Mathematical Models of Cardiac Pacemaking Function

Directory of Open Access Journals (Sweden)

Pan eLi

2013-10-01

Full Text Available Over the past half century, there has been intense and fruitful interaction between experimental and computational investigations of cardiac function. This interaction has, for example, led to deep understanding of cardiac excitation-contraction coupling; how it works, as well as how it fails. However, many lines of inquiry remain unresolved, among them the initiation of each heartbeat. The sinoatrial node, a cluster of specialized pacemaking cells in the right atrium of the heart, spontaneously generates an electro-chemical wave that spreads through the atria and through the cardiac conduction system to the ventricles, initiating the contraction of cardiac muscle essential for pumping blood to the body. Despite the fundamental importance of this primary pacemaker, this process is still not fully understood, and ionic mechanisms underlying cardiac pacemaking function are currently under heated debate. Several mathematical models of sinoatrial node cell membrane electrophysiology have been constructed as based on different experimental data sets and hypotheses. As could be expected, these differing models offer diverse predictions about cardiac pacemaking activities. This paper aims to present the current state of debate over the origins of the pacemaking function of the sinoatrial node. Here, we will specifically review the state-of-the-art of cardiac pacemaker modeling, with a special emphasis on current discrepancies, limitations, and future challenges.

Special Education Teachers' Views on Using Technology in Teaching Mathematics

Science.gov (United States)

Baglama, Basak; Yikmis, Ahmet; Demirok, Mukaddes Sakalli

2017-01-01

Individuals with special needs require support in acquiring various academic and social skills and mathematical skills are one of the most important skills in which individuals with special needs need to acquire in order to maintain their daily lives. Current approaches in education emphasize the importance of integrating technology into special…

Inferentialism in mathematics education : introduction to a special issue

NARCIS (Netherlands)

Bakker, Arthur; Hußmann, Stephan

2017-01-01

Inferentialism, as developed by the philosopher Robert Brandom (1994, 2000), is a theory of meaning. The theory has wide-ranging implications in various fields but this special issue concentrates on the use and content of concepts. The key idea, relevant to mathematics education research, is that

The functions of mathematical physics

CERN Document Server

Hochstadt, Harry

2012-01-01

A modern classic, this clearly written, incisive textbook provides a comprehensive, detailed survey of the functions of mathematical physics, a field of study straddling the somewhat artificial boundary between pure and applied mathematics.In the 18th and 19th centuries, the theorists who devoted themselves to this field - pioneers such as Gauss, Euler, Fourier, Legendre, and Bessel - were searching for mathematical solutions to physical problems. Today, although most of the functions have practical applications, in areas ranging from the quantum-theoretical model of the atom to the vibrating

Advancements in Research on Creativity and Giftedness in Mathematics Education: Introduction to the Special Issue

Science.gov (United States)

Singer, Florence Mihaela; Sheffield, Linda Jensen; Leikin, Roza

2017-01-01

Creativity and giftedness in mathematics education research are topics of an increased interest in the education community during recent years. This introductory paper to the special issue on Mathematical Creativity and Giftedness in Mathematics Education has a twofold purpose: to offer a brief historical perspective on the study of creativity and…

Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics

CERN Document Server

Ismail, Mourad

2001-01-01

These are the proceedings of the conference "Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics" held at the Department of Mathematics, University of Florida, Gainesville, from November 11 to 13, 1999. The main emphasis of the conference was Com­ puter Algebra (i. e. symbolic computation) and how it related to the fields of Number Theory, Special Functions, Physics and Combinatorics. A subject that is common to all of these fields is q-series. We brought together those who do symbolic computation with q-series and those who need q-series in­ cluding workers in Physics and Combinatorics. The goal of the conference was to inform mathematicians and physicists who use q-series of the latest developments in the field of q-series and especially how symbolic computa­ tion has aided these developments. Over 60 people were invited to participate in the conference. We ended up having 45 participants at the conference, including six one hour plenary speakers and 28 half hour speakers. T...

Foreword to the Special Focus on Mathematics, Data and Knowledge

KAUST Repository

Chen, Xiaoyu

2013-12-01

There is a growing interest in applying mathematical theories and methods from topology, computational geometry, differential equations, fluid dynamics, quantum statistics, etc. to describe and to analyze scientific regularities of diverse, massive, complex, nonlinear, and fast changing data accumulated continuously around the world and in discovering and revealing valid, insightful, and valuable knowledge that data imply. With increasingly solid mathematical foundations, various methods and techniques have been studied and developed for data mining, modeling, and processing, and knowledge representation, organization, and verification; different systems and mechanisms have been designed to perform data-intensive tasks in many application fields for classification, predication, recommendation, ranking, filtering, etc. This special focus of Mathematics in Computer Science is organized to stimulate original research on the interaction of mathematics with data and knowledge, in particular the exploration of new mathematical theories and methodologies for data modeling and analysis and knowledge discovery and management, the study of mathematical models of big data and complex knowledge, and the development of novel solutions and strategies to enhance the performance of existing systems and mechanisms for data and knowledge processing. The present foreword provides a short review of some key ideas and techniques on how mathematics interacts with data and knowledge, together with a few selected research directions and problems and a brief introduction to the four papers published in the focus. © 2013 Springer Basel.

Using special functions to model the propagation of airborne diseases

Science.gov (United States)

Bolaños, Daniela

2014-06-01

Some special functions of the mathematical physics are using to obtain a mathematical model of the propagation of airborne diseases. In particular we study the propagation of tuberculosis in closed rooms and we model the propagation using the error function and the Bessel function. In the model, infected individual emit pathogens to the environment and this infect others individuals who absorb it. The evolution in time of the concentration of pathogens in the environment is computed in terms of error functions. The evolution in time of the number of susceptible individuals is expressed by a differential equation that contains the error function and it is solved numerically for different parametric simulations. The evolution in time of the number of infected individuals is plotted for each numerical simulation. On the other hand, the spatial distribution of the pathogen around the source of infection is represented by the Bessel function K0. The spatial and temporal distribution of the number of infected individuals is computed and plotted for some numerical simulations. All computations were made using software Computer algebra, specifically Maple. It is expected that the analytical results that we obtained allow the design of treatment rooms and ventilation systems that reduce the risk of spread of tuberculosis.

Mathematics as verbal behavior.

Science.gov (United States)

Marr, M Jackson

2015-04-01

"Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk. Copyright © 2015 Elsevier B.V. All rights reserved.

Effects of mathematics computer games on special education students’ multiplicative reasoning ability

NARCIS (Netherlands)

Bakker, M.|info:eu-repo/dai/nl/355337770; Van den Heuvel-Panhuizen, M.|info:eu-repo/dai/nl/069266255; Robitzsch, Alexander

2016-01-01

This study examined the effects of a teacher-delivered intervention with online math-ematics mini-games on special education students’ multiplicative reasoning ability(multiplication and division). The games involved declarative, procedural, as well asconceptual knowledge of multiplicative

Effects of mathematics computer games on special education students' multiplicative reasoning ability

NARCIS (Netherlands)

Bakker, M.; Heuvel-Panhuizen, M.H.A.M. van den; Robitzsch, A.

2016-01-01

This study examined the effects of a teacher-delivered intervention with online mathematics mini-games on special education students' multiplicative reasoning ability (multiplication and division). The games involved declarative, procedural, as well as conceptual knowledge of multiplicative

Higher-order automatic differentiation of mathematical functions

Science.gov (United States)

Charpentier, Isabelle; Dal Cappello, Claude

2015-04-01

Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faà di Bruno's formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.

2nd Tbilisi-Salerno Workshop on Modeling in Mathematics

CERN Document Server

Ricci, Paolo; Tavkhelidze, Ilia

2017-01-01

This book contains a collection of papers presented at the 2nd Tbilisi Salerno Workshop on Mathematical Modeling in March 2015. The focus is on applications of mathematics in physics, electromagnetics, biochemistry and botany, and covers such topics as multimodal logic, fractional calculus, special functions, Fourier-like solutions for PDE’s, Rvachev-functions and linear dynamical systems. Special chapters focus on recent uniform analytic descriptions of natural and abstract shapes using the Gielis Formula. The book is intended for a wide audience with interest in application of mathematics to modeling in the natural sciences.

Special software for computing the special functions of wave catastrophes

Directory of Open Access Journals (Sweden)

Andrey S. Kryukovsky

2015-01-01

Full Text Available The method of ordinary differential equations in the context of calculating the special functions of wave catastrophes is considered. Complementary numerical methods and algorithms are described. The paper shows approaches to accelerate such calculations using capabilities of modern computing systems. Methods for calculating the special functions of wave catastrophes are considered in the framework of parallel computing and distributed systems. The paper covers the development process of special software for calculating of special functions, questions of portability, extensibility and interoperability.

Effects of Mathematics Computer Games on Special Education Students' Multiplicative Reasoning Ability

Science.gov (United States)

Bakker, Marjoke; van den Heuvel-Panhuizen, Marja; Robitzsch, Alexander

2016-01-01

This study examined the effects of a teacher-delivered intervention with online mathematics mini-games on special education students' multiplicative reasoning ability (multiplication and division). The games involved declarative, procedural, as well as conceptual knowledge of multiplicative relations, and were accompanied with teacher-led lessons…

Contrasting two models of academic self-efficacy--domain-specific versus cross-domain--in children receiving and not receiving special instruction in mathematics.

Science.gov (United States)

Jungert, Tomas; Hesser, Hugo; Träff, Ulf

2014-10-01

In social cognitive theory, self-efficacy is domain-specific. An alternative model, the cross-domain influence model, would predict that self-efficacy beliefs in one domain might influence performance in other domains. Research has also found that children who receive special instruction are not good at estimating their performance. The aim was to test two models of how self-efficacy beliefs influence achievement, and to contrast children receiving special instruction in mathematics with normally-achieving children. The participants were 73 fifth-grade children who receive special instruction and 70 children who do not receive any special instruction. In year four and five, the children's skills in mathematics and reading were assessed by national curriculum tests, and in their fifth year, self-efficacy in mathematics and reading were measured. Structural equation modeling showed that in domains where children do not receive special instruction in mathematics, self-efficacy is a mediating variable between earlier and later achievement in the same domain. Achievement in mathematics was not mediated by self-efficacy in mathematics for children who receive special instruction. For normal achieving children, earlier achievement in the language domain had an influence on later self-efficacy in the mathematics domain, and self-efficacy beliefs in different domains were correlated. Self-efficacy is mostly domain specific, but may play a different role in academic performance depending on whether children receive special instruction. The results of the present study provided some support of the Cross-Domain Influence Model for normal achieving children. © 2014 Scandinavian Psychological Associations and John Wiley & Sons Ltd.

Computer algebra in quantum field theory integration, summation and special functions

CERN Document Server

Schneider, Carsten

2013-01-01

The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including

Special functions group theoretical aspects and applications

CERN Document Server

Schempp, Walter; Askey, Richard A

1984-01-01

Approach your problems from It isn't that they can't see the right end and begin with the solution. the answers. Then one day, It is that they can't see the perhaps you will find the problem. final question. G.K. Chesterton. The Scandal 'The Hermit Clad in Crane of Father Brown 'The Point of Feathers' in R. van Gulik's a Pin'. The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the ...

Socio-functional dynamics of the mathematical contents

Directory of Open Access Journals (Sweden)

Isabel Alonso-Berenguer

2018-01-01

Full Text Available The article presents a model of the socio-functional dynamics of the mathematical contents that offers a novel theoretical-methodological basement for the development of the process of teaching-learning of the mathematical one. The investigation, of theoretical character, used the methods of analysis-synthesis, inductive-deductive and historical-logical to elaborate the one mentioned model that leaves of considering that the future professors have appropriated previously of the mathematical contents, foreseen in the curriculum, and they are, therefore, under conditions of understanding the potentialities of the same ones to facilitate the formation of socio-functional values.   

Occupational Therapy Interventions Effect on Mathematical Problems in Students with Special Learning Disorders

Directory of Open Access Journals (Sweden)

Rogaieh Mohammadi

2009-10-01

Full Text Available Objectives: Dyscalculia is specific learning disabilities affecting the acquisition of mathematic skills in an otherwise normal child. The aim of this study was investigation of occupational therapy interventions effect on mathematical problems in students with special learning disorders. Methods: 40 students with dyscalculia (2-5 grades were selected and divided through randomized permuted blocks method into two groups 20 persons as intervention group and the others as the control group. Initially both of groups were administered by the "Iran Key math Test". Then intervention group received occupational therapy interventions for 20 sessions individually and two groups were administered by the Test again. Data was analyzed by using Paired and Independent t-tests. Results: By the paired sample t-test the mean of total marks of Iran Key math Test demonstrated statistically significant difference in both of groups (P<0.05, but the measure of difference in intervention group was more than control group. The mean of marks of Basic Concepts, Operations and Applications demonstrated statistically significant difference at intervention group. Discussion: Occupational therapy interventions had clinical effect on mathematical problems in students with special learning disorders.

