other topics

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...

Fundamentals of calculus

CERN Document Server

Morris, Carla C

2015-01-01

Fundamentals of Calculus encourages students to use power, quotient, and product rules for solutions as well as stresses the importance of modeling skills.  In addition to core integral and differential calculus coverage, the book features finite calculus, which lends itself to modeling and spreadsheets.  Specifically, finite calculus is applied to marginal economic analysis, finance, growth, and decay.  Includes: Linear Equations and FunctionsThe DerivativeUsing the Derivative Exponential and Logarithmic Functions Techniques of DifferentiationIntegral CalculusIntegration TechniquesFunctions

Semiclassical dynamics and magnetic Weyl calculus

International Nuclear Information System (INIS)

Lein, Maximilian Stefan

2011-01-01

Weyl quantization and related semiclassical techniques can be used to study conduction properties of crystalline solids subjected to slowly-varying, external electromagnetic fields. The case where the external magnetic field is constant, is not covered by existing theory as proofs involving usual Weyl calculus break down. This is the regime of the so-called quantum Hall effect where quantization of transverse conductance is observed. To rigorously derive semiclassical equations of motion, one needs to systematically develop a magnetic Weyl calculus which contains a semiclassical parameter. Mathematically, the operators involved in the analysis are magnetic pseudodifferential operators, a topic which by itself is of interest for the mathematics and mathematical physics community alike. Hence, we will devote two additional chapters to further understanding of properties of those operators. (orig.)

Semiclassical dynamics and magnetic Weyl calculus

Energy Technology Data Exchange (ETDEWEB)

Lein, Maximilian Stefan

2011-01-19

Weyl quantization and related semiclassical techniques can be used to study conduction properties of crystalline solids subjected to slowly-varying, external electromagnetic fields. The case where the external magnetic field is constant, is not covered by existing theory as proofs involving usual Weyl calculus break down. This is the regime of the so-called quantum Hall effect where quantization of transverse conductance is observed. To rigorously derive semiclassical equations of motion, one needs to systematically develop a magnetic Weyl calculus which contains a semiclassical parameter. Mathematically, the operators involved in the analysis are magnetic pseudodifferential operators, a topic which by itself is of interest for the mathematics and mathematical physics community alike. Hence, we will devote two additional chapters to further understanding of properties of those operators. (orig.)

Regularization of positive definite matrix fields based on multiplicative calculus

NARCIS (Netherlands)

Florack, L.M.J.; Bruckstein, A.M.; Haar Romeny, ter B.M.; Bronstein, A.M.; Bronstein, M.M.

2012-01-01

Multiplicative calculus provides a natural framework in problems involving positive images and positivity preserving operators. In increasingly important, complex imaging frameworks, such as diffusion tensor imaging, it complements standard calculus in a nontrivial way. The purpose of this article

Calculus refresher

CERN Document Server

Klaf, A A

1956-01-01

This book is unique in English as a refresher for engineers, technicians, and students who either wish to brush up their calculus or find parts of calculus unclear. It is not an ordinary textbook. It is, instead, an examination of the most important aspects of integral and differential calculus in terms of the 756 questions most likely to occur to the technical reader. It provides a very easily followed presentation and may also be used as either an introductory or supplementary textbook. The first part of this book covers simple differential calculus, with constants, variables, functions, inc

Quantum mechanics and umbral calculus

International Nuclear Information System (INIS)

Lopez-Sendino, J E; Negro, J; Olmo, M A del; Salgado, E

2008-01-01

In this paper we present the first steps for obtaining a discrete Quantum Mechanics making use of the Umbral Calculus. The idea is to discretize the continuous Schroedinger equation substituting the continuous derivatives by discrete ones and the space-time continuous variables by well determined operators that verify some Umbral Calculus conditions. In this way we assure that some properties of integrability and symmetries of the continuous equation are preserved and also the solutions of the continuous case can be recovered discretized in a simple way. The case of the Schroedinger equation with a potential depending only in the space variable is discussed.

The umbral calculus

CERN Document Server

Roman, Steven

2005-01-01

Geared toward upper-level undergraduates and graduate students, this elementary introduction to classical umbral calculus requires only an acquaintance with the basic notions of algebra and a bit of applied mathematics (such as differential equations) to help put the theory in mathematical perspective. Subjects include Sheffer sequences and operators and their adjoints, with numerous examples of associated and other sequences. Related topics encompass the connection constants problem and duplication formulas, the Lagrange inversion formula, operational formulas, inverse relations, and binomial

Vector Differential Calculus

OpenAIRE

HITZER, Eckhard MS

2002-01-01

This paper treats the fundamentals of the vector differential calculus part of universal geometric calculus. Geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. In order to make the treatment self-contained, I first compile all important geometric algebra relationships,which are necesssary for vector differential calculus. Then differentiation by vectors is introduced and a host of major ve...

Graphical calculus of volume, inverse volume and Hamiltonian operators in loop quantum gravity

Energy Technology Data Exchange (ETDEWEB)

Yang, Jinsong [Guizhou University, Department of Physics, Guiyang (China); Academia Sinica, Institute of Physics, Taipei (China); Ma, Yongge [Beijing Normal University, Department of Physics, Beijing (China)

2017-04-15

To adopt a practical method to calculate the action of geometrical operators on quantum states is a crucial task in loop quantum gravity. In this paper, the graphical calculus based on the original Brink graphical method is applied to loop quantum gravity along the line of previous work. The graphical method provides a very powerful technique for simplifying complicated calculations. The closed formula of the volume operator and the actions of the Euclidean Hamiltonian constraint operator and the so-called inverse volume operator on spin-network states with trivalent vertices are derived via the graphical method. By employing suitable and non-ambiguous graphs to represent the action of operators as well as the spin-network states, we use the simple rules of transforming graphs to obtain the resulting formula. Comparing with the complicated algebraic derivation in some literature, our procedure is more concise, intuitive and visual. The resulting matrix elements of the volume operator is compact and uniform, fitting for both gauge-invariant and gauge-variant spin-network states. Our results indicate some corrections to the existing results for the Hamiltonian operator and inverse volume operator in the literature. (orig.)

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, ...

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

Science.gov (United States)

Sonnert, Gerhard; Sadler, Philip M.

2014-11-01

Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and four-year colleges continues to grow, and these courses are well-populated with students who already took pre-calculus in high school. We examine student performance in college calculus, using regression discontinuity to estimate the effects of taking college pre-calculus or not, in a national US sample of 5507 students at 132 institutions. We find that students who take college pre-calculus do not earn higher calculus grades.

Two-parameter asymptotics in magnetic Weyl calculus

International Nuclear Information System (INIS)

Lein, Max

2010-01-01

This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter ε, the case of small coupling λ to the magnetic vector potential naturally occurs in this context. Magnetic Weyl calculus is adapted to incorporate both parameters, at least one of which needs to be small. Of particular interest is the expansion of the Weyl product which can be used to expand the product of operators in a small parameter, a technique which is prominent to obtain perturbation expansions. Three asymptotic expansions for the magnetic Weyl product of two Hoermander class symbols are proven as (i) ε<< 1 and λ<< 1, (ii) ε<< 1 and λ= 1, as well as (iii) ε= 1 and λ<< 1. Expansions (i) and (iii) are impossible to obtain with ordinary Weyl calculus. Furthermore, I relate the results derived by ordinary Weyl calculus with those obtained with magnetic Weyl calculus by one- and two-parameter expansions. To show the power and versatility of magnetic Weyl calculus, I derive the semirelativistic Pauli equation as a scaling limit from the Dirac equation up to errors of fourth order in 1/c.

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

Science.gov (United States)

Wan, Tien-Chun; Cheng, Fu-Yuan; Liu, Yu-Tse; Lin, Liang-Chuan; Sakata, Ryoichi

2009-12-01

The purpose of the study was to investigate bioactive compounds of in vitro cultured Calculus Suis and natural Calculus Bovis obtained as valuable by-products from animals used for meat production. The results showed that the components of natural Calculus Bovis were rich in bilirubin and biliverdin and had higher content of essential amino acids. The major amino acids of in vitro cultured Calculus Suis were identified as glycine, alanine, glutamic acid and aspartic acid, and those for natural Calculus Bovis were found to be glutamic acid, aspartic acid, proline, and arginine. The methionine and cysteine contents of precursors for glutathione in natural Calculus Bovis were significantly higher than those of in vitro cultured Calculus Suis. The mineral contents of zinc, iron and manganese of natural Calculus Bovis were significantly higher than those of in vitro cultured Calculus Suis. The major bile acids in both products were cholic acid and dehydrocholic acid, respectively. The chenodeoxycholic and ursodeoxycholic acid content of in vitro cultured Calculus Suis was significantly higher than that of natural Calculus Bovis.

Fractional vector calculus and fractional Maxwell's equations

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2008-01-01

The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using a fractional generalization of the Fundamental Theorem of Calculus. We define the differential and integral vector operations. The fractional Green's, Stokes' and Gauss's theorems are formulated. The proofs of these theorems are realized for simplest regions. A fractional generalization of exterior differential calculus of differential forms is discussed. Fractional nonlocal Maxwell's equations and the corresponding fractional wave equations are considered

Propositional Calculus in Coq

OpenAIRE

van Doorn, Floris

2015-01-01

I formalize important theorems about classical propositional logic in the proof assistant Coq. The main theorems I prove are (1) the soundness and completeness of natural deduction calculus, (2) the equivalence between natural deduction calculus, Hilbert systems and sequent calculus and (3) cut elimination for sequent calculus.

Noncausal stochastic calculus

CERN Document Server

Ogawa, Shigeyoshi

2017-01-01

This book presents an elementary introduction to the theory of noncausal stochastic calculus that arises as a natural alternative to the standard theory of stochastic calculus founded in 1944 by Professor Kiyoshi Itô. As is generally known, Itô Calculus is essentially based on the "hypothesis of causality", asking random functions to be adapted to a natural filtration generated by Brownian motion or more generally by square integrable martingale. The intention in this book is to establish a stochastic calculus that is free from this "hypothesis of causality". To be more precise, a noncausal theory of stochastic calculus is developed in this book, based on the noncausal integral introduced by the author in 1979. After studying basic properties of the noncausal stochastic integral, various concrete problems of noncausal nature are considered, mostly concerning stochastic functional equations such as SDE, SIE, SPDE, and others, to show not only the necessity of such theory of noncausal stochastic calculus but ...

Model Checking Processes Specified In Join-Calculus Algebra

Directory of Open Access Journals (Sweden)

Sławomir Piotr Maludziński

2014-01-01

Full Text Available This article presents a model checking tool used to verify concurrent systems specified in join-calculus algebra. The temporal properties of systems under verification are expressed in CTL logic. Join-calculus algebra with its operational semantics defined by the chemical abstract machine serves as the basic method for the specification of concurrent systems and their synchronization mechanisms, and allows the examination of more complex systems.

Renal calculus

CERN Document Server

Pyrah, Leslie N

1979-01-01

Stone in the urinary tract has fascinated the medical profession from the earliest times and has played an important part in the development of surgery. The earliest major planned operations were for the removal of vesical calculus; renal and ureteric calculi provided the first stimulus for the radiological investigation of the viscera, and the biochemical investigation of the causes of calculus formation has been the training ground for surgeons interested in metabolic disorders. It is therefore no surprise that stone has been the subject of a number of monographs by eminent urologists, but the rapid development of knowledge has made it possible for each one of these authors to produce something new. There is still a technical challenge to the surgeon in the removal of renal calculi, and on this topic we are always glad to have the advice of a master craftsman; but inevitably much of the interest centres on the elucidation of the causes of stone formation and its prevention. Professor Pyrah has had a long an...

Golden quantum oscillator and Binet–Fibonacci calculus

International Nuclear Information System (INIS)

Pashaev, Oktay K; Nalci, Sengul

2012-01-01

The Binet formula for Fibonacci numbers is treated as a q-number and a q-operator with Golden ratio bases q = φ and Q = −1/φ, and the corresponding Fibonacci or Golden calculus is developed. A quantum harmonic oscillator for this Golden calculus is derived so that its spectrum is given only by Fibonacci numbers. The ratio of successive energy levels is found to be the Golden sequence, and for asymptotic states in the limit n → ∞ it appears as the Golden ratio. We call this oscillator the Golden oscillator. Using double Golden bosons, the Golden angular momentum and its representation in terms of Fibonacci numbers and the Golden ratio are derived. Relations of Fibonacci calculus with a q-deformed fermion oscillator and entangled N-qubit states are indicated. (paper)

Golden quantum oscillator and Binet-Fibonacci calculus

Energy Technology Data Exchange (ETDEWEB)

Pashaev, Oktay K; Nalci, Sengul, E-mail: oktaypashaev@iyte.edu.tr [Department of Mathematics, Izmir Institute of Technology, Urla-Izmir 35430 (Turkey)

2012-01-13

The Binet formula for Fibonacci numbers is treated as a q-number and a q-operator with Golden ratio bases q = {phi} and Q = -1/{phi}, and the corresponding Fibonacci or Golden calculus is developed. A quantum harmonic oscillator for this Golden calculus is derived so that its spectrum is given only by Fibonacci numbers. The ratio of successive energy levels is found to be the Golden sequence, and for asymptotic states in the limit n {yields} {infinity} it appears as the Golden ratio. We call this oscillator the Golden oscillator. Using double Golden bosons, the Golden angular momentum and its representation in terms of Fibonacci numbers and the Golden ratio are derived. Relations of Fibonacci calculus with a q-deformed fermion oscillator and entangled N-qubit states are indicated. (paper)

Calculus II For Dummies

CERN Document Server

Zegarelli, Mark

2012-01-01

An easy-to-understand primer on advanced calculus topics Calculus II is a prerequisite for many popular college majors, including pre-med, engineering, and physics. Calculus II For Dummies offers expert instruction, advice, and tips to help second semester calculus students get a handle on the subject and ace their exams. It covers intermediate calculus topics in plain English, featuring in-depth coverage of integration, including substitution, integration techniques and when to use them, approximate integration, and improper integrals. This hands-on guide also covers sequences and series, wit

Quantum stochastic calculus associated with quadratic quantum noises

International Nuclear Information System (INIS)

Ji, Un Cig; Sinha, Kalyan B.

2016-01-01

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus

Quantum stochastic calculus associated with quadratic quantum noises

Energy Technology Data Exchange (ETDEWEB)

Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr [Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju, Chungbuk 28644 (Korea, Republic of); Sinha, Kalyan B., E-mail: kbs-jaya@yahoo.co.in [Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore-64, India and Department of Mathematics, Indian Institute of Science, Bangalore-12 (India)

2016-02-15

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus.

Periodic-drop-take calculus for stream transformers

NARCIS (Netherlands)

Mak, R.H.

2005-01-01

Stream transformers are a formalism to specify and reason about stream processing systems. Many application specific circuits, e.g. in the area of signal processing, classify as such systems. This paper presents a two- operator calculus to reason about a specific class of stream operators, viz. the

Early Vector Calculus: A Path through Multivariable Calculus

Science.gov (United States)

Robertson, Robert L.

2013-01-01

The divergence theorem, Stokes' theorem, and Green's theorem appear near the end of calculus texts. These are important results, but many instructors struggle to reach them. We describe a pathway through a standard calculus text that allows instructors to emphasize these theorems. (Contains 2 figures.)

Executable Behaviour and the π-Calculus (extended abstract

Directory of Open Access Journals (Sweden)

Bas Luttik

2015-08-01

Full Text Available Reactive Turing machines extend classical Turing machines with a facility to model observable interactive behaviour. We call a behaviour executable if, and only if, it is behaviourally equivalent to the behaviour of a reactive Turing machine. In this paper, we study the relationship between executable behaviour and behaviour that can be specified in the pi-calculus. We establish that all executable behaviour can be specified in the pi-calculus up to divergence-preserving branching bisimilarity. The converse, however, is not true due to (intended limitations of the model of reactive Turing machines. That is, the pi-calculus allows the specification of behaviour that is not executable up to divergence-preserving branching bisimilarity. Motivated by an intuitive understanding of executability, we then consider a restriction on the operational semantics of the pi-calculus that does associate with every pi-term executable behaviour, at least up to the version of branching bisimilarity that does not require the preservation of divergence.

Calculus

CERN Document Server

Spivak, Michael

2006-01-01

Spivak's celebrated textbook is widely held as one of the finest introductions to mathematical analysis. His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.

Boolean integral calculus

Science.gov (United States)

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

1988-01-01

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

Particular Solutions of the Confluent Hypergeometric Differential Equation by Using the Nabla Fractional Calculus Operator

Directory of Open Access Journals (Sweden)

Resat Yilmazer

2016-02-01

Full Text Available In this work; we present a method for solving the second-order linear ordinary differential equation of hypergeometric type. The solutions of this equation are given by the confluent hypergeometric functions (CHFs. Unlike previous studies, we obtain some different new solutions of the equation without using the CHFs. Therefore, we obtain new discrete fractional solutions of the homogeneous and non-homogeneous confluent hypergeometric differential equation (CHE by using a discrete fractional Nabla calculus operator. Thus, we obtain four different new discrete complex fractional solutions for these equations.

Tuplix calculus

NARCIS (Netherlands)

Bergstra, J.A.; Ponse, A.; van der Zwaag, M.B.

2008-01-01

We introduce a calculus for tuplices, which are expressions that generalize matrices and vectors. Tuplices have an underlying data type for quantities that are taken from a zero-totalized field. We start with the core tuplix calculus CTC for entries and tests, which are combined using conjunctive

Calculus with applications

CERN Document Server

Lax, Peter D

2014-01-01

This new edition of Lax, Burstein, and Lax's Calculus with Applications and Computing offers meaningful explanations of the important theorems of single variable calculus. Written with students in mathematics, the physical sciences, and engineering in mind, and revised with their help, it shows that the themes of calculation, approximation, and modeling are central to mathematics and the main ideas of single variable calculus. This edition brings the innovation of the first edition to a new generation of students. New sections in this book use simple, elementary examples to show that when applying calculus concepts to approximations of  functions, uniform convergence is more natural and easier to use than point-wise convergence. As in the original, this edition includes material that is essential for students in science and engineering, including an elementary introduction to complex numbers and complex-valued functions, applications of calculus to modeling vibrations and population dynamics, and an introduc...

Sampling, Splitting and Merging in Coinductive Stream Calculus

NARCIS (Netherlands)

M. Niqui (Milad); J.J.M.M. Rutten (Jan); C. Bolduc; J. Desharnais; B. Ktari

2010-01-01

textabstractWe study various operations for partitioning, projecting and merging streams of data. These operations are motivated by their use in dataflow programming and the stream processing languages. We use the framework of \\emph{stream calculus} and \\emph{stream circuits} for defining and

Sampling, splitting and merging in coinductive stream calculus

NARCIS (Netherlands)

M. Niqui (Milad); J.J.M.M. Rutten (Jan)

2009-01-01

htmlabstractWe study various operations for partitioning, projecting and merging streams of data. These operations are motivated by their use in dataflow programming and the stream processing languages. We use the framework of stream calculus and stream circuits for defining and proving properties

Calculus of one variable

CERN Document Server

Grossman, Stanley I

1986-01-01

Calculus of One Variable, Second Edition presents the essential topics in the study of the techniques and theorems of calculus.The book provides a comprehensive introduction to calculus. It contains examples, exercises, the history and development of calculus, and various applications. Some of the topics discussed in the text include the concept of limits, one-variable theory, the derivatives of all six trigonometric functions, exponential and logarithmic functions, and infinite series.This textbook is intended for use by college students.

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

OpenAIRE

Caputo, M. Cristina

2009-01-01

In this note we show how one can obtain results from the nabla calculus from results on the delta calculus and vice versa via a duality argument. We provide applications of the main results to the calculus of variations on time scales.

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

CERN Document Server

Banner, Adrian

2009-01-01

For many students, calculus can be the most mystifying and frustrating course they will ever take. The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it. All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of

On the refinement calculus

CERN Document Server

Vickers, Trevor

1992-01-01

On the Refinement Calculus gives one view of the development of the refinement calculus and its attempt to bring together - among other things - Z specifications and Dijkstra's programming language. It is an excellent source of reference material for all those seeking the background and mathematical underpinnings of the refinement calculus.

The perturbative Regge-calculus regime of loop quantum gravity

International Nuclear Information System (INIS)

Bianchi, Eugenio; Modesto, Leonardo

2008-01-01

The relation between loop quantum gravity and Regge calculus has been pointed out many times in the literature. In particular the large spin asymptotics of the Barrett-Crane vertex amplitude is known to be related to the Regge action. In this paper we study a semiclassical regime of loop quantum gravity and show that it admits an effective description in terms of perturbative area-Regge-calculus. The regime of interest is identified by a class of states given by superpositions of four-valent spin networks, peaked on large spins. As a probe of the dynamics in this regime, we compute explicitly two- and three-area correlation functions at the vertex amplitude level. We find that they match with the ones computed perturbatively in area-Regge-calculus with a single 4-simplex, once a specific perturbative action and measure have been chosen in the Regge-calculus path integral. Correlations of other geometric operators and the existence of this regime for other models for the dynamics are briefly discussed

Quantum calculus new concepts, impulsive IVPs and BVPs, inequalities

CERN Document Server

Ahmad, Bashir; Tariboon, Jessada

2016-01-01

The main objective of this book is to extend the scope of the q-calculus based on the definition of q-derivative [Jackson (1910)] to make it applicable to dense domains. As a matter of fact, Jackson's definition of q-derivative fails to work for impulse points while this situation does not arise for impulsive equations on q-time scales as the domains consist of isolated points covering the case of consecutive points. In precise terms, we study quantum calculus on finite intervals.In the first part, we discuss the concepts of qk-derivative and qk-integral, and establish their basic properties. As applications, we study initial and boundary value problems of impulsive qk-difference equations and inclusions equipped with different kinds of boundary conditions. We also transform some classical integral inequalities and develop some new integral inequalities for convex functions in the context of qk-calculus. In the second part, we develop fractional quantum calculus in relation to a new qk-shifting operator and e...

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

Science.gov (United States)

Sonnert, Gerhard; Sadler, Philip M.

2014-01-01

Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and…

Fractional Calculus in Hydrologic Modeling: A Numerical Perspective

Energy Technology Data Exchange (ETDEWEB)

David A. Benson; Mark M. Meerschaert; Jordan Revielle

2012-01-01

Fractional derivatives can be viewed either as a handy extension of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Levy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Levy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus.

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...

Foundations for relativistic quantum theory. I. Feynman's operator calculus and the Dyson conjectures

International Nuclear Information System (INIS)

Gill, Tepper L.; Zachary, W.W.

2002-01-01

In this paper, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson's second conjecture for quantum electrodynamics. In addition, we show that the expansion may be considered exact to any finite order by producing the remainder term. This implies that every nonperturbative solution has a perturbative expansion. Using a physical analysis of information from experiment versus that implied by our models, we reformulate our theory as a sum over paths. This allows us to relate our theory to Feynman's path integral, and to prove Dyson's first conjecture that the divergences are in part due to a violation of Heisenberg's uncertainly relations

Pre-calculus essentials

CERN Document Server

Woodward, Ernest

2012-01-01

REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Pre-Calculus reviews sets, numbers, operations and properties, coordinate geometry, fundamental algebraic topics, solving equations and inequalities, functions, trigonometry, exponents

An ellipsoidal calculus based on propagation and fusion.

Science.gov (United States)

Ros, L; Sabater, A; Thomas, F

2002-01-01

Presents an ellipsoidal calculus based solely on two basic operations: propagation and fusion. Propagation refers to the problem of obtaining an ellipsoid that must satisfy an affine relation with another ellipsoid, and fusion to that of computing the ellipsoid that tightly bounds the intersection of two given ellipsoids. These two operations supersede the Minkowski sum and difference, affine transformation and intersection tight bounding of ellipsoids on which other ellipsoidal calculi are based. Actually, a Minkowski operation can be seen as a fusion followed by a propagation and an affine transformation as a particular case of propagation. Moreover, the presented formulation is numerically stable in the sense that it is immune to degeneracies of the involved ellipsoids and/or affine relations. Examples arising when manipulating uncertain geometric information in the context of the spatial interpretation of line drawings are extensively used as a testbed for the presented calculus.

Multivariable calculus with applications

CERN Document Server

Lax, Peter D

2017-01-01

This text in multivariable calculus fosters comprehension through meaningful explanations. Written with students in mathematics, the physical sciences, and engineering in mind, it extends concepts from single variable calculus such as derivative, integral, and important theorems to partial derivatives, multiple integrals, Stokes’ and divergence theorems. Students with a background in single variable calculus are guided through a variety of problem solving techniques and practice problems. Examples from the physical sciences are utilized to highlight the essential relationship between calculus and modern science. The symbiotic relationship between science and mathematics is shown by deriving and discussing several conservation laws, and vector calculus is utilized to describe a number of physical theories via partial differential equations. Students will learn that mathematics is the language that enables scientific ideas to be precisely formulated and that science is a source for the development of mathemat...

Calculus

CERN Document Server

Grossman, Stanley I

1984-01-01

Calculus, Third Edition emphasizes the techniques and theorems of calculus, including many applied examples and exercises in both drill and applied-type problems.This book discusses shifting the graphs of functions, derivative as a rate of change, derivative of a power function, and theory of maxima and minima. The area between two curves, differential equations of exponential growth and decay, inverse hyperbolic functions, and integration of rational functions are also elaborated. This text likewise covers the fluid pressure, ellipse and translation of axes, graphing in polar coordinates, pro

Calculus of variations

CERN Document Server

Elsgolc, L E; Stark, M

1961-01-01

Calculus of Variations aims to provide an understanding of the basic notions and standard methods of the calculus of variations, including the direct methods of solution of the variational problems. The wide variety of applications of variational methods to different fields of mechanics and technology has made it essential for engineers to learn the fundamentals of the calculus of variations. The book begins with a discussion of the method of variation in problems with fixed boundaries. Subsequent chapters cover variational problems with movable boundaries and some other problems; sufficiency

Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

KAUST Repository

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.

Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes

Science.gov (United States)

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.

Intuitionistic fuzzy calculus

CERN Document Server

Lei, Qian

2017-01-01

This book offers a comprehensive and systematic review of the latest research findings in the area of intuitionistic fuzzy calculus. After introducing the intuitionistic fuzzy numbers’ operational laws and their geometrical and algebraic properties, the book defines the concept of intuitionistic fuzzy functions and presents the research on the derivative, differential, indefinite integral and definite integral of intuitionistic fuzzy functions. It also discusses some of the methods that have been successfully used to deal with continuous intuitionistic fuzzy information or data, which are different from the previous aggregation operators focusing on discrete information or data. Mainly intended for engineers and researchers in the fields of fuzzy mathematics, operations research, information science and management science, this book is also a valuable textbook for postgraduate and advanced undergraduate students alike.

Polynomial Calculus: Rethinking the Role of Calculus in High Schools

Science.gov (United States)

Grant, Melva R.; Crombie, William; Enderson, Mary; Cobb, Nell

2016-01-01

Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in…

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

Science.gov (United States)

Deni Akbar, Mohammad; Mizoguchi, Yoshihiro; Adiwijaya

2018-03-01

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

Equivariant calculus in the differential envelope

Energy Technology Data Exchange (ETDEWEB)

Kastler, D. (Centre National de la Recherche Scientifique, 13 - Marseille (France). Centre de Physique Theorique)

1991-01-01

The author shows how Z/2-graded cyclic cohomology is related to the equivariant calculus of S. Klimek, W. Kondracki, and A. Lesniewski (HUTMP 90/B247 (1990)). He uses the differential envelope of a complex unital differential algebra. After a presentation of fiber-preserved operators on equivariant functions valued in this algebra on a group he considers certain operators on this algebra. Finally he discusses explicitly the case G=Z/2. (HSI).

Equivariant calculus in the differential envelope

International Nuclear Information System (INIS)

Kastler, D.

1991-01-01

The author shows how Z/2-graded cyclic cohomology is related to the equivariant calculus of S. Klimek, W. Kondracki, and A. Lesniewski (HUTMP 90/B247 (1990)). He uses the differential envelope of a complex unital differential algebra. After a presentation of fiber-preserved operators on equivariant functions valued in this algebra on a group he considers certain operators on this algebra. Finally he discusses explicitly the case G=Z/2. (HSI)

A Fixpoint-Based Calculus for Graph-Shaped Computational Fields

DEFF Research Database (Denmark)

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

2015-01-01

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

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

Science.gov (United States)

Chaparala, Ramakrishna Prasad Chowdary; Patel, Rafiuddin; Guthrie, James Ahsley; Davies, Mervyn Huw; Guillou, Pierre J; Menon, Krishna V

2005-09-10

Pancreatic ductal calculi are most often associated with chronic pancreatitis. Radiological features of chronic pancreatitis are readily evident in the presence of these calculi. However, acute pancreatitis due to a solitary main pancreatic ductal calculus of biliary origin is rare. A 59-year-old man presented with a first episode of acute pancreatitis. Contrast enhanced computerized tomography (CT) scan and endoscopic retrograde cholangiopancreatography (ERCP) revealed a calculus in the main pancreatic duct in the head of the pancreas causing acute pancreatitis. There were no features suggestive of chronic pancreatitis on CT scanning. The episode acute pancreatitis was managed conservatively. ERCP extraction of the calculus failed as the stone was impacted in the main pancreatic duct resulting in severe acute pancreatitis. Once this resolved, a transduodenal exploration and extraction of the pancreatic ductal calculus was performed successfully. Crystallographic analysis revealed the composition of the calculus was different to that seen in chronic pancreatitis, but more in keeping with a calculus of biliary origin. This could be explained by migration of the biliary calculus via the common channel into the main pancreatic duct. Following the operation the patient made an uneventful recovery and was well at two-year follow up. Acute pancreatitis due to a solitary main pancreatic ductal calculus of biliary origin is rare. Failing endoscopic extraction, transduodenal exploration and extraction is a safe option after resolution of acute pancreatitis.