The analysis of mathematics teachers' learning on algebra function limit material based on teaching experience difference

Science.gov (United States)

Ma'rufi, Budayasa, I. Ketut; Juniati, Dwi

2017-08-01

The aim of this study was to describe the analysis of mathematics teachers' learning on algebra function limit material based on teaching experience difference. The purpose of this study is to describe the analysis of mathematics teacher's learning on limit algebraic functions in terms of the differences of teaching experience. Learning analysis focused on Pedagogical Content Knowledge (PCK) of teachers in mathematics on limit algebraic functions related to the knowledge of pedagogy. PCK of teachers on limit algebraic function is a type of specialized knowledge for teachers on how to teach limit algebraic function that can be understood by students. Subjects are two high school mathematics teacher who has difference of teaching experience they are one Novice Teacher (NP) and one Experienced Teacher (ET). Data are collected through observation of learning in the class, videos of learning, and then analyzed using qualitative analysis. Teacher's knowledge of Pedagogic defined as a knowledge and understanding of teacher about planning and organizing of learning, and application of learning strategy. The research results showed that the Knowledge of Pedagogy on subject NT in mathematics learning on the material of limit function algebra showed that the subject NT tended to describe procedurally, without explaining the reasons why such steps were used, asking questions which tended to be monotonous not be guiding and digging deeper, and less varied in the use of learning strategies while subject ET gave limited guidance and opportunities to the students to find their own answers, exploit the potential of students to answer questions, provide an opportunity for students to interact and work in groups, and subject ET tended to combine conceptual and procedural explanation.

Characterizing the Development of Specialized Mathematical Content Knowledge for Teaching in Algebraic Reasoning and Number Theory

Science.gov (United States)

Bair, Sherry L.; Rich, Beverly S.

2011-01-01

This article characterizes the development of a deep and connected body of mathematical knowledge categorized by Ball and Bass' (2003b) model of Mathematical Knowledge for Teaching (MKT), as Specialized Content Knowledge for Teaching (SCK) in algebraic reasoning and number sense. The research employed multiple cases across three years from two…

Mathematical Learning Disabilities in Special Populations: Phenotypic Variation and Cross-Disorder Comparisons

Science.gov (United States)

Dennis, Maureen; Berch, Daniel B.; Mazzocco, Michele M. M.

2009-01-01

What is mathematical learning disability (MLD)? The reviews in this special issue adopt different approaches to defining the construct of MLD. Collectively, they demonstrate the current status of efforts to establish a consensus definition and the challenges faced in this endeavor. In this commentary, we reflect upon the proposed pathways to…

Licensure tests for special education teachers: how well they assess knowledge of reading instruction and mathematics.

Science.gov (United States)

Stotsky, Sandra

2009-01-01

To determine the extent to which knowledge of evidence-based reading instruction and mathematics is assessed on licensure tests for prospective special education teachers, this study drew on information provided by Educational Testing Service (ETS), the American Board for Certification of Teacher Excellence, and National Evaluation Systems (now Evaluation Systems group of Pearson). It estimated the percentage of test items on phonemic awareness, phonics, and vocabulary knowledge and on mathematics content. It also analyzed descriptions of ETS's tests of "principles of teaching and learning." Findings imply that prospective special education teachers should be required to take both a dedicated test of evidence-based reading instructional knowledge, as in California, Massachusetts, and Virginia, and a test of mathematical knowledge, as in Massachusetts. States must design their own tests of teaching principles to assess knowledge of evidence-based educational theories.

Reprint of "Mathematics as verbal behavior".

Science.gov (United States)

Marr, M Jackson

2015-05-01

"Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk. Copyright © 2015 Elsevier B.V. All rights reserved.

Mathematical simulation of cascade-probabilistic functions for charged particles

International Nuclear Information System (INIS)

Kupchishin, A.A.; Kupchishin, A.I.; Smygaleva, T.A.

1998-01-01

Analytical expressions for cascade-probabilistic functions (CPF) for electrons, protons, α-particles and ions with taking into account energy losses are received. Mathematical analysis of these functions is carried out and main properties of function are determined. Algorithms of CPF are developed and their computer calculation were conducted. Regularities in behavior of function in dependence on initial particles energy, atomic number and registration depth are established. Book is intended to specialists on mathematical simulation of radiation defects, solid state physics, elementary particle physics and applied mathematics. There are 3 chapters in the book: 1. Cascade-probabilistic functions for electrons; 2. CPF for protons and α-particles; 3. CPF with taking unto account energy losses of ions. (author)

On computing special functions in marine engineering

Science.gov (United States)

Constantinescu, E.; Bogdan, M.

2015-11-01

Important modeling applications in marine engineering conduct us to a special class of solutions for difficult differential equations with variable coefficients. In order to be able to solve and implement such models (in wave theory, in acoustics, in hydrodynamics, in electromagnetic waves, but also in many other engineering fields), it is necessary to compute so called special functions: Bessel functions, modified Bessel functions, spherical Bessel functions, Hankel functions. The aim of this paper is to develop numerical solutions in Matlab for the above mentioned special functions. Taking into account the main properties for Bessel and modified Bessel functions, we shortly present analytically solutions (where possible) in the form of series. Especially it is studied the behavior of these special functions using Matlab facilities: numerical solutions and plotting. Finally, it will be compared the behavior of the special functions and point out other directions for investigating properties of Bessel and spherical Bessel functions. The asymptotic forms of Bessel functions and modified Bessel functions allow determination of important properties of these functions. The modified Bessel functions tend to look more like decaying and growing exponentials.

Mathematical analysis, approximation theory and their applications

CERN Document Server

Gupta, Vijay

2016-01-01

Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

Some applications of mathematics in theoretical physics - A review

International Nuclear Information System (INIS)

Bora, Kalpana

2016-01-01

Mathematics is a very beautiful subject−very much an indispensible tool for Physics, more so for Theoretical Physics (by which we mean here mainly Field Theory and High Energy Physics). These branches of Physics are based on Quantum Mechanics and Special Theory of Relativity, and many mathematical concepts are used in them. In this work, we shall elucidate upon only some of them, like−differential geometry, infinite series, Mellin transforms, Fourier and integral transforms, special functions, calculus, complex algebra, topology, group theory, Riemannian geometry, functional analysis, linear algebra, operator algebra, etc. We shall also present, some physics issues, where these mathematical tools are used. It is not wrong to say that Mathematics is such a powerful tool, without which, there can not be any Physics theory!! A brief review on our research work is also presented.

Some applications of mathematics in theoretical physics - A review

Energy Technology Data Exchange (ETDEWEB)

Bora, Kalpana [Physics Department, Gauhati University, Guwahati-781014, Assam (India)

2016-06-21

Mathematics is a very beautiful subject−very much an indispensible tool for Physics, more so for Theoretical Physics (by which we mean here mainly Field Theory and High Energy Physics). These branches of Physics are based on Quantum Mechanics and Special Theory of Relativity, and many mathematical concepts are used in them. In this work, we shall elucidate upon only some of them, like−differential geometry, infinite series, Mellin transforms, Fourier and integral transforms, special functions, calculus, complex algebra, topology, group theory, Riemannian geometry, functional analysis, linear algebra, operator algebra, etc. We shall also present, some physics issues, where these mathematical tools are used. It is not wrong to say that Mathematics is such a powerful tool, without which, there can not be any Physics theory!! A brief review on our research work is also presented.

Some applications of mathematics in theoretical physics - A review

Science.gov (United States)

Bora, Kalpana

2016-06-01

Mathematics is a very beautiful subject-very much an indispensible tool for Physics, more so for Theoretical Physics (by which we mean here mainly Field Theory and High Energy Physics). These branches of Physics are based on Quantum Mechanics and Special Theory of Relativity, and many mathematical concepts are used in them. In this work, we shall elucidate upon only some of them, like-differential geometry, infinite series, Mellin transforms, Fourier and integral transforms, special functions, calculus, complex algebra, topology, group theory, Riemannian geometry, functional analysis, linear algebra, operator algebra, etc. We shall also present, some physics issues, where these mathematical tools are used. It is not wrong to say that Mathematics is such a powerful tool, without which, there can not be any Physics theory!! A brief review on our research work is also presented.

Topics in mathematical analysis and applications

CERN Document Server

Tóth, László

2014-01-01

This volume presents significant advances in a number of theories and problems of Mathematical Analysis and its applications in disciplines such as Analytic Inequalities, Operator Theory, Functional Analysis, Approximation Theory, Functional Equations, Differential Equations, Wavelets, Discrete Mathematics and Mechanics. The contributions focus on recent developments and are written by eminent scientists from the international mathematical community. Special emphasis is given to new results that have been obtained in the above mentioned disciplines in which Nonlinear Analysis plays a central role. Some review papers published in this volume will be particularly useful for a broader readership in Mathematical Analysis, as well as for graduate students. An attempt is given to present all subjects in this volume in a unified and self-contained manner, to be particularly useful to the mathematical community.

A study about teaching quadratic functions using mathematical models and free software

Science.gov (United States)

Nepomucena, T. V.; da Silva, A. C.; Jardim, D. F.; da Silva, J. M.

2017-12-01

In the face of the reality of teaching Mathematics in Basic Education in Brazil, specially relating teach functions focusing their relevance to the student’s academic development in Basic and Superior Education, this work proposes the use of educational software to help the teaching of functions in Basic Education since the computers and software show as an outstanding option to help the teaching and learning processes. On the other hand, the study also proposes the use of Didactic Transposition as a methodology investigation and research. Along with this survey, some teaching interventions were applied to detect the main difficulties in the teaching process of functions in the Basic Education, analyzing the results obtained along the interventions in a qualitative form. Considering the discussion of the results at the end of the didactic interventions, it was verified that the results obtained were satisfactory.

Introduction to mathematical physics methods and concepts

CERN Document Server

Wong, Chun Wa

2013-01-01

Mathematical physics provides physical theories with their logical basis and the tools for drawing conclusions from hypotheses. Introduction to Mathematical Physics explains to the reader why and how mathematics is needed in the description of physical events in space. For undergraduates in physics, it is a classroom-tested textbook on vector analysis, linear operators, Fourier series and integrals, differential equations, special functions and functions of a complex variable. Strongly correlated with core undergraduate courses on classical and quantum mechanics and electromagnetism, it helps the student master these necessary mathematical skills. It contains advanced topics of interest to graduate students on relativistic square-root spaces and nonlinear systems. It contains many tables of mathematical formulas and references to useful materials on the Internet. It includes short tutorials on basic mathematical topics to help readers refresh their mathematical knowledge. An appendix on Mathematica encourages...

A course in mathematical methods for physicists

CERN Document Server

Herman, Russell L

2014-01-01

Based on the author’s junior-level undergraduate course, this introductory textbook is designed for a course in mathematical physics. Focusing on the physics of oscillations and waves, A Course in Mathematical Methods for Physicists helps students understand the mathematical techniques needed for their future studies in physics. It takes a bottom-up approach that emphasizes physical applications of the mathematics. The book offers: •A quick review of mathematical prerequisites, proceeding to applications of differential equations and linear algebra •Classroom-tested explanations of complex and Fourier analysis for trigonometric and special functions •Coverage of vector analysis and curvilinear coordinates for solving higher dimensional problems •Sections on nonlinear dynamics, variational calculus, numerical solutions of differential equations, and Green's functions

Orthogonal Polynomials and Special Functions

CERN Document Server

Assche, Walter

2003-01-01

The set of lectures from the Summer School held in Leuven in 2002 provide an up-to-date account of recent developments in orthogonal polynomials and special functions, in particular for algorithms for computer algebra packages, 3nj-symbols in representation theory of Lie groups, enumeration, multivariable special functions and Dunkl operators, asymptotics via the Riemann-Hilbert method, exponential asymptotics and the Stokes phenomenon. The volume aims at graduate students and post-docs working in the field of orthogonal polynomials and special functions, and in related fields interacting with orthogonal polynomials, such as combinatorics, computer algebra, asymptotics, representation theory, harmonic analysis, differential equations, physics. The lectures are self-contained requiring only a basic knowledge of analysis and algebra, and each includes many exercises.

An Introduction to Business Mathematics

OpenAIRE

Henk van Elst

2015-01-01

These lecture notes provide a self-contained introduction to the mathematical methods required in a Bachelor degree programme in Business, Economics, or Management. In particular, the topics covered comprise real-valued vector and matrix algebra, systems of linear algebraic equations, Leontief's stationary input-output matrix model, linear programming, elementary financial mathematics, as well as differential and integral calculus of real-valued functions of one real variable. A special focus...

Mathematics Programming on the Apple II and IBM PC.

Science.gov (United States)

Myers, Roy E.; Schneider, David I.

1987-01-01

Details the features of BASIC used in mathematics programming and provides the information needed to translate between the Apple II and IBM PC computers. Discusses inputing a user-defined function, setting scroll windows, displaying subscripts and exponents, variable names, mathematical characters and special symbols. (TW)

The Functions of Function Discourse--University Mathematics Teaching from a Commognitive Standpoint

Science.gov (United States)

Viirman, Olov

2014-01-01

This paper addresses a topic within university mathematics education which has been somewhat underexplored: the teaching practices actually used by university mathematics teachers when giving lectures. The study investigates the teaching practices of seven Swedish university teachers on the topic of functions using a discursive approach, the…

An Introduction to Equilibrium Thermodynamics: A Rational Approach to Its Teaching. Part 1: Notation and Mathematics.

Science.gov (United States)

Williams, Donald F.; Glasser, David

1991-01-01

Introduces and develops mathematical notation to assist undergraduate students in overcoming conceptual difficulties involving the underlying mathematics of state functions, which tend to be different from functions encountered by students in previous mathematical courses, because of the need to manipulate special types of partial derivatives and…

Mathematical tools for physicists

International Nuclear Information System (INIS)

Trigg, G.L.