Advanced calculus a transition to analysis

CERN Document Server

Dence, Thomas P

2010-01-01

Designed for a one-semester advanced calculus course, Advanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis -- providing a mathematically sophisticated introduction to functional analytical concepts. The text is interesting to read and includes many illustrative worked-out examples and instructive exercises, and precise historical notes to aid in further exploration of calculus. Ancillary list: * Companion website, Ebook- http://www.elsevierdirect.com/product.jsp?isbn=9780123749550 * Student Solutions Manual- To come * Instructor

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

Science.gov (United States)

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

1994-09-01

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

Continuous Slice Functional Calculus in Quaternionic Hilbert Spaces

Science.gov (United States)

Ghiloni, Riccardo; Moretti, Valter; Perotti, Alessandro

2013-04-01

The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest, the class of continuous functions to consider in this setting is the one of slice quaternionic functions. Slice functions generalize the concept of slice regular function, which comprises power series with quaternionic coefficients on one side and that can be seen as an effective generalization to quaternions of holomorphic functions of one complex variable. The notion of slice function allows to introduce suitable classes of real, complex and quaternionic C*-algebras and to define, on each of these C*-algebras, a functional calculus for quaternionic normal operators. In particular, we establish several versions of the spectral map theorem. Some of the results are proved also for unbounded operators. However, the mentioned continuous functional calculi are defined only for bounded normal operators. Some comments on the physical significance of our work are included.

Maxima and Minima Without Calculus.

Science.gov (United States)

Birnbaum, Ian

1982-01-01

Approaches to extrema that do not require calculus are presented to help free maxima/minima problems from the confines of calculus. Many students falsely suppose that these types of problems can only be dealt with through calculus, since few, if any, noncalculus examples are usually presented. (MP)

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)

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

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

Science.gov (United States)

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

A desired outcome of scaling and root planing is the complete removal of calculus and infected root tissue and preservation of healthy cementum for rapid healing of periodontal tissues. Conventional periodontal treatments for calculus removal, such as hand instrument scaling and ultrasonic scaling, often deeply scrape the surface of the underlying hard tissue and may leave behind a smear layer. Pulsed lasers emitting at violet wavelengths (specifically, 380 to 400 nm) are a potential alternative treatment since they can selectively ablate dental calculus without ablating pristine hard tissue (i.e., enamel, cementum, and dentin). In this study, light and scanning electron microscopy are used to compare and contrast the efficacy of in vitro calculus removal for several conventional periodontal treatments (hand instruments, ultrasonic scaler, and Er:YAG laser) to calculus removal with a frequency-doubled Ti:sapphire (λ = 400 nm). After calculus removal, enamel and cementum surfaces are investigated for calculus debris and damage to the underlying hard tissue surface. Compared to the smear layer, grooves, and unintentional hard tissue removal typically found using these conventional treatments, calculus removal using the 400-nm laser is complete and selective without any removal of pristine dental hard tissue. Based on these results, selective ablation from the 400-nm laser appears to produce a root surface that would be more suitable for successful healing of periodontal tissues.

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

[Fluorescence control of dental calculus removal].

Science.gov (United States)

Bakhmutov, D N; Gonchukov, S A; Lonkina, T V; Sukhinina, A V

2012-01-01

The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In the frames of this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise detection of tooth-calculus interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing (as ultrasonic or laser devices).

A Calculus for Context-Awareness

DEFF Research Database (Denmark)

Zimmer, Pascal

2005-01-01

In order to answer the challenge of pervasive computing, we propose a new process calculus, whose aim is to describe dynamic systems composed of agents able to move and react differently depending on their location. This Context-Aware Calculus features a hierarchical structure similar to mobile...... ambients, and a generic multi-agent synchronization mechanism, inspired from the join-calculus. After general ideas and introduction, we review the full calculus' syntax and semantics, as well as some motivating examples, study its expressiveness, and show how the notion of computation itself can be made...

Simulations of incompressible Navier Stokes equations on curved surfaces using discrete exterior calculus

Science.gov (United States)

Samtaney, Ravi; Mohamed, Mamdouh; Hirani, Anil

2015-11-01

We present examples of numerical solutions of incompressible flow on 2D curved domains. The Navier-Stokes equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. A conservative discretization of Navier-Stokes equations on simplicial meshes is developed based on discrete exterior calculus (DEC). The discretization is then carried out by substituting the corresponding discrete operators based on the DEC framework. By construction, the method is conservative in that both the discrete divergence and circulation are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step. Numerical examples include Taylor vortices on a sphere, Stuart vortices on a sphere, and flow past a cylinder on domains with varying curvature. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1401-01.

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

Science.gov (United States)

Gibson, Megan

2013-01-01

Due in part to the growing popularity of the Advanced Placement program, an increasingly large percentage of entering college students are enrolling in calculus courses having already taken calculus in high school. Many students do not score high enough on the AP calculus examination to place out of Calculus I, and many do not take the…

Hands-On Calculus

Science.gov (United States)

Sutherland, Melissa

2006-01-01

In this paper we discuss manipulatives and hands-on investigations for Calculus involving volume, arc length, and surface area to motivate and develop formulae which can then be verified using techniques of integration. Pre-service teachers in calculus courses using these activities experience a classroom in which active learning is encouraged and…

The malliavin calculus and related topics

CERN Document Server

Nualart, David

1995-01-01

The Malliavin calculus (or stochastic calculus of variations) is an infinite-dimensional differential calculus on the Wiener space Originally, it was developed to prove a probabilistic proof to Hörmander's "sum of squares" theorem, but more recently it has found application in a variety of stochastic differential equation problems This monograph presents the main features of the Malliavin calculus and discusses in detail its connection with the anticipating stochastic calculus The author begins by developing analysis on the Wiener space, and then uses this to analyze the regularity of probability laws and to prove Hörmander's theorem Subsequent chapters apply the Malliavin calculus to anticipating stochastic differential equations and to studying the Markov property of solutions to stochastic differential equations with boundary conditions

The Vectorial $\\lambda$-Calculus

OpenAIRE

Arrighi, Pablo; Díaz-Caro, Alejandro; Valiron, Benoît

2013-01-01

We describe a type system for the linear-algebraic $\\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\\lambda$-calculus: it is able to statically describe the linear combinations of terms that will be obtained when reducing the programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. We prove that the resulting typed $\\lambda$-calculus is strongly normalising and fea...

Teaching the Calculus

Science.gov (United States)

Sauerheber, Richard D.

2012-01-01

Methods of teaching the Calculus are presented in honour of Sir Isaac Newton, by discussing an extension of his original proofs and discoveries. The methods, requested by Newton to be used that reflect the historical sequence of the discovered Fundamental Theorems, allow first-time students to grasp quickly the basics of the Calculus from its…

Dental Calculus Arrest of Dental Caries.

Science.gov (United States)

Keyes, Paul H; Rams, Thomas E

An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human teeth for the presence and location of dental caries, dental calculus, and dental plaque biofilms. A total of 1,200 teeth were preserved in 10% buffered formal saline, and viewed while moist by a single experienced examiner using a research stereomicroscope at 15-25× magnification. Representative teeth were sectioned and photographed, and their dental plaque biofilms subjected to gram-stain examination with light microscopy at 100× magnification. Dental calculus was observed on 1,140 (95%) of the extracted human teeth, and no dental carious lesions were found underlying dental calculus-covered surfaces on 1,139 of these teeth. However, dental calculus arrest of dental caries was found on one (0.54%) of 187 evaluated teeth that presented with unrestored proximal enamel caries. On the distal surface of a maxillary premolar tooth, dental calculus mineralization filled the outer surface cavitation of an incipient dental caries lesion. The dental calculus-covered carious lesion extended only slightly into enamel, and exhibited a brown pigmentation characteristic of inactive or arrested dental caries. In contrast, the tooth's mesial surface, without a superficial layer of dental calculus, had a large carious lesion going through enamel and deep into dentin. These observations further document the potential protective effects of dental calculus mineralization against dental caries.

Dental Calculus Arrest of Dental Caries

Science.gov (United States)

Keyes, Paul H.; Rams, Thomas E.

2016-01-01

Background An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human teeth for the presence and location of dental caries, dental calculus, and dental plaque biofilms. Materials and methods A total of 1,200 teeth were preserved in 10% buffered formal saline, and viewed while moist by a single experienced examiner using a research stereomicroscope at 15-25× magnification. Representative teeth were sectioned and photographed, and their dental plaque biofilms subjected to gram-stain examination with light microscopy at 100× magnification. Results Dental calculus was observed on 1,140 (95%) of the extracted human teeth, and no dental carious lesions were found underlying dental calculus-covered surfaces on 1,139 of these teeth. However, dental calculus arrest of dental caries was found on one (0.54%) of 187 evaluated teeth that presented with unrestored proximal enamel caries. On the distal surface of a maxillary premolar tooth, dental calculus mineralization filled the outer surface cavitation of an incipient dental caries lesion. The dental calculus-covered carious lesion extended only slightly into enamel, and exhibited a brown pigmentation characteristic of inactive or arrested dental caries. In contrast, the tooth's mesial surface, without a superficial layer of dental calculus, had a large carious lesion going through enamel and deep into dentin. Conclusions These observations further document the potential protective effects of dental calculus mineralization against dental caries. PMID:27446993

Pre-calculus workbook for dummies

CERN Document Server

Kuang, Yang

2011-01-01

Get the confidence and math skills you need to get started with calculus Are you preparing for calculus? This hands-on workbook helps you master basic pre-calculus concepts and practice the types of problems you'll encounter in the course. You'll get hundreds of valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every problem. You'll also memorize the most frequently used equations, see how to avoid common mistakes, understand tricky trig proofs, and much more. Pre-Calculus Workbook For Dummies is the perfect tool for anyone who wa

Initialized Fractional Calculus

Science.gov (United States)

Lorenzo, Carl F.; Hartley, Tom T.

2000-01-01

This paper demonstrates the need for a nonconstant initialization for the fractional calculus and establishes a basic definition set for the initialized fractional differintegral. This definition set allows the formalization of an initialized fractional calculus. Two basis calculi are considered; the Riemann-Liouville and the Grunwald fractional calculi. Two forms of initialization, terminal and side are developed.

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

Toward lattice fractional vector calculus

International Nuclear Information System (INIS)

Tarasov, Vasily E

2014-01-01

An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity. (papers)

Toward lattice fractional vector calculus

Science.gov (United States)

Tarasov, Vasily E.

2014-09-01

An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.

Vector calculus in non-integer dimensional space and its applications to fractal media

Science.gov (United States)

Tarasov, Vasily E.

2015-02-01

We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are defined. For simplification we consider scalar and vector fields that are independent of angles. We formulate a generalization of vector calculus for rotationally covariant scalar and vector functions. This generalization allows us to describe fractal media and materials in the framework of continuum models with non-integer dimensional space. As examples of application of the suggested calculus, we consider elasticity of fractal materials (fractal hollow ball and fractal cylindrical pipe with pressure inside and outside), steady distribution of heat in fractal media, electric field of fractal charged cylinder. We solve the correspondent equations for non-integer dimensional space models.

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...

Advanced calculus

CERN Document Server

Nickerson, HK; Steenrod, NE

2011-01-01

""This book is a radical departure from all previous concepts of advanced calculus,"" declared the Bulletin of the American Mathematics Society, ""and the nature of this departure merits serious study of the book by everyone interested in undergraduate education in mathematics."" Classroom-tested in a Princeton University honors course, it offers students a unified introduction to advanced calculus. Starting with an abstract treatment of vector spaces and linear transforms, the authors introduce a single basic derivative in an invariant form. All other derivatives - gradient, divergent, curl,

Differential Calculus on Quantum Spheres

OpenAIRE

Welk, Martin

1998-01-01

We study covariant differential calculus on the quantum spheres S_q^2N-1. Two classification results for covariant first order differential calculi are proved. As an important step towards a description of the noncommutative geometry of the quantum spheres, a framework of covariant differential calculus is established, including a particular first order calculus obtained by factorization, higher order calculi and a symmetry concept.

Disappearing renal calculus.

Science.gov (United States)

Cui, Helen; Thomas, Johanna; Kumar, Sunil

2013-04-10

We present a case of a renal calculus treated solely with antibiotics which has not been previously reported in the literature. A man with a 17 mm lower pole renal calculus and concurrent Escherichia coli urine infection was being worked up to undergo percutaneous nephrolithotomy. However, after a course of preoperative antibiotics the stone was no longer seen on retrograde pyelography or CT imaging.

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.)

Fractional dynamic calculus and fractional dynamic equations on time scales

CERN Document Server

Georgiev, Svetlin G

2018-01-01

Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger’s basic theories on time scales and examines recent developments within the field of fractional calculus and fractional equations. Useful tools are provided for solving differential and integral equations as well as various problems involving special functions of mathematical physics and their extensions and generalizations in one and more variables. Much discussion is devoted to Riemann-Liouville fractional dynamic equations and Caputo fractional dynamic equations.  Intended for use in the field and designed for students without an extensive mathematical background, this book is suitable for graduate courses and researchers looking for an introduction to fractional dynamic calculus and equations on time scales. .

Essential calculus with applications

CERN Document Server

Silverman, Richard A

1989-01-01

Rigorous but accessible text introduces undergraduate-level students to necessary background math, then clear coverage of differential calculus, differentiation as a tool, integral calculus, integration as a tool, and functions of several variables. Numerous problems and a supplementary section of ""Hints and Answers."" 1977 edition.

Factors Associated with Success in College Calculus II

Science.gov (United States)

Rosasco, Margaret E.

2013-01-01

Students are entering college having earned credit for college Calculus 1 based on their scores on the College Board's Advanced Placement (AP) Calculus AB exam. Despite being granted credit for college Calculus 1, it is unclear whether these students are adequately prepared for college Calculus 2. College calculus classes are often taught from a…

Leveraging Prior Calculus Study with Embedded Review

Science.gov (United States)

Nikolov, Margaret C.; Withers, Wm. Douglas

2016-01-01

We propose a new course structure to address the needs of college students with previous calculus study but no course validations as an alternative to repeating the first year of calculus. Students are introduced directly to topics from Calculus III unpreceded by a formal review of topics from Calculus I or II, but with additional syllabus time…

Vector 33: A reduce program for vector algebra and calculus in orthogonal curvilinear coordinates

Science.gov (United States)

Harper, David

1989-06-01

This paper describes a package with enables REDUCE 3.3 to perform algebra and calculus operations upon vectors. Basic algebraic operations between vectors and between scalars and vectors are provided, including scalar (dot) product and vector (cross) product. The vector differential operators curl, divergence, gradient and Laplacian are also defined, and are valid in any orthogonal curvilinear coordinate system. The package is written in RLISP to allow algebra and calculus to be performed using notation identical to that for operations. Scalars and vectors can be mixed quite freely in the same expression. The package will be of interest to mathematicians, engineers and scientists who need to perform vector calculations in orthogonal curvilinear coordinates.

Generalized Gaussian Error Calculus

CERN Document Server

Grabe, Michael

2010-01-01

For the first time in 200 years Generalized Gaussian Error Calculus addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. Since experimentalists realized that measurements in general are burdened by unknown systematic errors, the classical, widespread used evaluation procedures scrutinizing the consequences of random errors alone turned out to be obsolete. As a matter of course, the error calculus to-be, treating random and unknown systematic errors side by side, should ensure the consistency and traceability of physical units, physical constants and physical quantities at large. The generalized Gaussian error calculus considers unknown systematic errors to spawn biased estimators. Beyond, random errors are asked to conform to the idea of what the author calls well-defined measuring conditions. The approach features the properties of a building kit: any overall uncertainty turns out to be the sum of a contribution due to random errors, to be taken from a confidence inter...

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

Science.gov (United States)

Davydov, Aleksandr; Sturm-Beiss, Rachel

2008-01-01

The orders of presentation of pre-calculus and calculus topics, and the notation used, deserve careful study as they affect clarity and ultimately students' level of understanding. We introduce an alternate approach to some of the topics included in this sequence. The suggested alternative is based on years of teaching in colleges within and…

Abdominal fat distribution on computed tomography predicts ureteric calculus fragmentation by shock wave lithotripsy

Energy Technology Data Exchange (ETDEWEB)

Juan, Hsu-Cheng; Chou, Yii-Her [Kaohsiung Medical University Hospital, Department of Urology, Kaohsiung (China); Lin, Hung-Yu [Kaohsiung Medical University, Graduate Institute of Medicine, Kaohsiung (China); E-Da Hospital/ I-Shou University, Department of Urology, Kaohsiung (China); Yang, Yi-Hsin [Kaohsiung Medical University, Institute of Oral Health Sciences, Kaohsiung (China); Shih, Paul Ming-Chen [Kaohsiung Municipal Hsiao-Kang Hospital, Department of Radiology, Kaohsiung (China); Kaohsiung Medical University, Department of Radiology, Kaohsiung (China); Chuang, Shu-Mien [Yuh-Ing Junior College of Health Care and Management, Kaohsiung (China); Shen, Jung-Tsung [Kaohsiung Municipal Hsiao-Kang Hospital, Department of Urology, Kaohsiung (China); Juan, Yung-Shun [Kaohsiung Medical University Hospital, Department of Urology, Kaohsiung (China); Kaohsiung Medical University, Graduate Institute of Medicine, Kaohsiung (China); Kaohsiung Medical University, Department of Urology, Faculty of Medicine, Kaohsiung (China)

2012-08-15

To assess the effects of abdominal fat on shock wave lithotripsy (SWL). We used pre-SWL unenhanced computed tomography (CT) to evaluate the impact of abdominal fat distribution and calculus characteristics on the outcome of SWL. One hundred and eighty-five patients with a solitary ureteric calculus treated with SWL were retrospectively reviewed. Each patient underwent unenhanced CT within 1 month before SWL treatment. Treatment outcomes were evaluated 1 month later. Unenhanced CT parameters, including calculus surface area, Hounsfield unit (HU) density, abdominal fat area and skin to calculus distance (SSD) were analysed. One hundred and twenty-eight of the 185 patients were found to be calculus-free following treatment. HU density, total fat area, visceral fat area and SSD were identified as significant variables on multivariate logistic regression analysis. The receiver-operating characteristic analyses showed that total fat area, para/perirenal fat area and visceral fat area were sensitive predictors of SWL outcomes. This study revealed that higher quantities of abdominal fat, especially visceral fat, are associated with a lower calculus-free rate following SWL treatment. Unenhanced CT is a convenient technique for diagnosing the presence of a calculus, assessing the intra-abdominal fat distribution and thereby helping to predict the outcome of SWL. (orig.)

Abdominal fat distribution on computed tomography predicts ureteric calculus fragmentation by shock wave lithotripsy

International Nuclear Information System (INIS)

Juan, Hsu-Cheng; Chou, Yii-Her; Lin, Hung-Yu; Yang, Yi-Hsin; Shih, Paul Ming-Chen; Chuang, Shu-Mien; Shen, Jung-Tsung; Juan, Yung-Shun

2012-01-01

To assess the effects of abdominal fat on shock wave lithotripsy (SWL). We used pre-SWL unenhanced computed tomography (CT) to evaluate the impact of abdominal fat distribution and calculus characteristics on the outcome of SWL. One hundred and eighty-five patients with a solitary ureteric calculus treated with SWL were retrospectively reviewed. Each patient underwent unenhanced CT within 1 month before SWL treatment. Treatment outcomes were evaluated 1 month later. Unenhanced CT parameters, including calculus surface area, Hounsfield unit (HU) density, abdominal fat area and skin to calculus distance (SSD) were analysed. One hundred and twenty-eight of the 185 patients were found to be calculus-free following treatment. HU density, total fat area, visceral fat area and SSD were identified as significant variables on multivariate logistic regression analysis. The receiver-operating characteristic analyses showed that total fat area, para/perirenal fat area and visceral fat area were sensitive predictors of SWL outcomes. This study revealed that higher quantities of abdominal fat, especially visceral fat, are associated with a lower calculus-free rate following SWL treatment. Unenhanced CT is a convenient technique for diagnosing the presence of a calculus, assessing the intra-abdominal fat distribution and thereby helping to predict the outcome of SWL. (orig.)

A κ-symmetry calculus for superparticles

International Nuclear Information System (INIS)

Gauntlett, J.P.

1991-01-01

We develop a κ-symmetry calculus for the d=2 and d=3, N=2 massive superparticles, which enables us to construct higher order κ-invariant actions. The method relies on a reformulation of these models as supersymmetric sigma models that are invariant under local worldline superconformal transformations. We show that the κ-symmetry is embedded in the superconformal symmetry so that a calculus for the κ-symmetry is equivalent to a tensor calculus for the latter. We develop such a calculus without the introduction of a wordline supergravity multiplet. (orig.)

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

International Nuclear Information System (INIS)

Gao Feng; Ye Chunhua; Wang Kanger; Sun Yan

2009-01-01

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

An AP Calculus Classroom Amusement Park

Science.gov (United States)

Ferguson, Sarah

2016-01-01

Throughout the school year, AP Calculus teachers strive to teach course content comprehensively and swiftly in an effort to finish all required material before the AP Calculus exam. As early May approaches and the AP Calculus test looms, students and teachers nervously complete lessons, assignments, and assessments to ensure student preparation.…

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.

Discounted Duration Calculus

DEFF Research Database (Denmark)

Ody, Heinrich; Fränzle, Martin; Hansen, Michael Reichhardt

2016-01-01

To formally reason about the temporal quality of systems discounting was introduced to CTL and LTL. However, these logic are discrete and they cannot express duration properties. In this work we introduce discounting for a variant of Duration Calculus. We prove decidability of model checking...... for a useful fragment of discounted Duration Calculus formulas on timed automata under mild assumptions. Further, we provide an extensive example to show the usefulness of the fragment....

A Formal Calculus for Categories

DEFF Research Database (Denmark)

Cáccamo, Mario José

This dissertation studies the logic underlying category theory. In particular we present a formal calculus for reasoning about universal properties. The aim is to systematise judgements about functoriality and naturality central to categorical reasoning. The calculus is based on a language which...... extends the typed lambda calculus with new binders to represent universal constructions. The types of the languages are interpreted as locally small categories and the expressions represent functors. The logic supports a syntactic treatment of universality and duality. Contravariance requires a definition...... of universality generous enough to deal with functors of mixed variance. Ends generalise limits to cover these kinds of functors and moreover provide the basis for a very convenient algebraic manipulation of expressions. The equational theory of the lambda calculus is extended with new rules for the definitions...

Testicular calculus: A rare case.

Science.gov (United States)

Sen, Volkan; Bozkurt, Ozan; Demır, Omer; Tuna, Burcin; Yorukoglu, Kutsal; Esen, Adil

2015-01-01

Testicular calculus is an extremely rare case with unknown etiology and pathogenesis. To our knowledge, here we report the third case of testicular calculus. A 31-year-old man was admitted to our clinic with painful solid mass in left testis. After diagnostic work-up for a possible testicular tumour, he underwent inguinal orchiectomy and histopathologic examination showed a testicular calculus. Case hypothesis: Solid testicular lesions in young adults generally correspond to testicular cancer. Differential diagnosis should be done carefully. Future implications: In young adults with painful and solid testicular mass with hyperechogenic appearance on scrotal ultrasonography, testicular calculus must be kept in mind in differential diagnosis. Further reports on this topic may let us do more clear recommendations about the etiology and treatment of this rare disease.

Improving student learning in calculus through applications

Science.gov (United States)

Young, C. Y.; Georgiopoulos, M.; Hagen, S. C.; Geiger, C. L.; Dagley-Falls, M. A.; Islas, A. L.; Ramsey, P. J.; Lancey, P. M.; Straney, R. A.; Forde, D. S.; Bradbury, E. E.

2011-07-01

Nationally only 40% of the incoming freshmen Science, Technology, Engineering and Mathematics (STEM) majors are successful in earning a STEM degree. The University of Central Florida (UCF) EXCEL programme is a National Science Foundation funded STEM Talent Expansion Programme whose goal is to increase the number of UCF STEM graduates. One of the key requirements for STEM majors is a strong foundation in Calculus. To improve student learning in calculus, the EXCEL programme developed two special courses at the freshman level called Applications of Calculus I (Apps I) and Applications of Calculus II (Apps II). Apps I and II are one-credit classes that are co-requisites for Calculus I and II. These classes are teams taught by science and engineering professors whose goal is to demonstrate to students where the calculus topics they are learning appear in upper level science and engineering classes as well as how faculty use calculus in their STEM research programmes. This article outlines the process used in producing the educational materials for the Apps I and II courses, and it also discusses the assessment results pertaining to this specific EXCEL activity. Pre- and post-tests conducted with experimental and control groups indicate significant improvement in student learning in Calculus II as a direct result of the application courses.

Lacroix and the calculus

CERN Document Server

Domingues, João Caramalho

2008-01-01

Silvestre François Lacroix (Paris, 1765 - ibid., 1843) was a most influential mathematical book author. His most famous work is the three-volume Traité du calcul différentiel et du calcul intégral (1797-1800; 2nd ed. 1810-1819) – an encyclopedic appraisal of 18th-century calculus which remained the standard reference on the subject through much of the 19th century, in spite of Cauchy's reform of the subject in the 1820's. Lacroix and the Calculus is the first major study of Lacroix’s large Traité. It uses the unique and massive bibliography given by Lacroix to explore late 18th-century calculus, and the way it is reflected in Lacroix’s account. Several particular aspects are addressed in detail, including: the foundations of differential calculus, analytic and differential geometry, conceptions of the integral, and types of solutions of differential equations (singular/complete/general integrals, geometrical interpretations, and generality of arbitrary functions). Lacroix’s large Traité... was a...

[Factors affecting residual stones after percutaneous nephrolithotomy in patients with renal calculus].

Science.gov (United States)

Qiao, Mingzhou; Zhang, Haifang; Zhou, Chenlong

2015-11-24

To explore the factors affecting the residual stones after percutaneous nephrolithotomy (PCNL) in patients with renal calculus. A retrospective analysis was performed for 1 200 patients who were affected by renal calculus and treated with PCNL between Jan 2008 and May 2014 in People's Hospital of Anyang City. Among those patients, 16 were diagnosed as bilateral renal stone and had two successive operations. The size, location and number of stones, previous history of surgery, the degree of hydronephrosis, urinary infection were included in the univariate analysis. Significant factors in univariate analysis were included in the multivariate analysis to determine factors affecting stone residual. A total of 385 cases developed stone residual after surgery. The overall residual rate was 31.7%. In univariate analysis, renal pelvis combined with caliceal calculus (P=0.006), stone size larger than 4 cm (P=0.005), stone number more than 4 (P=0.002), the amount of bleeding more than 200 ml (P=0.025), operation time longer than 120 minutes (P=0.028) were associated with an increased rate of stone residual. When subjected to the Cox multivariate analysis, the independent risk factors for residual stones were renal pelvis combined with caliceal calculus (P=0.049), stone size larger than 4 cm (P=0.038) and stone number more than 4 (P=0.018). Factors affecting the incidence of residual stones after PCNL are the size, location and number of stones. Larger size stone and the presence of renal pelvis combined with caliceal calculus are significantly associated with residual stones. Nevertheless, stone number less than 4 indicates an increased stone clearance rate.

CLEP calculus

CERN Document Server

Hill, Gregory

2013-01-01

Earn College Credit with REA's Test Prep for CLEP* Calculus Everything you need to pass the exam and get the college credit you deserve.Our test prep for CLEP* Calculus and the free online tools that come with it, will allow you to create a personalized CLEP* study plan that can be customized to fit you: your schedule, your learning style, and your current level of knowledge.Here's how it works:Diagnostic exam at the REA Study Center focuses your studyOur online diagnostic exam pinpoints your strengths and shows you exactly where you need to focus your study. Armed with this information, you

Null-strut calculus. II. Dynamics

International Nuclear Information System (INIS)

Kheyfets, A.; LaFave, N.J.; Miller, W.A.

1990-01-01

In this paper, we continue from the preceding paper to develop a fully functional Regge calculus geometrodynamic algorithm from the null-strut-calculus construction. The developments discussed include (a) the identification of the Regge calculus analogue of the constraint and evolution equations on the null-strut lattice, (b) a description of the Minkowski solid geometry for the simplicial blocks of the null-strut lattice, (c) a description of the evolution algorithm for the geometrodynamic scheme and an analysis of its consistency, and (d) a presentation of the dynamical degrees of freedom for a simplicial hypersurface and the description of an initial-value prescription. To demonstrate qualitatively this new approach to geometrodynamics, we present the most simple application of null-strut calculus that we know of---the Friedmann cosmology using the three-boundary of a 600-cell simplicial polytope to model the simplicial hypersurface

A Higher-Order Calculus for Categories

DEFF Research Database (Denmark)

Cáccamo, Mario José; Winskel, Glynn

2001-01-01

A calculus for a fragment of category theory is presented. The types in the language denote categories and the expressions functors. The judgements of the calculus systematise categorical arguments such as: an expression is functorial in its free variables; two expressions are naturally isomorphic...... in their free variables. There are special binders for limits and more general ends. The rules for limits and ends support an algebraic manipulation of universal constructions as opposed to a more traditional diagrammatic approach. Duality within the calculus and applications in proving continuity are discussed...... with examples. The calculus gives a basis for mechanising a theory of categories in a generic theorem prover like Isabelle....

The calculus primer

CERN Document Server

Schaaf, William L

2011-01-01

Comprehensive but concise, this introduction to differential and integral calculus covers all the topics usually included in a first course. The straightforward development places less emphasis on mathematical rigor, and the informal manner of presentation sets students at ease. Many carefully worked-out examples illuminate the text, in addition to numerous diagrams, problems, and answers.Bearing the needs of beginners constantly in mind, the treatment covers all the basic concepts of calculus: functions, derivatives, differentiation of algebraic and transcendental functions, partial different

Computing for calculus

CERN Document Server

Christensen, Mark J

1981-01-01

Computing for Calculus focuses on BASIC as the computer language used for solving calculus problems.This book discusses the input statement for numeric variables, advanced intrinsic functions, numerical estimation of limits, and linear approximations and tangents. The elementary estimation of areas, numerical and string arrays, line drawing algorithms, and bisection and secant method are also elaborated. This text likewise covers the implicit functions and differentiation, upper and lower rectangular estimates, Simpson's rule and parabolic approximation, and interpolating polynomials. Other to

Putting Differentials Back into Calculus

Science.gov (United States)

Dray, Tevian; Manogue, Corrine A.

2010-01-01

We argue that the use of differentials in introductory calculus courses is useful and provides a unifying theme, leading to a coherent view of the calculus. Along the way, we meet several interpretations of differentials, some better than others.

Giant calculus: review and report of a case.

Science.gov (United States)

Woodmansey, Karl; Severine, Anthony; Lembariti, Bakari S

2013-01-01

Dental calculus is a common oral finding. The term giant calculus is used to describe unusually large deposits of dental calculus. Several extreme cases have been reported in the dental literature. The specific etiology of these cases remains uncertain. This paper reviews previously reported cases, and presents another extreme example of giant calculus.

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....

Calculus with vectors

CERN Document Server

Treiman, Jay S

2014-01-01

Calculus with Vectors grew out of a strong need for a beginning calculus textbook for undergraduates who intend to pursue careers in STEM. fields. The approach introduces vector-valued functions from the start, emphasizing the connections between one-variable and multi-variable calculus. The text includes early vectors and early transcendentals and includes a rigorous but informal approach to vectors. Examples and focused applications are well presented along with an abundance of motivating exercises. All three-dimensional graphs have rotatable versions included as extra source materials and may be freely downloaded and manipulated with Maple Player; a free Maple Player App is available for the iPad on iTunes. The approaches taken to topics such as the derivation of the derivatives of sine and cosine, the approach to limits, and the use of "tables" of integration have been modified from the standards seen in other textbooks in order to maximize the ease with which students may comprehend the material. Additio...

Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus

Science.gov (United States)

Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.

2015-05-01

We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.

From lattice BF gauge theory to area-angle Regge calculus

International Nuclear Information System (INIS)

Bonzom, Valentin

2009-01-01

We consider Riemannian 4D BF lattice gauge theory, on a triangulation of spacetime. Introducing the simplicity constraints which turn BF theory into simplicial gravity, some geometric quantities of Regge calculus, areas, and 3D and 4D dihedral angles, are identified. The parallel transport conditions are taken care of to ensure a consistent gluing of simplices. We show that these gluing relations, together with the simplicity constraints, contain the constraints of area-angle Regge calculus in a simple way, via the group structure of the underlying BF gauge theory. This provides a precise road from constrained BF theory to area-angle Regge calculus. Doing so, a framework combining variables of lattice BF theory and Regge calculus is built. The action takes a form a la Regge and includes the contribution of the Immirzi parameter. In the absence of simplicity constraints, the standard spin foam model for BF theory is recovered. Insertions of local observables are investigated, leading to Casimir insertions for areas and reproducing for 3D angles known results obtained through angle operators on spin networks. The present formulation is argued to be suitable for deriving spin foam models from discrete path integrals and to unravel their geometric content.

Calculus and analysis in Euclidean space

CERN Document Server

Shurman, Jerry

2016-01-01

The graceful role of analysis in underpinning calculus is often lost to their separation in the curriculum. This book entwines the two subjects, providing a conceptual approach to multivariable calculus closely supported by the structure and reasoning of analysis. The setting is Euclidean space, with the material on differentiation culminating in the inverse and implicit function theorems, and the material on integration culminating in the general fundamental theorem of integral calculus. More in-depth than most calculus books but less technical than a typical analysis introduction, Calculus and Analysis in Euclidean Space offers a rich blend of content to students outside the traditional mathematics major, while also providing transitional preparation for those who will continue on in the subject. The writing in this book aims to convey the intent of ideas early in discussion. The narrative proceeds through figures, formulas, and text, guiding the reader to do mathematics resourcefully by marshaling the skil...

Dental calculus detection using the VistaCam.

Science.gov (United States)

Shakibaie, Fardad; Walsh, Laurence J

2016-12-01

The VistaCam® intra-oral camera system (Dürr Dental, Bietigheim-Bissingen, Germany) is a fluorescence system using light emitting diodes that produce a 405-nm violet light. This wavelength has potential application for detection of dental calculus based on red emissions from porphyrin molecules. This study assessed the digital scores obtained for both supragingival and subgingival calculus on 60 extracted teeth and compared these with lesions of dental caries. It has also examined the effect of saliva and blood on the fluorescence readings for dental calculus. VistaCam fluorescence scores for both supragingival (1.7-3.3) and subgingival calculus (1.3-2.4) were higher than those for sound root surfaces (0.9-1.1) and dental caries (0.9-2.2) ( p  calculus samples were not affected by the presence of saliva or blood. These results suggest that the use of violet light fluorescence could be a possible adjunct to clinical examination for deposits of dental calculus.

Two-dimensional calculus

CERN Document Server

Osserman, Robert

2011-01-01

The basic component of several-variable calculus, two-dimensional calculus is vital to mastery of the broader field. This extensive treatment of the subject offers the advantage of a thorough integration of linear algebra and materials, which aids readers in the development of geometric intuition. An introductory chapter presents background information on vectors in the plane, plane curves, and functions of two variables. Subsequent chapters address differentiation, transformations, and integration. Each chapter concludes with problem sets, and answers to selected exercises appear at the end o

On Some Syntactic Properties of the Modalized Heyting Calculus

OpenAIRE

Muravitsky, Alexei

2016-01-01

We show that the modalized Heyting calculus introduced by Leo Esakia admits a normal axiomatization. Then, we prove that the inference rules $\\square\\alpha/\\alpha$ and $\\square\\alpha\\rightarrow\\alpha/\\alpha$ are admissible in this calculus. Finally, we show that this calculus and intuitionistic propositional calculus are assertorically equipollent, which leads to a variant of limited separation property for the modalized Heyting calculus.

The calculus a genetic approach

CERN Document Server

Toeplitz, Otto

2007-01-01

When first published posthumously in 1963, this book presented a radically different approach to the teaching of calculus.  In sharp contrast to the methods of his time, Otto Toeplitz did not teach calculus as a static system of techniques and facts to be memorized. Instead, he drew on his knowledge of the history of mathematics and presented calculus as an organic evolution of ideas beginning with the discoveries of Greek scholars, such as Archimedes, Pythagoras, and Euclid, and developing through the centuries in the work of Kepler, Galileo, Fermat, Newton, and Leibniz. Through this unique a

Pre-calculus workbook for dummies

CERN Document Server

Gilman, Michelle Rose; Neal, Karina

2009-01-01

Get the confidence and the math skills you need to get started with calculus! Are you preparing for calculus? This easy-to-follow, hands-on workbook helps you master basic pre-calculus concepts and practice the types of problems you'll encounter in your cour sework. You get valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every problem. You'll also memorize the most frequently used equations, see how to avoid common mistakes, understand tricky trig proofs, and much more. 100s of Problems! Detailed, fully worked-out solutions to problem

Mathematics for physics with calculus

CERN Document Server

Das, Biman

2005-01-01

Designed for students who plan to take or who are presently taking calculus-based physics courses. This book will develop necessary mathematical skills and help students gain the competence to use precalculus, calculus, vector algebra, vector calculus, and the statistical analysis of experimental data. Students taking intermediate physics, engineering, and other science courses will also find the book useful-and will be able to use the book as a mathematical resource for these intermediate level courses. The book emphasizes primarily the use of mathematical techniques and mathematical concepts in Physics and does not go into their rigorous developments.

On exterior variational calculus

International Nuclear Information System (INIS)

Aldrovandi, R.; Kraenkel, R.A.

1987-01-01

Exterior variational calculus is introduced through examples in field theory. It provides a very simple technique to decide on the existence of Lagrangians for given equations of motions and, in the case, to find them. Only local aspects are discussed but the analogy to exterior calculus on finite dimensional manifolds is complete, strongly suggesting its suitability to the study of topological aspects. (Author) [pt

ASSESSING STUDENTS' UNDERSTANDING OF PRE-CALCULUS CONCEPTS

OpenAIRE

Dr. Jyoti Sharma

2017-01-01

Calculus is one of the most momentous achievements of the human intellect (Boyer, 1949). It has given a new direction to the work of mathematicians and scientists. Calculus has exponentially expanded the scope and use of mathematics in other fields. Learning calculus is important to pursue career in applied mathematics.

Feynman's Operational Calculi: Spectral Theory for Noncommuting Self-adjoint Operators

International Nuclear Information System (INIS)

Jefferies, Brian; Johnson, Gerald W.; Nielsen, Lance

2007-01-01

The spectral theorem for commuting self-adjoint operators along with the associated functional (or operational) calculus is among the most useful and beautiful results of analysis. It is well known that forming a functional calculus for noncommuting self-adjoint operators is far more problematic. The central result of this paper establishes a rich functional calculus for any finite number of noncommuting (i.e. not necessarily commuting) bounded, self-adjoint operators A 1 ,..., A n and associated continuous Borel probability measures μ 1 , ?, μ n on [0,1]. Fix A 1 ,..., A n . Then each choice of an n-tuple (μ 1 ,...,μ n ) of measures determines one of Feynman's operational calculi acting on a certain Banach algebra of analytic functions even when A 1 , ..., A n are just bounded linear operators on a Banach space. The Hilbert space setting along with self-adjointness allows us to extend the operational calculi well beyond the analytic functions. Using results and ideas drawn largely from the proof of our main theorem, we also establish a family of Trotter product type formulas suitable for Feynman's operational calculi

Dental Calculus Arrest of Dental Caries

OpenAIRE

Keyes, Paul H.; Rams, Thomas E.

2016-01-01

Background An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human t...

Jet-calculus approach including coherence effects

International Nuclear Information System (INIS)

Jones, L.M.; Migneron, R.; Narayanan, K.S.S.

1987-01-01

We show how integrodifferential equations typical of jet calculus can be combined with an averaging procedure to obtain jet-calculus-based results including the Mueller interference graphs. Results in longitudinal-momentum fraction x for physical quantities are higher at intermediate x and lower at large x than with the conventional ''incoherent'' jet calculus. These results resemble those of Marchesini and Webber, who used a Monte Carlo approach based on the same dynamics

Functional Fractional Calculus

CERN Document Server

Das, Shantanu

2011-01-01

When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with 'ordinary' differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematic

Computer tomography urography assisted real-time ultrasound-guided percutaneous nephrolithotomy on renal calculus.

Science.gov (United States)

Fang, You-Qiang; Wu, Jie-Ying; Li, Teng-Cheng; Zheng, Hao-Feng; Liang, Guan-Can; Chen, Yan-Xiong; Hong, Xiao-Bin; Cai, Wei-Zhong; Zang, Zhi-Jun; Di, Jin-Ming

2017-06-01

This study aimed to assess the role of pre-designed route on computer tomography urography (CTU) in the ultrasound-guided percutaneous nephrolithotomy (PCNL) for renal calculus.From August 2013 to May 2016, a total of 100 patients diagnosed with complex renal calculus in our hospital were randomly divided into CTU group and control group (without CTU assistance). CTU was used to design a rational route for puncturing in CTU group. Ultrasound was used in both groups to establish a working trace in the operation areas. Patients' perioperative parameters and postoperative complications were recorded.All operations were successfully performed, without transferring to open surgery. Time of channel establishment in CTU group (6.5 ± 4.3 minutes) was shorter than the control group (10.0 ± 6.7 minutes) (P = .002). In addition, there was shorter operation time, lower rates of blood transfusion, secondary operation, and less establishing channels. The incidence of postoperative complications including residual stones, sepsis, severe hemorrhage, and perirenal hematoma was lower in CTU group than in control group.Pre-designing puncture route on CTU images would improve the puncturing accuracy, lessen establishing channels as well as improve the security in the ultrasound-guided PCNL for complex renal calculus, but at the cost of increased radiation exposure.

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...

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...

A primer on exterior differential calculus

Directory of Open Access Journals (Sweden)

Burton D.A.

2003-01-01

Full Text Available A pedagogical application-oriented introduction to the cal­culus of exterior differential forms on differential manifolds is presented. Stokes' theorem, the Lie derivative, linear con­nections and their curvature, torsion and non-metricity are discussed. Numerous examples using differential calculus are given and some detailed comparisons are made with their tradi­tional vector counterparts. In particular, vector calculus on R3 is cast in terms of exterior calculus and the traditional Stokes' and divergence theorems replaced by the more powerful exterior expression of Stokes' theorem. Examples from classical continuum mechanics and spacetime physics are discussed and worked through using the language of exterior forms. The numerous advantages of this calculus, over more traditional ma­chinery, are stressed throughout the article. .

Model-checking dense-time Duration Calculus

DEFF Research Database (Denmark)

Fränzle, Martin

2004-01-01

Since the seminal work of Zhou Chaochen, M. R. Hansen, and P. Sestoft on decidability of dense-time Duration Calculus [Zhou, Hansen, Sestoft, 1993] it is well-known that decidable fragments of Duration Calculus can only be obtained through withdrawal of much of the interesting vocabulary...... of this logic. While this was formerly taken as an indication that key-press verification of implementations with respect to elaborate Duration Calculus specifications were also impossible, we show that the model property is well decidable for realistic designs which feature natural constraints...... suitably sparser model classes we obtain model-checking procedures for rich subsets of Duration Calculus. Together with undecidability results also obtained, this sheds light upon the exact borderline between decidability and undecidability of Duration Calculi and related logics....

Proof Nets for Lambek Calculus

NARCIS (Netherlands)

Roorda, Dirk

1992-01-01

The proof nets of linear logic are adapted to the non-commutative Lambek calculus. A different criterion for soundness of proof nets is given, which gives rise to new algorithms for proof search. The order sensitiveness of the Lambek calculus is reflected by the planarity condition on proof nets;

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.

The Calculus of a Vase

Science.gov (United States)

Scherger, Nicole

2012-01-01

Of the most universal applications in integral calculus are those involved with finding volumes of solids of revolution. These profound problems are typically taught with traditional approaches of the disk and shell methods, after which most calculus curriculums will additionally cover arc length and surfaces of revolution. Even in these visibly…

Miniature endoscopic optical coherence tomography for calculus detection.

Science.gov (United States)

Kao, Meng-Chun; Lin, Chun-Li; Kung, Che-Yen; Huang, Yi-Fung; Kuo, Wen-Chuan

2015-08-20

The effective treatment of periodontitis involves the detection and removal of subgingival dental calculus. However, subgingival calculus is more difficult to detect than supragingival calculus because it is firmly attached to root surfaces within periodontal pockets. To achieve a smooth root surface, clinicians often remove excessive amounts of root structure because of decreased visibility. In addition, enamel pearl, a rare type of ectopic enamel formation on the root surface, can easily be confused with dental calculus in the subgingival environment. In this study, we developed a fiber-probe swept-source optical coherence tomography (SSOCT) technique and combined it with the quantitative measurement of an optical parameter [standard deviation (SD) of the optical coherence tomography (OCT) intensity] to differentiate subgingival calculus from sound enamel, including enamel pearl. Two-dimensional circumferential images were constructed by rotating the miniprobe (0.9 mm diameter) while acquiring image lines, and the adjacent lines in each rotation were stacked to generate a three-dimensional volume. In OCT images, compared to sound enamel and enamel pearls, dental calculus showed significant differences (Pdental calculus.

Area Regge calculus and continuum limit

International Nuclear Information System (INIS)

Khatsymovsky, V.M.

2002-01-01

Encountered in the literature generalisations of general relativity to independent area variables are considered, the discrete (generalised Regge calculus) and continuum ones. The generalised Regge calculus can be either with purely area variables or, as we suggest, with area tensor-connection variables. Just for the latter, in particular, we prove that in analogy with corresponding statement in ordinary Regge calculus (by Feinberg, Friedberg, Lee and Ren), passing to the (appropriately defined) continuum limit yields the generalised continuum area tensor-connection general relativity

Applications of fractional calculus in physics

CERN Document Server

2000-01-01

Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus.This volume provides an introduction to fractional calculus for physicists, and co

Enriching an effect calculus with linear types

DEFF Research Database (Denmark)

Egger, Jeff; Møgelberg, Rasmus Ejlers; Simpson, Alex

2009-01-01

We define an ``enriched effect calculus'' by conservatively extending  a type theory for computational effects with primitives from linear logic. By doing so, we obtain a generalisation of linear type theory, intended as a formalism for expressing linear aspects of effects. As a worked example, we...... formulate  linearly-used continuations in the enriched effect calculus. These are captured by a fundamental translation of the enriched effect calculus into itself, which extends existing call-by-value and call-by-name linearly-used CPS translations. We show that our translation is involutive. Full...... completeness results for the various linearly-used CPS translations  follow. Our main results, the conservativity of enriching the effect calculus with linear primitives, and the involution property of the fundamental translation, are proved using a category-theoretic semantics for the enriched effect calculus...

Detection, removal and prevention of calculus: Literature Review

Directory of Open Access Journals (Sweden)

Deepa G. Kamath

2014-01-01

Full Text Available Dental plaque is considered to be a major etiological factor in the development of periodontal disease. Accordingly, the elimination of supra- and sub-gingival plaque and calculus is the cornerstone of periodontal therapy. Dental calculus is mineralized plaque; because it is porous, it can absorb various toxic products that can damage the periodontal tissues. Hence, calculus should be accurately detected and thoroughly removed for adequate periodontal therapy. Many techniques have been used to identify and remove calculus deposits present on the root surface. The purpose of this review was to compile the various methods and their advantages for the detection and removal of calculus.

Łukasiewicz mu-Calculus

Directory of Open Access Journals (Sweden)

Matteo Mio

2013-08-01

Full Text Available The paper explores properties of Łukasiewicz mu-calculus, a version of the quantitative/probabilistic modal mu-calculus containing both weak and strong conjunctions and disjunctions from Łukasiewicz (fuzzy logic. We show that this logic encodes the well-known probabilistic temporal logic PCTL. And we give a model-checking algorithm for computing the rational denotational value of a formula at any state in a finite rational probabilistic nondeterministic transition system.

Calculus of bivariant function

OpenAIRE

PTÁČNÍK, Jan

2011-01-01

This thesis deals with the introduction of function of two variables and differential calculus of this function. This work should serve as a textbook for students of elementary school's teacher. Each chapter contains a summary of basic concepts and explanations of relationships, then solved model exercises of the topic and finally the exercises, which should solve the student himself. Thesis have transmit to students basic knowledges of differential calculus of functions of two variables, inc...

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.

Geometric calculus: a new computational tool for Riemannian geometry

International Nuclear Information System (INIS)

Moussiaux, A.; Tombal, P.

1988-01-01

We compare geometric calculus applied to Riemannian geometry with Cartan's exterior calculus method. The correspondence between the two methods is clearly established. The results obtained by a package written in an algebraic language and doing general manipulations on multivectors are compared. We see that the geometric calculus is as powerful as exterior calculus

Abdominal fat distribution on computed tomography predicts ureteric calculus fragmentation by shock wave lithotripsy.

Science.gov (United States)

Juan, Hsu-Cheng; Lin, Hung-Yu; Chou, Yii-Her; Yang, Yi-Hsin; Shih, Paul Ming-Chen; Chuang, Shu-Mien; Shen, Jung-Tsung; Juan, Yung-Shun

2012-08-01

To assess the effects of abdominal fat on shock wave lithotripsy (SWL). We used pre-SWL unenhanced computed tomography (CT) to evaluate the impact of abdominal fat distribution and calculus characteristics on the outcome of SWL. One hundred and eighty-five patients with a solitary ureteric calculus treated with SWL were retrospectively reviewed. Each patient underwent unenhanced CT within 1 month before SWL treatment. Treatment outcomes were evaluated 1 month later. Unenhanced CT parameters, including calculus surface area, Hounsfield unit (HU) density, abdominal fat area and skin to calculus distance (SSD) were analysed. One hundred and twenty-eight of the 185 patients were found to be calculus-free following treatment. HU density, total fat area, visceral fat area and SSD were identified as significant variables on multivariate logistic regression analysis. The receiver-operating characteristic analyses showed that total fat area, para/perirenal fat area and visceral fat area were sensitive predictors of SWL outcomes. This study revealed that higher quantities of abdominal fat, especially visceral fat, are associated with a lower calculus-free rate following SWL treatment. Unenhanced CT is a convenient technique for diagnosing the presence of a calculus, assessing the intra-abdominal fat distribution and thereby helping to predict the outcome of SWL. • Unenhanced CT is now widely used to assess ureteric calculi. • The same CT protocol can provide measurements of abdominal fat distribution. • Ureteric calculi are usually treated by shock wave lithotripsy (SWL). • Greater intra-abdominal fat stores are generally associated with poorer SWL results.

Critical Analysis of the Mathematical Formalism of Theoretical Physics. II. Foundations of Vector Calculus

Science.gov (United States)

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.

Smooth vectors and Weyl-Pedersen calculus for representations of nilpotent Lie groups

OpenAIRE

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.

Fluorescence detection of dental calculus

International Nuclear Information System (INIS)

Gonchukov, S; Sukhinina, A; Vdovin, Yu; Biryukova, T

2010-01-01

This work is devoted to the optimization of fluorescence dental calculus diagnostics in optical spectrum. The optimal wavelengths for fluorescence excitation and registration are determined. Two spectral ranges 620 – 645 nm and 340 – 370 nm are the most convenient for supra- and subgingival calculus determination. The simple implementation of differential method free from the necessity of spectrometer using was investigated. Calculus detection reliability in the case of simple implementation is higher than in the case of spectra analysis at optimal wavelengths. The use of modulated excitation light and narrowband detection of informative signal allows us to decrease essentially its diagnostic intensity even in comparison with intensity of the low level laser dental therapy

Fluorescence detection of dental calculus

Science.gov (United States)

Gonchukov, S.; Biryukova, T.; Sukhinina, A.; Vdovin, Yu

2010-11-01

This work is devoted to the optimization of fluorescence dental calculus diagnostics in optical spectrum. The optimal wavelengths for fluorescence excitation and registration are determined. Two spectral ranges 620 - 645 nm and 340 - 370 nm are the most convenient for supra- and subgingival calculus determination. The simple implementation of differential method free from the necessity of spectrometer using was investigated. Calculus detection reliability in the case of simple implementation is higher than in the case of spectra analysis at optimal wavelengths. The use of modulated excitation light and narrowband detection of informative signal allows us to decrease essentially its diagnostic intensity even in comparison with intensity of the low level laser dental therapy.

Essential AOP: The A Calculus

DEFF Research Database (Denmark)

De Fraine, Bruno; Ernst, Erik; Südholt, Mario

2012-01-01

Aspect-oriented programming (AOP) has produced interesting language designs, but also ad hoc semantics that needs clarification. We contribute to this clarification with a calculus that models essential AOP, both simpler and more general than existing formalizations. In AOP, advice may intercept......-oriented code. Two well-known pointcut categories, call and execution, are commonly considered similar.We formally expose their differences, and resolve the associated soundness problem. Our calculus includes type ranges, an intuitive and concise alternative to explicit type variables that allows advice...... to be polymorphic over intercepted methods. We use calculus parameters to cover type safety for a wide design space of other features. Type soundness is verified in Coq....

An infinite-dimensional calculus for gauge theories

OpenAIRE

Mendes, Rui Vilela

2010-01-01

A space for gauge theories is defined, using projective limits as subsets of Cartesian products of homomorphisms from a lattice on the structure group. In this space, non-interacting and interacting measures are defined as well as functions and operators. From projective limits of test functions and distributions on products of compact groups, a projective gauge triplet is obtained, which provides a framework for the infinite-dimensional calculus in gauge theories. The gauge measure behavior ...

Topology, calculus and approximation

CERN Document Server

Komornik, Vilmos

2017-01-01

Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...

Recursive sequences in first-year calculus

Science.gov (United States)

Krainer, Thomas

2016-02-01

This article provides ready-to-use supplementary material on recursive sequences for a second-semester calculus class. It equips first-year calculus students with a basic methodical procedure based on which they can conduct a rigorous convergence or divergence analysis of many simple recursive sequences on their own without the need to invoke inductive arguments as is typically required in calculus textbooks. The sequences that are accessible to this kind of analysis are predominantly (eventually) monotonic, but also certain recursive sequences that alternate around their limit point as they converge can be considered.

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

OpenAIRE

Ayebo, Abraham; Ukkelberg, Sarah; Assuah, Charles

2017-01-01

Calculus at the college level has significantpotential to serve as a pump for increasing the number of students majoring inSTEM fields. It is a foundation course for all STEM majors and, if mastered well,should provide students with a positive and successful first-year experienceand gateway into more advanced courses. Studies have shown that a high percentage of studentsfailing college calculus has caused a shortage of individuals entering fieldsthat are heavily dependent on mathematics. Many...

Dental calculus image based on optical coherence tomography

Science.gov (United States)

Hsieh, Yao-Sheng; Ho, Yi-Ching; Lee, Shyh-Yuan; Chuang, Ching-Cheng; Wang, Chun-Yang; Sun, Chia-Wei

2011-03-01

In this study, the dental calculus was characterized and imaged by means of swept-source optical coherence tomography (SSOCT). The refractive indices of enamel, dentin, cementum and calculus were measured as 1.625+/-0.024, 1.534+/-0.029, 1.570+/-0.021 and 1.896+/-0.085, respectively. The dental calculus lead strong scattering property and thus the region can be identified under enamel with SSOCT imaging. An extracted human tooth with calculus was covered by gingiva tissue as in vitro sample for SSOCT imaging.

Calculus detection technologies: where do we stand now?

Science.gov (United States)

Archana, V

2014-01-01

Epidemiological studies have implicated dental calculus as an ideal substrate for subgingival microbial colonization. Therefore, the main objective of periodontal therapy is to eliminate the microbial biofilm along with the calculus deposits from the root surface by root surface debridement. Over the past years, a large number of clinical and laboratory studies have been conducted to evaluate the efficacy of calculus removal by various methods. None of these conventional methods or devices was effective in completely eliminating all the calculus from the diseased root surfaces. In this context, a number of newer technologies have been developed to identify and selectively remove the dental calculus. Regarding this fact, the present article highlights a critical review of these devices based on published clinical and experimental data.

Calculus detection technologies: where do we stand now?

Science.gov (United States)

Archana, V

2014-01-01

Epidemiological studies have implicated dental calculus as an ideal substrate for subgingival microbial colonization. Therefore, the main objective of periodontal therapy is to eliminate the microbial biofilm along with the calculus deposits from the root surface by root surface debridement. Over the past years, a large number of clinical and laboratory studies have been conducted to evaluate the efficacy of calculus removal by various methods. None of these conventional methods or devices was effective in completely eliminating all the calculus from the diseased root surfaces. In this context, a number of newer technologies have been developed to identify and selectively remove the dental calculus. Regarding this fact, the present article highlights a critical review of these devices based on published clinical and experimental data. PMID:25870667

Characteristics of subgingival calculus detection by multiphoton fluorescence microscopy

Science.gov (United States)

Tung, Oi-Hong; Lee, Shyh-Yuan; Lai, Yu-Lin; Chen, How-Foo

2011-06-01

Subgingival calculus has been recognized as a major cause of periodontitis, which is one of the main chronic infectious diseases of oral cavities and a principal cause of tooth loss in humans. Bacteria deposited in subgingival calculus or plaque cause gingival inflammation, function deterioration, and then periodontitis. However, subgingival calculus within the periodontal pocket is a complicated and potentially delicate structure to be detected with current dental armamentaria, namely dental x-rays and dental probes. Consequently, complete removal of subgingival calculus remains a challenge to periodontal therapies. In this study, the detection of subgingival calculus employing a multiphoton autofluorescence imaging method was characterized in comparison with a one-photon confocal fluorescence imaging technique. Feasibility of such a system was studied based on fluorescence response of gingiva, healthy teeth, and calculus with and without gingiva covered. The multiphoton fluorescence technology perceived the tissue-covered subgingival calculus that cannot be observed by the one-photon confocal fluorescence method.

Dental calculus formation in children and adolescents undergoing hemodialysis.

Science.gov (United States)

Martins, Carla; Siqueira, Walter Luiz; Oliveira, Elizabeth; Nicolau, José; Primo, Laura Guimarães

2012-10-01

This study aimed to determine whether dental calculus formation is really higher among patients with chronic kidney disease undergoing hemodialysis than among controls. Furthermore, the study evaluated correlations between dental calculus formation and dental plaque, variables that are related to renal disease and/or saliva composition. The Renal Group was composed of 30 patients undergoing hemodialysis, whereas the Healthy Group had 30 clinically healthy patients. Stimulated whole saliva and parotid saliva were collected. Salivary flow rate and calcium and phosphate concentrations were determined. In the Renal Group the saliva collection was carried out before and after a hemodialysis session. Patients from both groups received intraoral exams, oral hygiene instructions, and dental scaling. Three months later, the dental calculus was measured by the Volpe-Manhold method to determine the rate of dental calculus formation. The Renal Group presented a higher rate of dental calculus formation (p dental calculus formation and whole saliva flow rate in the Renal Group after a hemodialysis session (r = 0.44, p dental calculus was associated with phosphate concentration in whole saliva from the Renal Group (p dental calculus formation, probably due to salivary variables.

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

Science.gov (United States)

Bakhmutov, D.; Gonchukov, S.; Sukhinina, A.

2010-05-01

The aim of the present study was to investigate the fluorescence properties of dental calculus in comparison with the properties of adjacent unaffected tooth structure using both lasers and LEDs in the UV-visible range for fluorescence excitation. The influence of calculus color on the informative signal is demonstrated. The optimal spectral bands of excitation and registration of the fluorescence are determined.

Brownian motion, martingales, and stochastic calculus

CERN Document Server

Le Gall, Jean-François

2016-01-01

This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested i...

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....

A type system for continuation calculus

NARCIS (Netherlands)

Geuvers, J.H.; Geraedts, W.; Geron, B.; Stegeren, van J.; Oliva, P.

2014-01-01

Continuation Calculus (CC), introduced by Geron and Geuvers, is a simple foundational model for functional computation. It is closely related to lambda calculus and term rewriting, but it has no variable binding and no pattern matching. It is Turing complete and evaluation is deterministic. Notions

Differential calculus on deformed E(2) group

International Nuclear Information System (INIS)

Giller, S.; Gonera, C.; Kosinski, P.; Maslanka, P.

1997-01-01

Four dimensional bi-covariant differential *-calculus on quantum E(2) group is constructed. The relevant Lie algebra is obtained and covariant differential calculus on quantum plane is found. (author)

Restricted diversity of dental calculus methanogens over five centuries, France

OpenAIRE

Hong T. T. Huynh; Vanessa D. Nkamga; Michel Signoli; Stéfan Tzortzis; Romuald Pinguet; Gilles Audoly; Gérard Aboudharam; Michel Drancourt

2016-01-01

Methanogens are acknowledged archaeal members of modern dental calculus microbiota and dental pathogen complexes. Their repertoire in ancient dental calculus is poorly known. We therefore investigated archaea in one hundred dental calculus specimens collected from individuals recovered from six archaeological sites in France dated from the 14th to 19th centuries AD. Dental calculus was demonstrated by macroscopic and cone-beam observations. In 56 calculus specimens free of PCR inhibition, PCR...

Series expansion in fractional calculus and fractional differential equations

OpenAIRE

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

2009-01-01

Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this theorem, in this paper we introduce fractional series expansion method to fractional calculus. We define a kind of fractional Taylor series of an infinitely fractionally-differentiable function. Further, based on our definition we generalize hypergeometric functio...

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...