2005-01-01

Mathematical Tools for Physisists is a unique collection of 18 review articles, each one written by a renowned expert of its field. Their professional style will be beneficial for advanced students as well as for the scientist at work. The first may find a comprehensive introduction while the latter use it as a quick reference. Great attention was paid to ensuring fast access to the information, and each carefully reviewed article includes a glossary of terms and a guide to further reading. The contributions range from fundamental methods right up to the latest applications, including: - Algebraic Methods - Analytic Methods - Fourier and Other Mathematical Transforms - Fractal Geometry - Geometrical Methods - Green's Functions - Group Theory - Mathematical Modeling - Monte Carlo Methods - Numerical Methods - Perturbation Methods - Quantum Computation - Quantum Logic - Special Functions - Stochastic Processes - Symmetries and Conservation Laws - Topology - Variational Methods. (orig.)

Modeling of morpho-functional profile of sportsmen of high qualification who specialize in swimming in way butterfly stroke at distances of various lengths.

Directory of Open Access Journals (Sweden)

Olga Pilipko

2017-02-01

Full Text Available Purpose: the development of modern morpho-functional models of sportsmen of high qualification who specialize in swimming in way butterfly stroke at distances of various lengths. Material & Methods: the analysis of scientifically-methodical literature, timekeeping, measurement of morpho-functional indicators with application of private techniques, methods of mathematical statistics. The contingent of the investigated was made by sportsmen who specialized in distances of 50, 100 and 200 meters in way butterfly stroke and had the level of sports qualification: MSU, MSIC. Results: it is established that the morpho-functional profile of the sportsmen specializing in swimming in way butterfly stroke at distances of various length has the features; model morpho-functional characteristics of sportsmen, who act in swimming in way butterfly stroke at distances of 50, 100 and 200 meters, are developed. Conclusions: the definition of compliance of individual characteristics of the sportsman to the morpho-functional status will allow choosing correctly remote specialization of the swimmer, to open his potential opportunities most fully.

The Main Properties of q-Functions

OpenAIRE

Nina O. Virchenko; Olena V. Ovcharenko

2017-01-01

Background.  The new generalization of the function of complex variable (q-function) is considered, its main properties are investigated. Such distributions have a special place among the special functions due to their widespread use in many areas of applied mathematics. Objective. The aim of the paper is to study the new generalization of the function of complex variable for application in applied sciences. Methods. To obtain scientific results the general methods of the mathematical a...

Special functions and the theory of group representations

CERN Document Server

Vilenkin, N Ja

1968-01-01

A standard scheme for a relation between special functions and group representation theory is the following: certain classes of special functions are interpreted as matrix elements of irreducible representations of a certain Lie group, and then properties of special functions are related to (and derived from) simple well-known facts of representation theory. The book combines the majority of known results in this direction. In particular, the author describes connections between the exponential functions and the additive group of real numbers (Fourier analysis), Legendre and Jacobi polynomials and representations of the group SU(2), and the hypergeometric function and representations of the group SL(2,R), as well as many other classes of special functions.

Mathematic-Graphical Formalization of Switch Point Control Circuit Function

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Juraj Zdansky

2004-01-01

Full Text Available This article describes authors designed method then enables mathematic – graphical formalization of system’s functional specification. The result of this method is algebraic system – finite automata that is written in transition table. This transition table is possible to overwrite to graphic form (state diagram or to mathematic form (transition and output function. This method is described by example of switch point control circuit.

Executive functioning predicts reading, mathematics, and theory of mind during the elementary years.

Science.gov (United States)

Cantin, Rachelle H; Gnaedinger, Emily K; Gallaway, Kristin C; Hesson-McInnis, Matthew S; Hund, Alycia M

2016-06-01

The goal of this study was to specify how executive functioning components predict reading, mathematics, and theory of mind performance during the elementary years. A sample of 93 7- to 10-year-old children completed measures of working memory, inhibition, flexibility, reading, mathematics, and theory of mind. Path analysis revealed that all three executive functioning components (working memory, inhibition, and flexibility) mediated age differences in reading comprehension, whereas age predicted mathematics and theory of mind directly. In addition, reading mediated the influence of executive functioning components on mathematics and theory of mind, except that flexibility also predicted mathematics directly. These findings provide important details about the development of executive functioning, reading, mathematics, and theory of mind during the elementary years. Copyright © 2016 Elsevier Inc. All rights reserved.

How special are teachers of specialized schools? : a quantitative investigation of Turkish mathematics teachers' self-confidence levels in the technology domain

OpenAIRE

Çatma, Zehra

2013-01-01

Ankara : The Program of Curriculum and Instruction, Bilkent University, 2013. Thesis (Master's) -- Bilkent University, 2013. Includes bibliographical refences. The purpose of the current study was to investigate whether specialized high school mathematics teachers, who were selected to educate selected students, were mentally ready to integrate Fatih project technologies into their teaching. The sample consisted of 40 teachers, who voluntarily participated the study and work...

A summary of numerical computation for special functions

International Nuclear Information System (INIS)

Zhang Shanjie

1992-01-01

In the paper, special functions frequently encountered in science and engineering calculations are introduced. The computation of the values of Bessel function and elliptic integrals are taken as the examples, and some common algorithms for computing most special functions, such as series expansion for small argument, asymptotic approximations for large argument, polynomial approximations, recurrence formulas and iteration method, are discussed. In addition, the determination of zeros of some special functions, and the other questions related to numerical computation are also discussed

Special-purpose interactive programming shell for the open-quotes POLEclose quotes system

International Nuclear Information System (INIS)

Rvachev, V.L.; Kurpa, L.I.

1995-01-01

The development of the theory of R-functions has stimulated the emergence of efficient numerical-analytical methods for a wide class of problems associated with physico-mechanical fields. R-functions are the basis for computer-aided level source language, which is sufficiently close to an ordinary mathematical language. Despite the powerful capabilities of the POLE family systems and the extensive support for the analysis of computation results, these systems are still not widely used in practice, as they assume a user with special mathematical qualifications. It is therefore necessary to develop special-purpose systems that do not require the user to be proficient in mathematical physics, the theory of R-functions, variational methods, etc. In other words, we need systems that are oriented toward technical-profile engineers specializing in design and calculations. In this article, we propose some principles for the construction of a special-purpose interactive programming system POLE-PLAST capable of solving problems in the mechanics of deformable solids of complex shape. As the specific application domain for the description of the system we have chosen problems that deal with bending, stability, and vibration of elements of thin-walled constructions modeled by thin plates

Special solutions of neutral functional differential equations

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Győri István

2001-01-01

Full Text Available For a system of nonlinear neutral functional differential equations we prove the existence of an -parameter family of "special solutions" which characterize the asymptotic behavior of all solutions at infinity. For retarded functional differential equations the special solutions used in this paper were introduced by Ryabov.

Behavioral Executive Functions Among Adolescents With Mathematics Difficulties.

Science.gov (United States)

Holm, Marja E; Aunio, Pirjo; Björn, Piia M; Klenberg, Liisa; Korhonen, Johan; Hannula, Markku S

2017-07-01

This study investigates behavioral executive functions (EFs) in the mathematics classroom context among adolescents with different mathematics performance levels. The EF problems were assessed by teachers using a behavioral rating inventory. Using cutoff scores on a standardized mathematics assessment, groups with mathematics difficulties (MD; n = 124), low mathematics performance (LA; n = 140), and average or higher scores (AC; n = 355) were identified. Results showed that the MD group had more problems with distractibility, directing attention, shifting attention, initiative, execution of action, planning, and evaluation than the LA group, whereas the differences in hyperactivity, impulsivity, and sustaining attention were not significant. Compared to the AC group, the MD group showed more problems with all behavioral EFs except hyperactivity and impulsivity, while the LA group showed more problems only with shifting attention. Male adolescents showed more behavioral EF problems than female adolescents, but this gender difference was negligible within the MD group. The practical implications of the results are discussed.

Mathematical methods for physicists and engineers

CERN Document Server

Collins, Royal Eugene

2011-01-01

This practical, highly readable text provides physics and engineering students with the essential mathematical tools for thorough comprehension of their disciplines. Featuring all the necessary topics in applied mathematics in the form of programmed instruction, the text can be understood by advanced undergraduates and beginning graduate students without any assistance from the instructor. Topics include elementary vector calculus, matrix algebra, and linear vector operations; the many and varied methods of solving linear boundary value problems, including the more common special functions o

Mathematical analysis I

CERN Document Server

Zorich, Vladimir A

2015-01-01

VLADIMIR A. ZORICH is professor of mathematics at Moscow State University. His areas of specialization are analysis, conformal geometry, quasiconformal mappings, and mathematical aspects of thermodynamics. He solved the problem of global homeomorphism for space quasiconformal mappings. He holds a patent in the technology of mechanical engineering, and he is also known by his book Mathematical Analysis of Problems in the Natural Sciences . This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems...

Assessment of efficiency of functioning the infocommunication systems a special purpose in the conditions of violation quality of relevance information

Science.gov (United States)

Parinov, A. V.; Korotkikh, L. P.; Desyatov, D. B.; Stepanov, L. V.

2018-03-01

The uniqueness of information processing mechanisms in special-purpose infocommunication systems and the increased interest of intruders lead to an increase in the relevance of the problems associated with their protection. The paper considers the issues of building risk-models for the violation of the relevance and value of information in infocommunication systems for special purposes. Also, special attention is paid to the connection between the qualities of relevance and the value of information obtained as a result of the operation of infocommunication systems for special purposes. Analytical expressions for the risk and damage function in the time range in special-purpose infocommunication systems are obtained, which can serve as a mathematical basis for risk assessment. Further, an analytical expression is obtained to assess the chance of obtaining up-to-date information in the operation of infocommunication systems up to the time the information quality is violated. An analytical expression for estimating the chance can be used to calculate the effectiveness of a special-purpose infocommunication system.

Teachers' Understanding of the Role of Executive Functions in Mathematics Learning.

Science.gov (United States)

Gilmore, Camilla; Cragg, Lucy

2014-09-01

Cognitive psychology research has suggested an important role for executive functions, the set of skills that monitor and control thought and action, in learning mathematics. However, there is currently little evidence about whether teachers are aware of the importance of these skills and, if so, how they come by this information. We conducted an online survey of teachers' views on the importance of a range of skills for mathematics learning. Teachers rated executive function skills, and in particular inhibition and shifting, to be important for mathematics. The value placed on executive function skills increased with increasing teaching experience. Most teachers reported that they were aware of these skills, although few knew the term "executive functions." This awareness had come about through their teaching experience rather than from formal instruction. Researchers and teacher educators could do more to highlight the importance of these skills to trainee or new teachers.

The relationship model of technical and tactical and morpho-functional characteristics of highly skilled swimmers specializing in 50 m butterfly

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Оlena Politko

2016-06-01

Full Text Available Purpose: development of model of the technical and tactical actions, morpho-functional characteristics of highly qualified athletes-swimmers specializing in the 50m butterfly way. Material & Methods: the analytical synthesis of scientific literature data, filming of competitive activity, getting of timing, anthropometry, methods of mathematical statistics. Results: developed model of technical and tactical actions, morphofunctional characteristics of highly qualified swimmers and determined the most important factors affecting athletic performance. Conclusions: the identification and assessment of the most important for the success of sports perfection indicators will allow to draw conclusions about the correctness of the training process according to chosen swimming specialization.

Cluster algebras in mathematical physics

International Nuclear Information System (INIS)

Francesco, Philippe Di; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

2014-01-01

This special issue of Journal of Physics A: Mathematical and Theoretical contains reviews and original research articles on cluster algebras and their applications to mathematical physics. Cluster algebras were introduced by S Fomin and A Zelevinsky around 2000 as a tool for studying total positivity and dual canonical bases in Lie theory. Since then the theory has found diverse applications in mathematics and mathematical physics. Cluster algebras are axiomatically defined commutative rings equipped with a distinguished set of generators (cluster variables) subdivided into overlapping subsets (clusters) of the same cardinality subject to certain polynomial relations. A cluster algebra of rank n can be viewed as a subring of the field of rational functions in n variables. Rather than being presented, at the outset, by a complete set of generators and relations, it is constructed from the initial seed via an iterative procedure called mutation producing new seeds successively to generate the whole algebra. A seed consists of an n-tuple of rational functions called cluster variables and an exchange matrix controlling the mutation. Relations of cluster algebra type can be observed in many areas of mathematics (Plücker and Ptolemy relations, Stokes curves and wall-crossing phenomena, Feynman integrals, Somos sequences and Hirota equations to name just a few examples). The cluster variables enjoy a remarkable combinatorial pattern; in particular, they exhibit the Laurent phenomenon: they are expressed as Laurent polynomials rather than more general rational functions in terms of the cluster variables in any seed. These characteristic features are often referred to as the cluster algebra structure. In the last decade, it became apparent that cluster structures are ubiquitous in mathematical physics. Examples include supersymmetric gauge theories, Poisson geometry, integrable systems, statistical mechanics, fusion products in infinite dimensional algebras, dilogarithm

Teachers' Understanding of the Role of Executive Functions in Mathematics Learning

Science.gov (United States)

Gilmore, Camilla; Cragg, Lucy

2014-01-01

Cognitive psychology research has suggested an important role for executive functions, the set of skills that monitor and control thought and action, in learning mathematics. However, there is currently little evidence about whether teachers are aware of the importance of these skills and, if so, how they come by this information. We conducted an online survey of teachers' views on the importance of a range of skills for mathematics learning. Teachers rated executive function skills, and in particular inhibition and shifting, to be important for mathematics. The value placed on executive function skills increased with increasing teaching experience. Most teachers reported that they were aware of these skills, although few knew the term “executive functions.” This awareness had come about through their teaching experience rather than from formal instruction. Researchers and teacher educators could do more to highlight the importance of these skills to trainee or new teachers. PMID:25674156

Luigi Gatteschi's work on asymptotics of special functions and their zeros

Science.gov (United States)

Gautschi, Walter; Giordano, Carla

2008-12-01

A good portion of Gatteschi's research publications-about 65%-is devoted to asymptotics of special functions and their zeros. Most prominently among the special functions studied figure classical orthogonal polynomials, notably Jacobi polynomials and their special cases, Laguerre polynomials, and Hermite polynomials by implication. Other important classes of special functions dealt with are Bessel functions of the first and second kind, Airy functions, and confluent hypergeometric functions, both in Tricomi's and Whittaker's form. This work is reviewed here, and organized along methodological lines.

Mathematical methods for mathematicians, physical scientists and engineers

CERN Document Server

Dunning-Davies, J

2003-01-01

This practical introduction encapsulates the entire content of teaching material for UK honours degree courses in mathematics, physics, chemistry and engineering, and is also appropriate for post-graduate study. It imparts the necessary mathematics for use of the techniques, with subject-related worked examples throughout. The text is supported by challenging problem exercises (and answers) to test student comprehension. Index notation used in the text simplifies manipulations in the sections on vectors and tensors. Partial differential equations are discussed, and special functions introduced

Dissemination of 3D Visualizations of Complex Function Data for the NIST Digital Library of Mathematical Functions

Directory of Open Access Journals (Sweden)

Qiming Wang

2007-03-01

Full Text Available The National Institute of Standards and Technology (NIST is developing a digital library to replace the widely used National Bureau of Standards Handbook of Mathematical Functions published in 1964. The NIST Digital Library of Mathematical Functions (DLMF will include formulas, methods of computation, references, and links to software for over forty functions. It will be published both in hardcopy format and as a website featuring interactive navigation, a mathematical equation search, 2D graphics, and dynamic interactive 3D visualizations. This paper focuses on the development and accessibility of the 3D visualizations for the digital library. We examine the techniques needed to produce accurate computations of function data, and through a careful evaluation of several prototypes, we address the advantages and disadvantages of using various technologies, including the Virtual Reality Modeling Language (VRML, interactive embedded graphics, and video capture to render and disseminate the visualizations in an environment accessible to users on various platforms.

International Conference on Recent Trends in Mathematical Analysis and its Applications 2014

CERN Document Server

Mohapatra, R; Singh, Uaday; Srivastava, H

2015-01-01

This book discusses recent developments in and the latest research on mathematics, statistics and their applications. All contributing authors are eminent academics, scientists, researchers and scholars in their respective fields, hailing from around the world. The book presents roughly 60 unpublished, high-quality and peer-reviewed research papers that cover a broad range of areas including approximation theory, harmonic analysis, operator theory, fixed-point theory, functional differential equations, dynamical and control systems, complex analysis, special functions, function spaces, summability theory, Fourier and wavelet analysis, and numerical analysis – all of which are topics of great interest to the research community – while further papers highlight important applications of mathematical analysis in science, engineering and related areas. This conference aims at bringing together experts and young researchers in mathematics from all over the world to discuss the latest advances in mathematical an...

Phonological Storage and Executive Function Deficits in Children with Mathematics Difficulties

Science.gov (United States)

Peng, Peng; Congying, Sun; Beilei, Li; Sha, Tao

2012-01-01

Children with mathematics difficulties suffer from working memory deficits. This study investigated the deficit profile of phonological storage and executive functions in working memory among children with mathematics difficulties. Based on multiple instruments and two assessment points, 68 children were screened out of 805 fifth graders. Of these…

Students with ‘Special Rights' for mathematics education

DEFF Research Database (Denmark)

Lindenskov, Lena; Gervasoni, Ann

2011-01-01

The issues of equity and quality have been central to international debates on mathematics in research, policy, curriculum and teaching. This book covers a wide variety of topics in the research and practice of mathematics education, demonstrating how equity and quality are inherently political...... equity and quality within various educational contexts and with a variety of marginalized populations. Written by teachers, researchers and academics from all over the world, this book represents a powerful response to the international call for quality education of all students in mathematics around...... terms whose political bedrock is obscured by them being taken for granted. Mapping Equity and Quality in Mathematics Education is broken into four parts. Section 1 addresses the constructs of equity and quality from a variety of theoretical perspectives and outlines new directions to approach...

Functions in Contemporary Secondary Mathematics Textbook Series in the United States

Science.gov (United States)

Ross, Daniel J.

2011-01-01

Textbooks play a central role in US mathematics classrooms (Stein, Remillard, & Smith, 2007) and functions are a key topic in secondary mathematics (Carlson, Jacobs, Coe, Larsen, & Hsu, 2002). This study presents results from an analysis of this essential topic in the latest editions of three textbook series: the Glencoe Mathematics…

Students' Conceptions of Function Transformation in a Dynamic Mathematical Environment

Science.gov (United States)

Daher, Wajeeh; Anabousy, Ahlam

2015-01-01

The study of function transformations helps students understand the function concept which is a basic and main concept in mathematics, but this study is problematic to school students as well as college students, especially when transformations are performed on non-basic functions. The current research tried to facilitate grade 9 students'…

Developing mathematics learning set for special-needs junior high school student oriented to learning interest and achievement

Directory of Open Access Journals (Sweden)

Ai Sadidah

2016-11-01

Full Text Available This study aims to produce a mathematics learning set for special-needs students (mathematical learning disability and mathematically gifted of Junior High School Grade VIII Second Semester oriented to learning interests and achievement which is valid, practical, and effective. This study was a research and development study using the Four-D development model consisting of four stages: (1 define, (2 design, (3 develop, and (4 disseminate. The quality of learning set consisting of the following three criterions: (1 validity, (2 practicality, and (3 effectiveness.  The data analysis technique used in this study is a descriptive quantitative analysis. The research produced learning set consisting of lesson plans and student worksheets. The result of the research shows that: (1 the learning set fulfill the valid criteria base on experts’ appraisal; (2 the learning set fulfill the practical criterion base on teacher’s and students’ questionnaire, and observation of learning implementation; (3 the learning set fulfill the effectiveness criterion base on learning interest and achievement.

INFORMATIONAL-METHODICAL SUPPORT OF THE COURSE «MATHEMATICAL LOGIC AND THEORY OF ALGORITHMS»

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Y. I. Sinko

2010-06-01

Full Text Available In this article the basic principles of training technique of future teachers of mathematics to foundations of mathematical logic and theory of algorithms in the Kherson State University with the use of information technologies are examined. General description of functioning of the methodical system of learning of mathematical logic with the use of information technologies, in that variant, when information technologies are presented by the integrated specialized programmatic environment of the educational purpose «MatLog» is given.

Mathematical Formalization Of Theories Of Motivation Proposed By Abraham Maslow And Frederick Herzberg

OpenAIRE

Ivan Kotliarov

2008-01-01

the present article gives an outline of a mathematical model of theories of motivation proposed by Abraham Maslow and Frederick Herzberg. This model is built on a basis of special non-continuous functions.

Orthogonal rational functions on the unit circle: from the scalar to the matrix case.

NARCIS (Netherlands)

Bultheel, A.; Gonzalez-Vera, P.; Hendriksen, E.; Njastad, O.

2006-01-01

Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? In the twentieth century the emphasis was on special functions satisfying linear differential equations,

Algebraic special functions and SO(3,2)

International Nuclear Information System (INIS)

Celeghini, E.; Olmo, M.A. del

2013-01-01

A ladder structure of operators is presented for the associated Legendre polynomials and the sphericas harmonics. In both cases these operators belong to the irreducible representation of the Lie algebra so(3,2) with quadratic Casimir equals to −5/4. As both are also bases of square-integrable functions, the universal enveloping algebra of so(3,2) is thus shown to be homomorphic to the space of linear operators acting on the L 2 functions defined on (−1,1)×Z and on the sphere S 2 , respectively. The presence of a ladder structure is suggested to be the general condition to obtain a Lie algebra representation defining in this way the “algebraic special functions” that are proposed to be the connection between Lie algebras and square-integrable functions so that the space of linear operators on the L 2 functions is homomorphic to the universal enveloping algebra. The passage to the group, by means of the exponential map, shows that the associated Legendre polynomials and the spherical harmonics support the corresponding unitary irreducible representation of the group SO(3,2). -- Highlights: •The algebraic ladder structure is constructed for the associated Legendre polynomials (ALP). •ALP and spherical harmonics support a unitary irreducible SO(3,2)-representation. •A ladder structure is the condition to get a Lie group representation defining “algebraic special functions”. •The “algebraic special functions” connect Lie algebras and L 2 functions

A Comparison of Functional and Imperative Programming Techniques for Mathematical Software Development

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Scott Frame

2014-04-01

Full Text Available Functional programming has traditionally been considered elegant and powerful, but also somewhat impractical for ordinary computing. Proponents of functional programming claim that the evolution of functional languages makes their use feasible in many domains. In this work, a popular imperative language (C++ and the leading functional language (Haskell are compared in a math-intensive, real-world application using a variety of criteria: ease of implementation, efficiency, and readability. The programming tasks that were used as benchmarks involved mathematical transformations between local and global coordinate systems. Details regarding the application area and how language features of both languages were used to solve critical problems are described. The paper closes with some conclusions regarding applicability of functional programming for mathematical applications.

An analysis of teacher’s preparation in implementing 2013 revision edition curriculum on mathematics specialization learning

Science.gov (United States)

Susilo, T.; Suryawan, A.

2018-05-01

This study aimed to determine the pedagogical competence of teachers, the readiness of planning and implementation of learning related to the implementation 2013 revised edition curriculum on mathematics specialization learning for senior high schools Wonogiri. Informants in this study there are 6 high school mathematics teachers X and XI class who teach in the school district Wonogiri. Data were collected using questionnaire method, interview, observation and documentation. Qualitative data analysis is done interactively through 4 paths: data collection, data reduction, data display, drawing conclusion. The results showed that high school mathematics teacher class X and XI in school district of Wonogiri City. The results show that most high school mathematics teachers in grade X and XI are ready to implement the 2013 revised edition curriculum and a few have not been able to implement due to internal or external factors. High school math teachers at Wonogiri district who are ready to face the 2013 revised edition curriculum have applied 10 teacher pedagogic competency indicators according to Regulation of the national education ministry Number 16 Year 2007 in learning. The readiness and implementation of mathematics learning is in line with the demands of the 2013 revised edition curriculum. Based on the teachers who are not ready, data on issues that arise in the implementation of the 2013 revised edition curriculum. Especially the problems in learning, namely mismatch of Core Competence (KI) and Basic Competence (KD) in teacher manual, material disregard in student handbook and lack of examples of problems that exist in teacher manual.

Contributions of executive function and spatial skills to preschool mathematics achievement.

Science.gov (United States)

Verdine, Brian N; Irwin, Casey M; Golinkoff, Roberta Michnick; Hirsh-Pasek, Kathryn

2014-10-01

Early mathematics achievement is highly predictive of later mathematics performance. Here we investigated the influence of executive function (EF) and spatial skills, two generalizable skills often overlooked in mathematics curricula, on mathematics performance in preschoolers. Children (N=44) of varying socioeconomic status (SES) levels were assessed at 3 years of age on a new assessment of spatial skill (Test of Spatial Assembly, TOSA) and a vocabulary measure (Peabody Picture Vocabulary Test, PPVT). The same children were tested at 4 years of age on the Beery Test of Visual-Motor Integration (VMI) as well as on measures of EF and mathematics. The TOSA was created specifically as an assessment for 3-year-olds, allowing the investigation of links among spatial, EF, and mathematical skills earlier than previously possible. Results of a hierarchical regression indicate that EF and spatial skills predict 70% of the variance in mathematics performance without an explicit math test, EF is an important predictor of math performance as prior research suggested, and spatial skills uniquely predict 27% of the variance in mathematics skills. Additional research is needed to understand whether EF is truly malleable and whether EF and spatial skills may be leveraged to support early mathematics skills, especially for lower SES children who are already falling behind in these skill areas by 3 and 4 years of age. These findings indicate that both skills are part of an important foundation for mathematics performance and may represent pathways for improving school readiness for mathematics. Copyright © 2014 Elsevier Inc. All rights reserved.

Working Memory Training and the Effect on Mathematical Achievement in Children with Attention Deficits and Special Needs

Science.gov (United States)

Dahlin, Karin I. E.

2013-01-01

Working Memory (WM) has a central role in learning. It is suggested to be malleable and is considered necessary for several aspects of mathematical functioning. This study investigated whether work with an interactive computerised working memory training programme at school could affect the mathematical performance of young children. Fifty-seven…

Special relativity

International Nuclear Information System (INIS)

Taylor, J.G.