Advanced calculus of a single variable

CERN Document Server

Geveci, Tunc

2016-01-01

This advanced undergraduate textbook is based on a one-semester course on single variable calculus that the author has been teaching at San Diego State University for many years. The aim of this classroom-tested book is to deliver a rigorous discussion of the concepts and theorems that are dealt with informally in the first two semesters of a beginning calculus course. As such, students are expected to gain a deeper understanding of the fundamental concepts of calculus, such as limits (with an emphasis on ε-δ definitions), continuity (including an appreciation of the difference between mere pointwise and uniform continuity), the derivative (with rigorous proofs of various versions of L’Hôpital’s rule) and the Riemann integral (discussing improper integrals in-depth, including the comparison and Dirichlet tests). Success in this course is expected to prepare students for more advanced courses in real and complex analysis and this book will help to accomplish this. The first semester of advanced calculus...

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

Science.gov (United States)

Robinson, William Baker

1970-01-01

The predicted and actual achievement in college calculus is compared for students who had studied two semesters of calculus in high school. The regression equation used for prediction was calculated from the performance data of similar students who had not had high school calculus. (CT)

Computer Managed Instruction Homework Modules for Calculus I.

Science.gov (United States)

Goodman-Petrushka, Sharon; Roitberg, Yael

This booklet contains 11 modules (290 multiple-choice items) designed for use in the first course of a three-course calculus sequence using the textbook "Calculus with Analytic Geometry" (Dennis G. Zill). In each module, relevant sections of the textbook are identified for users. It can, however, be used in conjunction with any calculus textbook.…

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

Science.gov (United States)

Wang, Yimin; Chen, Shanwen; Wang, Wei; Liu, Jianyong; Jin, Baiye

2015-07-02

Renal vein thrombosis (RVT) with flank pain, and hematuria, is often mistaken with renal colic originating from ureteric or renal calculus. Especially in young and otherwise healthy patients, clinicians are easily misled by clinical presentation and calcified RVT. A 38-year-old woman presented with flank pain and hematuria suggestive of renal calculus on ultrasound. She underwent extracorporeal shock wave lithotripsy that failed, leading to the recommendation that percutaneous lithotomy was necessary to remove the renal calculus. In preoperative view of the unusual shape of the calculus without hydronephrosis, noncontrast computed tomography was taken and demonstrated left ureteric calculus. However computed tomography angiography revealed, to our surprise, a calcified RVT that was initially thought to be a urinary calculus. This case shows that a calcified RVT might mimic a urinary calculus on conventional ultrasonography and ureteric calculus on noncontrast computed tomography. Subsequent computed tomography angiography disclosed that a calcified RVT caused the imaging findings, thus creating a potentially dangerous clinical pitfall. Hence, it is suggested that the possibility of a RVT needs to be considered in the differential diagnosis whenever one detects an uncommon shape for a urinary calculus.

Pre-calculus 1,001 practice problems for dummies

CERN Document Server

Sterling, Mary Jane; Sterling

2014-01-01

Prepare for calculus the smart way, with customizable pre-calculus practice 1,001 Pre-Calculus Practice Problems For Dummies offers 1,001 opportunities to gain confidence in your math skills. Much more than a workbook, this study aid provides pre-calculus problems ranked from easy to advanced, with detailed explanations and step-by-step solutions for each one. The companion website gives you free online access to all 1,001 practice problems and solutions, and you can track your progress and ID where you should focus your study time. Accessible on the go by smart phone, tablet, o

A Snapshot of the Calculus Classroom

Science.gov (United States)

Weathers, Tony D.; Latterell, Carmen M.

2003-01-01

Essentially a focus group to discuss textbook related issues, a meeting of calculus instructors from a wide variety of environments was convened and sponsored by McGraw Hill to provide feedback on the current state of the calculus classroom. This paper provides a description of the group's discussions.

Imagine Yourself in This Calculus Classroom

Science.gov (United States)

Bryan, Luajean

2007-01-01

The efforts to attract students to precalculus, trigonometry, and calculus classes became more successful at the author's school when projects-based classes were offered. Data collection from an untethered hot air balloon flight for calculus students was planned to maximize enrollment. The data were analyzed numerically, graphically, and…

A calculus for quality

DEFF Research Database (Denmark)

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

2013-01-01

for default behaviour in case the ideal behaviour fails due to unreliable communication and thereby to increase the quality of service offered by the systems. The development is facilitated by a SAT-based robustness analysis to determine whether or not the code is vulnerable to unreliable communication......A main challenge of programming component-based software is to ensure that the components continue to behave in a reasonable manner even when communication becomes unreliable. We propose a process calculus, the Quality Calculus, for programming software components where it becomes natural to plan...

Schaum's outline of calculus

CERN Document Server

Ayres, Frank

1999-01-01

Students can gain a thorough understanding of differential and integral calculus with this powerful study tool. They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guide­­--more than 104,000 copies were bought of the prior edition--­­includes problems and examples using graphing calculators.

A Giant Urethral Calculus.

Science.gov (United States)

Sigdel, G; Agarwal, A; Keshaw, B W

2014-01-01

Urethral calculi are rare forms of urolithiasis. Majority of the calculi are migratory from urinary bladder or upper urinary tract. Primary urethral calculi usually occur in presence of urethral stricture or diverticulum. In this article we report a case of a giant posterior urethral calculus measuring 7x3x2 cm in a 47 years old male. Patient presented with acute retention of urine which was preceded by burning micturition and dribbling of urine for one week. The calculus was pushed in to the bladder through the cystoscope and was removed by suprapubic cystolithotomy.

Discrete Calculus by Analogy

CERN Document Server

Izadi, F A; Bagirov, G

2009-01-01

With its origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. The topics covered here usually arise in many branches of science and technology, especially in discrete mathematics, numerical analysis, statistics and probability theory as well as in electrical engineering, but our viewpoint here is that these topics belong to a much more general realm of mathematics; namely calculus and differential equations because of the remarkable analogy of the subject to this branch of mathemati

AP calculus AB & BC crash course

CERN Document Server

Rosebush, J

2012-01-01

AP Calculus AB & BC Crash Course - Gets You a Higher Advanced Placement Score in Less Time Crash Course is perfect for the time-crunched student, the last-minute studier, or anyone who wants a refresher on the subject. AP Calculus AB & BC Crash Course gives you: Targeted, Focused Review - Study Only What You Need to Know Crash Course is based on an in-depth analysis of the AP Calculus AB & BC course description outline and actual AP test questions. It covers only the information tested on the exams, so you can make the most of your valuable study time. Written by experienced math teachers, our

Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

KAUST Repository

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

RAMAN-SPECTRA OF HUMAN DENTAL CALCULUS

NARCIS (Netherlands)

TSUDA, H; ARENDS, J

1993-01-01

Raman spectra of human dental calculus have been observed for the first time by use of micro-Raman spectroscopy. The spectral features of calculus were influenced easily by heating caused by laser irradiation. Therefore, the measurements were carried out at relatively low power (5 mW, 1-mu m spot

An Introductory Calculus-Based Mechanics Investigation

Science.gov (United States)

Allen, Bradley

2017-01-01

One challenge for the introductory physics teacher is incorporating calculus techniques into the laboratory setting. It can be difficult to strike a balance between presenting an experimental task for which calculus is essential and making the mathematics accessible to learners who may be apprehensive about applying it. One-dimensional kinematics…

Using Dynamic Software to Address Common College Calculus Stumbling Blocks

Science.gov (United States)

Seneres, Alice W.; Kerrigan, John A.

2014-01-01

There are specific topics in college calculus that can be major stumbling blocks for students. Having taught college calculus for four years to over a thousand students, we observed that even the students who have already taken pre-calculus or calculus during their high school careers had common misunderstandings. Students may remember a technique…

Extending Stochastic Network Calculus to Loss Analysis

Directory of Open Access Journals (Sweden)

Chao Luo

2013-01-01

Full Text Available Loss is an important parameter of Quality of Service (QoS. Though stochastic network calculus is a very useful tool for performance evaluation of computer networks, existing studies on stochastic service guarantees mainly focused on the delay and backlog. Some efforts have been made to analyse loss by deterministic network calculus, but there are few results to extend stochastic network calculus for loss analysis. In this paper, we introduce a new parameter named loss factor into stochastic network calculus and then derive the loss bound through the existing arrival curve and service curve via this parameter. We then prove that our result is suitable for the networks with multiple input flows. Simulations show the impact of buffer size, arrival traffic, and service on the loss factor.

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

Science.gov (United States)

Huynh, Hong T T; Nkamga, Vanessa D; Signoli, Michel; Tzortzis, Stéfan; Pinguet, Romuald; Audoly, Gilles; Aboudharam, Gérard; Drancourt, Michel

2016-05-11

Methanogens are acknowledged archaeal members of modern dental calculus microbiota and dental pathogen complexes. Their repertoire in ancient dental calculus is poorly known. We therefore investigated archaea in one hundred dental calculus specimens collected from individuals recovered from six archaeological sites in France dated from the 14(th) to 19(th) centuries AD. Dental calculus was demonstrated by macroscopic and cone-beam observations. In 56 calculus specimens free of PCR inhibition, PCR sequencing identified Candidatus Methanobrevibacter sp. N13 in 44.6%, Methanobrevibacter oralis in 19.6%, a new Methanomassiliicoccus luminyensis-like methanogen in 12.5%, a Candidatus Nitrososphaera evergladensis-like in one and Methanoculleus bourgensis in one specimen, respectively. One Candidatus Methanobrevibacter sp. N13 dental calculus was further documented by fluorescent in situ hybridization. The prevalence of dental calculus M. oralis was significantly lower in past populations than in modern populations (P = 0.03, Chi-square test). This investigation revealed a previously unknown repertoire of archaea found in the oral cavity of past French populations as reflected in preserved dental calculus.

Ancient DNA analysis of dental calculus.

Science.gov (United States)

Weyrich, Laura S; Dobney, Keith; Cooper, Alan

2015-02-01

Dental calculus (calcified tartar or plaque) is today widespread on modern human teeth around the world. A combination of soft starchy foods, changing acidity of the oral environment, genetic pre-disposition, and the absence of dental hygiene all lead to the build-up of microorganisms and food debris on the tooth crown, which eventually calcifies through a complex process of mineralisation. Millions of oral microbes are trapped and preserved within this mineralised matrix, including pathogens associated with the oral cavity and airways, masticated food debris, and other types of extraneous particles that enter the mouth. As a result, archaeologists and anthropologists are increasingly using ancient human dental calculus to explore broad aspects of past human diet and health. Most recently, high-throughput DNA sequencing of ancient dental calculus has provided valuable insights into the evolution of the oral microbiome and shed new light on the impacts of some of the major biocultural transitions on human health throughout history and prehistory. Here, we provide a brief historical overview of archaeological dental calculus research, and discuss the current approaches to ancient DNA sampling and sequencing. Novel applications of ancient DNA from dental calculus are discussed, highlighting the considerable scope of this new research field for evolutionary biology and modern medicine. Copyright © 2014 Elsevier Ltd. All rights reserved.

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

Science.gov (United States)

Hall, Angela Renee

2011-01-01

This investigative research focuses on the level of readiness of Science, Technology, Engineering, and Mathematics (STEM) students entering Historically Black Colleges and Universities (HBCU) in the college Calculus sequence. Calculus is a fundamental course for STEM courses. The level of readiness of the students for Calculus can very well play a…

Thematization of the Calculus Graphing Schema

Science.gov (United States)

Cooley, Laurel; Baker, Bernadette; Trigueros, Maria

2003-01-01

This article is the result of an investigation of students' conceptualizations of calculus graphing techniques after they had completed at least two semesters of calculus. The work and responses of 27 students to a series of questions that solicit information about the graphical implications of the first derivative, second derivative, continuity,…

A Cross-National Study of Calculus

Science.gov (United States)

Chai, Jun; Friedler, Louis M.; Wolff, Edward F.; Li, Jun; Rhea, Karen

2015-01-01

The results from a cross-national study comparing calculus performance of students at East China Normal University (ECNU) in Shanghai and students at the University of Michigan before and after their first university calculus course are presented. Overall, ECNU significantly outperformed Michigan on both the pre- and post-tests, but the Michigan…

Command injection attacks, continuations, and the Lambek calculus

Directory of Open Access Journals (Sweden)

Hayo Thielecke

2016-06-01

Full Text Available This paper shows connections between command injection attacks, continuations, and the Lambek calculus: certain command injections, such as the tautology attack on SQL, are shown to be a form of control effect that can be typed using the Lambek calculus, generalizing the double-negation typing of continuations. Lambek's syntactic calculus is a logic with two implicational connectives taking their arguments from the left and right, respectively. These connectives describe how strings interact with their left and right contexts when building up syntactic structures. The calculus is a form of propositional logic without structural rules, and so a forerunner of substructural logics like Linear Logic and Separation Logic.

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

Science.gov (United States)

Bagley, Spencer Franklin

The quality of education in science, technology, engineering, and mathematics (STEM) fields is an issue of particular educational and economic importance, and Calculus I is a linchpin course in STEM major tracks. A national study is currently being conducted examining the characteristics of successful programs in college calculus (CSPCC, 2012). In work related to the CSPCC program, this study examines the effects on student outcomes of four different teaching strategies used at a single institution. The four classes were a traditional lecture, a lecture with discussion, a lecture incorporating both discussion and technology, and an inverted model. This dissertation was guided by three questions: (1) What impact do these four instructional approaches have on students' persistence, beliefs about mathematics, and conceptual and procedural achievement in calculus? (2) How do students at the local institution compare to students in the national database? And (3) How do the similarities and differences in opportunities for learning presented in the four classes contribute to the similarities and differences in student outcomes? Quantitative analysis of surveys and exams revealed few statistically significant differences in outcomes, and students in the inverted classroom often had poorer outcomes than those in other classes. Students in the technology-enhanced class scored higher on conceptual items on the final exam than those in other classes. Comparing to the national database, local students had similar switching rates but less expert-like attitudes and beliefs about mathematics than the national average. Qualitative analysis of focus group interviews, classroom observations, and student course evaluations showed that several implementation issues, some the result of pragmatic constraints, others the result of design choice, weakened affordances provided by innovative features and shrunk the differences between classes. There were substantial differences between the

Neutrosophic Precalculus and Neutrosophic Calculus

OpenAIRE

Florentin Smarandache

2015-01-01

Neutrosophic Analysis is a generalization of Set Analysis, which in its turn is a generalization of Interval Analysis. Neutrosophic Precalculus is referred to indeterminate staticity, while Neutrosophic Calculus is the mathematics of indeterminate change. The Neutrosophic Precalculus and Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the methods used to deal with such indeterminacy. In this book, the author presents a few examples o...

Endoscopic vs. tactile evaluation of subgingival calculus.

Science.gov (United States)

Osborn, Joy B; Lenton, Patricia A; Lunos, Scott A; Blue, Christine M

2014-08-01

Endoscopic technology has been developed to facilitate imagery for use during diagnostic and therapeutic phases of periodontal care. The purpose of this study was to compare the level of subgingival calculus detection using a periodontal endoscope with that of conventional tactile explorer in periodontitis subjects. A convenience sample of 26 subjects with moderate periodontitis in at least 2 quadrants was recruited from the University of Minnesota School of Dentistry to undergo quadrant scaling and root planing. One quadrant from each subject was randomized for tactile calculus detection alone and the other quadrant for tactile detection plus the Perioscope ™ (Perioscopy Inc., Oakland, Cali). A calculus index on a 0 to 3 score was performed at baseline and at 2 post-scaling and root planing visits. Sites where calculus was detected at visit 1 were retreated. T-tests were used to determine within-subject differences between Perioscope™ and tactile measures, and changes in measures between visits. Significantly more calculus was detected using the Perioscope™ vs. tactile explorer for all 3 subject visits (pcalculus detection from baseline to visit 1 were statistically significant for both the Perioscope™ and tactile quadrants (pcalculus detection from visit 1 to visit 2 was only significant for the Perioscope™ quadrant (pcalculus at this visit. It was concluded that the addition of a visual component to calculus detection via the Perioscope™ was most helpful in the re-evaluation phase of periodontal therapy. Copyright © 2014 The American Dental Hygienists’ Association.

Educating about Sustainability while Enhancing Calculus

Science.gov (United States)

Pfaff, Thomas J.

2011-01-01

We give an overview of why it is important to include sustainability in mathematics classes and provide specific examples of how to do this for a calculus class. We illustrate that when students use "Excel" to fit curves to real data, fundamentally important questions about sustainability become calculus questions about those curves. (Contains 5…

Introductory analysis a deeper view of calculus

CERN Document Server

Bagby, Richard J

2000-01-01

Introductory Analysis addresses the needs of students taking a course in analysis after completing a semester or two of calculus, and offers an alternative to texts that assume that math majors are their only audience. By using a conversational style that does not compromise mathematical precision, the author explains the material in terms that help the reader gain a firmer grasp of calculus concepts.* Written in an engaging, conversational tone and readable style while softening the rigor and theory* Takes a realistic approach to the necessary and accessible level of abstraction for the secondary education students* A thorough concentration of basic topics of calculus* Features a student-friendly introduction to delta-epsilon arguments * Includes a limited use of abstract generalizations for easy use* Covers natural logarithms and exponential functions* Provides the computational techniques often encountered in basic calculus

Calculus of tensors and differential forms

CERN Document Server

Sinha, Rajnikant

2014-01-01

Calculus of tensors and differential forms is an introductory-level textbook. Through this book, students will familiarize themselves with tools they need in order to use for further study on general relativity and research, such as affine tensors, tensor calculus on manifolds, relative tensors, Lie derivatives, wedge products, differential forms, and Stokes' theorem. The treatment is concrete and in detail, so that abstract concepts do not deter even physics and engineering students. This self contained book requires undergraduate-level calculus of several variables and linear algebra as prerequisite. Fubini's theorem in real analysis, to be used in Stokes' theorem, has been proved earlier than Stokes' theorem so that students don't have to search elsewhere.

Quantum geometry in dynamical Regge calculus

International Nuclear Information System (INIS)

Hagura, Hiroyuki

2002-01-01

We study geometric properties of dynamical Regge calculus which is a hybridization of dynamical triangulation and quantum Regge calculus. Lattice diffeomorphisms are generated by certain elementary moves on a simplicial lattice in the hybrid model. At the semiclassical level, we discuss a possibility that the lattice diffeomorphisms give a simple explanation for the Bekenstein-Hawking entropy of a black hole. At the quantum level, numerical calculations of 3D pure gravity show that a fractal structure of the hybrid model is the same as that of dynamical triangulation in the strong-coupling phase. In the weak-coupling phase, on the other hand, space-time becomes a spiky configuration, which often occurs in quantum Regge calculus

Anisotropic fractal media by vector calculus in non-integer dimensional space

Energy Technology Data Exchange (ETDEWEB)

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)

2014-08-15

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

Anisotropic fractal media by vector calculus in non-integer dimensional space

Science.gov (United States)

Tarasov, Vasily E.

2014-08-01

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

Anisotropic fractal media by vector calculus in non-integer dimensional space

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2014-01-01

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media

The dagger lambda calculus

Directory of Open Access Journals (Sweden)

Philip Atzemoglou

2014-12-01

Full Text Available We present a novel lambda calculus that casts the categorical approach to the study of quantum protocols into the rich and well established tradition of type theory. Our construction extends the linear typed lambda calculus with a linear negation of "trivialised" De Morgan duality. Reduction is realised through explicit substitution, based on a symmetric notion of binding of global scope, with rules acting on the entire typing judgement instead of on a specific subterm. Proofs of subject reduction, confluence, strong normalisation and consistency are provided, and the language is shown to be an internal language for dagger compact categories.

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

Science.gov (United States)

Corraini, Priscila; López, Rodrigo

2015-04-01

To assess the intra-examiner reliability of recordings of subgingival calculus detected using an ultrasonic device, and to investigate the influence of subject-, tooth- and site-level factors on the reliability of these subgingival calculus recordings. On two occasions, within a 1-week interval, 147 adult periodontitis patients received a full-mouth clinical periodontal examination by a single trained examiner. Duplicate subgingival calculus recordings, in six sites per tooth, were obtained using an ultrasonic device for calculus detection and removal. Agreement was observed in 65 % of the 22,584 duplicate subgingival calculus recordings, ranging 45 % to 83 % according to subject. Using hierarchical modeling, disagreements in the subgingival calculus duplicate recordings were more likely in all other sites than the mid-buccal, and in sites harboring supragingival calculus. Disagreements were less likely in sites with PD ≥  4 mm and with furcation involvement  ≥  degree 2. Bleeding on probing or suppuration did not influence the reliability of subgingival calculus. At the subject-level, disagreements were less likely in patients presenting with the highest and lowest extent categories of the covariate subgingival calculus. The reliability of subgingival calculus recordings using the ultrasound technology is reasonable. The results of the present study suggest that the reliability of subgingival calculus recordings is not influenced by the presence of inflammation. Moreover, subgingival calculus can be more reliably detected using the ultrasound device at sites with higher need for periodontal therapy, i.e., sites presenting with deep pockets and premolars and molars with furcation involvement.

Malliavin Calculus With Applications to Stochastic Partial Differential Equations

CERN Document Server

Sanz-Solé, Marta

2005-01-01

Developed in the 1970s to study the existence and smoothness of density for the probability laws of random vectors, Malliavin calculus--a stochastic calculus of variation on the Wiener space--has proven fruitful in many problems in probability theory, particularly in probabilistic numerical methods in financial mathematics.This book presents applications of Malliavin calculus to the analysis of probability laws of solutions to stochastic partial differential equations driven by Gaussian noises that are white in time and coloured in space. The first five chapters introduce the calculus itself

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.

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

Science.gov (United States)

Gonchukov, S.; Sukhinina, A.; Bakhmutov, D.; Biryukova, T.

2013-02-01

The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise noninvasive detection of calculus-tooth interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing.

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

International Nuclear Information System (INIS)

Gonchukov, S; Sukhinina, A; Bakhmutov, D; Biryukova, T

2013-01-01

The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise noninvasive detection of calculus-tooth interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing.

Areas and Volumes in Pre-Calculus

Science.gov (United States)

Jarrett, Joscelyn A.

2008-01-01

This article suggests the introduction of the concepts of areas bounded by plane curves and the volumes of solids of revolution in Pre-calculus. It builds on the basic knowledge that students bring to a pre-calculus class, derives a few more formulas, and gives examples of some problems on plane areas and the volumes of solids of revolution that…

A call-by-value lambda-calculus with lists and control

Directory of Open Access Journals (Sweden)

Robbert Krebbers

2012-10-01

Full Text Available Calculi with control operators have been studied to reason about control in programming languages and to interpret the computational content of classical proofs. To make these calculi into a real programming language, one should also include data types. As a step into that direction, this paper defines a simply typed call-by-value lambda calculus with the control operators catch and throw, a data type of lists, and an operator for primitive recursion (a la Goedel's T. We prove that our system satisfies subject reduction, progress, confluence for untyped terms, and strong normalization for well-typed terms.

Programming Language Concepts - The Lambda Calculus Approach

NARCIS (Netherlands)

Fokkinga, M.M.; Asveld, P.R.J.; Nijholt, Antinus

1987-01-01

The Lambda Calculus is a formal system, originally intended as a tool in the foundation of mathematics, but mainly used to study the concepts of algorithm and effective computability. Recently, the Lambda Calculus and related systems acquire attention from Computer Science for another reason too:

[Endoscopy-assisted sialolithectomy for the calculus of the Stensen's duct].

Science.gov (United States)

Ye, Xin; Xie, Xiaoyan; Liu, Denggao; Zhang, Lei; Zhang, Zuyan; Yu, Guangyan

2014-11-01

To investigate the clinical effects of endoscopy-assisted sialolithectomy for the calculus in the Stensen's duct. From August 2005 to July 2013, 67 consecutive patients with calculus (or foreign bodies) in the Stensen's duct underwent explorative and interventional endoscopy in our hospital. The stones (or foreign bodies) were removed by endoscopy-assisted technique. After operation, the patients were followed-up periodically, and treatment effects were analyzed. Among the 67 patients, the stones (or foreign bodies) were completely removed in 58 cases, and almost completely removed in 3 cases, with a success rate of 87% (58/67). Among the 61 stone-removed cases, treatment options included direct removal with aid of basket or forceps (24 cases), basket entrapment and opening-up of the ostium (21 cases), basket entrapment and mucosal incision near the ostium (8 cases), open removal via buccal incision (2 cases) and open removal via pre-auricular flap (6 cases). During the 6-90 months' follow-up of the 61 cases, 48 cases were asymptomatic, 7 had mild symptoms, 3 developed ductal obturation, 1 had numbness in the parotid region, and the remaining 2 were missed. Endoscopy-assisted sialolithectomy is a safe and effective gland-preservation technique for the patients with parotid gland calculus.

Relativistic collapse using Regge calculus: Pt. 1

International Nuclear Information System (INIS)

Dubal, M.R.; Leicester Univ.

1989-01-01

Regge calculus is used to simulate the dynamical collapse of model stars. In this paper we describe the general methodology of including a perfect fluid in dynamical Regge calculus spacetimes. The Regge-Einstein equations for spherical collapse are obtained and are then specialised to mimic a particular continuum gauge. The equivalent continuum problem is also set up. This is to be solved using standard numerical techniques (i.e. the method of finite difference). A subsequent paper will consider the solution of the equations presented here and will use the continuum problem for comparison purposes in order to check the Regge calculus results. (author)

A Transition Course from Advanced Placement to College Calculus

Science.gov (United States)

Lucas, Timothy A.; Spivey, Joseph

2011-01-01

In the Spring of 2007, a group of highly motivated mathematics graduate students conducted a review of Duke's Calculus curriculum. They focused on two main problems. The first problem is the result of a very positive trend: a growing number of students are earning AP credit for Calculus I in high school. However, this results in Calculus II…

Everyday calculus discovering the hidden math all around us

CERN Document Server

Fernandez, Oscar E

2014-01-01

Calculus. For some of us, the word conjures up memories of ten-pound textbooks and visions of tedious abstract equations. And yet, in reality, calculus is fun, accessible, and surrounds us everywhere we go. In Everyday Calculus, Oscar Fernandez shows us how to see the math in our coffee, on the highway, and even in the night sky. Fernandez uses our everyday experiences to skillfully reveal the hidden calculus behind a typical day's events. He guides us through how math naturally emerges from simple observations-how hot coffee cools down, for example-and in discussions of over fifty familia

Towards Model Checking a Spi-Calculus Dialect

NARCIS (Netherlands)

Gnesi, S.; Latella, D.; Lenzini, Gabriele

We present a model checking framework for a spi-calculus dialect which uses a linear time temporal logic for expressing security properties. We have provided our spi-calculus dialect, called SPID, with a semantics based on labeled transition systems (LTS), where the intruder is modeled in the

On flipping first-semester calculus: a case study

Science.gov (United States)

Petrillo, Joseph

2016-05-01

High failure rates in calculus have plagued students, teachers, and administrators for decades, while science, technology, engineering, and mathematics programmes continue to suffer from low enrollments and high attrition. In an effort to affect this reality, some educators are 'flipping' (or inverting) their classrooms. By flipping, we mean administering course content outside of the classroom and replacing the traditional in-class lectures with discussion, practice, group work, and other elements of active learning. This paper presents the major results from a three-year study of a flipped, first-semester calculus course at a small, comprehensive, American university with a well-known engineering programme. The data we have collected help quantify the positive and substantial effects of our flipped calculus course on failure rates, scores on the common final exam, student opinion of calculus, teacher impact on measurable outcomes, and success in second-semester calculus. While flipping may not be suitable for every teacher, every student, and in every situation, this report provides some evidence that it may be a viable option for those seeking an alternative to the traditional lecture model.

Geometric calculus according to the Ausdehnungslehre of H. Grassmann

CERN Document Server

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...

Introduction to Differential Calculus Systematic Studies with Engineering Applications for Beginners

CERN Document Server

Rohde, Ulrich L; Poddar, Ajay K; Ghosh, A K

2011-01-01

Enables readers to apply the fundamentals of differential calculus to solve real-life problems in engineering and the physical sciences Introduction to Differential Calculus fully engages readers by presenting the fundamental theories and methods of differential calculus and then showcasing how the discussed concepts can be applied to real-world problems in engineering and the physical sciences. With its easy-to-follow style and accessible explanations, the book sets a solid foundation before advancing to specific calculus methods, demonstrating the connections between differential calculus

Science 101: How Do We Use Calculus in Science?

Science.gov (United States)

Robertson, Bill

2014-01-01

How is calculus used in science? That might seem like an odd question to answer in a magazine intended primarily for elementary school teachers. After all, how much calculus gets used in elementary science? Here the author guesses that quite a few readers of this column do not know a whole lot about calculus and have not taken a course in…

Elementary calculus an infinitesimal approach

CERN Document Server

Keisler, H Jerome

2012-01-01

This first-year calculus book is centered around the use of infinitesimals, an approach largely neglected until recently for reasons of mathematical rigor. It exposes students to the intuition that originally led to the calculus, simplifying their grasp of the central concepts of derivatives and integrals. The author also teaches the traditional approach, giving students the benefits of both methods.Chapters 1 through 4 employ infinitesimals to quickly develop the basic concepts of derivatives, continuity, and integrals. Chapter 5 introduces the traditional limit concept, using approximation p

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...

On power series expansions of the S-resolvent operator and the Taylor formula

Science.gov (United States)

Colombo, Fabrizio; Gantner, Jonathan

2016-12-01

The S-functional calculus is based on the theory of slice hyperholomorphic functions and it defines functions of n-tuples of not necessarily commuting operators or of quaternionic operators. This calculus relays on the notion of S-spectrum and of S-resolvent operator. Since most of the properties that hold for the Riesz-Dunford functional calculus extend to the S-functional calculus, it can be considered its non commutative version. In this paper we show that the Taylor formula of the Riesz-Dunford functional calculus can be generalized to the S-functional calculus. The proof is not a trivial extension of the classical case because there are several obstructions due to the non commutativity of the setting in which we work that have to be overcome. To prove the Taylor formula we need to introduce a new series expansion of the S-resolvent operators associated to the sum of two n-tuples of operators. This result is a crucial step in the proof of our main results, but it is also of independent interest because it gives a new series expansion for the S-resolvent operators. This paper is addressed to researchers working in operator theory and in hypercomplex analysis.

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

Science.gov (United States)

Brede, O.; Schelle, F.; Krueger, S.; Oehme, B.; Dehn, C.; Frentzen, M.; Braun, A.

2011-03-01

The aim of this study was to assess the difference of fluorescence signals of cement and calculus using a 405 nm excitation wavelength. A total number of 20 freshly extracted teeth was used. The light source used for this study was a blue LED with a wavelength of 405nm. For each tooth the spectra of calculus and cementum were measured separately. Fluorescence light was collimated into an optical fibre and spectrally analyzed using an echelle spectrometer (aryelle 200, Lasertechnik Berlin, Germany) with an additionally bandpass (fgb 67, Edmund Industrial Optics, Karlsruhe, Germany). From these 40 measurements the median values were calculated over the whole spectrum, leading to two different median spectra, one for calculus and one for cementum. For further statistical analysis we defined 8 areas of interest (AOI) in wavelength regions, showing remarkable differences in signal strength. In 7 AOIs the intensity of the calculus spectrum differed statistically significant from the intensity of the cementum spectrum (p calculus and cement between 600nm and 700nm. Thus, we can conclude that fluorescence of calculus shows a significant difference to the fluorescence of cement. A differentiation over the intensity is possible as well as over the spectrum. Using a wavelength of 405nm, it is possible to distinguish between calculus and cement. These results could be used for further devices to develop a method for feedback controlled calculus removal.

Subgingival calculus imaging based on swept-source optical coherence tomography

Science.gov (United States)

Hsieh, Yao-Sheng; Ho, Yi-Ching; Lee, Shyh-Yuan; Lu, Chih-Wei; Jiang, Cho-Pei; Chuang, Ching-Cheng; Wang, Chun-Yang; Sun, Chia-Wei

2011-07-01

We characterized and imaged dental calculus using swept-source optical coherence tomography (SS-OCT). The refractive indices of enamel, dentin, cementum, and calculus were measured as 1.625 +/- 0.024, 1.534 +/- 0.029, 1.570 +/- 0.021, and 2.097 +/- 0.094, respectively. Dental calculus leads strong scattering properties, and thus, the region can be identified from enamel with SS-OCT imaging. An extracted human tooth with calculus is covered with gingiva tissue as an in vitro sample for tomographic imaging.

Calculator calculus

CERN Document Server

McCarty, George

1982-01-01

How THIS BOOK DIFFERS This book is about the calculus. What distinguishes it, however, from other books is that it uses the pocket calculator to illustrate the theory. A computation that requires hours of labor when done by hand with tables is quite inappropriate as an example or exercise in a beginning calculus course. But that same computation can become a delicate illustration of the theory when the student does it in seconds on his calculator. t Furthermore, the student's own personal involvement and easy accomplishment give hi~ reassurance and en­ couragement. The machine is like a microscope, and its magnification is a hundred millionfold. We shall be interested in limits, and no stage of numerical approximation proves anything about the limit. However, the derivative of fex) = 67.SgX, for instance, acquires real meaning when a student first appreciates its values as numbers, as limits of 10 100 1000 t A quick example is 1.1 , 1.01 , 1.001 , •••• Another example is t = 0.1, 0.01, in the functio...

Intitialization, Conceptualization, and Application in the Generalized Fractional Calculus

Science.gov (United States)

Lorenzo, Carl F.; Hartley, Tom T.

1998-01-01

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions.

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

Science.gov (United States)

Lorenzo, Carl F; Hartley, Tom T

2007-01-01

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions.

Calculus in High School--At What Cost?

Science.gov (United States)

Sorge, D. H.; Wheatley, G. H.

1977-01-01

Evidence on the decline in preparation of entering calculus students and the relationship to high school preparation is presented, focusing on the trend toward the de-emphasis of trigonometry and analytic geometry in favor of calculus. Data on students' perception of the adequacy of their preparation are also presented. (Author/MN)

Calculus and Success in a Business School

Science.gov (United States)

Kim, Dong-gook; Garcia, Fernando; Dey, Ishita

2012-01-01

Many business schools or colleges require calculus as a prerequisite for certain classes or for continuing to upper division courses. While there are many studies investigating the relationship between performance in calculus and performance in a single course, such as economics, statistics, and finance, there are very few studies investigating…

Fractal physiology and the fractional calculus: a perspective

Directory of Open Access Journals (Sweden)

Bruce J West

2010-10-01

Full Text Available This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. We review the allometric aggregation approach to the processing of physiologic time series as a way of determining the fractal character of the underlying phenomena. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. Fractional operators acting on fractal functions yield fractal functions, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process. Control of physiologic complexity is one of the goals of medicine. Allometric control incorporates long-time memory, inverse power-law (IPL correlations, and long-range interactions in complex phenomena as manifest by IPL distributions. We hypothesize that allometric control, rather than homeostatic control, maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can be described using the fractional calculus to capture the dynamics of complex physiologic networks. This hypothesis is supported by a number of physiologic time series data.

Generalized Cartan Calculus in general dimension

Science.gov (United States)

Wang, Yi-Nan

2015-07-01

We develop the generalized Cartan Calculus for the groups and SO(5 , 5). They are the underlying algebraic structures of d = 9 , 7 , 6 exceptional field theory, respectively. These algebraic identities are needed for the "tensor hierarchy" structure in exceptional field theory. The validity of Poincaré lemmas in this new differential geometry is also discussed. Finally we explore some possible extension of the generalized Cartan calculus beyond the exceptional series.

Superconformal tensor calculus in five dimensions

International Nuclear Information System (INIS)

Fujita, Tomoyuki; Ohashi, Keisuke

2001-01-01

We present a full superconformal tensor calculus in five spacetime dimensions in which the Weyl multiplet has 32 Bose plus 32 Fermi degrees of freedom. It is derived using dimensional reduction from the 6D superconformal tensor calculus. We present two types of 32+32 Weyl multiplets, a vector multiplet, linear multiplet, hypermultiplet and nonlinear multiplet. Their superconformal transformation laws and the embedding and invariant action formulas are given. (author)

Null-strut calculus. I. Kinematics

International Nuclear Information System (INIS)

Kheyfets, A.; LaFave, N.J.; Miller, W.A.

1990-01-01

This paper describes the kinematics of null-strut calculus---a 3+1 Regge calculus approach to general relativity. We show how to model the geometry of spacetime with simplicial spacelike three-geometries (TET's) linked to ''earlier'' and ''later'' momentumlike lattice surfaces (TET * ) entirely by light rays or ''null struts.'' These three-layered lattice spacetime geometries are defined and analyzed using combinatorial formulas for the structure of polytopes. The following paper in this series describes how these three-layered spacetime lattices are used to model spacetimes in full conformity with Einstein's theory of gravity

Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric

Science.gov (United States)

Balankin, Alexander S.; Bory-Reyes, Juan; Shapiro, Michael

2016-02-01

One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.

Teaching and learning of pre-calculus: an insights of educators ...

African Journals Online (AJOL)

The high-failure of Calculus courses has bring dilemma to the educators worldwide. This study has focus on teaching and learning of Pre-Calculus, a fundamental course for higher level Calculus courses. A well-designed questionnaire was distributed to all respondents to find the difficulties faced by both lecturers and ...

Backpropagation and ordered derivatives in the time scales calculus.

Science.gov (United States)

Seiffertt, John; Wunsch, Donald C

2010-08-01

Backpropagation is the most widely used neural network learning technique. It is based on the mathematical notion of an ordered derivative. In this paper, we present a formulation of ordered derivatives and the backpropagation training algorithm using the important emerging area of mathematics known as the time scales calculus. This calculus, with its potential for application to a wide variety of inter-disciplinary problems, is becoming a key area of mathematics. It is capable of unifying continuous and discrete analysis within one coherent theoretical framework. Using this calculus, we present here a generalization of backpropagation which is appropriate for cases beyond the specifically continuous or discrete. We develop a new multivariate chain rule of this calculus, define ordered derivatives on time scales, prove a key theorem about them, and derive the backpropagation weight update equations for a feedforward multilayer neural network architecture. By drawing together the time scales calculus and the area of neural network learning, we present the first connection of two major fields of research.

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

Science.gov (United States)

Zhang, Jian J; Rajabhandharaks, Danop; Xuan, Jason Rongwei; Wang, Hui; Chia, Ray W J; Hasenberg, Tom; Kang, Hyun Wook

2015-01-01

Q-switched (QS) Tm:YAG laser ablation mechanisms on urinary calculi are still unclear to researchers. Here, dependence of water content in calculus phantom on calculus ablation performance was investigated. White gypsum cement was used as a calculus phantom model. The calculus phantoms were ablated by a total 3-J laser pulse exposure (20 mJ, 100 Hz, 1.5 s) and contact mode with N=15 sample size. Ablation volume was obtained on average 0.079, 0.122, and 0.391  mm3 in dry calculus in air, wet calculus in air, and wet calculus in-water groups, respectively. There were three proposed ablation mechanisms that could explain the effect of water content in calculus phantom on calculus ablation performance, including shock wave due to laser pulse injection and bubble collapse, spallation, and microexplosion. Increased absorption coefficient of wet calculus can cause stronger spallation process compared with that caused by dry calculus; as a result, higher calculus ablation was observed in both wet calculus in air and wet calculus in water. The test result also indicates that the shock waves generated by short laser pulse under the in-water condition have great impact on the ablation volume by Tm:YAG QS laser.

Anastomotic Urethroplasty for an Obstructing Calculus Within a Bulbar Urethral Diverticulum and Urethral Stricture

Directory of Open Access Journals (Sweden)

Pooya Banapour

2017-01-01

Full Text Available A 61-year-old male with prior history of endoscopic urethral calculus removal presented to the emergency room with urinary retention and a palpable perineal mass. A CT showed a large calcification within the bulbar urethra. After multiple unsuccessful attempts at foley catheter insertion, the urology service was consulted. The patient was taken to the operating room where an obstructing urethral calculus with associated urethral stricture was visualized on cystoscopy. We present an exceedingly rare case of recurrent urethrolithiasis with associated urethral stricture managed with initial suprapubic tube and delayed primary end-to-end urethroplasty, excision of urethral stricture and urethral diverticulectomy.

Supergravity tensor calculus in 5D from 6D

International Nuclear Information System (INIS)

Kugo, Taichiro; Ohashi, Keisuke

2000-01-01

Supergravity tensor calculus in five spacetime dimensions is derived by dimensional reduction from the d=6 superconformal tensor calculus. In particular, we obtain an off-shell hypermultiplet in 5D from the on-shell hypermultiplet in 6D. Our tensor calculus retains the dilatation gauge symmetry, so that it is a trivial gauge fixing to make the Einstein term canonical in a general matter-Yang-Mills-supergravity coupled system. (author)

The Enriched Effect Calculus: Syntax and Semantics

DEFF Research Database (Denmark)

Møgelberg, Rasmus Ejlers; Simpson, Alex; Egger, Jeff

2014-01-01

This article introduces the enriched effect calculus, which extends established type theories for computational effects with primitives from linear logic. The new calculus provides a formalism for expressing linear aspects of computational effects; e.g. the linear usage of imperative features....... The second half of the article investigates models for the enriched effect calculus, based on enriched category theory. We give several examples of such models, relating them to models of standard effect calculi (such as those based on monads), and to models of intuitionistic linear logic. We also prove...

Discrete Calculus as a Bridge between Scales

Science.gov (United States)

Degiuli, Eric; McElwaine, Jim

2012-02-01

Understanding how continuum descriptions of disordered media emerge from the microscopic scale is a fundamental challenge in condensed matter physics. In many systems, it is necessary to coarse-grain balance equations at the microscopic scale to obtain macroscopic equations. We report development of an exact, discrete calculus, which allows identification of discrete microscopic equations with their continuum equivalent [1]. This allows the application of powerful techniques of calculus, such as the Helmholtz decomposition, the Divergence Theorem, and Stokes' Theorem. We illustrate our results with granular materials. In particular, we show how Newton's laws for a single grain reproduce their continuum equivalent in the calculus. This allows introduction of a discrete Airy stress function, exactly as in the continuum. As an application of the formalism, we show how these results give the natural mean-field variation of discrete quantities, in agreement with numerical simulations. The discrete calculus thus acts as a bridge between discrete microscale quantities and continuous macroscale quantities. [4pt] [1] E. DeGiuli & J. McElwaine, PRE 2011. doi: 10.1103/PhysRevE.84.041310

A calculus for attribute-based communication

DEFF Research Database (Denmark)

Alrahman, Yehia Abd; De Nicola, Rocco; Loreti, Michele

2015-01-01

The notion of attribute-based communication seems promising to model and analyse systems with huge numbers of interacting components that dynamically adjust and combine their behaviour to achieve specific goals. A basic process calculus, named AbC, is introduced that has as primitive construct...... of how well-established process calculi could be encoded into AbC is given by considering the translation into AbC of a proto-typical π-calculus process....

Regge calculus from discontinuous metrics

International Nuclear Information System (INIS)

Khatsymovsky, V.M.

2003-01-01

Regge calculus is considered as a particular case of the more general system where the linklengths of any two neighbouring 4-tetrahedra do not necessarily coincide on their common face. This system is treated as that one described by metric discontinuous on the faces. In the superspace of all discontinuous metrics the Regge calculus metrics form some hypersurface defined by continuity conditions. Quantum theory of the discontinuous metric system is assumed to be fixed somehow in the form of quantum measure on (the space of functionals on) the superspace. The problem of reducing this measure to the Regge hypersurface is addressed. The quantum Regge calculus measure is defined from a discontinuous metric measure by inserting the δ-function-like phase factor. The requirement that continuity conditions be imposed in a 'face-independent' way fixes this factor uniquely. The term 'face-independent' means that this factor depends only on the (hyper)plane spanned by the face, not on it's form and size. This requirement seems to be natural from the viewpoint of existence of the well-defined continuum limit maximally free of lattice artefacts

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

Science.gov (United States)

Krisdapong, Sudaduang; Prasertsom, Piyada; Rattanarangsima, Khanit; Sheiham, Aubrey; Tsakos, Georgios

2012-09-01

To assess associations of socio-demographic, behavioural and the extent of gingivitis and calculus with oral health-related quality of life (OHRQoL) in nationally representative samples of 12- and 15-year-old Thai children. In the Thailand National Oral Health Survey, 1,063 twelve-year olds and 811 fifteen-year olds were clinically examined and interviewed for OHRQoL using the Child-OIDP and OIDP indices, respectively, and completed a behavioural questionnaire. We assessed associations of condition-specific impacts (CS-impacts) with gingivitis and calculus, adjusted for socio-demographic and behavioural factors. Gingivitis and calculus were highly prevalent: 79.3% in 12-year and 81.5% in 15-year olds. CS-impacts relating to calculus and/or gingivitis were reported by 26.0% of 12-year and 29.6% of 15-year olds. Except for calculus without gingivitis, calculus and/or gingivitis in any form was significantly related to any level of CS-impacts. At a moderate or higher level of CS-impacts, there were significant relationships with extensive calculus and/or gingivitis in 12-year olds and for extensive gingivitis and gingivitis without calculus in 15-year olds. Gingivitis was generally associated with any level of CS-impacts attributed to calculus and/or gingivitis. CS-impacts were related more to gingivitis than to calculus. © 2012 John Wiley & Sons A/S.

Giant Calculus In The Mouth Of Partially Edentulous Woman, (Case ...

African Journals Online (AJOL)

Objective: This case report is to create awareness of the presence of giant calculus in the mouth, the possible causes and its prevention. Report: This describes the oral condition of a partially edentulous woman with a giant calculus in the mouth. It highlights the effect of such an enormous calculus in the oral cavity.

Improving Calculus II and III through the Redistribution of Topics

Science.gov (United States)

George, C. Yousuf; Koetz, Matt; Lewis, Heather A.

2016-01-01

Three years ago our mathematics department rearranged the topics in second and third semester calculus, moving multivariable calculus to the second semester and series to the third semester. This paper describes the new arrangement of topics, and how it could be adapted to calculus curricula at different schools. It also explains the benefits we…

Partial Fractions in Calculus, Number Theory, and Algebra

Science.gov (United States)

Yackel, C. A.; Denny, J. K.

2007-01-01

This paper explores the development of the method of partial fraction decomposition from elementary number theory through calculus to its abstraction in modern algebra. This unusual perspective makes the topic accessible and relevant to readers from high school through seasoned calculus instructors.

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

Science.gov (United States)

Ferguson, Leann J.

2012-01-01

Calculus is an important tool for building mathematical models of the world around us and is thus used in a variety of disciplines, such as physics and engineering. These disciplines rely on calculus courses to provide the mathematical foundation needed for success in their courses. Unfortunately, due to the basal conceptions of what it means to…

Thunks and the λ-calculus

DEFF Research Database (Denmark)

Hatcliff, John; Danvy, Olivier

1997-01-01

Thirty-five years ago, thunks were used to simulate call-by-name under call-by-value in Algol 60. Twenty years ago, Plotkin presented continuation-based simulations of call-by-name under call-by-value and vice versa in the λ-calculus. We connect all three of these classical simulations by factori......Thirty-five years ago, thunks were used to simulate call-by-name under call-by-value in Algol 60. Twenty years ago, Plotkin presented continuation-based simulations of call-by-name under call-by-value and vice versa in the λ-calculus. We connect all three of these classical simulations...

Area Regge calculus and discontinuous metrics

International Nuclear Information System (INIS)

Wainwright, Chris; Williams, Ruth M

2004-01-01

Taking the triangle areas as independent variables in the theory of Regge calculus can lead to ambiguities in the edge lengths, which can be interpreted as discontinuities in the metric. We construct solutions to area Regge calculus using a triangulated lattice and find that on a spacelike or timelike hypersurface no such discontinuity can arise. On a null hypersurface however, we can have such a situation and the resulting metric can be interpreted as a so-called refractive wave

A Graph Calculus for Predicate Logic

Directory of Open Access Journals (Sweden)

Paulo A. S. Veloso

2013-03-01

Full Text Available We introduce a refutation graph calculus for classical first-order predicate logic, which is an extension of previous ones for binary relations. One reduces logical consequence to establishing that a constructed graph has empty extension, i. e. it represents bottom. Our calculus establishes that a graph has empty extension by converting it to a normal form, which is expanded to other graphs until we can recognize conflicting situations (equivalent to a formula and its negation.

Sandboxing in a Distributed Pi-Calculus

DEFF Research Database (Denmark)

Hüttel, Hans; Kühnrich, Morten

2006-01-01

This paper presents an extension of the Dpi-calculus due to Hennessy and Riely with constructs for signing and authenticating code and for sandboxing. A sort system, built on Milner's sort systems for the polyadic pi-calculus, is presented and proven sound with respect to an error predicate which...... ensures that errors do not occur outside sandboxes and that authentication and migration only happen when allowed. Futhermore a weak subject reduction result involving partial well sortedness is presented....

A MATLAB companion for multivariable calculus

CERN Document Server

Cooper, Jeffery

2001-01-01

Offering a concise collection of MatLab programs and exercises to accompany a third semester course in multivariable calculus, A MatLab Companion for Multivariable Calculus introduces simple numerical procedures such as numerical differentiation, numerical integration and Newton''s method in several variables, thereby allowing students to tackle realistic problems. The many examples show students how to use MatLab effectively and easily in many contexts. Numerous exercises in mathematics and applications areas are presented, graded from routine to more demanding projects requiring some programming. Matlab M-files are provided on the Harcourt/Academic Press web site at http://www.harcourt-ap.com/matlab.html.* Computer-oriented material that complements the essential topics in multivariable calculus* Main ideas presented with examples of computations and graphics displays using MATLAB * Numerous examples of short code in the text, which can be modified for use with the exercises* MATLAB files are used to implem...

The dental calculus metabolome in modern and historic samples

DEFF Research Database (Denmark)

Velsko, Irina M.; Overmyer, Katherine A.; Speller, Camilla

2017-01-01

Introduction: Dental calculus is a mineralized microbial dental plaque biofilm that forms throughout life by precipitation of salivary calcium salts. Successive cycles of dental plaque growth and calcification make it an unusually well-preserved, long-term record of host-microbial interaction...... in the archaeological record. Recent studies have confirmed the survival of authentic ancient DNA and proteins within historic and prehistoric dental calculus, making it a promising substrate for investigating oral microbiome evolution via direct measurement and comparison of modern and ancient specimens. Objective: We...... present the first comprehensive characterization of the human dental calculus metabolome using a multi-platform approach. Methods: Ultra performance liquid chromatography-tandem mass spectrometry (UPLC–MS/MS) quantified 285 metabolites in modern and historic (200 years old) dental calculus, including...

Equality and fixpoints in the calculus of structures

DEFF Research Database (Denmark)

Chaudhuri, Kaustuv; Guenot, Nicolas

2014-01-01

The standard proof theory for logics with equality and fixpoints suffers from limitations of the sequent calculus, where reasoning is separated from computational tasks such as unification or rewriting. We propose in this paper an extension of the calculus of structures, a deep inference formalism...

Quantum stochastic calculus and representations of Lie superalgebras

CERN Document Server

Eyre, Timothy M W

1998-01-01

This book describes the representations of Lie superalgebras that are yielded by a graded version of Hudson-Parthasarathy quantum stochastic calculus. Quantum stochastic calculus and grading theory are given concise introductions, extending readership to mathematicians and physicists with a basic knowledge of algebra and infinite-dimensional Hilbert spaces. The develpment of an explicit formula for the chaotic expansion of a polynomial of quantum stochastic integrals is particularly interesting. The book aims to provide a self-contained exposition of what is known about Z_2-graded quantum stochastic calculus and to provide a framework for future research into this new and fertile area.

Discrete Quantum Gravity in the Regge Calculus Formalism

International Nuclear Information System (INIS)

Khatsymovsky, V.M.

2005-01-01

We discuss an approach to the discrete quantum gravity in the Regge calculus formalism that was developed in a number of our papers. The Regge calculus is general relativity for a subclass of general Riemannian manifolds called piecewise flat manifolds. The Regge calculus deals with a discrete set of variables, triangulation lengths, and contains continuous general relativity as a special limiting case where the lengths tend to zero. In our approach, the quantum length expectations are nonzero and of the order of the Plank scale, 10 -33 cm, implying a discrete spacetime structure on these scales

On the Lipschitz condition in the fractal calculus

International Nuclear Information System (INIS)

Golmankhaneh, Alireza K.; Tunc, Cemil

2017-01-01

In this paper, the existence and uniqueness theorems are proved for the linear and non-linear fractal differential equations. The fractal Lipschitz condition is given on the F"α-calculus which applies for the non-differentiable function in the sense of the standard calculus. More, the metric spaces associated with fractal sets and about functions with fractal supports are defined to build fractal Cauchy sequence. Furthermore, Picard iterative process in the F"α-calculus which have important role in the numerical and approximate solution of fractal differential equations is explored. We clarify the results using the illustrative examples.

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

The absolute differential calculus calculus of tensors

CERN Document Server

Levi-Cività, Tullio

1926-01-01

Written by a towering figure of twentieth-century mathematics, this classic examines the mathematical background necessary for a grasp of relativity theory. Tullio Levi-Civita provides a thorough treatment of the introductory theories that form the basis for discussions of fundamental quadratic forms and absolute differential calculus, and he further explores physical applications.Part one opens with considerations of functional determinants and matrices, advancing to systems of total differential equations, linear partial differential equations, algebraic foundations, and a geometrical intro

Covariant differential calculus on the quantum hyperplane

International Nuclear Information System (INIS)

Wess, J.

1991-01-01

We develop a differential calculus on the quantum hyperplane covariant with respect to the action of the quantum group GL q (n). This is a concrete example of noncommutative differential geometry. We describe the general constraints for a noncommutative differential calculus and verify that the example given here satisfies all these constraints. We also discuss briefly the integration over the quantum plane. (orig.)

The giant calculus within the prostatic urethra.

Science.gov (United States)

Demir, Omer; Kefi, Aykut; Cahangirov, Asif; Cihan, Ahmet; Obuz, Funda; Esen, Adil Ahmet; Celebi, Ilhan

2011-08-01

The giant calculus within the prostatic urethra is a rare clinical entity in the young population. Most of the calculi within the urethra migrate from the urinary bladder and obliterate the urethra. These stones are often composed of calcium phosphate or calcium oxalate. The decision of treatment strategy is affected by the size, shape and position of the calculus and by the status of the urethra. If the stone is large and immovable, it may be extracted via the perineal or the suprapubic approach. In most cases, the giant calculi were extracted via the transvesical approach and external urethrotomy. Our case is the biggest prostatic calculus, known in the literature so far, which was treated endoscopically by the combination of laser and the pneumatic lithotriptor.

Calculus Instructors' and Students' Discourses on the Derivative

Science.gov (United States)

Park, Jungeun

2011-01-01

Recently, there has been an increasing interest in collegiate mathematics education, especially teaching and learning calculus (e.g., Oehrtman, Carlson, & Thompson, 2008; Speer, Smith, & Horvath, 2010). Of many calculus concepts, the derivative is known as a difficult concept for students to understand because it involves various concepts…

Reflections on Our First Calculus Undergraduate Teaching Assistant

Science.gov (United States)

Deshler, Jessica M.

2016-01-01

This article describes some reflections from the first Calculus I undergraduate teaching assistant in our department as she explored the various ways in which she was able to support both novice and experienced Calculus teachers and the effect of her experience on her academic and career plans.

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

Science.gov (United States)

Baris, O; Demir, T; Gulluce, M

2017-12-01

Although it is known that bacterial mechanisms are involved in dental calculus formation, which is a predisposing factor in periodontal diseases, there have been few studies of such associations, and therefore, information available is limited. The purpose of this study was to isolate and identify aerobic bacteria responsible for direct calcification from supragingival calculus samples. The study was conducted using supragingival calculus samples from patients with periodontal disease, which was required as part of conventional treatment. Isolations were performed by sampling the supragingival calculus with buffer and inoculating the samples on media on which crystallization could be observed. The 16S recombinant DNA of the obtained pure cultures was then amplified and sequenced. A few bacterial species that have not previously been associated with mineralization or identified on bacterial plaque or calculus were detected. The bacteria that caused mineralization an aerobic environment are identified as Neisseria flava, Aggregatibacter segnis, Streptococcus tigurinus, and Morococcus cerebrosus. These findings proved that bacteria potentially play a role in the etiopathology of supragingival calculus. The association between the effects of the identified bacteria on periodontal diseases and calculus formation requires further studies.

Introduction to Integral Calculus Systematic Studies with Engineering Applications for Beginners

CERN Document Server

Rohde, Ulrich L; Poddar, Ajay K; Ghosh, A K

2011-01-01

An accessible introduction to the fundamentals of calculus needed to solve current problems in engineering and the physical sciences I ntegration is an important function of calculus, and Introduction to Integral Calculus combines fundamental concepts with scientific problems to develop intuition and skills for solving mathematical problems related to engineering and the physical sciences. The authors provide a solid introduction to integral calculus and feature applications of integration, solutions of differential equations, and evaluation methods. With logical organization coupled with cle

Dependence of calculus retropulsion dynamics on fiber size and radiant exposure during Ho:YAG lithotripsy.

Science.gov (United States)

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.

Length expectation values in quantum Regge calculus

International Nuclear Information System (INIS)

Khatsymovsky, V.M.

2004-01-01

Regge calculus configuration superspace can be embedded into a more general superspace where the length of any edge is defined ambiguously depending on the 4-tetrahedron containing the edge. Moreover, the latter superspace can be extended further so that even edge lengths in each the 4-tetrahedron are not defined, only area tensors of the 2-faces in it are. We make use of our previous result concerning quantization of the area tensor Regge calculus which gives finite expectation values for areas. Also our result is used showing that quantum measure in the Regge calculus can be uniquely fixed once we know quantum measure on (the space of the functionals on) the superspace of the theory with ambiguously defined edge lengths. We find that in this framework quantization of the usual Regge calculus is defined up to a parameter. The theory may possess nonzero (of the order of Planck scale) or zero length expectation values depending on whether this parameter is larger or smaller than a certain value. Vanishing length expectation values means that the theory is becoming continuous, here dynamically in the originally discrete framework

Enabling quaternion derivatives: the generalized HR calculus

Science.gov (United States)

Xu, Dongpo; Jahanchahi, Cyrus; Took, Clive C.; Mandic, Danilo P.

2015-01-01

Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutativity of quaternion algebra. To address this issue, we introduce the generalized HR (GHR) derivatives which employ quaternion rotations in a general orthogonal system and provide the left- and right-hand versions of the quaternion derivative of general functions. The GHR calculus also solves the long-standing problems of product and chain rules, mean-value theorem and Taylor's theorem in the quaternion field. At the core of the proposed GHR calculus is quaternion rotation, which makes it possible to extend the principle to other functional calculi in non-commutative settings. Examples in statistical learning theory and adaptive signal processing support the analysis. PMID:26361555

Utilizing Microsoft Mathematics in Teaching and Learning Calculus

Science.gov (United States)

Oktaviyanthi, Rina; Supriani, Yani

2015-01-01

The experimental design was conducted to investigate the use of Microsoft Mathematics, free software made by Microsoft Corporation, in teaching and learning Calculus. This paper reports results from experimental study details on implementation of Microsoft Mathematics in Calculus, students' achievement and the effects of the use of Microsoft…

Calculation of spontaneous emission from a V-type three-level atom in photonic crystals using fractional calculus

International Nuclear Information System (INIS)

Huang, Chih-Hsien; Hsieh, Wen-Feng; Wu, Jing-Nuo; Cheng, Szu-Cheng; Li, Yen-Yin

2011-01-01

Fractional time derivative, an abstract mathematical operator of fractional calculus, is used to describe the real optical system of a V-type three-level atom embedded in a photonic crystal. A fractional kinetic equation governing the dynamics of the spontaneous emission from this optical system is obtained as a fractional Langevin equation. Solving this fractional kinetic equation by fractional calculus leads to the analytical solutions expressed in terms of fractional exponential functions. The accuracy of the obtained solutions is verified through reducing the system into the special cases whose results are consistent with the experimental observation. With accurate physical results and avoiding the complex integration for solving this optical system, we propose fractional calculus with fractional time derivative as a better mathematical method to study spontaneous emission dynamics from the optical system with non-Markovian dynamics.

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

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

Science.gov (United States)

Dawkins, Paul Christian; Mendoza Epperson, James A.