1975-01-01

It is stated that the early chapters review special relativity from an elementary mathematical viewpoint, and include discussion of recent experiments which set out to test Einstein's predictions. The theory of relativity is then reformulated in more sophisticated mathematical language to show its relation to electro-magnetism, and to lay the foundation for more general viewpoints. The final chapter discusses in simple terms where activity in the field is currently centred, and where future interest lies. Chapter headings include: the constant speed of light; measuring time and distance; the Lorentz transformation (relativity of simultaneity, space-time and causality); relativistic kinematics (including - the Dopper effect); relativistic dynamics (including - nuclear binding energy, particle creation, electrodynamics); the structure of special relativity (including - the Lorentz group, the rotation group, elementary particle scattering); extensions of special relativity. (U.K.)

Mathematical model for research and analyze relations and functions between enterprises, members of cluster

Science.gov (United States)

Angelov, Kiril; Kaynakchieva, Vesela

2017-12-01

The aim of the current study is to research and analyze Mathematical model for research and analyze of relations and functions between enterprises, members of cluster, and its approbation in given cluster. Subject of the study are theoretical mechanisms for the definition of mathematical models for research and analyze of relations and functions between enterprises, members of cluster. Object of the study are production enterprises, members of cluster. Results of this study show that described theoretical mathematical model is applicable for research and analyze of functions and relations between enterprises, members of cluster from different industrial sectors. This circumstance creates alternatives for election of cluster, where is experimented this model for interaction improvement between enterprises, members of cluster.

Exp-function method for solving Maccari's system

International Nuclear Information System (INIS)

Zhang Sheng

2007-01-01

In this Letter, the Exp-function method is used to seek exact solutions of Maccari's system. As a result, single and combined generalized solitonary solutions are obtained, from which some known solutions obtained by extended sine-Gordon equation method and improved hyperbolic function method are recovered as special cases. It is shown that the Exp-function method provides a very effective and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics

MATHEMATICS LANGUAGE IN-CLASS INSTRUCTION

Directory of Open Access Journals (Sweden)

Jasmina KARIKJ

2010-11-01

Full Text Available The goal of the research was to compare the level of mathematic language acquisition between students of lower grades in special elementary schools for children who are hearing impaired and students of a mainstream elementary school. A total of 239 children attending mainstream and special schools in the territory of Serbia were included in the research. Instruction of mathematics in schools for students who are hearing impaired has a different character as it contains elements of native language instruction. Obtained results show a significant difference in some fields. A conclusion stating that the level of language acquisition is in direct correlation with the level of acquisition of mathematics language imposes itself. What that means is that hearing impaired children have not only to comprehend mathematics relations, but also to learn mathematics terms in a completely different way as compared to children who are hearing.

Contributions of Motivation, Early Numeracy Skills, and Executive Functioning to Mathematical Performance. A Longitudinal Study.

Science.gov (United States)

Mercader, Jessica; Miranda, Ana; Presentación, M Jesús; Siegenthaler, Rebeca; Rosel, Jesús F

2017-01-01

The main goal of this longitudinal study is to examine the power of different variables and its dynamic interactions in predicting mathematical performance. The model proposed in this study includes indicators of motivational constructs (learning motivation and attributions), executive functioning (inhibition and working memory), and early numeracy skills (logical operations, counting, and magnitude comparison abilities), assessed during kindergarten, and mathematical performance in the second year of Primary Education. The sample consisted of 180 subjects assessed in two moments (5-6 and 7-8 years old). The results showed an indirect effect of initial motivation on later mathematical performance. Executive functioning and early numeracy skills mediated the effect of motivation on later mathematic achievement. Practical implications of these findings for mathematics education are discussed.

Heat kernels and zeta functions on fractals

International Nuclear Information System (INIS)

Dunne, Gerald V

2012-01-01

On fractals, spectral functions such as heat kernels and zeta functions exhibit novel features, very different from their behaviour on regular smooth manifolds, and these can have important physical consequences for both classical and quantum physics in systems having fractal properties. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (paper)

Mathematics Teaching and Inclusion

DEFF Research Database (Denmark)

This volume contains the proceedings of the 3rd Nordic Research Conference on Special Needs Education in Mathematics, which took place in Rebild organised by Aalborg University in November 23-25, 2005. The theme of the conference was Mathematics Education and Inclusion. The conference theme...

Do preschool special education services make a difference in kindergarten reading and mathematics skills?: A propensity score weighting analysis.

Science.gov (United States)

Sullivan, Amanda L; Field, Samuel

2013-04-01

The purpose of this study was to examine the average treatment effect of preschool special education services on children's kindergarten academic skills. Using data from a nationally representative sample of United States children who participated in the Early Childhood Longitudinal Study-Birth Cohort, we examined the effectiveness of preschool special education services by comparing reading and math outcomes for children who received special education services at preschool-age to a propensity-score-weighted sample of children who did not receive these services. Results indicated that the receipt of these special education services had a statistically significant moderate negative effect on children's kindergarten skills in both reading (d=-0.21) and mathematics (d=-0.29). These findings have implications for the implementation and evaluation of services for young children experiencing developmental delays or disabilities. Copyright © 2012 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.

Mathematical Modeling and Pure Mathematics

Science.gov (United States)

Usiskin, Zalman

2015-01-01

Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

Contributions of Motivation, Early Numeracy Skills, and Executive Functioning to Mathematical Performance. A Longitudinal Study

Directory of Open Access Journals (Sweden)

Jessica Mercader

2018-01-01

Full Text Available The main goal of this longitudinal study is to examine the power of different variables and its dynamic interactions in predicting mathematical performance. The model proposed in this study includes indicators of motivational constructs (learning motivation and attributions, executive functioning (inhibition and working memory, and early numeracy skills (logical operations, counting, and magnitude comparison abilities, assessed during kindergarten, and mathematical performance in the second year of Primary Education. The sample consisted of 180 subjects assessed in two moments (5–6 and 7–8 years old. The results showed an indirect effect of initial motivation on later mathematical performance. Executive functioning and early numeracy skills mediated the effect of motivation on later mathematic achievement. Practical implications of these findings for mathematics education are discussed.

Undergraduate Mathematics Students' Understanding of the Concept of Function

Science.gov (United States)

Bardini, Caroline; Pierce, Robyn; Vincent, Jill; King, Deborah

2014-01-01

Concern has been expressed that many commencing undergraduate mathematics students have mastered skills without conceptual understanding. A pilot study carried out at a leading Australian university indicates that a significant number of students, with high tertiary entrance ranks, have very limited understanding of the concept of function,…

Mathematics

CERN Document Server

Stein, Sherman K

2010-01-01

Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi

Biomedical Mathematics, Unit VII: Exponential and Logarithmic Functions. Student Text. Revised Version, 1977.

Science.gov (United States)

Biomedical Interdisciplinary Curriculum Project, Berkeley, CA.

This collection of lessons, exercises, and experiments deals with exponential and logarithmic mathematical functions in the context of biomedical situations. Typical units in this collection provide discussion of the biomedical problem or setting, discussion of the mathematical concept, several example problems and solutions, and a set of problems…

Developing Students’ Reflections about the Function and Status of Mathematical Modeling in Different Scientific Practices

DEFF Research Database (Denmark)

Kjeldsen, Tinne Hoff; Blomhøj, Morten

2013-01-01

position held by the modeler(s) and the practitioners in the extra-mathematical domain. For students to experience the significance of different scientific practices and cultures for the function and status of mathematical modeling in other sciences, students need to be placed in didactical situations......Mathematical models and mathematical modeling play different roles in the different areas and problems in which they are used. The function and status of mathematical modeling and models in the different areas depend on the scientific practice as well as the underlying philosophical and theoretical...... where such differences are exposed and made into explicit objects of their reflections. It can be difficult to create such situations in the teaching of contemporary science in which modeling is part of the culture. In this paper we show how history can serve as a means for students to be engaged...

The specialization of function: cognitive and neural perspectives.

Science.gov (United States)

Mahon, Bradford Z; Cantlon, Jessica F

2011-05-01

A unifying theme that cuts across all research areas and techniques in the cognitive and brain sciences is whether there is specialization of function at levels of processing that are "abstracted away" from sensory inputs and motor outputs. Any theory that articulates claims about specialization of function in the mind/brain confronts the following types of interrelated questions, each of which carries with it certain theoretical commitments. What methods are appropriate for decomposing complex cognitive and neural processes into their constituent parts? How do cognitive processes map onto neural processes, and at what resolution are they related? What types of conclusions can be drawn about the structure of mind from dissociations observed at the neural level, and vice versa? The contributions that form this Special Issue of Cognitive Neuropsychology represent recent reflections on these and other issues from leading researchers in different areas of the cognitive and brain sciences.

Functional specialization of ramets in a clonal plant network functional specialization of ramets in a clonal plant network

NARCIS (Netherlands)

Ikegami, M.

2004-01-01

Functional specialization of ramets and co-operation between interconnected ramets in heterogeneous environments are studied in this thesis. Since clonal plants can spread horizontally by vegetative growth, a genet has the potential to grow across a heterogeneous environment. Therefore, ramets can

Mathematics without boundaries surveys in pure mathematics

CERN Document Server

Pardalos, Panos

2014-01-01

The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the  latest information.

Teaching Mathematical Functions Using Geometric Functions Approach and Its Effect on Ninth Grade Students' Motivation

Science.gov (United States)

Akçakin, Veysel

2018-01-01

The purpose of this study is to investigate the effects of using geometric functions approach on 9th grade students' motivation levels toward mathematics in functions unit. Participants of this study were 87 students who were ongoing in the first year of high school in Turkey. In this research, pretest and posttest control group quasiexperimental…

Using an Augmented Reality Enhanced Tabletop System to Promote Learning of Mathematics: A Case Study with Students with Special Educational Needs

Science.gov (United States)

Cascales-Martínez, Antonia; Martínez-Segura, María-José; Pérez-López, David; Contero, Manuel

2017-01-01

The main objective of this research is to determine the feasibility of using a multi touch tabletop system for applied mathematics learning in primary education with students with special needs (SEN). The instructional content designed on the tabletop focuses on understanding and managing money, coins, and banknotes. The study also analyzes the…

Trickle down Mathematics: Adult Pre-Service Elementary Teachers Gain Confidence in Mathematics--Enough to Pass It Along?

Science.gov (United States)

Ashun, Mary Apea; Reinink, John

2009-01-01

Much research (Ma, 1999; Cohen & Leung, 2004; English, 2003) has been done on mathematics education and pre-service teachers with special emphasis on how the mathematics is taught and the psychology of the pre-service teachers. While there is concern among North American mathematicians that mathematics instruction in K-12 grades needs to be…

Interactions between Mathematics and Physics: The History of the Concept of Function--Teaching with and about Nature of Mathematics

Science.gov (United States)

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-01-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another…

Mathematical modeling and visualization of functional neuroimages

DEFF Research Database (Denmark)

Rasmussen, Peter Mondrup

This dissertation presents research results regarding mathematical modeling in the context of the analysis of functional neuroimages. Specifically, the research focuses on pattern-based analysis methods that recently have become popular analysis tools within the neuroimaging community. Such methods...... neuroimaging data sets are characterized by relatively few data observations in a high dimensional space. The process of building models in such data sets often requires strong regularization. Often, the degree of model regularization is chosen in order to maximize prediction accuracy. We focus on the relative...... be carefully selected, so that the model and its visualization enhance our ability to interpret brain function. The second part concerns interpretation of nonlinear models and procedures for extraction of ‘brain maps’ from nonlinear kernel models. We assess the performance of the sensitivity map as means...

Mathematics Interventions for Students with High Functioning Autism/Asperger's Syndrome

Science.gov (United States)

Donaldson, Jeffrey B.; Zager, Dianne

2010-01-01

Teachers are often at a loss when considering how to address mathematics difficulties for students with high functioning autism/Asperger's syndrome (HFA/AS). Students may show difficulty remembering operations throughout an equation, organizing information on the page, and comprehending the language in instructions of word problems. These…

Intelligent mathematics II applied mathematics and approximation theory

CERN Document Server

Duman, Oktay

2016-01-01

This special volume is a collection of outstanding more applied articles presented in AMAT 2015 held in Ankara, May 28-31, 2015, at TOBB Economics and Technology University. The collection is suitable for Applied and Computational Mathematics and Engineering practitioners, also for related graduate students and researchers. Furthermore it will be a useful resource for all science and engineering libraries. This book includes 29 self-contained and well-edited chapters that can be among others useful for seminars in applied and computational mathematics, as well as in engineering.

Evaluation of integrals with hypergeometric and logarithmic functions

Directory of Open Access Journals (Sweden)

Sofo Anthony

2018-02-01

Full Text Available We provide an explicit analytical representation for a number of logarithmic integrals in terms of the Lerch transcendent function and other special functions. The integrals in question will be associated with both alternating harmonic numbers and harmonic numbers with positive terms. A few examples of integrals will be given an identity in terms of some special functions including the Riemann zeta function. In general none of these integrals can be solved by any currently available mathematical package.

Unitary symmetry, combinatorics, and special functions

Energy Technology Data Exchange (ETDEWEB)

Louck, J.D.

1996-12-31

From 1967 to 1994, Larry Biedenham and I collaborated on 35 papers on various aspects of the general unitary group, especially its unitary irreducible representations and Wigner-Clebsch-Gordan coefficients. In our studies to unveil comprehensible structures in this subject, we discovered several nice results in special functions and combinatorics. The more important of these will be presented and their present status reviewed.

Mathematical operations in cytogenetic dosimetry: Dosgen

International Nuclear Information System (INIS)

Garcia L, O.; Zequera J, T.

1996-01-01

Handling of formulas and mathematical procedures for fitting and using of dose-response relationships in cytogenetic dosimetry is often difficulted by the absence of collaborators specialized in mathematics and computation. DOSGEN program contains the main mathematical operations which are used in cytogenetic dosimetry. It is able to run in IBM compatible Pc's by non-specialized personnel.The program possibilities are: Poisson distribution fitting test for the number of aberration per cell, dose assessment for whole body irradiation, dose assessment for partial irradiation and determination of irradiated fraction. The program allows on screen visualization and printing of results. DOSGEN has been developed in turbo pascal and is 33Kb of size. (authors). 4 refs

Equations of mathematical physics

CERN Document Server

Tikhonov, A N

2011-01-01

Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri

Foundations of mathematics and literacy: The role of executive functioning components.

Science.gov (United States)

Purpura, David J; Schmitt, Sara A; Ganley, Colleen M

2017-01-01

The current study investigated the relations between the three cognitive processes that comprise executive functioning (EF)-response inhibition, working memory, and cognitive flexibility-and individual components of mathematics and literacy skills in preschool children. Participants were 125 preschool children ranging in age from 3.12 to 5.26years (M=4.17years, SD=0.58). Approximately 53.2% were female, and the sample was predominantly Caucasian (69.8%). Results suggest that the components of EF may be differentially related to the specific components of early mathematics and literacy. For mathematics, response inhibition was broadly related to most components. Working memory was related to more advanced mathematics skills that involve comparison or combination of numbers and quantities. Cognitive flexibility was related to more conceptual or abstract mathematics skills. For early literacy, response inhibition and cognitive flexibility were related to print knowledge, and working memory was related only to phonological awareness. None of the EF components was related to vocabulary. These findings provide initial evidence for better understanding the ways in which EF components and academic skills are related and measured. Furthermore, the findings provide a foundation for further study of the components of each domain using a broader and more diverse array of measures. Copyright © 2016 Elsevier Inc. All rights reserved.

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences; Search. Search. Proceedings – Mathematical Sciences. Title. Author. Keywords. Fulltext. Submit. Proceedings – Mathematical Sciences. Current Issue : Vol. 128, Issue 2. Current Issue Volume 128 | Issue 2. April 2018. Home · Volumes & Issues · Special Issues ...

Evidence of the Need to Prepare Prospective Teachers to Engage in Mathematics Consultations

Science.gov (United States)

van Ingen, Sarah; Eskelson, Samuel L.; Allsopp, David

2016-01-01

The mathematics consultation represents a powerful opportunity for mathematics teachers to leverage the knowledge base of special education professionals to advance equity for students with special education needs. Yet, most teacher preparation programs do not specifically prepare prospective teachers to engage in mathematics-specific…

Mathematics and culture II visual perfection : mathematics and creativity

CERN Document Server

Emmer, Michele

2005-01-01

This volume stresses the strong links between mathematics, culture and creativity in architecture, contemporary art, geometry, computer graphics, literature, theatre and cinema. It is designed not only for mathematicians but for anyone interested in culture, with a special emphasis on the visual aspects.

Developing Mathematical Knowledge for Teaching in a Methods Course: The Case of Function

Science.gov (United States)

Steele, Michael D.; Hillen, Amy F.; Smith, Margaret S.

2013-01-01

This study describes teacher learning in a teaching experiment consisting of a content-focused methods course involving the mathematical knowledge for teaching function. Prospective and practicing teachers in the course showed growth in their ability to define function, to provide examples of functions and link them to the definition, in the…

Benchmarks of programming languages for special purposes in the space station

Science.gov (United States)

Knoebel, Arthur

1986-01-01

Although Ada is likely to be chosen as the principal programming language for the Space Station, certain needs, such as expert systems and robotics, may be better developed in special languages. The languages, LISP and Prolog, are studied and some benchmarks derived. The mathematical foundations for these languages are reviewed. Likely areas of the space station are sought out where automation and robotics might be applicable. Benchmarks are designed which are functional, mathematical, relational, and expert in nature. The coding will depend on the particular versions of the languages which become available for testing.

Mathematical formalization of theories of motivation proposed by Maslow and Herzberg

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Ivan Kotliarov

2008-12-01

Full Text Available Maslow's theory is by far the most known theory of motivation, and the most common in the business and management practice. Herzberg's theory fits the observations and explains some aspects of human motivation left unexplained by Maslow. However, these theories have never been formalized on a strictly mathematical basis. The present article gives an outline of a mathematical model of theories of motivation proposed by Abraham Maslow and Frederick Herzberg. This model is built on a basis of special non-continuous functions. This description may be a good basis for HR software and may be useful for business and management.

The Mathematics of Knots

CERN Document Server

Banagl, Markus

2011-01-01

The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested

Series of Bessel and Kummer-type functions

CERN Document Server

Baricz, Arpad; Pogány, Tibor K

2017-01-01

This book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schlömilch, Dini and Fourier series of Bessel and other special functions, such as Struve and von Lommel functions. The aim is also to find the coefficients of the Neumann and Kapteyn series, as well as closed-form expressions and summation formulas for the series of Bessel functions considered. Some integral representations are deduced using techniques from the theory of differential equations. The text is aimed at a mathematical audience, including graduate students and those in the scientific community who are interested in a new perspective on Fourier–Bessel series, and their manifold and polyvalent applications, mainly in general classical analysis, applied mathematics and mathematical physics.

Sociocultural context as a facilitator of student learning of function concepts in mathematics

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Evangelina Díaz Obando

2016-03-01

Full Text Available In Costa Rica, many secondary students have serious difficulties to establish relationships between mathematics and real-life contexts. They question the utilitarian role of the school mathematics. This fact motivated the research object of this report which evidences the need to overcome methodologies unrelated to students’ reality, toward new didactical options that help students to value mathematics, reasoning and its  applications, connecting it with their socio-cultural context. The research used a case study as a qualitative methodology and the social constructivism as an educational paradigm in which the knowledge is built by the student; as a product of his social interactions. A collection of learning situations was designed, validated, and implemented. It allowed establishing relationships between mathematical concepts and the socio-cultural context of participants. It analyzed the impact of students’socio-cultural context in their mathematics learning of basic concepts of real variable functions, consistent with the Ministry of Education (MEP Official Program.  Among the results, it was found that using students’sociocultural context improved their motivational processes, mathematics sense making, and promoted cooperative social interactions. It was evidenced that contextualized learning situations favored concepts comprehension that allow students to see mathematics as a discipline closely related with their every-day life.

Mathematical handbook for scientists and engineers definitions, theorems, and formulas for reference and review

CERN Document Server

Korn, Granino A

2000-01-01

A reliable source of definitions, theorems, and formulas, this authoritative handbook provides convenient access to information from every area of mathematics. Coverage includes Fourier transforms, Z transforms, linear and nonlinear programming, calculus of variations, random-process theory, special functions, combinatorial analysis, numerical methods, game theory, and much more.

Some aspects of executive functions as predictors of understanding textual mathematical tasks in students with mild intellectual disability

Directory of Open Access Journals (Sweden)

Japundža-Milisavljević Mirjana

2016-01-01

Full Text Available The most significant segment during the process of solving mathematical tasks is translation from mathematical to native language, in the basis o which, among others, are the following factors: resistance to distraction and forming adequate verbal strategies. The goal of this research is to evaluate the contribution of some aspects of executive functions in explaining the variance of solving illustrative mathematical tasks in students with mild intellectual disability. The sample consists of 90 students with mild intellectual disability aged from 12 to 16 (M=14.7; SD=1.6, of both sexes (44.4% boys and 55.6% girls. The Twenty questions test and the Stroop test were used to estimate the executive functions. Verbal problem tasks were used for the purpose of understanding mathematical language The obtained results show that the estimated aspects of executive functions are significant predictors of understanding mathematical language in students with intellectual disabilities. The strongest predictor is distraction resistance (p=0.01.

[Survival functions and life tables at the origins of actuarial mathematics].

Science.gov (United States)

Spelta, D

1997-01-01

"In the determination of death probabilities of an insured subject one can use either statistical data or a mathematical function. In this paper a survey of the relationship between mortality tables and survival functions from the origins until the first half of the nineteenth century is presented. The author has tried to find the methodological grounds which have induced the actuaries to prefer either of these tools." (EXCERPT)

The learning evaluations of the concept function in the mathematical subject I

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Wilmer Valle Castañeda

2018-03-01

Full Text Available The evaluation must be one of the most complex tasks that teachers face today, both for the process itself and for having to issue an assessment about the achievements and deficiencies of the students. It is for them that techniques and instruments were developed, which allow the evaluation of the function concept in the Mathematics I subject´s. Methods of the theoretical level, of the empirical level such as the historical-logical analysis, the surveys, were used in the research carried out. The documentary analyses, as well as procedures such as the analysis - synthesis that made it possible to investigate the theoretical and practical fundament´s learning evaluation´s. The evaluation instruments presented allowed for the evaluation of the students in Mathematics I, less than one of the most important functions of the evaluation: the formative or educational function. These constituted a reference for the continuous improvement of student learning.

Lectures on constructive mathematical analysis

CERN Document Server

Kushner, B A

1984-01-01

The basis of this book was a special course given by the author at the Mechanics-Mathematics Faculty of Moscow University. The material presumes almost no previous knowledge and is completely understandable to a reader who is in command of a standard course of mathematical analysis. There are an extensive bibliography and indexes which will be helpful to students.

A mathematical model of functioning of channels of distribution of freight traffic

OpenAIRE

Shramenko, N.

2006-01-01

The mathematical model of functioning of channels of distribution of freight traffics is developed at international transportations which allows to optimize technological parameters of separate parts and to minimize expenses along the logistical chain.

ASSESSING CONCEPTUAL UNDERSTANDING IN MATHEMATICS: Using Derivative Function to Solve Connected Problems

Directory of Open Access Journals (Sweden)

Nevin ORHUN

2013-07-01

Full Text Available Open and distance education plays an important role in the actualization of cultural goals as well as in societal developments. This is an independent teaching and learning method for mathematics which forms the dynamic of scientific thinking. Distance education is an important alternative to traditional teaching applications. These contributions brought by technology enable students to participate actively in having access to information and questioning it. Such an application increases students’ motivation and teaches how mathematics can be used in daily life. Derivative is a mathematical concept which can be used in many areas of daily life. The aim of this study is to enable the concept of derivatives to be understood well by using the derivative function in the solution of various problems. It also aims at interpreting difficulties theoretically in the solution of problems and determining mistakes in terms of teaching methods. In this study, how various aspects of derivatives are understood is emphasized. These aspects concern the explanation of concepts and process, and also their application to certain concepts in physics. Students’ depth of understanding of derivatives was analyzed based on two aspects of understanding; theoretical analysis and contextual application. Follow-up interviews were conducted with five students. The results show that the students preferred to apply an algebraic symbolic aspect instead of using logical meanings of function and its derivative. In addition, in relation to how the graph of the derivative function affects the aspect of function, it was determined that the students displayed low performance.

Applied Computational Mathematics in Social Sciences

CERN Document Server

Damaceanu, Romulus-Catalin

2010-01-01

Applied Computational Mathematics in Social Sciences adopts a modern scientific approach that combines knowledge from mathematical modeling with various aspects of social science. Special algorithms can be created to simulate an artificial society and a detailed analysis can subsequently be used to project social realities. This Ebook specifically deals with computations using the NetLogo platform, and is intended for researchers interested in advanced human geography and mathematical modeling studies.

Mathematical methods in systems biology.

Science.gov (United States)

Kashdan, Eugene; Duncan, Dominique; Parnell, Andrew; Schattler, Heinz

2016-12-01

The editors of this Special Issue of Mathematical Biosciences and Engineering were the organizers for the Third International Workshop "Mathematical Methods in System Biology" that took place on June 15-18, 2015 at the University College Dublin in Ireland. As stated in the workshop goals, we managed to attract a good mix of mathematicians and statisticians working on biological and medical applications with biologists and clinicians interested in presenting their challenging problems and looking to find mathematical and statistical tools for their solutions.

Comprehensive basic mathematics

CERN Document Server

Veena, GR

2005-01-01

Salient Features As per II PUC Basic Mathematics syllabus of Karnataka. Provides an introduction to various basic mathematical techniques and the situations where these could be usefully employed. The language is simple and the material is self-explanatory with a large number of illustrations. Assists the reader in gaining proficiency to solve diverse variety of problems. A special capsule containing a gist and list of formulae titled ''REMEMBER! Additional chapterwise arranged question bank and 3 model papers in a separate section---''EXAMINATION CORNER''.

Mathematics computer-based training tool for pupils with special educational needs

OpenAIRE

Čeponienė, Lina

2010-01-01

Mathematics has a great influence on the development of world science and education, technology and human culture. Ukeje observes that without mathematics there is no science, without science there is no modern technology and without modern technology there is no modern society. In other words, mathematics is the precursor and the queen of science and technology and the indispensable single element in modern societal development. So, it plays a vital role in developing learners abilities to c...

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...