2014-08-01

This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate this blended instruction as a local representative of the US calculus reform movements that helped foster it. These reform movements tended to emphasize problem-solving as well as multiple mathematical registers and quantitative modelling. Our statistical analysis reveals the influence of the blended traditional/reform calculus instruction on students' ability to solve calculus-related, non-routine problems through repeated measures over the semester. The calculus instruction in this study significantly improved students' performance on non-routine problems, though performance improved more regarding strategies and accuracy than it did for drawing conclusions and providing justifications. We identified problem-solving behaviours that characterized top performance or attrition in the course. Top-performing students displayed greater algebraic proficiency, calculus skills, and more general heuristics than their peers, but overused algebraic techniques even when they proved cumbersome or inappropriate. Students who subsequently withdrew from calculus often lacked algebraic fluency and understanding of the graphical register. The majority of participants, when given a choice, relied upon less sophisticated trial-and-error approaches in the numerical register and rarely used the graphical register, contrary to the goals of US calculus reform. We provide explanations for these patterns in students' problem-solving performance in view of both their preparation for university calculus and the courses' assessment structure, which preferentially rewarded algebraic reasoning. While instruction improved students' problem

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

CERN Document Server

Sabatier, J; Machado, J A Teneiro

2007-01-01

Fractional Calculus is a new growing field. Up to this point, researchers, scientists, and engineers have been reluctant to accept the fact that Fractional Calculus can be used in the analysis and design of many systems of practical interests, whereas in similar applications the traditional calculus either fails or provides poor solutionsMany engineers, scientists, and applied mathematicians are looking for books that can provide many applications of Fractional Calculus. This book will provide a partial solution to this problem. Since it covers recent applications of Fractional Calculus, it will be attractive to many engineers, scientists, and applied mathematicians.

Multivariate calculus and geometry

CERN Document Server

Dineen, Seán

2014-01-01

Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.

Representing and reasoning about program in situation calculus

Science.gov (United States)

Yang, Bo; Zhang, Ming-yi; Wu, Mao-nian; Xie, Gang

2011-12-01

Situation calculus is an expressive tool for modeling dynamical system in artificial intelligence, changes in a dynamical world is represented naturally by the notions of action, situation and fluent in situation calculus. Program can be viewed as a discrete dynamical system, so it is possible to model program with situation calculus. To model program written in a smaller core programming language CL, notion of fluent is expanded for representing value of expression. Together with some functions returning concerned objects from expressions, a basic action theory of CL programming is constructed. Under such a theory, some properties of program, such as correctness and termination can be reasoned about.

Reggeon calculus at collider energies

International Nuclear Information System (INIS)

Pajares, C.; Varias, A.; Yepes, P.

1983-01-01

The phenomenology of the perturbative reggeon calculus at collider energies is studied. It is found that the graphs which were neglected at ISR energies are still negligeable at √s=540 GeV. The perturbative series for the total cross section still converges reasonably fast. The values of the different parameters which describe rightly the data up to ISR energies give rise to a total cross section of around 60 mb at √s=540 GeV. For these values, the corresponding low mass and high mass eikonal series converges much more slowly. The non perturbative reggeon calculus gives rise to a total cross section less than 60 mb. (orig.)

Sequent Calculus and Equational Programming

Directory of Open Access Journals (Sweden)

Nicolas Guenot

2015-07-01

Full Text Available Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus. A typed functional language is presented, based on a sequent calculus, that we relate to the syntax and internal language of Agda. In particular, we discuss the use of patterns and case splittings, as well as rules implementing inductive reasoning and dependent products and sums.

Advanced Placement Mathematics Calculus, Grade 12 Curriculum Guide.

Science.gov (United States)

Scharf, John; And Others

This document is a guide to the advanced placement program in calculus for grade 12 in the city schools in Warren, Ohio. The program covers analytic geometry, differential and integral calculus of algebraic functions, elementary transcendental functions, and applications of differentiation and integration. The philosophy and aims of the program…

DIFFERENTIAL AND INTEGRAL CALCULUS. A TENTATIVE CURRICULUM GUIDE.

Science.gov (United States)

BRANT, VINCENT; GERARDI, WILLIAM

A GUIDE FOR A 1-YEAR COURSE IN DIFFERENTIAL AND INTEGRAL CALCULUS PREREQUISITED KNOWLEDGE IN ALGEBRA, ANALYTIC TRIGONOMETRY, AND ELEMENTARY ANALYSIS. EACH ASSIGNMENT CONTAINED BOTH NEW AND REVIEW WORK TO REINFORCE THE NEW WORK. THERE WERE ELEVEN UNITS OF STUDY USING THE FOLLOWING FOUR BOOKS--"CALCULUS AND ANALYTIC GEOMETRY, THIRD…

Catwalk: First-Semester Calculus.

Science.gov (United States)

Speiser, Bob; Walter, Chuck

1994-01-01

Describes the use of time-lapse photographs of a running cat as a model to investigate the concepts of function and derivative in a college calculus course. Discusses student difficulties and implications for teachers. (MKR)

Coordinating Multiple Representations in a Reform Calculus Textbook

Science.gov (United States)

Chang, Briana L.; Cromley, Jennifer G.; Tran, Nhi

2016-01-01

Coordination of multiple representations (CMR) is widely recognized as a critical skill in mathematics and is frequently demanded in reform calculus textbooks. However, little is known about the prevalence of coordination tasks in such textbooks. We coded 707 instances of CMR in a widely used reform calculus textbook and analyzed the distributions…

A phenomenological calculus of Wiener description space.

Science.gov (United States)

Richardson, I W; Louie, A H

2007-10-01

The phenomenological calculus is a categorical example of Robert Rosen's modeling relation. This paper is an alligation of the phenomenological calculus and generalized harmonic analysis, another categorical example. Our epistemological exploration continues into the realm of Wiener description space, in which constitutive parameters are extended from vectors to vector-valued functions of a real variable. Inherent in the phenomenology are fundamental representations of time and nearness to equilibrium.

Fractional and multivariable calculus model building and optimization problems

CERN Document Server

Mathai, A M

2017-01-01

This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable ...

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

Science.gov (United States)

Hayashizaki, Junko; Ban, Seiji; Nakagaki, Haruo; Okumura, Akihiko; Yoshii, Saori; Robinson, Colin

2008-02-01

Dental calculus has been implicated in the aetiology of several periodontal conditions. Its prevention and removal are therefore desirable clinical goals. While it is known that calculus is very variable in chemical composition, crystallinity and crystallite size little is known about site specific variability within a dentition and between individuals. With this in mind, a study was undertaken to investigate the comparative site specific nature and composition of human dental supra-gingival dental calculus obtained from 66 male patients visiting for their dental check-up using fluorescent X-ray spectroscopy, X-ray diffractometry and Fourier transform infrared spectroscopy. The supra-gingival dental calculus formed on the lingual surfaces of lower anterior teeth and the buccal surfaces of upper molar teeth were classified into four types based on calcium phosphate phases present. There was significant difference in composition of the crystal phase types between lower and upper teeth (pdental calculus on anterior or molar teeth of all samples. The degree of crystallinity of dental calculus formed on the upper molar teeth was higher than that formed on the lower anterior teeth (pdental calculus formed on the lower anterior teeth were higher than on upper molar teeth (pdental supra-gingival dental calculus is related to its location in the mouth.

A many-sorted calculus based on resolution and paramodulation

CERN Document Server

Walther, Christoph

1987-01-01

A Many-Sorted Calculus Based on Resolution and Paramodulation emphasizes the utilization of advantages and concepts of many-sorted logic for resolution and paramodulation based automated theorem proving.This book considers some first-order calculus that defines how theorems from given hypotheses by pure syntactic reasoning are obtained, shifting all the semantic and implicit argumentation to the syntactic and explicit level of formal first-order reasoning. This text discusses the efficiency of many-sorted reasoning, formal preliminaries for the RP- and ?RP-calculus, and many-sorted term rewrit

Dental hygiene faculty calibration in the evaluation of calculus detection.

Science.gov (United States)

Garland, Kandis V; Newell, Kathleen J

2009-03-01

The purpose of this pilot study was to explore the impact of faculty calibration training on intra- and interrater reliability regarding calculus detection. After IRB approval, twelve dental hygiene faculty members were recruited from a pool of twenty-two for voluntary participation and randomized into two groups. All subjects provided two pre- and two posttest scorings of calculus deposits on each of three typodonts by recording yes or no indicating if they detected calculus. Accuracy and consistency of calculus detection were evaluated using an answer key. The experimental group received three two-hour training sessions to practice a prescribed exploring sequence and technique for calculus detection. Participants immediately corrected their answers, received feedback from the trainer, and reconciled missed areas. Intra- and interrater reliability (pre- and posttest) was determined using Cohen's Kappa and compared between groups using repeated measures (split-plot) ANOVA. The groups did not differ from pre- to posttraining (intrarater reliability p=0.64; interrater reliability p=0.20). Training had no effect on reliability levels for simulated calculus detection in this study. Recommendations for future studies of faculty calibration when evaluating students include using patients for assessing rater reliability, employing larger samples at multiple sites, and assessing the impact on students' attitudes and learning outcomes.

Calculus and Geometry

Indian Academy of Sciences (India)

IAS Admin

Sphere–Cylinder Theorem, vol- ume and surface area of the torus, volume and surface area of a slice of a solid sphere. The author earned his PhD degree in mathematics. (topology), in 2000, from. Panjab University,. Chandigarh and since then he has been teaching analysis, algebra, calculus and discrete mathematics at.

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

Science.gov (United States)

Miladipour, Amir Hossein; Shakhssalim, Nasser; Parvin, Mahmoud; Azadvari, Mohaddeseh

2012-01-01

Even though dehydration could aggravate formation of urinary calculi, the effects of fluid and food restriction on calculus formation is not thoroughly defined. The purpose of this study is to evaluate the effects of fluid and food restriction in Ramadan fasting on urinary factors in kidney and urinary calculus formation. Fifty-seven men aged 30 to 55 years old, including 37 recurrent calcium calculus formers and 20 with no history of kidney calculi were evaluated for blood tests, ultrasonography investigations, urinalysis, urine culture, and also 24-hour urine collection test. Metabolites including calcium, oxalate, citrate, uric acid, magnesium, phosphate, potassium, sodium, and creatinine were measured before and during Ramadan fasting. The values of calculus-precipitating solutes as well as inhibitory factors were documented thoroughly. Total excretion of calcium, phosphate, and magnesium in 24-hour urine and also urine volume during fasting were significantly lower than those in the nonfasting period. Urine concentration of calcium during fasting was significantly lower than nonfasting (P calculus formation. We did not find enough evidence in favor of increased risks of calculus formation during Ramadan fasting.

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...

Multivariable dynamic calculus on time scales

CERN Document Server

Bohner, Martin

2016-01-01

This book offers the reader an overview of recent developments of multivariable dynamic calculus on time scales, taking readers beyond the traditional calculus texts. Covering topics from parameter-dependent integrals to partial differentiation on time scales, the book’s nine pedagogically oriented chapters provide a pathway to this active area of research that will appeal to students and researchers in mathematics and the physical sciences. The authors present a clear and well-organized treatment of the concept behind the mathematics and solution techniques, including many practical examples and exercises.

Essay on Fractional Riemann-Liouville Integral Operator versus Mikusinski’s

Directory of Open Access Journals (Sweden)

Ming Li

2013-01-01

Full Text Available This paper presents the representation of the fractional Riemann-Liouville integral by using the Mikusinski operators. The Mikusinski operators discussed in the paper may yet provide a new view to describe and study the fractional Riemann-Liouville integral operator. The present result may be useful for applying the Mikusinski operational calculus to the study of fractional calculus in mathematics and to the theory of filters of fractional order in engineering.

Graphical calculus for Gaussian pure states

International Nuclear Information System (INIS)

Menicucci, Nicolas C.; Flammia, Steven T.; Loock, Peter van

2011-01-01

We provide a unified graphical calculus for all Gaussian pure states, including graph transformation rules for all local and semilocal Gaussian unitary operations, as well as local quadrature measurements. We then use this graphical calculus to analyze continuous-variable (CV) cluster states, the essential resource for one-way quantum computing with CV systems. Current graphical approaches to CV cluster states are only valid in the unphysical limit of infinite squeezing, and the associated graph transformation rules only apply when the initial and final states are of this form. Our formalism applies to all Gaussian pure states and subsumes these rules in a natural way. In addition, the term 'CV graph state' currently has several inequivalent definitions in use. Using this formalism we provide a single unifying definition that encompasses all of them. We provide many examples of how the formalism may be used in the context of CV cluster states: defining the 'closest' CV cluster state to a given Gaussian pure state and quantifying the error in the approximation due to finite squeezing; analyzing the optimality of certain methods of generating CV cluster states; drawing connections between this graphical formalism and bosonic Hamiltonians with Gaussian ground states, including those useful for CV one-way quantum computing; and deriving a graphical measure of bipartite entanglement for certain classes of CV cluster states. We mention other possible applications of this formalism and conclude with a brief note on fault tolerance in CV one-way quantum computing.

Regge calculus: applications to classical and quantum gravity

International Nuclear Information System (INIS)

Lewis, S.M.

1983-01-01

Regge calculus is a simplicial approximation to general relativity which preserves many topological and geometrical properties of the exact theory. After discussing the foundations of this technique and deriving some basic identities, specific solutions to Regge calculus are analyzed. In particular, the flat Friedmann-Robertson-Walker (FRW) model is shown. This particular model is used in the discussion of the initial value problem for Regge calculus. An Arnowitt-Deser-Misner type of 3 + 1 decomposition is possible only under very special circumstances; solutions with a non-spatially constant lapse can not generally be decomposed. The flat FRW model is also used to compute the accuracy of this approximation method developed by Regge. A three-dimensional toy model of quantum gravity is discussed that was originally formulated by Ponzano and Regge. A more thorough calculation is performed that takes into account additional terms. The renormalization properties of this model are shown. Finally, speculations are made on the interaction of the geometry, topology and quantum effects using Regge calculus, which, because of its simplicial nature, makes these effects more amenable to calculation and intuition

Three-plus-one formulation of Regge calculus

International Nuclear Information System (INIS)

Piran, T.; Williams, R.M.

1986-01-01

Following the work of Lund and Regge for homogeneous spaces, we construct the action for Regge calculus in its three-plus-one form for general space-times. This is achieved in two ways: a first-order formalism and a second-order formalism. We describe the Regge-calculus analogue of solving the initial-value equations using conformal transformations. The second-order formalism is used to study the time development of two simple model universes

Reggeon calculus as a low-order perturbation theory for the Pomeron

International Nuclear Information System (INIS)

DeTar, C.

1975-01-01

We review the foundations of the Gribov Reggeon calculus with an emphasis on the relationship between the energy-plane and J-plane descriptions of the diagrams of the calculus. The question of the ''large-rapidity-gap cutoff'' for the Pomeron and the problem of signature are treated in more detail than in the traditional approach to the calculus. Except for some slight differences, the main results agree with Gribov's original formulation. We advocate the use of the Reggeon calculus as a refinement on the contemporary ''two-component'' model for the Pomeron and collect some formulas useful for phenomenological applications

Secure Data Flow in a Calculus for Context Awareness

DEFF Research Database (Denmark)

Bucur, Doina; Nielsen, Mogens

2008-01-01

We present a Mobile-Ambients-based process calculus to describe context-aware computing in an infrastructure-based Ubiquitous Computing setting. In our calculus, computing agents can provide and discover contextual information and are owners of security policies. Simple access control to contextual...

Visual Thinking and Gender Differences in High School Calculus

Science.gov (United States)

Haciomeroglu, Erhan Selcuk; Chicken, Eric

2012-01-01

This study sought to examine calculus students' mathematical performances and preferences for visual or analytic thinking regarding derivative and antiderivative tasks presented graphically. It extends previous studies by investigating factors mediating calculus students' mathematical performances and their preferred modes of thinking. Data were…

Metric regularity and subdifferential calculus

International Nuclear Information System (INIS)

Ioffe, A D

2000-01-01

The theory of metric regularity is an extension of two classical results: the Lyusternik tangent space theorem and the Graves surjection theorem. Developments in non-smooth analysis in the 1980s and 1990s paved the way for a number of far-reaching extensions of these results. It was also well understood that the phenomena behind the results are of metric origin, not connected with any linear structure. At the same time it became clear that some basic hypotheses of the subdifferential calculus are closely connected with the metric regularity of certain set-valued maps. The survey is devoted to the metric theory of metric regularity and its connection with subdifferential calculus in Banach spaces

The dental calculus metabolome in modern and historic samples.

Science.gov (United States)

Velsko, Irina M; Overmyer, Katherine A; Speller, Camilla; Klaus, Lauren; Collins, Matthew J; Loe, Louise; Frantz, Laurent A F; Sankaranarayanan, Krithivasan; Lewis, Cecil M; Martinez, Juan Bautista Rodriguez; Chaves, Eros; Coon, Joshua J; Larson, Greger; Warinner, Christina

2017-01-01

Dental calculus is a mineralized microbial dental plaque biofilm that forms throughout life by precipitation of salivary calcium salts. Successive cycles of dental plaque growth and calcification make it an unusually well-preserved, long-term record of host-microbial interaction in the archaeological record. Recent studies have confirmed the survival of authentic ancient DNA and proteins within historic and prehistoric dental calculus, making it a promising substrate for investigating oral microbiome evolution via direct measurement and comparison of modern and ancient specimens. We present the first comprehensive characterization of the human dental calculus metabolome using a multi-platform approach. Ultra performance liquid chromatography-tandem mass spectrometry (UPLC-MS/MS) quantified 285 metabolites in modern and historic (200 years old) dental calculus, including metabolites of drug and dietary origin. A subset of historic samples was additionally analyzed by high-resolution gas chromatography-MS (GC-MS) and UPLC-MS/MS for further characterization of metabolites and lipids. Metabolite profiles of modern and historic calculus were compared to identify patterns of persistence and loss. Dipeptides, free amino acids, free nucleotides, and carbohydrates substantially decrease in abundance and ubiquity in archaeological samples, with some exceptions. Lipids generally persist, and saturated and mono-unsaturated medium and long chain fatty acids appear to be well-preserved, while metabolic derivatives related to oxidation and chemical degradation are found at higher levels in archaeological dental calculus than fresh samples. The results of this study indicate that certain metabolite classes have higher potential for recovery over long time scales and may serve as appropriate targets for oral microbiome evolutionary studies.

Calculus

CERN Document Server

Zandy, Bernard V

2003-01-01

We take great notes-and make learning a snap When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core Calculus concepts-from functions, limits, and derivatives to differentials, integration, and definite integrals- and get the best possible grade. At CliffsNotes, we're dedicated to helping you do your best, no matter how challenging the subject. Our authors are veteran teachers and talented writers who know how to cut to the chase- and zero in on the essential information you need to succeed.

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.

Giant vesical calculus

African Journals Online (AJOL)

Giant vesical calculus. A case report. H. H. LAUBSCHER. Summary. An exceptional case of bladder stone is presented. The case is unusual as regards the size of the stone and the fact that the patient did··not seek medical assistance much earlier, as this was readily avail- able. Furthermore, recovery after removal of the.

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

Science.gov (United States)

Mackie, Meaghan; Hendy, Jessica; Lowe, Abigail D; Sperduti, Alessandra; Holst, Malin; Collins, Matthew J; Speller, Camilla F

2017-01-01

Proteomic analysis of dental calculus is emerging as a powerful tool for disease and dietary characterisation of archaeological populations. To better understand the variability in protein results from dental calculus, we analysed 21 samples from three Roman-period populations to compare: 1) the quantity of extracted protein; 2) the number of mass spectral queries; and 3) the number of peptide spectral matches and protein identifications. We found little correlation between the quantity of calculus analysed and total protein identifications, as well as no systematic trends between site location and protein preservation. We identified a wide range of individual variability, which may be associated with the mechanisms of calculus formation and/or post-depositional contamination, in addition to taphonomic factors. Our results suggest dental calculus is indeed a stable, long-term reservoir of proteins as previously reported, but further systematic studies are needed to identify mechanisms associated with protein entrapment and survival in dental calculus.

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

Science.gov (United States)

Ashkenazi, M; Miller, R; Levin, L

2012-10-01

To evaluate the occurrence of supra-gingival calculus in children aged 6-9 years with disuse conditions such as: presence of dental pain, open-bite or erupting teeth. A cohort of 327 children aged 7.64±2.12 (range: 6-9) years (45% girls) were screened for presence of supra-gingival calculus in relation to open bite, erupting teeth and dental pain. Presence of dental calculus was evaluated dichotomically in the buccal, palatinal/lingual and occlusal surfaces. Plaque index (PI) and gingival index (GI) were also evaluated. Supra-gingival calculus was found in 15.9% of the children mainly in the mandibular incisors. Children aged 6-7 years had a higher prevalence of calculus as compared to children aged 7-8 years (23% vs. 13.5%, p=0.057) or 8-9 years (23% vs. 12.4%, p=0.078), respectively. No statistical relation was found between plaque and gingival indices and presence of calculus. The prevalence of calculus among children with openbite was significantly higher than that of children without open-bite (29.4% vs. 10.7%, p=0.0006, OR=3.489). The prevalence of calculus among children with erupting teeth in their oral cavity was higher than that of children without erupting teeth (17.7% vs. 9%, respectively, p=0.119). No statistical correlation was found between presence of dental pain and calculus (15.4% vs. 15.9%; p=0.738). Accumulation of calculus in children aged 6-10 years was found mainly in the mandibular incisors, decreased with age and was correlated with open-bite.

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

Science.gov (United States)

Chong, Hong-Heng; An, Geng

2009-02-15

To study the percentage of uric acid calculus in uroliths and its metabolic character in Dongjiang River valley. To analyze the chemical composition of 290 urinary stones by infrared (IR) spectroscopy and study the ratio changes of uric acid calculus. Uric acid calculus patients and healthy people were studied. Personal characteristics, dietary habits were collected. Conditional logistic regression was used for data analysis and studied the dietary risk factors of uric acid calculus. Patients with uric acid calculus, calcium oxalate and those without urinary calculus were undergone metabolic evaluation analysis. The results of uric acid calculus patients compared to another two groups to analysis the relations between the formation of uric acid calculus and metabolism factors. Uric acid calculi were found in 53 cases (18.3%). The multiple logistic regression analysis suggested that low daily water intake, eating more salted and animal food, less vegetable were very closely associated with uric acid calculus. Comparing to calcium oxalate patients, the urine volume, the value of pH, urine calcium, urine oxalic acid were lower, but uric acid was higher than it. The value of pH, urine oxalic acid and citric acid were lower than them, but uric acid and urine calcium were higher than none urinary calculus peoples. Blood potassium and magnesium were lower than them. The percentage of uric acid stones had obvious advanced. Less daily water intake, eating salted food, eating more animal food, less vegetables and daily orange juice intake, eating sea food are the mainly dietary risk factors to the formation of uric acid calculus. Urine volume, the value of pH, citric acid, urine calcium, urine uric acid and the blood natrium, potassium, magnesium, calcium, uric acid have significant influence to the information of uric acid stones.

Fuzzy relational calculus theory, applications and software

CERN Document Server

Peeva, Ketty

2004-01-01

This book examines fuzzy relational calculus theory with applications in various engineering subjects. The scope of the text covers unified and exact methods with algorithms for direct and inverse problem resolution in fuzzy relational calculus. Extensive engineering applications of fuzzy relation compositions and fuzzy linear systems (linear, relational and intuitionistic) are discussed. Some examples of such applications include solutions of equivalence, reduction and minimization problems in fuzzy machines, pattern recognition in fuzzy languages, optimization and inference engines in textile and chemical engineering, etc. A comprehensive overview of the authors' original work in fuzzy relational calculus is also provided in each chapter. The attached CD-Rom contains a toolbox with many functions for fuzzy calculations, together with an original algorithm for inverse problem resolution in MATLAB. This book is also suitable for use as a textbook in related courses at advanced undergraduate and graduate level...

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

Science.gov (United States)

Rechmann, Peter; Hennig, Thomas

1996-01-01

The aim of the study was the selective removal of dental calculus by means of pulsed lasers. In a first approach the optical characteristics of subgingival calculus were calculated using fluorescence emission spectroscopy (excitation laser: N2-laser, wavelength 337 nm, pulse duration 4 ns). Subgingival calculus seems to absorb highly in the ultraviolet spectral region up to 420 nm. According to these measurements a frequency doubled Alexandrite-laser (wavelength 377 nm, pulse duration 100 ns, repetition rate 110 Hz) was used to irradiate calculus located on enamel, at the cementum enamel junction and on the root surface (located on dentin or on cementum). Irradiation was performed perpendicular to the root surface with a laser fluence of 1 Jcm-2. During the irradiation procedure an effective water cooling-system was engaged. Histological investigations were done on undecalcified sections. As a result, engaging low fluences allows a fast and strictly selective removal of subgingival calculus. Even more the investigations revealed that supragingival calculus can be removed in a strictly selective manner engaging a frequency doubled Alexandrite-laser. No adverse side effects to the surrounding tissues could be found.

Prostatic fossa calculus | El Abiad | Pan African Medical Journal

African Journals Online (AJOL)

As part of the evaluation, a plain radiograph was performed and incidentally showed a radiopaque prostatic calculus (Red arrows). A retrograde urethrocystography, performed after a 10-days course of antibiotics, confirmed the presence of an approximately 35 mm non-obstructive calculus occupying almost the whole ...

A compositional proof system for the modal μ-calculus

DEFF Research Database (Denmark)

Andersen, Henrik Reif; Stirling, C.; Winskel,, G.

1994-01-01

We present a proof system for determining satisfaction between processes in a fairly general process algebra and assertions of the modal μ-calculus. The proof system is compositional in the structure of processes. It extends earlier work on compositional reasoning within the modal μ-calculus and ...

Non-commutative residue of projections in Boutet de Monvel's calculus

DEFF Research Database (Denmark)

Gaarde, Anders

2007-01-01

Using results by Melo, Nest, Schick, and Schrohe on the K-theory of Boutet de Monvel's calculus of boundary value problems, we show that the non-commutative residue introduced by Fedosov, Golse, Leichtnam, and Schrohe vanishes on projections in the calculus. This partially answers a question raised...... in a recent collaboration with Grubb, namely whether the residue is zero on sectorial projections for boundary value problems: This is confirmed to be true when the sectorial projections is in the calculus....

Application of Quantum Process Calculus to Higher Dimensional Quantum Protocols

Directory of Open Access Journals (Sweden)

Simon J. Gay

2014-07-01

Full Text Available We describe the use of quantum process calculus to describe and analyze quantum communication protocols, following the successful field of formal methods from classical computer science. We have extended the quantum process calculus to describe d-dimensional quantum systems, which has not been done before. We summarise the necessary theory in the generalisation of quantum gates and Bell states and use the theory to apply the quantum process calculus CQP to quantum protocols, namely qudit teleportation and superdense coding.

Stochastic integration by parts and functional Itô calculus

CERN Document Server

Vives, Josep

2016-01-01

This volume contains lecture notes from the courses given by Vlad Bally and Rama Cont at the Barcelona Summer School on Stochastic Analysis (July 2012). The notes of the course by Vlad Bally, co-authored with Lucia Caramellino, develop integration by parts formulas in an abstract setting, extending Malliavin's work on abstract Wiener spaces. The results are applied to prove absolute continuity and regularity results of the density for a broad class of random processes. Rama Cont's notes provide an introduction to the Functional Itô Calculus, a non-anticipative functional calculus that extends the classical Itô calculus to path-dependent functionals of stochastic processes. This calculus leads to a new class of path-dependent partial differential equations, termed Functional Kolmogorov Equations, which arise in the study of martingales and forward-backward stochastic differential equations. This book will appeal to both young and senior researchers in probability and stochastic processes, as well as to pract...

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

Science.gov (United States)

Patel, Rita Manubhai; McCombs, Paul; Zollman, Alan

2014-01-01

Novice students have difficulty with the topic of limits in calculus. We believe this is in part because of the multiple perspectives and shifting metaphors available to solve items correctly. We investigated college calculus instructors' personal concepts of limits. Based upon previous research investigating introductory calculus student…

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

Science.gov (United States)

Dawkins, Paul Christian; Epperson, James A. Mendoza

2014-01-01

This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate…

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

Science.gov (United States)

Mokry, Jeanette

2016-01-01

This article discusses preparation assignments used in a Calculus II course that cover material from prerequisite courses. Prior to learning new material, students work on problems outside of class involving concepts from algebra, trigonometry, and Calculus I. These problems are directly built upon in order to answer Calculus II questions,…

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

Science.gov (United States)

Sadler, Philip; Sonnert, Gerhard

2018-01-01

This study addresses a longstanding question among high school mathematics teachers and college mathematics professors: Which is the best preparation for college calculus-- (a) a high level of mastery of mathematics considered preparatory for calculus (algebra, geometry, precalculus) or (b) taking calculus itself in high school? We used a data set…

Type Inference for Session Types in the Pi-Calculus

DEFF Research Database (Denmark)

Graversen, Eva Fajstrup; Harbo, Jacob Buchreitz; Huttel, Hans

2014-01-01

In this paper we present a direct algorithm for session type inference for the π-calculus. Type inference for session types has previously been achieved by either imposing limitations and restriction on the π-calculus, or by reducing the type inference problem to that for linear types. Our approach...

A large primary vaginal calculus in a woman with paraplegia.

Science.gov (United States)

Avsar, Ayse Filiz; Keskin, Huseyin Levent; Catma, Tuba; Kaya, Basak; Sivaslioglu, Ahmet Akın

2013-01-01

The study aimed to report a primary vaginal stone, an extremely rare entity, without vesicovaginal fistula in a woman with disability. We describe the case of a large primary vaginal calculus in a 22-year-old woman with paraplegia, which, surprisingly, was not diagnosed until she was examined under general anesthesia during a preparation for laparoscopy for an adnexal mass. The stone had not been identified by physical examination with the patient in a recumbent position or by transabdominal ultrasonography and pelvic tomography during the preoperative preparation. Vaginoscopy was not performed because the vagina was completely filled with the mass. As a result of its size and hard consistency, a right-sided episiotomy was performed and a 136-g stone was removed using ring forceps. A vesicovaginal fistula was excluded. There was no evidence of a foreign body or other nidus on the cut section of the stone, and it was determined to be composed of 100% struvite (ammonium magnesium phosphate). Culture of urine obtained via catheter showed Escherichia coli. After the surgical removal of the calculus without complications, a program of intermittent catheterization was started. The follow-up period was uneventful, and the patient was symptom free at 6 months after the operation. We postulate that the calculus formed as a consequence of urinary contamination of the vagina in association with incontinence and prolonged maintenance in a recumbent posture. This report is important because it highlights that, although vaginal stones are very rare, their possibility should be considered in the differential diagnosis of individuals with long-term paraplegia.