Practical mathematical optimization basic optimization theory and gradient-based algorithms

CERN Document Server

Snyman, Jan A

2018-01-01

This textbook presents a wide range of tools for a course in mathematical optimization for upper undergraduate and graduate students in mathematics, engineering, computer science, and other applied sciences. Basic optimization principles are presented with emphasis on gradient-based numerical optimization strategies and algorithms for solving both smooth and noisy discontinuous optimization problems. Attention is also paid to the difficulties of expense of function evaluations and the existence of multiple minima that often unnecessarily inhibit the use of gradient-based methods. This second edition addresses further advancements of gradient-only optimization strategies to handle discontinuities in objective functions. New chapters discuss the construction of surrogate models as well as new gradient-only solution strategies and numerical optimization using Python. A special Python module is electronically available (via springerlink) that makes the new algorithms featured in the text easily accessible and dir...

A practical guide to averaging functions

CERN Document Server

Beliakov, Gleb; Calvo Sánchez, Tomasa

2016-01-01

This book offers an easy-to-use and practice-oriented reference guide to mathematical averages. It presents different ways of aggregating input values given on a numerical scale, and of choosing and/or constructing aggregating functions for specific applications. Building on a previous monograph by Beliakov et al. published by Springer in 2007, it outlines new aggregation methods developed in the interim, with a special focus on the topic of averaging aggregation functions. It examines recent advances in the field, such as aggregation on lattices, penalty-based aggregation and weakly monotone averaging, and extends many of the already existing methods, such as: ordered weighted averaging (OWA), fuzzy integrals and mixture functions. A substantial mathematical background is not called for, as all the relevant mathematical notions are explained here and reported on together with a wealth of graphical illustrations of distinct families of aggregation functions. The authors mainly focus on practical applications ...

Zeta function methods and quantum fluctuations

International Nuclear Information System (INIS)

Elizalde, Emilio

2008-01-01

A review of some recent advances in zeta function techniques is given, in problems of pure mathematical nature but also as applied to the computation of quantum vacuum fluctuations in different field theories, and specially with a view to cosmological applications

Representation of mathematical expectation of symmetrical functionals in the particle transport theory

International Nuclear Information System (INIS)

Uchajkin, V.V.

1977-01-01

The two-dimensional functional is used to show that the mathematical expectation of symmetrical functionals may be represented as a nonlinear functional obtained from the solution of the Boltzman equations (Green's function). For the highest moments of additive detector readings, which are a particular case of symmetrical functionals, a similar result was obtained by the author previously when he studied particles transport with and without multiplication. In physical terms such a concept is conditioned by the absence of moving particles with one another, the assumption of which is the basis of the linear transport theory

Mathematics Reform Curricula and Special Education: Identifying Intersections and Implications for Practice

Science.gov (United States)

Sayeski, Kristin L.; Paulsen, Kim J.

2010-01-01

In many general education classrooms today, teachers are using "reform" mathematics curricula. These curricula emphasize the application of mathematics in real-life contexts and include such practices as collaborative, group problem solving and student-generated algorithms. Students with learning disabilities in the area of mathematics can…

Challenges and Opportunities in Teaching Mathematics

Science.gov (United States)

Goos, Merrilyn

2016-01-01

At the special conference celebrating the 50th anniversary of the Australian Association of Mathematics Teachers (AAMT), the author was asked to speak about the challenges and opportunities in teaching mathematics as a stimulus for discussion of AAMT's "future directions". With an open invitation to be a little provocative, the author…

Centrins in unicellular organisms: functional diversity and specialization.

Science.gov (United States)

Zhang, Yu; He, Cynthia Y

2012-07-01

Centrins (also known as caltractins) are conserved, EF hand-containing proteins ubiquitously found in eukaryotes. Similar to calmodulins, the calcium-binding EF hands in centrins fold into two structurally similar domains separated by an alpha-helical linker region, shaping like a dumbbell. The small size (15-22 kDa) and domain organization of centrins and their functional diversity/specialization make them an ideal system to study protein structure-function relationship. Here, we review the work on centrins with a focus on their structures and functions characterized in unicellular organisms.

Special issue on Computational Neuroscience - PREFACE

DEFF Research Database (Denmark)

Ditlevsen, Susanne; Lansky, Petr

2014-01-01

This Special Issue of Mathematical Biosciences and Engineering contains ten selected papers presented at the Neural Coding 2012 workshop. Neuroscience is traditionally very close to mathematics which stems from the famous theoretical work of McCulloch--Pitts and Hodgkin--Huxley in the middle...

Mathematical models in medicine: Diseases and epidemics

International Nuclear Information System (INIS)

Witten, M.

1987-01-01

This volume presents the numerous applications of mathematics in the life sciences and medicine, and demonstrates how mathematics and computers have taken root in these fields. The work covers a variety of techniques and applications including mathematical and modelling methodology, modelling/simulation technology, and philosophical issues in model formulation, leading to speciality medical modelling, artificial intelligence, psychiatric models, medical decision making, and molecular modelling

A Brief Historical Development of Classical Mathematics before the Renaissance

Science.gov (United States)

Debnath, Lokenath

2011-01-01

This article deals with a short history of mathematics and mathematical scientists during the ancient and medieval periods. Included are some major developments of the ancient, Indian, Arabic, Egyptian, Greek and medieval mathematics and their significant impact on the Renaissance mathematics. Special attention is given to many results, theorems,…

Mathematics Anxiety in Young Children: Concurrent and Longitudinal Associations with Mathematical Performance

Science.gov (United States)

Vukovic, Rose K.; Kieffer, Michael J.; Bailey, Sean P.; Harari, Rachel R.

2013-01-01

This study explored mathematics anxiety in a longitudinal sample of 113 children followed from second to third grade. We examined how mathematics anxiety related to different types of mathematical performance concurrently and longitudinally and whether the relations between mathematics anxiety and mathematical performance differed as a function of…

Brain State-dependent Functional Hemispheric Specialization in Men but not in Women

OpenAIRE

Mohr, Christine; Michel, Christoph M.; Lantz, Goran; Ortigue, Stephanie; Viaud-Delmon, Isabelle; Landis, Theodor

2017-01-01

Hemispheric specialization is reliably demonstrated in patients with unilateral lesions or disconnected hemispheres, but is inconsistent in healthy populations. The reason for this paradox is unclear. We propose that functional hemispheric specialization in healthy participants depends upon functional brain states at stimulus arrival (FBS). Brain activity was recorded from 123 surface electrodes while 22 participants (11 women) performed lateralized lexical decisions (left hemisphere processi...

Mathematical simulation of gamma-radiation angle distribution measurements

International Nuclear Information System (INIS)

Batij, V.G.; Batij, E.V.; Egorov, V.V.; Fedorchenko, D.V.; Kochnev, N.A.

2008-01-01

We developed mathematical model of the facility for gamma-radiation angle distribution measurement and calculated response functions for gamma-radiation intensities. We developed special software for experimental data processing, the 'Shelter' object radiation spectra unfolding and Sphere detector (ShD) angle resolution estimation. Neuronet method using for detection of the radiation directions is given. We developed software based on the neuronet algorithm, that allows obtaining reliable distribution of gamma-sources that make impact on the facility detectors at the measurement point. 10 refs.; 15 figs.; 4 tab

Mappings for Special Functions on Cantor Sets and Special Integral Transforms via Local Fractional Operators

Directory of Open Access Journals (Sweden)

Yang Zhao

2013-01-01

Full Text Available The mappings for some special functions on Cantor sets are investigated. Meanwhile, we apply the local fractional Fourier series, Fourier transforms, and Laplace transforms to solve three local fractional differential equations, and the corresponding nondifferentiable solutions were presented.

A review of mathematical functions for the analysis of growth in poultry

NARCIS (Netherlands)

Darmani Kuhi, H.; Porter, T.; Lopez, S.; Kebreab, E.; Strathe, A.B.; Dumas, A.; Dijkstra, J.; France, J.

2010-01-01

Poultry industries face various decisions in the production cycle that affect the profitability of an operation. Predictions of growth when the birds are ready for sale are important factors that contribute to the economy of poultry operations. Mathematical functions called ‘growth functions’ have

Working with Functions without Understanding: An Assessment of the Perceptions of Basotho College Mathematics Specialists on the Idea of Function

Science.gov (United States)

Polaki, Mokaeane Victor

2005-01-01

It is a well-known fact that the idea of function plays a unifying role in the development of mathematical concepts. Yet research has shown that many students do not understand it adequately even though they have experienced a great deal of success in performing a plethora of operations on function, and on using functions to solve various types of…

Mathematical problems in meteorological modelling

CERN Document Server

Csomós, Petra; Faragó, István; Horányi, András; Szépszó, Gabriella

2016-01-01

This book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives. The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting. The book arose from the workshop “Mathematical Problems in Meteorological Modelling” held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the de...

Mathematical foundations of thermodynamics

CERN Document Server

Giles, R; Stark, M; Ulam, S

2013-01-01

Mathematical Foundations of Thermodynamics details the core concepts of the mathematical principles employed in thermodynamics. The book discusses the topics in a way that physical meanings are assigned to the theoretical terms. The coverage of the text includes the mechanical systems and adiabatic processes; topological considerations; and equilibrium states and potentials. The book also covers Galilean thermodynamics; symmetry in thermodynamics; and special relativistic thermodynamics. The book will be of great interest to practitioners and researchers of disciplines that deal with thermodyn

Lectures in the history of mathematics

CERN Document Server

Bos, Henk J M

1993-01-01

"[These lectures] are about themes of the history of mathematics which, for various reasons, are dear to me. The early differential and integral calculus, the work of Christiaan Huygens, and the concept of construction in seventeenth- and eighteenth-century mathematics are the three themes around which much of my research has concentrated and which continue to fascinate me by the insights they offer in the development of that special human activity called mathematics." -from the Introduction This volume contains eleven lectures ranging over a variety of topics in the history of mathematics. The lectures, presented between 1970 and 1987, were delivered in a variety of venues and appeared only in less accessible publications. Those who teach mathematics, as well as mathematics historians, will appreciate this insightful, wide-ranging book.

Revisiting the reliability of published mathematical proofs: where do we go next?

Directory of Open Access Journals (Sweden)

Joachim Frans

2014-08-01

Full Text Available Mathematics seems to have a special status when compared to other areas of human knowledge. This special status is linked with the role of proof. Mathematicians all too often believe that this type of argumentation leaves no room for errors or unclarity. In this paper we take a closer look at mathematical practice, more precisely at the publication process in mathematics. We argue that the apparent view that mathematical literature is also more reliable is too naive. We will discuss several problems in the publication process that threaten this view, and give several suggestions on how this could be countered.

A mathematical function for the description of nutrient-response curve.

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Hamed Ahmadi

Full Text Available Several mathematical equations have been proposed to modeling nutrient-response curve for animal and human justified on the goodness of fit and/or on the biological mechanism. In this paper, a functional form of a generalized quantitative model based on Rayleigh distribution principle for description of nutrient-response phenomena is derived. The three parameters governing the curve a has biological interpretation, b may be used to calculate reliable estimates of nutrient response relationships, and c provide the basis for deriving relationships between nutrient and physiological responses. The new function was successfully applied to fit the nutritional data obtained from 6 experiments including a wide range of nutrients and responses. An evaluation and comparison were also done based simulated data sets to check the suitability of new model and four-parameter logistic model for describing nutrient responses. This study indicates the usefulness and wide applicability of the new introduced, simple and flexible model when applied as a quantitative approach to characterizing nutrient-response curve. This new mathematical way to describe nutritional-response data, with some useful biological interpretations, has potential to be used as an alternative approach in modeling nutritional responses curve to estimate nutrient efficiency and requirements.

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences. SENJO SHIMIZU. Articles written in Proceedings – Mathematical Sciences. Volume 127 Issue 5 November 2017 pp 815-831 Special Issue. Qualitative behaviour of incompressible two-phase flows with phase transitions: The isothermal case · JAN PRÜSS SENJO ...

Pedagogical content knowledge: Knowledge of pedagogy novice teachers in mathematics learning on limit algebraic function

Science.gov (United States)

Ma'rufi, Budayasa, I. Ketut; Juniati, Dwi

2017-02-01

Teacher is one of the key aspects of student's achievement. Teachers should master content material taught, how to teach it, and can interpret the students' thinking so that students easily understand the subject matter. This research was a qualitative research that aimed at describing profile of PCK's teachers in mathematics on limit algebraic functions in terms of the differences of teaching experience. Pedagogical Content Knowledge (PCK) and understanding of teachers is defined as involving the relationship between knowledge of teaching materials, how to transfer the subject matter, and the knowledge of students in mathematics on limit algebraic functions that the subject matter may be understood by students. The PCK components in this research were knowledge of subject matter, knowledge of pedagogy, and knowledge of students. Knowledge of pedagogy defines as knowledge and understanding of teachers about the planning and organization of the learning and teaching strategy of limit algebraic function. The subjects were two mathematics high school teachers who teach in class XI IPS. Data were collected through observation of learning during five meetings and interviews before and after the lesson continued with qualitative data analysis. Focus of this article was to describe novice teacher's knowledge of student in mathematics learning on limit algebraic function. Based on the results of the analysis of qualitative data the data concluded that novice teacher's knowledge of pedagogy in mathematics on limit algebraic function showed: 1) in teaching the definitions tend to identify prior knowledge of the student experience with the material to be studied, but not in the form of a problem, 2) in posing the questions tend to be monotonous non lead and dig, 3) in response to student questions preservice teachers do not take advantage of the characteristics or the potential of other students, 4) in addressing the problem of students, tend to use the drill approach and did

Mathematical omnibus thirty lectures on classic mathematics

CERN Document Server

Fuchs, Dmitry; Fuchs, Dmitry

2007-01-01

The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an accomplished artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.