ANALYTICAL MODEL FOR LATHE TOOL DISPLACEMENTS CALCULUS IN THE MANUFACTURING P ROCESS

Directory of Open Access Journals (Sweden)

Catălin ROŞU

2014-01-01

Full Text Available In this paper, we present an analytical model for lathe tools displacements calculus in the manufacturing process. We will present step by step the methodology for the displacements calculus and in the end we will insert these relations in a program for automatic calculus and we extract the conclusions. There is taken into account only the effects of the bending moments (because these insert the highest displacements. The simplifying assumptions and the calculus relations for the displacements (linea r and angular ones are presented in an original way.

Feynman path integral in area tensor Regge calculus and positivity

International Nuclear Information System (INIS)

Khatsymovsky, V.M.

2004-01-01

The versions of quantum measure in the area tensor Regge calculus constructed in the previous paper are studied on the simplest configurations of the system. These are found to be positively defined in the Euclidean case on physical surface corresponding to the ordinary Regge calculus (but not outside this surface), that is, adopt probabilistic interpretation. (Since Euclidean measure is defined via analytical continuation, positivity is not evident property.) An argument for positivity on physical surface on general configurations of area tensor Regge calculus is given

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

Science.gov (United States)

Mao, Zhiguo; Xu, Jing; Ye, Chaoyang; Chen, Dongping; Mei, Changlin

2013-08-01

Kidney stones in patients with autosomal dominant polycystic kidney disease are common, regarded as the consequence of the combination of anatomic abnormality and metabolic risk factors. However, complete staghorn calculus is rare in polycystic kidney disease and predicts a gloomy prognosis of kidney. For general population, recent data showed metabolic factors were the dominant causes for staghorn calculus, but for polycystic kidney disease patients, the cause for staghorn calculus remained elusive. We report a case of complete staghorm calculus in a polycystic kidney disease patient induced by repeatedly urinary tract infections. This 37-year-old autosomal dominant polycystic kidney disease female with positive family history was admitted in this hospital for repeatedly upper urinary tract infection for 3 years. CT scan revealed the existence of a complete staghorn calculus in her right kidney, while there was no kidney stone 3 years before, and the urinary stone component analysis showed the composition of calculus was magnesium ammonium phosphate. UTI is an important complication for polycystic kidney disease and will facilitate the formation of staghorn calculi. As staghorn calculi are associated with kidney fibrosis and high long-term renal deterioration rate, prompt control of urinary tract infection in polycystic kidney disease patient will be beneficial in preventing staghorn calculus formation.

Model checking biological systems described using ambient calculus

DEFF Research Database (Denmark)

Mardare, Radu Iulian; Priami, Corrado; Qualia, Paola

2005-01-01

Model checking biological systems described using ambient calculus. In Proc. of the second International Workshop on Computational Methods in Systems Biology (CMSB04), Lecture Notes in Bioinformatics 3082:85-103, Springer, 2005.......Model checking biological systems described using ambient calculus. In Proc. of the second International Workshop on Computational Methods in Systems Biology (CMSB04), Lecture Notes in Bioinformatics 3082:85-103, Springer, 2005....

Eye Irritation Test of Bovis Calculus Pharmacopuncture Solutions for Eye Drop

Directory of Open Access Journals (Sweden)

Hyeong-sik Seo

2008-06-01

Full Text Available Objective : This study was done to investigate the safety of Bovis Calculus pharmacopuncture solution manufactured with freezing dryness method to use eye drop. Methods : The eye irritation test of this material was performed according to the Regulation of Korea Food & Drug Administration (2005. 10. 21, KFDA 2005-60. After Bovis Calculus pharmacopuncture solution was medicated in the left eye of the rabbits, the auther observed eye irritation of the cornea, iris, conjunctiva at 1, 2, 3, 4 & 7day. Results : 1. After Bovis Calculus pharmacopuncture solution was medicated in the left eye of the rabbits, there wasn’t physical problem at 9 rabbits. 2. After Bovis Calculus pharmacopuncture solutionwas medicated in the left eye of the rabbits, there wasn’t eye irritation of the cornea, iris, conjunctiva at 1, 2, 3, 4 & 7day. Conclusions : I suggested that Bovis Calculus pharmacopuncture solution didn’t induced eye irritation in rabbits.

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

Science.gov (United States)

Gupta, Swati; Jain, P K; Kumra, Madhumani; Rehani, Shweta; Mathias, Yulia; Gupta, Ramakant; Mehendiratta, Monica; Chander, Anil

2016-07-01

Chronic inflammatory periodontal diseases i.e. gingivitis and periodontitis are one of the most common afflictions faced by human beings. Dental plaque, which is a pool of pathogenic microorganisms, remains to be current mainstay in etiopathogenesis. Dental calculus, which is a mineralized product of this plaque remains ignored and is considered merely as an ash heap of minor significance. However, the intriguing array in disease etiopathogenesis bulldozed researchers to suspect the role of calculus in disease chrysalis but still the viability of bacteria inside calculus and thus its pathogenicity remains an intricacy; the answer to which lies in the Pandora's Box. The present study was undertaken to investigate the viability of bacteria within dental calculus along with their identification. Also, to classify dental calculus on the basis of mineralization and to observe the variation of viable microflora found in dental calculus with the extent of mineralization and disease severity. A total of 60 samples were obtained, by harvesting two samples of supragingival calculus from each patient having chronic inflammatory periodontal disease. These samples were divided into two groups (Group A and Group B). Samples of Group A were kept non-irradiated and samples of Group B were exposed to UV radiation. The samples were categorized into less, moderately and highly mineralized according to the force required for crushing them. All the crushed calculus samples were then divided into three parts. These were used for dark-field microscopy, gram staining and bacterial cultures. Bacterial identification of the cultures obtained was also carried out by performing various biochemical assays. The present study revealed the presence of motile spirochaetes within the samples under dark-field microscope. Gram staining revealed presence of numerous gram positive cocci and gram negative bacilli. Bacterial cultures showed growth of variety of aerobic and capnophilic microorganisms. The

Initial data for time-symmetric gravitational radiation using Regge calculus

International Nuclear Information System (INIS)

Dubal, M.R.

1989-01-01

We apply Regge calculus to the construction of initial data for Brill waves: axisymmetric non-rotating vacuum solutions of Einstein's equation. The Regge calculus solutions are compared with those of the continuum theory, with encouraging results. (author)

Spiral CT biliary virtual endoscopy: preliminary clinical applications in the detection of biliary calculus

International Nuclear Information System (INIS)

Xiong Minghui; Wang Dong; Song Yunlong; Zhang Wanshi; Xu Jiaxing

2000-01-01

Objective: To evaluate imaging features and clinical value of CT biliary virtual endoscopy in the detection of biliary calculus. Methods: Eighteen patients with biliary calculi underwent volume scanning using spiral CT (Hispeed Advantage CT/i GE ). All data were transferred to computer workstation, and CT biliary virtual endoscopy images with pseudocolor encoding were generated from the volumetric data using the Navigator Smooth soft-ware. All cases were proved by ultrasound, axial CT or operation. Results: Among 18 cases, gallstones were found 8 in cases, common bile duct stones in 2 cases, gallstones and bile duct stones in 6 cases. The stones were 0.3-3.2 cm in size. CT biliary virtual endoscopy correctly demonstrated the surface details of stones which were viewed from extra- or intraluminal orientation in a 3D fashion. The findings were consistent with those of US, CT or operation. Conclusion: The CT virtual biliary endoscopy is a further development of virtual endoscopy for observing biliary calculus from intra- and extra-luminal views and providing three dimensional information of stone

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

NARCIS (Netherlands)

Rochel, J.

2016-01-01

We investigate the relationship between finite terms in lambda-letrec, the lambda calculus with letrec, and the infinite lambda terms they express. We say that a lambda-letrec term expresses a lambda term if the latter can be obtained as an infinite unfolding of the former. Unfolding is the process

Means and Variances without Calculus

Science.gov (United States)

Kinney, John J.

2005-01-01

This article gives a method of finding discrete approximations to continuous probability density functions and shows examples of its use, allowing students without calculus access to the calculation of means and variances.

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

Science.gov (United States)

Ziauddin, S M; Yoshimura, A; Montenegro Raudales, J L; Ozaki, Y; Higuchi, K; Ukai, T; Kaneko, T; Miyazaki, T; Latz, E; Hara, Y

2018-06-01

Dental calculus is a mineralized deposit attached to the tooth surface. We have shown that cellular uptake of dental calculus triggers nucleotide-binding oligomerization domain-like receptor family pyrin domain-containing 3 (NLRP3) inflammasome activation, leading to the processing of the interleukin-1β precursor into its mature form in mouse and human phagocytes. The activation of the NLRP3 inflammasome also induced a lytic form of programmed cell death, pyroptosis, in these cells. However, the effects of dental calculus on other cell types in periodontal tissue have not been investigated. The aim of this study was to determine whether dental calculus can induce cell death in oral epithelial cells. HSC-2 human oral squamous carcinoma cells, HOMK107 human primary oral epithelial cells and immortalized mouse macrophages were exposed to dental calculus or 1 of its components, hydroxyapatite crystals. For inhibition assays, the cells were exposed to dental calculus in the presence or absence of cytochalasin D (endocytosis inhibitor), z-YVAD-fmk (caspase-1 inhibitor) or glyburide (NLRP3 inflammasome inhibitor). Cytotoxicity was determined by measuring lactate dehydrogenase (LDH) release and staining with propidium iodide. Tumor necrosis factor-α production was quantified by enzyme-linked immunosorbent assay. Oral epithelial barrier function was examined by permeability assay. Dental calculus induced cell death in HSC-2 cells, as judged by LDH release and propidium iodide staining. Dental calculus also induced LDH release from HOMK107 cells. Following heat treatment, dental calculus lost its capacity to induce tumor necrosis factor-α in mouse macrophages, but could induce LDH release in HSC-2 cells, indicating a major role of inorganic components in cell death. Hydroxyapatite crystals also induced cell death in both HSC-2 and HOMK107 cells, as judged by LDH release, indicating the capacity of crystal particles to induce cell death. Cell death induced by dental

A Calculus of Circular Proofs and its Categorical Semantics

DEFF Research Database (Denmark)

Santocanale, Luigi

2002-01-01

We present a calculus of "circular proofs": the graph underlying a proof is not a finite tree but instead it is allowed to contain a certain amount of cycles.The main challenge in developing a theory for the calculus is to define the semantics of proofs, since the usual method by induction...

A Calculus of Circular Proofs and its Categorical Semantics

DEFF Research Database (Denmark)

Santocanale, Luigi

2002-01-01

We present a calculus of “circular proofs”: the graph underlying a proof is not a finite tree but instead it is allowed to contain a certain amount of cycles.The main challenge in developing a theory for the calculus is to define the semantics of proofs, since the usual method by induction...

Descartes' Calculus of Subnormals: What Might Have Been

Science.gov (United States)

Boudreaux, Gregory Mark; Walls, Jess E.

2013-01-01

Rene Descartes' method for finding tangents (equivalently, subnormals) depends on geometric and algebraic properties of a family of circles intersecting a given curve. It can be generalized to establish a calculus of subnormals, an alternative to the calculus of Newton and Leibniz. Here we prove subnormal counterparts of the well-known…

Variational calculus with constraints on general algebroids

Energy Technology Data Exchange (ETDEWEB)

Grabowska, Katarzyna [Physics Department, Division of Mathematical Methods in Physics, University of Warsaw, Hoza 69, 00-681 Warszawa (Poland); Grabowski, Janusz [Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, PO Box 21, 00-956 Warszawa (Poland)], E-mail: konieczn@fuw.edu.pl, E-mail: jagrab@impan.gov.pl

2008-05-02

Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and geometrical settings. The constrained Euler-Lagrange equations are derived for analogs of holonomic, vakonomic and nonholonomic constraints. This general model covers the majority of first-order Lagrangian systems which are present in the literature and reduces to the standard variational calculus and the Euler-Lagrange equations in classical mechanics for E = TM.

Variational calculus with constraints on general algebroids

International Nuclear Information System (INIS)

Grabowska, Katarzyna; Grabowski, Janusz

2008-01-01

Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and geometrical settings. The constrained Euler-Lagrange equations are derived for analogs of holonomic, vakonomic and nonholonomic constraints. This general model covers the majority of first-order Lagrangian systems which are present in the literature and reduces to the standard variational calculus and the Euler-Lagrange equations in classical mechanics for E = TM

A sequent calculus for signed interval logic

DEFF Research Database (Denmark)

Rasmussen, Thomas Marthedal

2001-01-01

We propose and discuss a complete sequent calculus formulation for Signed Interval Logic (SIL) with the chief purpose of improving proof support for SIL in practice. The main theoretical result is a simple characterization of the limit between decidability and undecidability of quantifier-free SIL....... We present a mechanization of SIL in the generic proof assistant Isabelle and consider techniques for automated reasoning. Many of the results and ideas of this report are also applicable to traditional (non-signed) interval logic and, hence, to Duration Calculus....

Modular invariance and covariant loop calculus

International Nuclear Information System (INIS)

Petersen, J.L.; Roland, K.O.; Sidenius, J.R.

1988-01-01

The covariant loop calculus provides an efficient technique for computing explicit expressions for the density on moduli space corresponding to arbitrary (bosonic string) loop diagrams. Since modular invariance is not manifest, however, we carry out a detailed comparison with known explicit two- and three-loop results derived using analytic geometry (one loop is known to be okay). We establish identity to 'high' order in some moduli and exactly in others. Agreement is found as a result of various nontrivial cancellations, in part related to number theory. We feel our results provide very strong support for the correctness of the covariant loop calculus approach. (orig.)

Modular invariance and covariant loop calculus

International Nuclear Information System (INIS)

Petersen, J.L.; Roland, K.O.; Sidenius, J.R.

1988-01-01

The covariant loop calculus provides and efficient technique for computing explicit expressions for the density on moduli space corresponding to arbitrary (bosonic string) loop diagrams. Since modular invariance is not manifest, however, we carry out a detailed comparison with known explicit 2- and 3- loop results derived using analytic geometry (1 loop is known to be ok). We establish identity to 'high' order in some moduli and exactly in others. Agreement is found as a result of various non-trivial cancellations, in part related to number theory. We feel our results provide very strong support for the correctness of the covariant loop calculus approach. (orig.)

Dynamical Regge calculus as lattice gravity

International Nuclear Information System (INIS)

Hagura, Hiroyuki

2001-01-01

We propose a hybrid approach to lattice quantum gravity by combining simultaneously the dynamical triangulation with the Regge calculus, called the dynamical Regge calculus (DRC). In this approach lattice diffeomorphism is realized as an exact symmetry by some hybrid (k, l) moves on the simplicial lattice. Numerical study of 3D pure gravity shows that an entropy of the DRC is not exponetially bounded if we adopt the uniform measure Π i dl i . On the other hand, using the scale-invariant measure Π i dl i /l i , we can calculate observables and observe a large hysteresis between two phases that indicates the first-order nature of the phase transition

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

Science.gov (United States)

Silva, Lidia Brión; Hodges, Kathleen O; Calley, Kristin Hamman; Seikel, John A

2012-01-01

This pilot study compared the clinical endpoints of the magnetostrictive and piezoelectric ultrasonic instruments on calculus removal. The null hypothesis stated that there is no statistically significant difference in calculus removal between the 2 instruments. A quasi-experimental pre- and post-test design was used. Eighteen participants were included. The magnetostrictive and piezoelectric ultrasonic instruments were used in 2 assigned contra-lateral quadrants on each participant. A data collector, blind to treatment assignment, assessed the calculus on 6 predetermined tooth sites before and after ultrasonic instrumentation. Calculus size was evaluated using ordinal measurements on a 4 point scale (0, 1, 2, 3). Subjects were required to have size 2 or 3 calculus deposit on the 6 predetermined sites. One clinician instrumented the pre-assigned quadrants. A maximum time of 20 minutes of instrumentation was allowed with each technology. Immediately after instrumentation, the data collector then conducted the post-test calculus evaluation. The repeated analysis of variance (ANOVA) was used to analyze the pre- and post-test calculus data (p≤0.05). The null hypothesis was accepted indicating that there is no statistically significant difference in calculus removal when comparing technologies (p≤0.05). Therefore, under similar conditions, both technologies removed the same amount of calculus. This research design could be used as a foundation for continued research in this field. Future studies include implementing this study design with a larger sample size and/or modifying the study design to include multiple clinicians who are data collectors. Also, deposit removal with periodontal maintenance patients could be explored.

Differential calculus and its applications

CERN Document Server

Field, Michael J

2013-01-01

Based on undergraduate courses in advanced calculus, the treatment covers a wide range of topics, from soft functional analysis and finite-dimensional linear algebra to differential equations on submanifolds of Euclidean space. 1976 edition.

Dental calculus is associated with death from heart infarction.

Science.gov (United States)

Söder, Birgitta; Meurman, Jukka H; Söder, Per-Östen

2014-01-01

We studied whether the amount of dental calculus is associated with death from heart infarction in the dental infection-atherosclerosis paradigm. Participants were 1676 healthy young Swedes followed up from 1985 to 2011. At the beginning of the study all subjects underwent oral clinical examination including dental calculus registration scored with calculus index (CI). Outcome measure was cause of death classified according to WHO International Classification of Diseases. Unpaired t-test, Chi-square tests, and multiple logistic regressions were used. Of the 1676 participants, 2.8% had died during follow-up. Women died at a mean age of 61.5 years and men at 61.7 years. The difference in the CI index score between the survivors versus deceased patients was significant by the year 2009 (P dental visits, dental plaque, periodontal pockets, education, income, socioeconomic status, and pack-years of smoking, CI score appeared to be associated with 2.3 times the odds ratio for cardiac death. The results confirmed our study hypothesis by showing that dental calculus indeed associated statistically with cardiac death due to infarction.

Wick calculus on spaces of generalized functions of compound poisson white noise

Science.gov (United States)

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).

Stochastic Pi-calculus Revisited

DEFF Research Database (Denmark)

Cardelli, Luca; Mardare, Radu Iulian

2013-01-01

We develop a version of stochastic Pi-calculus with a semantics based on measure theory. We dene the behaviour of a process in a rate environment using measures over the measurable space of processes induced by structural congruence. We extend the stochastic bisimulation to include the concept of...

Extending the Extensional Lambda Calculus with Surjective Pairing is Conservative

DEFF Research Database (Denmark)

Støvring, Kristian

2006-01-01

We answer Klop and de Vrijer's question whether adding surjective-pairing axioms to the extensional lambda calculus yields a conservative extension. The answer is positive. As a byproduct we obtain a "syntactic" proof that the extensional lambda calculus with surjective pairing is consistent....

Advanced calculus

CERN Document Server

Fitzpatrick, Patrick M

2009-01-01

Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclide

Matrix calculus

CERN Document Server

Bodewig, E

1959-01-01

Matrix Calculus, Second Revised and Enlarged Edition focuses on systematic calculation with the building blocks of a matrix and rows and columns, shunning the use of individual elements. The publication first offers information on vectors, matrices, further applications, measures of the magnitude of a matrix, and forms. The text then examines eigenvalues and exact solutions, including the characteristic equation, eigenrows, extremum properties of the eigenvalues, bounds for the eigenvalues, elementary divisors, and bounds for the determinant. The text ponders on approximate solutions, as well

Giant urinary bladder calculus: Case report | Otieno | East African ...

African Journals Online (AJOL)

A vertical calculus weighing more than 100 g is categorised as a giant urinary bladder stone. Giant urinary bladder stones are very rare and very few cases have been reported in English literature and only one case from Africa. This is a case report of a patient with a giant urinary bladder calculus presenting as a rectal ...

Effects of Clicker Use on Calculus Students' Mathematics Anxiety

Science.gov (United States)

Batchelor, John

2015-01-01

This paper reports the results of a survey study of clicker use and mathematics anxiety among students enrolled in an undergraduate calculus course during the Fall 2013 semester. Students in two large lecture sections of calculus completed surveys at the beginning and end of the course. One class used clickers, whereas the other class was taught…

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)

Projects for calculus the language of change

CERN Document Server

Stroyan, Keith D

1999-01-01

Projects for Calculus is designed to add depth and meaning to any calculus course. The fifty-two projects presented in this text offer the opportunity to expand the use and understanding of mathematics. The wide range of topics will appeal to both instructors and students. Shorter, less demanding projects can be managed by the independent learner, while more involved, in-depth projects may be used for group learning. Each task draws on special mathematical topics and applications from subjects including medicine, engineering, economics, ecology, physics, and biology.Subjects including:* Medicine* Engineering* Economics* Ecology* Physics* Biology

Data Quality Indicators Composition and Calculus: Engineering and Information Systems Approaches

Directory of Open Access Journals (Sweden)

Leon REZNIK

2015-02-01

Full Text Available Big Data phenomenon is a result of novel technological developments in sensor, computer and communication technologies. Nowadays more and more data are produced by nanoscale photonic, optoelectronic and electronic devices. However, their quality characteristics could be very low. The paper proposes new methods of the data management with huge data amounts that is based on associating of data quality indicators with each data entity. To achieve this goal, one needs to define the composition of the data quality indicators and to develop their integration calculus. As data quality evaluation involves multi-disciplinary research, various metrics have been investigated. The paper describes two major approaches in assigning the data quality indicators and developing their integration calculus. The information systems approach employs traditional high-level metrics like data accuracy, consistency and completeness. The engineering approach utilizes signal characteristics processed with the probability based calculus. The data quality metrics composition and calculus are discussed. The tools developed to automate the metrics selection and calculus procedures are presented. The user- friendly interface examples are provided.

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

Science.gov (United States)

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

2005-01-01

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

On commuting operator exponentials, II

Indian Academy of Sciences (India)

where N is an unbounded normal operator and M is a bounded normal operator in the. Hilbert space. Keywords. Self-adjoint and normal operator; commuting normal operator exponent- ials; Borel functional calculus. 1. Introduction. Let E be a complex Hilbert space and let B(E) be the algebra of bounded linear operators.

Outcome analysis of holmium laser and pneumatic lithotripsy in the endoscopic management of lower ureteric calculus in pediatric patients: a prospective study

Directory of Open Access Journals (Sweden)

Ankur Jhanwar

Full Text Available ABSTRACT Objective: To analyse outcomes of holmium laser and pneumatic lithotripsy in treatment of lower ureteric calculus in pediatric patients. Materials and methods: Prospective study conducted between August 2013 and July 2015. Inclusion criteria were lower ureteric calculus with stone size ≤1.5cms. Exclusion criteria were other than lower ureteric calculus, stone size ≥1.5cms, congenital renal anomalies, previous ureteral stone surgery. Patients were divided into two groups. Group A underwent pneumatic and group B underwent laser lithotripsy procedure. Patient's baseline demographic and peri-operative data were recorded and analysed. Post operatively X-ray/ultrasound KUB (Kidney, ureter and bladder was performed to assess stone free status. Results: A total of 76 patients who met the inclusion criteria to ureteroscopic intracorporeal lithotripsy were included. Group A and B included 38 patients in each. Mean age was 12.5±2.49 in Group A and 11.97±2.74 years in Group B respectively (p=0.38. Overall success rate was 94.73% in Group A and 100% in Group B, respectively (p=0.87. Conclusion: Holmium Laser lithotripsy is as efficacious as pneumatic lithotripsy and can be used safely for the endoscopic management of lower ureteric calculus in pediatric patients. However, holmium laser requires more expertise and it is a costly alternative.

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...

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...

Bisimulations for Delimited-Control Operators

OpenAIRE

Biernacki , Dariusz; Lenglet , Sergueï; Polesiuk , Piotr

2017-01-01

We propose a survey of the behavioral theory of an untyped lambda-calculus extended with the delimited-control operators shift and reset. We define a contextual equivalence for this calculus, that we then aim to characterize with coinductively defined relations, called bisimilarities. We study different styles of bisimilarities (namely applicative, normal form, and environmental), and we give several examples to illustrate their respective strengths and weaknesses. We also discuss how to exte...

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

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.

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

Science.gov (United States)

Scannicchio, Thomas Henry

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

Cartooning in Algebra and Calculus

Science.gov (United States)

Moseley, L. Jeneva

2014-01-01

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

Making an Interactive Calculus Textbook.

Science.gov (United States)

Larson, Timothy R.

1995-01-01

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

A Tutorial Review on Fractal Spacetime and Fractional Calculus

Science.gov (United States)

He, Ji-Huan

2014-11-01

This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.

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

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

Science.gov (United States)

Liu, Ping; He, Xinrong; Guo, Mei

2010-04-01

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

Advanced calculus

CERN Document Server

Friedman, Avner

2007-01-01

This rigorous two-part treatment advances from functions of one variable to those of several variables. Intended for students who have already completed a one-year course in elementary calculus, it defers the introduction of functions of several variables for as long as possible, and adds clarity and simplicity by avoiding a mixture of heuristic and rigorous arguments.The first part explores functions of one variable, including numbers and sequences, continuous functions, differentiable functions, integration, and sequences and series of functions. The second part examines functions of several

Unification and matching in Church's Original Lambda Calculus

OpenAIRE

Hustadt, U.

1992-01-01

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

Stochastic calculus an introduction through theory and exercises

CERN Document Server

Baldi, Paolo

2017-01-01

This book provides a comprehensive introduction to the theory of stochastic calculus and some of its applications. It is the only textbook on the subject to include more than two hundred exercises with complete solutions. After explaining the basic elements of probability, the author introduces more advanced topics such as Brownian motion, martingales and Markov processes. The core of the book covers stochastic calculus, including stochastic differential equations, the relationship to partial differential equations, numerical methods and simulation, as well as applications of stochastic processes to finance. The final chapter provides detailed solutions to all exercises, in some cases presenting various solution techniques together with a discussion of advantages and drawbacks of the methods used. Stochastic Calculus will be particularly useful to advanced undergraduate and graduate students wishing to acquire a solid understanding of the subject through the theory and exercises. Including full mathematical ...

Generalized calculus with applications to matter and forces

CERN Document Server

Campos, L M B C

2014-01-01

Combining mathematical theory, physical principles, and engineering problems, Generalized Calculus with Applications to Matter and Forces examines generalized functions, including the Heaviside unit jump and the Dirac unit impulse and its derivatives of all orders, in one and several dimensions. The text introduces the two main approaches to generalized functions: (1) as a nonuniform limit of a family of ordinary functions, and (2) as a functional over a set of test functions from which properties are inherited. The second approach is developed more extensively to encompass multidimensional generalized functions whose arguments are ordinary functions of several variables. As part of a series of books for engineers and scientists exploring advanced mathematics, Generalized Calculus with Applications to Matter and Forces presents generalized functions from an applied point of view, tackling problem classes such as: •Gauss and Stokes’ theorems in the differential geometry, tensor calculus, and theory of ...

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

Science.gov (United States)

Liang, Jiajuan; Martin, Linda

2008-01-01

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

Experimental Design: Utilizing Microsoft Mathematics in Teaching and Learning Calculus

Science.gov (United States)

Oktaviyanthi, Rina; Supriani, Yani

2015-01-01

The experimental design was conducted to investigate the use of Microsoft Mathematics, free software made by Microsoft Corporation, in teaching and learning Calculus. This paper reports results from experimental study details on implementation of Microsoft Mathematics in Calculus, students' achievement and the effects of the use of Microsoft…

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

Directory of Open Access Journals (Sweden)

Pablo Buiras

2012-03-01

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

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

OpenAIRE

Kehr, Flavius; Wentzel, Daniel; Mayer, Peter

2013-01-01

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

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

Science.gov (United States)

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

2016-06-01

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

Calculus in physics classes at UFRGS: an exploratory study

Directory of Open Access Journals (Sweden)

Maria Cecilia Pereira Santarosa

2011-11-01

Full Text Available This study is part f a larger one whose general objective is to investigate and to develop a new strategy for teaching Differential and Integral Calculus I, specifically for physics majors, through a possible integration with the teaching of General and Experimental Physics I. With the specific objective of identifying physics problem-situations that may help in making sense of the mathematical concepts used in Calculus I, and languages and notations that might be used in the teaching of Calculus to favor physics learning, it was investigates, through an ethnographic study, the may mathematics is transposed to classes of General and Experimental Physics I, in classes of physics courses at the Federal University of Rio Grande do Sul (UFRGS. Some findings of this study confirmed those reported in the literature regarding the teaching and learning process in introductory college physics courses. These findings will subsidize the preparation of potentially meaningful instructional materials that will be used in a second stage of the research designed to investigate the learning of declarative and procedural knowledge in basic college physics under an approach that integrates problem-situation in physics and calculus mathematical concepts.

Calculus Student Descending a Staircase.

Science.gov (United States)

Mueller, William

1999-01-01

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

q-fractional calculus and equations

CERN Document Server

Annaby, Mahmoud H

2012-01-01

This nine-chapter monograph introduces a rigorous investigation of q-difference operators in standard and fractional settings. It starts with elementary calculus of q-differences and integration of Jackson’s type before turning to q-difference equations. The existence and uniqueness theorems are derived using successive approximations, leading to systems of equations with retarded arguments. Regular  q-Sturm–Liouville theory is also introduced; Green’s function is constructed and the eigenfunction expansion theorem is given. The monograph also discusses some integral equations of Volterra and Abel type, as introductory material for the study of fractional q-calculi. Hence fractional q-calculi of the types Riemann–Liouville; Grünwald–Letnikov;  Caputo;  Erdélyi–Kober and Weyl are defined analytically. Fractional q-Leibniz rules with applications  in q-series are  also obtained with rigorous proofs of the formal  results of  Al-Salam-Verma, which remained unproved for decades. In working ...

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

Science.gov (United States)

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

2017-06-14

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

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...

Calculus Courses' Assessment Data

Science.gov (United States)

Pauna, Matti

2017-01-01

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

Generalizing Automath by means of a lambda-typed lambda calculus

NARCIS (Netherlands)

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

1994-01-01

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

Calculus domains modelled using an original bool algebra based on polygons

Science.gov (United States)

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

2016-08-01

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

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

Science.gov (United States)

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

2016-01-01

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

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

Science.gov (United States)

Akcalı, Aliye; Lang, Niklaus P

2018-02-01

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

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

Science.gov (United States)

Fuller, Robert G., Ed.; And Others

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

Understanding the calculus

OpenAIRE

Tall, David

1985-01-01

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

Quantum Stratonovich calculus and the quantum Wong-Zakai theorem

International Nuclear Information System (INIS)

Gough, John

2006-01-01

We extend the Ito(bar sign)-to-Stratonovich analysis or quantum stochastic differential equations, introduced by Gardiner and Collett for emission (creation), absorption (annihilation) processes, to include scattering (conservation) processes. Working within the framework of quantum stochastic calculus, we define Stratonovich calculus as an algebraic modification of the Ito(bar sign) one and give conditions for the existence of Stratonovich time-ordered exponentials. We show that conversion formula for the coefficients has a striking resemblance to Green's function formulas from standard perturbation theory. We show that the calculus conveniently describes the Markov limit of regular open quantum dynamical systems in much the same way as in the Wong-Zakai approximation theorems of classical stochastic analysis. We extend previous limit results to multiple-dimensions with a proof that makes use of diagrammatic conventions

Evaluating the Use of Learning Objects for Improving Calculus Readiness

Science.gov (United States)

Kay, Robin; Kletskin, Ilona

2010-01-01

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

On Flipping the Classroom in Large First Year Calculus Courses

Science.gov (United States)

Jungic, Veselin; Kaur, Harpreet; Mulholland, Jamie; Xin, Cindy

2015-01-01

Over the course of two years, 2012-2014, we have implemented a "flipping" the classroom approach in three of our large enrolment first year calculus courses: differential and integral calculus for scientists and engineers. In this article we describe the details of our particular approach and share with the reader some experiences of…

Modelling the Landing of a Plane in a Calculus Lab

Science.gov (United States)

Morante, Antonio; Vallejo, Jose A.

2012-01-01

We exhibit a simple model of a plane landing that involves only basic concepts of differential calculus, so it is suitable for a first-year calculus lab. We use the computer algebra system Maxima and the interactive geometry software GeoGebra to do the computations and graphics. (Contains 5 figures and 1 note.)

Newton Binomial Formulas in Schubert Calculus

OpenAIRE

Cordovez, Jorge; Gatto, Letterio; Santiago, Taise

2008-01-01

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

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

DEFF Research Database (Denmark)

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

2015-01-01

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

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

Science.gov (United States)

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

2015-01-01

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

Dental wax decreases calculus accumulation in small dogs.

Science.gov (United States)

Smith, Mark M; Smithson, Christopher W

2014-01-01

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

The early period of the calculus of variations

CERN Document Server

Freguglia, Paolo

2016-01-01

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

A huge bladder calculus causing acute renal failure.

Science.gov (United States)

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

2013-02-01

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

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

A Simplified Stabilizer ZX-calculus

Directory of Open Access Journals (Sweden)

Miriam Backens

2017-01-01

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

Beyond the spectral theorem: Spectrally decomposing arbitrary functions of nondiagonalizable operators

Science.gov (United States)

Riechers, Paul M.; Crutchfield, James P.

2018-06-01

Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, the familiar linear operator techniques that one would then hope to use often fail since the operators cannot be diagonalized. The curse of nondiagonalizability also plays an important role even in finite-dimensional linear operators, leading to analytical impediments that occur across many scientific domains. We show how to circumvent it via two tracks. First, using the well-known holomorphic functional calculus, we develop new practical results about spectral projection operators and the relationship between left and right generalized eigenvectors. Second, we generalize the holomorphic calculus to a meromorphic functional calculus that can decompose arbitrary functions of nondiagonalizable linear operators in terms of their eigenvalues and projection operators. This simultaneously simplifies and generalizes functional calculus so that it is readily applicable to analyzing complex physical systems. Together, these results extend the spectral theorem of normal operators to a much wider class, including circumstances in which poles and zeros of the function coincide with the operator spectrum. By allowing the direct manipulation of individual eigenspaces of nonnormal and nondiagonalizable operators, the new theory avoids spurious divergences. As such, it yields novel insights and closed-form expressions across several areas of physics in which nondiagonalizable dynamics arise, including memoryful stochastic processes, open nonunitary quantum systems, and far-from-equilibrium thermodynamics. The technical contributions include the first full treatment of arbitrary powers of an operator, highlighting the special role of the zero eigenvalue. Furthermore, we show that the Drazin inverse, previously only defined axiomatically, can be derived as the negative-one power of singular operators within the meromorphic functional calculus and we give a new general

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

Science.gov (United States)

Stenberg, Warren; Walker, Robert J.

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

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

NARCIS (Netherlands)

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

2015-01-01

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

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)

Integration on supermanifolds and a generalized Cartan calculus

International Nuclear Information System (INIS)

Picken, R.F.; Sundermeyer, K.

1986-01-01

A suggestion by Berezin for a method of integration on supermanifolds is given a precise differential geometric meaning by assuming that a supermanifold is the total space of a fibre bundle with connection. The relevant objects for integration are identified as suitable horizontal/vertical projections of hyperforms. The latter are generalizations of differential forms having both covariant and contravariant indices. The exterior calculus of these projected hyperforms is developed, analogously to the Cartan calculus, by introducing appropriate derivations and determining their commutators, respectively anticommutators. (orig.)

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...

A primer on the calculus of variations and optimal control theory

CERN Document Server

Mesterton-Gibbons, Mike

2009-01-01

The calculus of variations is used to find functions that optimize quantities expressed in terms of integrals. Optimal control theory seeks to find functions that minimize cost integrals for systems described by differential equations. This book is an introduction to both the classical theory of the calculus of variations and the more modern developments of optimal control theory from the perspective of an applied mathematician. It focuses on understanding concepts and how to apply them. The range of potential applications is broad: the calculus of variations and optimal control theory have been widely used in numerous ways in biology, criminology, economics, engineering, finance, management science, and physics. Applications described in this book include cancer chemotherapy, navigational control, and renewable resource harvesting. The prerequisites for the book are modest: the standard calculus sequence, a first course on ordinary differential equations, and some facility with the use of mathematical softwa...

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

Science.gov (United States)

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

2013-04-01

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

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

Science.gov (United States)

Ayebo, Abraham; Ukkelberg, Sarah; Assuah, Charles

2017-01-01

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

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

Science.gov (United States)

Singh, Udita; Goel, Saurabh

2017-01-01

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

One Answer to "What Is Calculus?"

Science.gov (United States)

Shilgalis, Thomas W.

1979-01-01

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

Calculus diaries

CERN Document Server

Ouellette,, Jennifer

2011-01-01

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

Higher order differential calculus on SLq(N)

International Nuclear Information System (INIS)

Heckenberger, I.; Schueler, A.

1997-01-01

Let Γ be a bicovariant first order differential calculus on a Hopf algebra A. There are three possibilities to construct a differential N 0 -graded Hopf algebra Γcirconflex which contains Γ as its first order part. In all cases Γcirconflex is a quotient Γcirconflex = Γ x /J of the tensor algebra by some suitable ideal. We distinguish three possible choices u J, s J, and w J, where the first one generates the universal differential calculus (over Γ) and the last one is Woronowicz' external algebra. Let q be a transcendental complex number and let Γ be one of the N 2 -dimensional bicovariant first order differential calculi on the quantum group SL q (N). Then for N ≥ 3 the three ideals coincide. For Woronowicz' external algebra we calculate the dimensions of the spaces of left-invariant and bi-invariant k-forms. In this case each bi-invariant form is closed. In case of 4D ± calculi on SL q (2) the universal calculus is strictly larger than the other two calculi. In particular, the bi-invariant 1-form is not closed. (author)

Bicovariant differential calculus on quantum groups and wave mechanics

International Nuclear Information System (INIS)

Carow-Watamura, U.; Watamura, S.; Hebecker, A.; Schlieker, M.; Weich, W.

1992-01-01

The bicovariant differential calculus on quantum groups defined by Woronowicz and later worked out explicitly by Carow-Watamura et al. and Jurco for the real quantum groups SU q (N) and SO q (N) through a systematic construction of the bicovariant bimodules of these quantum groups, is reviewed for SU q (2) and SO q (N). The resulting vector fields build representations of the quantized universal enveloping algebras acting as covariant differential operators on the quantum groups and their associated quantum spaces. As an application, a free particle stationary wave equation on quantum space is formulated and solved in terms of a complete set of energy eigenfunctions. (author) 15 refs

Fractal physiology and the fractional calculus: a perspective.

Science.gov (United States)

West, Bruce J

2010-01-01

This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a

A flow calculus of mwp-bounds for complexity analysis

DEFF Research Database (Denmark)

Jones, Neil; Kristiansen, Lars

2010-01-01

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

On flipping the classroom in large first year calculus courses

Science.gov (United States)

Jungić, Veselin; Kaur, Harpreet; Mulholland, Jamie; Xin, Cindy

2015-05-01

Over the course of two years, 2012--2014, we have implemented a 'flipping' the classroom approach in three of our large enrolment first year calculus courses: differential and integral calculus for scientists and engineers. In this article we describe the details of our particular approach and share with the reader some experiences of both instructors and students.

Calculus III essentials

CERN Document Server

REA, Editors of

2012-01-01

REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Calculus III includes vector analysis, real valued functions, partial differentiation, multiple integrations, vector fields, and infinite series.

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...

Differentiated Instruction in a Calculus Curriculum for College Students in Taiwan

Science.gov (United States)

Chen, Jing-Hua; Chen, Yi-Chou

2018-01-01

Objectives: To explore differentiated instruction within a calculus curriculum. For college students to learn concentration, motivation and the impact of academic achievement; explore the attitudes and ideas of students on differentiated instruction within a calculus curriculum; build up the diversity of mathematics education within varied…

Electron microscopy of octacalcium phosphate in the dental calculus.

Science.gov (United States)

Kakei, Mitsuo; Sakae, Toshiro; Yoshikawa, Masayoshi

2009-12-01

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

Dental Calculus Is Associated with Death from Heart Infarction

Directory of Open Access Journals (Sweden)

Birgitta Söder

2014-01-01

Full Text Available Objectives. We studied whether the amount of dental calculus is associated with death from heart infarction in the dental infection—atherosclerosis paradigm. Materials. Participants were 1676 healthy young Swedes followed up from 1985 to 2011. At the beginning of the study all subjects underwent oral clinical examination including dental calculus registration scored with calculus index (CI. Outcome measure was cause of death classified according to WHO International Classification of Diseases. Unpaired t-test, Chi-square tests, and multiple logistic regressions were used. Results. Of the 1676 participants, 2.8% had died during follow-up. Women died at a mean age of 61.5 years and men at 61.7 years. The difference in the CI index score between the survivors versus deceased patients was significant by the year 2009 (P<0.01. In multiple regression analysis of the relationship between death from heart infarction as a dependent variable and CI as independent variable with controlling for age, gender, dental visits, dental plaque, periodontal pockets, education, income, socioeconomic status, and pack-years of smoking, CI score appeared to be associated with 2.3 times the odds ratio for cardiac death. Conclusions. The results confirmed our study hypothesis by showing that dental calculus indeed associated statistically with cardiac death due to infarction.

Covariant differential calculus on the quantum exterior vector space

International Nuclear Information System (INIS)

Parashar, P.; Soni, S.K.

1992-01-01

We formulate a differential calculus on the quantum exterior vector space spanned by the generators of a non-anticommutative algebra satisfying r ij = θ i θ j +B kl ij θ k θ l =0 i, j=1, 2, ..., n. and (θ i ) 2 =(θ j ) 2 =...=(θ n ) 2 =0, where B kl ij is the most general matrix defined in terms of complex deformation parameters. Following considerations analogous to those of Wess and Zumino, we are able to exhibit covariance of our calculus under ( 2 n )+1 parameter deformation of GL(n) and explicitly check that the non-anticommutative differential calculus satisfies the general constraints given by them, such as the 'linear' conditions dr ij ≅0 and the 'quadratic' condition r ij x n ≅0 where x n =dθ n are the differentials of the variables. (orig.)

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

Science.gov (United States)

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

2017-01-01

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

Hermeneutics of differential calculus in eighteenth-century northern Germany.

Science.gov (United States)

Blanco, Mónica

2008-01-01

This paper applies comparative textbook analysis to studying the mathematical development of differential calculus in northern German states during the eighteenth century. It begins with describing how the four textbooks analyzed presented the foundations of calculus and continues with assessing the influence each of these foundational approaches exerted on the resolution of problems, such as the determination of tangents and extreme values, and even on the choice of coordinates for both algebraic and transcendental curves.

Numerical convergence of discrete exterior calculus on arbitrary surface meshes

KAUST Repository

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.

Instructor's manual to accompany calculus with analytic geometry

CERN Document Server

Zhou, Yong

1978-01-01

Instructor's Manual to Accompany Calculus with Analytic Geometry is an instructor's manual on calculus with analytic geometry. It contains answers to even-numbered exercises and solutions of selected even- and odd-numbered exercises. Comments on selected exercises are included.Comprised of 18 chapters, this book first presents answers and solutions to exercises relating to functions and graphs. The next chapter is about derivatives and covers topics ranging from the slope problem to limits, sums and products, and quotients and square roots, along with limits and continuity. Subsequent chapters

About the differential calculus on the quantum groups

International Nuclear Information System (INIS)

Bernard, D.

1992-01-01

Given a solution R of the Yang-Baxter equation admitting a quasi-triangular decomposition we define a quasi-triangular quantum Lie algebra. We describe how to any quasi-triangular quantum Lie algebra U(G R ) is associated a Hopf algebra F(G R ) with a differential calculus on it such that the algebra of the quantum Lie derivatives is the algebra U(G R ). This allows us to make the connection between the differential calculus on quantum groups and the exchange algebras of the algebraic Bethe ansatz. (orig.)

Differential calculus for Dirichlet forms: The measure-valued gradient preserved by image

OpenAIRE

Bouleau, Nicolas

2005-01-01

In order to develop a differential calculus for error propagation we study local Dirichlet forms on probability spaces with square field operator $\\Gamma$ -- i.e. error structures -- and we are looking for an object related to $\\Gamma$ which is linear and with a good behaviour by images. For this we introduce a new notion called the measure valued gradient which is a randomized square root of $\\Gamma$. The exposition begins with inspecting some natural notions candidate to solve the problem b...

Meshes optimized for discrete exterior calculus (DEC).

Energy Technology Data Exchange (ETDEWEB)

Mousley, Sarah C. [Univ. of Illinois, Urbana-Champaign, IL (United States); Deakin, Michael [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Knupp, Patrick [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Mitchell, Scott A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-12-01

We study the optimization of an energy function used by the meshing community to measure and improve mesh quality. This energy is non-traditional because it is dependent on both the primal triangulation and its dual Voronoi (power) diagram. The energy is a measure of the mesh's quality for usage in Discrete Exterior Calculus (DEC), a method for numerically solving PDEs. In DEC, the PDE domain is triangulated and this mesh is used to obtain discrete approximations of the continuous operators in the PDE. The energy of a mesh gives an upper bound on the error of the discrete diagonal approximation of the Hodge star operator. In practice, one begins with an initial mesh and then makes adjustments to produce a mesh of lower energy. However, we have discovered several shortcomings in directly optimizing this energy, e.g. its non-convexity, and we show that the search for an optimized mesh may lead to mesh inversion (malformed triangles). We propose a new energy function to address some of these issues.

Brownian motion and stochastic calculus

CERN Document Server

Karatzas, Ioannis

1998-01-01

This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large num...

Discrete calculus methods for counting

CERN Document Server

Mariconda, Carlo

2016-01-01

This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii’s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. Although several books touch on one or more of these aspects, precious few cover all of them. The authors, both pure mathematicians, have attempted to develop methods that will allow the student to formulate a given problem in a precise mathematical framework. The aim is to equip readers with a sound strategy for classifying and solving problems by pursuing a mathematically rigorous yet ...

An operational calculus framework to characterize droplet size populations from turbulent breakup by a small number of parameters

International Nuclear Information System (INIS)

Vazquez, Rafael; Ganan-Calvo, Alfonso M

2010-01-01

A systematic operational calculus framework that characterizes droplet/bubble size distributions resulting from turbulent breakup of an immiscible fluid into a carrier one is presented. The proposed formulation is derived from dynamical arguments; a finite-difference formulation of the integro-differential continuous coagulation and fragmentation equation is shown to exhibit the same structure as a discrete sequence of Mellin convolutions between the probability distribution of the evolving dispersed phase and a generic kernel. This kernel may have its physical correspondence with the probability distribution resulting from a single breakup event, e.g. a liquid ligament breakup in a ligament-mediated spray formation. The number of convolution steps in the sequence can be reduced to a single parameter. As an illustration, this procedure is applied to the exponential and the gamma distributions, obtaining as a result the Frechet distribution earlier used by Rosin and Rammler (1934 Kolloid-Zeitschrift 67 16-26), and by Nukiyama and Tanasawa (1939 Trans. Soc. Mech. Eng. Japan 5 62-7). Thus, the framework introduced in this work provides a physical foundation for the success of the Frechet distribution in accurately fitting experimentally measured droplet size distributions in sprays and emulsions.

An operational calculus framework to characterize droplet size populations from turbulent breakup by a small number of parameters

Energy Technology Data Exchange (ETDEWEB)

Vazquez, Rafael; Ganan-Calvo, Alfonso M, E-mail: amgc@us.e [Departamento de IngenierIa Aeroespacial y Mecanica de Fluidos, Universidad de Sevilla, e-41092 Sevilla (Spain)

2010-05-07

A systematic operational calculus framework that characterizes droplet/bubble size distributions resulting from turbulent breakup of an immiscible fluid into a carrier one is presented. The proposed formulation is derived from dynamical arguments; a finite-difference formulation of the integro-differential continuous coagulation and fragmentation equation is shown to exhibit the same structure as a discrete sequence of Mellin convolutions between the probability distribution of the evolving dispersed phase and a generic kernel. This kernel may have its physical correspondence with the probability distribution resulting from a single breakup event, e.g. a liquid ligament breakup in a ligament-mediated spray formation. The number of convolution steps in the sequence can be reduced to a single parameter. As an illustration, this procedure is applied to the exponential and the gamma distributions, obtaining as a result the Frechet distribution earlier used by Rosin and Rammler (1934 Kolloid-Zeitschrift 67 16-26), and by Nukiyama and Tanasawa (1939 Trans. Soc. Mech. Eng. Japan 5 62-7). Thus, the framework introduced in this work provides a physical foundation for the success of the Frechet distribution in accurately fitting experimentally measured droplet size distributions in sprays and emulsions.

6th Conference on Non-integer Order Calculus and Its Applications

CERN Document Server

Łukaniszyn, Marian; Stanisławski, Rafał

2015-01-01

This volume presents selected aspects of non-integer, or fractional order systems, whose analysis, synthesis and applications have increasingly become a real challenge for various research communities, ranging from science to engineering. The spectrum of applications of the fractional order calculus has incredibly expanded, in fact it would be hard to find a science/engineering-related subject area where the fractional calculus had not been incorporated. The content of the fractional calculus is ranged from pure mathematics to engineering implementations and so is the content of this volume. The volume is subdivided into six parts, reflecting particular aspects of the fractional order calculus. The first part contains a single invited paper on a new formulation of fractional-order descriptor observers for fractional-order descriptor continous LTI systems. The second part provides new elements to the mathematical theory of fractional-order systems. In the third part of this volume, a bunch of new results in ap...

Dental Calculus Stimulates Interleukin-1β Secretion by Activating NLRP3 Inflammasome in Human and Mouse Phagocytes.

Directory of Open Access Journals (Sweden)

Jorge Luis Montenegro Raudales

Full Text Available Dental calculus is a mineralized deposit associated with periodontitis. The bacterial components contained in dental calculus can be recognized by host immune sensors, such as Toll-like receptors (TLRs, and induce transcription of proinflammatory cytokines, such as IL-1β. Studies have shown that cellular uptake of crystalline particles may trigger NLRP3 inflammasome activation, leading to the cleavage of the IL-1β precursor to its mature form. Phagocytosis of dental calculus in the periodontal pocket may therefore lead to the secretion of IL-1β, promoting inflammatory responses in periodontal tissues. However, the capacity of dental calculus to induce IL-1β secretion in human phagocytes has not been explored. To study this, we stimulated human polymorphonuclear leukocytes (PMNs and peripheral blood mononuclear cells (PBMCs with dental calculus collected from periodontitis patients, and measured IL-1β secretion by ELISA. We found that calculus induced IL-1β secretion in both human PMNs and PBMCs. Calculus also induced IL-1β in macrophages from wild-type mice, but not in macrophages from NLRP3- and ASC-deficient mice, indicating the involvement of NLRP3 and ASC. IL-1β induction was inhibited by polymyxin B, suggesting that LPS is one of the components of calculus that induces pro-IL-1β transcription. To analyze the effect of the inorganic structure, we baked calculus at 250°C for 1 h. This baked calculus failed to induce pro-IL-1β transcription. However, it did induce IL-1β secretion in lipid A-primed cells, indicating that the crystalline structure of calculus induces inflammasome activation. Furthermore, hydroxyapatite crystals, a component of dental calculus, induced IL-1β in mouse macrophages, and baked calculus induced IL-1β in lipid A-primed human PMNs and PBMCs. These results indicate that dental calculus stimulates IL-1β secretion via NLRP3 inflammasome in human and mouse phagocytes, and that the crystalline structure has a

Dental Calculus Stimulates Interleukin-1β Secretion by Activating NLRP3 Inflammasome in Human and Mouse Phagocytes.

Science.gov (United States)

Montenegro Raudales, Jorge Luis; Yoshimura, Atsutoshi; Sm, Ziauddin; Kaneko, Takashi; Ozaki, Yukio; Ukai, Takashi; Miyazaki, Toshihiro; Latz, Eicke; Hara, Yoshitaka

2016-01-01

Dental calculus is a mineralized deposit associated with periodontitis. The bacterial components contained in dental calculus can be recognized by host immune sensors, such as Toll-like receptors (TLRs), and induce transcription of proinflammatory cytokines, such as IL-1β. Studies have shown that cellular uptake of crystalline particles may trigger NLRP3 inflammasome activation, leading to the cleavage of the IL-1β precursor to its mature form. Phagocytosis of dental calculus in the periodontal pocket may therefore lead to the secretion of IL-1β, promoting inflammatory responses in periodontal tissues. However, the capacity of dental calculus to induce IL-1β secretion in human phagocytes has not been explored. To study this, we stimulated human polymorphonuclear leukocytes (PMNs) and peripheral blood mononuclear cells (PBMCs) with dental calculus collected from periodontitis patients, and measured IL-1β secretion by ELISA. We found that calculus induced IL-1β secretion in both human PMNs and PBMCs. Calculus also induced IL-1β in macrophages from wild-type mice, but not in macrophages from NLRP3- and ASC-deficient mice, indicating the involvement of NLRP3 and ASC. IL-1β induction was inhibited by polymyxin B, suggesting that LPS is one of the components of calculus that induces pro-IL-1β transcription. To analyze the effect of the inorganic structure, we baked calculus at 250°C for 1 h. This baked calculus failed to induce pro-IL-1β transcription. However, it did induce IL-1β secretion in lipid A-primed cells, indicating that the crystalline structure of calculus induces inflammasome activation. Furthermore, hydroxyapatite crystals, a component of dental calculus, induced IL-1β in mouse macrophages, and baked calculus induced IL-1β in lipid A-primed human PMNs and PBMCs. These results indicate that dental calculus stimulates IL-1β secretion via NLRP3 inflammasome in human and mouse phagocytes, and that the crystalline structure has a partial role in

Dental Calculus Stimulates Interleukin-1β Secretion by Activating NLRP3 Inflammasome in Human and Mouse Phagocytes

Science.gov (United States)

Montenegro Raudales, Jorge Luis; Yoshimura, Atsutoshi; SM, Ziauddin; Kaneko, Takashi; Ozaki, Yukio; Ukai, Takashi; Miyazaki, Toshihiro; Latz, Eicke; Hara, Yoshitaka

2016-01-01

Dental calculus is a mineralized deposit associated with periodontitis. The bacterial components contained in dental calculus can be recognized by host immune sensors, such as Toll-like receptors (TLRs), and induce transcription of proinflammatory cytokines, such as IL-1β. Studies have shown that cellular uptake of crystalline particles may trigger NLRP3 inflammasome activation, leading to the cleavage of the IL-1β precursor to its mature form. Phagocytosis of dental calculus in the periodontal pocket may therefore lead to the secretion of IL-1β, promoting inflammatory responses in periodontal tissues. However, the capacity of dental calculus to induce IL-1β secretion in human phagocytes has not been explored. To study this, we stimulated human polymorphonuclear leukocytes (PMNs) and peripheral blood mononuclear cells (PBMCs) with dental calculus collected from periodontitis patients, and measured IL-1β secretion by ELISA. We found that calculus induced IL-1β secretion in both human PMNs and PBMCs. Calculus also induced IL-1β in macrophages from wild-type mice, but not in macrophages from NLRP3- and ASC-deficient mice, indicating the involvement of NLRP3 and ASC. IL-1β induction was inhibited by polymyxin B, suggesting that LPS is one of the components of calculus that induces pro-IL-1β transcription. To analyze the effect of the inorganic structure, we baked calculus at 250°C for 1 h. This baked calculus failed to induce pro-IL-1β transcription. However, it did induce IL-1β secretion in lipid A-primed cells, indicating that the crystalline structure of calculus induces inflammasome activation. Furthermore, hydroxyapatite crystals, a component of dental calculus, induced IL-1β in mouse macrophages, and baked calculus induced IL-1β in lipid A-primed human PMNs and PBMCs. These results indicate that dental calculus stimulates IL-1β secretion via NLRP3 inflammasome in human and mouse phagocytes, and that the crystalline structure has a partial role in

Algorithms, The λ Calculus and Programming

Indian Academy of Sciences (India)

IAS Admin

developed a model to understand ... Hence the ¸ calculus also served as an alternate model ...... Practical programming using usual languages based on .... and return values as. 'answers'. This style of programming that emerges is therefore.

Answers to selected problems in multivariable calculus with linear algebra and series

CERN Document Server

Trench, William F

1972-01-01

Answers to Selected Problems in Multivariable Calculus with Linear Algebra and Series contains the answers to selected problems in linear algebra, the calculus of several variables, and series. Topics covered range from vectors and vector spaces to linear matrices and analytic geometry, as well as differential calculus of real-valued functions. Theorems and definitions are included, most of which are followed by worked-out illustrative examples.The problems and corresponding solutions deal with linear equations and matrices, including determinants; vector spaces and linear transformations; eig

[Calculus formation in the prostatic cavity after transurethral resection of the prostate: causes, treatment and prevention].

Science.gov (United States)

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.

Management of calculus anuria using ureteroscopic lithotripsy as a first line treatment: its efficacy and safety.

Science.gov (United States)

Savić, Slaviša; Vukotić, Vinka; Lazić, Miodrag; Savić, Nataša

2014-05-06

To present our experience with emergency ureteroscopic lithotripsy (URSL) for ureteral calculi associated with acute kidney injury (AKI). We retrospectively evaluated the 61 patients consisted of 90 ureteral units (UU), who underwent URSL. The cause of anuria was bilateral calculus obstructions in 29 cases, and unilateral calculus obstruction with, absent, nephrectomized contralateral kidney in 32 cases. In the case of bilateral synchronous ureteric calculi same-session bilateral ureteroscopy (SBBU) was done. The duration of anuria varied between 12 to 72 hours. At the end of the procedure, ureteral stent was systematically left in place in all patients. Surgery was performed 6-12 hours after admission to hospital. Patients were followed at least 1 month postoperatively. The stone free rates (SFR) were determined as baseline, on the first post-operative day, and as overall on the 30 days after procedure. The greatest success was achieved in the distal localization of stones up to 10 mm (93%). Renal function returned in 51 (83.6%) patients within 7 days. In 18 (29.5%) patients [18 (20%) UU] we performed second procedure as extracorporeal shockwave lithotripsy in 16.7% and open surgery in 2.2%. In 43 (70.5%) patients URSL was a successful therapeutic approach in dealing with pain, obstruction and calculus. Calculus anuria is a medical emergency that requires rapid diagnosis and prompt treatment for the purpose of decompression. URSL is the proper method of choice for selected patients and can be performed safely and has high success rates with minimal morbidity.

Advanced calculus of several variables

CERN Document Server

Edwards, C H

1995-01-01

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

A Calculus for Trust Management

DEFF Research Database (Denmark)

Carbone, Marco; Nielsen, Mogens; Sassone, Vladimiro

2004-01-01

principals to policies. We elect to formalise policies using a Datalog-like logic, and to express protocols in the process algebra style. This yields an expressive calculus very suitable for the global computing scenarios, and provides a formalisation of notions such as trust evolution. For ctm we define...

Portfolio Analysis for Vector Calculus

Science.gov (United States)

Kaplan, Samuel R.

2015-01-01

Classic stock portfolio analysis provides an applied context for Lagrange multipliers that undergraduate students appreciate. Although modern methods of portfolio analysis are beyond the scope of vector calculus, classic methods reinforce the utility of this material. This paper discusses how to introduce classic stock portfolio analysis in a…

Graded tensor calculus

International Nuclear Information System (INIS)

Scheunert, M.

1982-10-01

We develop a graded tensor calculus corresponding to arbitrary Abelian groups of degrees and arbitrary commutation factors. The standard basic constructions and definitions like tensor products, spaces of multilinear mappings, contractions, symmetrization, symmetric algebra, as well as the transpose, adjoint, and trace of a linear mapping, are generalized to the graded case and a multitude of canonical isomorphisms is presented. Moreover, the graded versions of the classical Lie algebras are introduced and some of their basic properties are described. (orig.)

Evidence for calcifying nanoparticles in gingival crevicular fluid and dental calculus in periodontitis.

Science.gov (United States)

Zhang, Song-Mei; Tian, Fei; Jiang, Xin-Quan; Li, Jing; Xu, Chun; Guo, Xiao-Kui; Zhang, Fu-Qiang

2009-09-01

Calcifying nanoparticles (CNPs), also known as nanobacteria, can produce carbonate apatite on their cell walls and initiate pathologic calcification. The objective of this study was to determine whether CNPs are present in the gingival crevicular fluid (GCF) from subjects with periodontal disease and whether they can induce the pathologic calcification of primary cultured human gingival epithelial cells. GCF and dental calculus samples were collected from 10 subjects with gingivitis and 10 subjects with chronic periodontitis. CNPs in GCF and calculus filtrates were detected with nanocapture enzyme-linked immunosorbent assay kits. The CNPs in cultures of dental calculus filtrates were also identified using immunofluorescence staining, transmission electron microscopy (TEM), and chemical analysis. Pathologic changes in the CNP-treated gingival epithelial cells were observed with TEM, alizarin red staining, and disk-scanning confocal microscopy. CNPs were found in GCF samples from two subjects with chronic periodontitis. Based on chemical analysis, the surface-associated material from CNPs isolated and cultured from calculus has a composition similar to dental calculus. The pathologic calcification of CNP-treated gingival epithelial cells was also observed. Self-replicating calcifying nanoparticles can be cultured and identified from dental calculus. This raises the issue of whether CNPs contribute to the pathogenesis of periodontitis.