International Conference on Quantum Mathematical Physics : a Bridge between Mathematics and Physics

CERN Document Server

Kleiner, Johannes; Röken, Christian; Tolksdorf, Jürgen

2016-01-01

Quantum physics has been highly successful for more than 90 years. Nevertheless, a rigorous construction of interacting quantum field theory is still missing. Moreover, it is still unclear how to combine quantum physics and general relativity in a unified physical theory. Attacking these challenging problems of contemporary physics requires highly advanced mathematical methods as well as radically new physical concepts. This book presents different physical ideas and mathematical approaches in this direction. It contains a carefully selected cross-section of lectures which took place in autumn 2014 at the sixth conference ``Quantum Mathematical Physics - A Bridge between Mathematics and Physics'' in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fu...

Features of projectile motion in the special theory of relativity

International Nuclear Information System (INIS)

Shahin, Ghassan Y

2006-01-01

A relativistic projectile motion in a vacuum is examined by means of elementary consequences of special relativity. Exact analytical expressions were found for the kinematics variables using basic mathematical tools. The trajectory equation was established and the area under the trajectory traversed by the relativistic projectile was determined. It was found that, unlike non-relativistic projectile motion, the launching angles that maximize both the horizontal range as well as the area under the trajectory are functions of the initial speed. It is anticipated that this paper will be consistent with the intuition of students and serve as a resource for further problems usually encountered in the special theory of relativity

Mathematics

CERN Document Server

Eringen, A Cemal

2013-01-01

Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th

Specialized functional diversity and interactions of the Na,K-ATPase

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Igor I. Krivoi

2016-05-01

Full Text Available Na,K-ATPase is a protein ubiquitously expressed in the plasma membrane of all animal cells and vitally essential for their functions. A specialized functional diversity of the Na,K-ATPase isozymes is provided by molecular heterogeneity, distinct subcellular localizations and functional interactions with molecular environment. Studies over the last decades clearly demonstrated complex and isoform-specific reciprocal functional interactions between the Na,K-ATPase and neighboring proteins and lipids. These interactions are enabled by a spatially restricted ion homeostasis, direct protein-protein/lipid interactions and protein kinase signaling pathways. In addition to its ‘classical’ function in ion translocation, the Na,K-ATPase is now considered as one of the most important signaling molecules in neuronal, epithelial, skeletal, cardiac and vascular tissues. Accordingly, the Na,K-ATPase forms specialized sub-cellular multimolecular microdomains which act as receptors to circulating endogenous cardiotonic steroids triggering a number of signaling pathways. Changes in these endogenous cardiotonic steroid levels and initiated signaling responses have significant adaptive values for tissues and whole organisms under numerous physiological and pathophysiological conditions. This review discusses recent progress in the studies of functional interactions between the Na,K-ATPase and molecular microenvironment, the Na,K-ATPase-dependent signaling pathways and their significance for diversity of cell function.

Mathematical modeling and visualization of functional neuroimages

DEFF Research Database (Denmark)

Rasmussen, Peter Mondrup

This dissertation presents research results regarding mathematical modeling in the context of the analysis of functional neuroimages. Specifically, the research focuses on pattern-based analysis methods that recently have become popular within the neuroimaging community. Such methods attempt...... sets are characterized by relatively few data observations in a high dimensional space. The process of building models in such data sets often requires strong regularization. Often, the degree of model regularization is chosen in order to maximize prediction accuracy. We focus on the relative influence...... be carefully selected, so that the model and its visualization enhance our ability to interpret the brain. The second part concerns interpretation of nonlinear models and procedures for extraction of ‘brain maps’ from nonlinear kernel models. We assess the performance of the sensitivity map as means...

Understanding mathematical proof

CERN Document Server

Taylor, John

2014-01-01

Introduction The need for proof The language of mathematics Reasoning Deductive reasoning and truth Example proofs Logic and ReasoningIntroduction Propositions, connectives, and truth tables Logical equivalence and logical implication Predicates and quantification Logical reasoning Sets and Functions Introduction Sets and membership Operations on setsThe Cartesian product Functions and composite functions Properties of functions The Structure of Mathematical ProofsIntroduction Some proofs dissected An informal framework for proofs Direct proof A more formal framework Finding Proofs Direct proo

On certain properties of some generalized special functions

International Nuclear Information System (INIS)

Pathan, M.A.; Khan, Subuhi

2002-06-01

In this paper, we derive a result concerning eigenvector for the product of two operators defined on a Lie algebra of endomorphisms of a vector space. The results given by Radulescu, Mandal and authors follow as special cases of this result. Further using these results, we deduce certain properties of generalized Hermite polynomials and Hermite Tricomi functions. (author)

Automatic optimization of constants and special mathematic ensuring algorithms SKALA-micro system of RBMK-1000 reactor self-certification in operation

International Nuclear Information System (INIS)

Aleksandrov, S.I.; Dmitrenko, V.V.; Postnikov, V.V.; Sviridenkov, A.N.; Yurkin, G.V.; Yakunin, I.S.

2007-01-01

Paper dwells upon problems dealing with accuracy improvement of the energy release distribution and the safety margin of the RBMK-1000 operation. The accuracy is improved through the automatic optimization of some constants used in the SKALA-micro system special mathematic ensuring program and the regular self-validation of the algorithm to determine the energy release distribution calculation error. The validation based on the regular scanning of the reactor core by a calibrating detector and through the sequence disabling of the internal detectors is shown to give the close results [ru

The functionality of canoeists specializing in competitive distance 200 meters.

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Guo Penchen

2011-09-01

Full Text Available The article shows the importance of reactive properties to realize the potential of canoeist of south-east Asia specializing in the 200 meters established on a specialized focus of the training process sprinter. The parameters of functionality of athletes based on integrated aerobic and anaerobic ensure competitive distance of 200 m. They are based on assessing level of aerobic power and capacity of energy supply and properties of the cardiorespiratory system in actively increasing metabolic acidosis.

Upper Primary School Teachers' Mathematical Knowledge for Teaching Functional Thinking in Algebra

Science.gov (United States)

Wilkie, Karina J.

2014-01-01

This article is based on a project that investigated teachers' knowledge in teaching an important aspect of algebra in the middle years of schooling--functions, relations and joint variation. As part of the project, 105 upper primary teachers were surveyed during their participation in Contemporary Teaching and Learning of Mathematics, a research…

Insights into teaching mathematics

CERN Document Server

Orton, Anthony

2004-01-01

Providing essential guidance and background information about teaching mathematics, this book is intended particularly for teachers who do not regard themselves as specialists in mathematics. It deals with issues of learning and teaching, including the delivery of content and the place of problems and investigations. Difficulties which pupils encounter in connection with language and symbols form important sections of the overall discussion of how to enhance learning. The curriculum is considered in brief under the headings of number, algebra, shape and space, and data handling, and special at

Physical mathematics

CERN Document Server

Cahill, Kevin

2013-01-01

Unique in its clarity, examples and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theory.

The study of the value of applying the special functions of DSA during uterine artery embolization

International Nuclear Information System (INIS)

Wang Ting; Zhao Zhenhua; Lv Weigong

2007-01-01

Objective: To study the value of applying the special functions of DSA during uterine artery embolization. Methods: 122 cases were performed uterine artery embolization, including 67 cases with traditional operation and 55 cases with applying the special functions of DSA: rotary DSA angiography, the best work position and road map technology. We recorded the correlative operative indices to compare and analyse the mean exposure time, the mean operative time, the mean dosage of contrast medium, the probability of vasospasm and injury of blood vessel during operation. Results: The mean exposure time, mean operative time and the mean dosage of contrast medium were reduced with the special functions of DSA during uterine artery embolization. There is significant difference between traditional operation and the operation applying the special functions of DSA (P<0.01). Conclusion: Applying the special functions of DSA during uterine artery embolization can reduce the operative time, operative risk and economic burden. (authors)

Low and High Achivers in Mathematics

DEFF Research Database (Denmark)

Overgaard, Steffen; Tonnesen, Pia Beck

2016-01-01

achievers - within their first years of schooling think mathematically, as background to initiate more effective teaching of the two groups of students. In autumn 2014, 328 Grade 2 students (born in 2006) received an individual special teaching, early intervention, based on the same model and material, 20...... to enhance the teaching of low and high mathematics achievers so as to increase their mathematical knowledge and confidence.......Every mathematics teacher has a challenge in coping with the gap between low and high achievers in the classroom. The purpose of the the project, Early Math Intervention for Marginalized Students, TMTM 2014, is to bring forth knowledge of how these marginalized students - low as well as high...

Teaching the Relevance of Mathematics in Information Technologies through Functional Programming in Secondary School

Science.gov (United States)

Ruiz, Rosario Vera

2011-01-01

From the point of view of functional programming, a computational process to solve a problem is described as a mathematical function taking some arguments (corresponding to the data of the problem) and returning as a result its solution. Turtle Graphics can be used to describe the movements of a virtual turtle, which leaves a trail along his path…

Completeness, special functions and uncertainty principles over q-linear grids

International Nuclear Information System (INIS)

Abreu, LuIs Daniel

2006-01-01

We derive completeness criteria for sequences of functions of the form f(xλ n ), where λ n is the nth zero of a suitably chosen entire function. Using these criteria, we construct complete nonorthogonal systems of Fourier-Bessel functions and their q-analogues, as well as other complete sets of q-special functions. We discuss connections with uncertainty principles over q-linear grids and the completeness of certain sets of q-Bessel functions is used to prove that, if a function f and its q-Hankel transform both vanish at the points {q -n } ∞ n=1 , 0 n } ∞ n=-∞

Generalized fractional integration of the \\overline{H}-function

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Praveen Agarwal

2012-11-01

Full Text Available A significantly large number of earlier works on the subject of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, special functions, summation of series, et cetera. In the present paper, we study and develop the generalized fractional integral operators given by Saigo. First, we establish two Theorems that give the images of the product of H-function and a general class of polynomials inSaigo operators. On account of the general nature of the Saigo operators, H-function and a general class of polynomials a large number of new and known Images involving Riemann-Liouville and Erdélyi-Kober fractional integral operators and several special functions notably generalized Wright hypergeometric function, generalized Wright-Bessel function, the polylogarithm and Mittag-Leffler functions follow as special cases of our main findings.

Application of a functional mathematical index for antibacterial and anticarcinogenic effects of tea catechins.

Science.gov (United States)

Finotti, Enrico; Bersani, Enrico; Friedman, Mendel

2011-02-09

Tea leaves produce secondary metabolites that are involved in the defense of the plants against invading pathogens. In the case of green teas, these metabolites are polyphenolic compounds called catechins. Previous studies developed a mathematical formula called functional mathematical index (FMI) that was used to describe the quality of different olive oils and potatoes in terms of compositional parameters and antioxidative properties of individual components. This study extends the development of the FMI concept to define an "optimum tea" based on reported relationships between the content of structurally different catechins of a large number of teas and their dual beneficial effects: antimicrobial activities against a foodborne pathogen and inhibition of human cancer cell lines. The described mathematical approach may be useful for predicting relative beneficial effects of new teas based on their catechin content.

Mathematical quantization

CERN Document Server

Weaver, Nik

2001-01-01

With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures. This approach makes possible, with minimal mathematical detail, a unified treatment of a variety of topics.Detailed here for the first time, the fundamental idea of mathematical quantization is that sets are replaced by Hilbert spaces. Building on this idea, and most importantly on the fact that scalar-valued functions on a set correspond to operators on a Hilbert space, one can determine quantum analogs of a variety of classical structures. In particular, because topologies and measure classes on a set can be treated in terms of scalar-valued functions, we can transfer these constructions to the quantum realm, giving rise to C*- and von Neumann algebras.In the first half of the book, the author quickly builds the operator algebra setting. He uses this ...

On the mathematics of fuzziness

International Nuclear Information System (INIS)

Kerre, E.

1994-01-01

During the past twenty-five years, the scientific community has been working very extensively on the development of reliable models for the representation and manipulation of impreciseness and uncertainty that pervade the real world. Fuzzy set theory is one of the most popular theories able to treat incomplete information. In this paper, the basic mathematical principles underlying fuzzy set theory are outlined. Special attention is paid to the way that set theory has influenced the development of mathematics in a positive way

On the mathematics of fuzziness

Energy Technology Data Exchange (ETDEWEB)

Kerre, E. [Ghent Univ. (Belgium)

1994-12-31

During the past twenty-five years, the scientific community has been working very extensively on the development of reliable models for the representation and manipulation of impreciseness and uncertainty that pervade the real world. Fuzzy set theory is one of the most popular theories able to treat incomplete information. In this paper, the basic mathematical principles underlying fuzzy set theory are outlined. Special attention is paid to the way that set theory has influenced the development of mathematics in a positive way.

Exploring Turkish Mathematics Teachers' Content Knowledge of Quadrilaterals

Science.gov (United States)

Butuner, Suphi Onder; Filiz, Mehmet

2017-01-01

The aim of this research was to examine mathematics teachers' performances in defining special types of quadrilaterals, identifying their family and hierarchically classifying them. In this vein, 33 of 58 primary school mathematics teachers working in the province of Yozgat, Turkey were voluntarily recruited for this survey, and they were asked to…

Orientations toward Mathematical Processes of Prospective Secondary Mathematics Teachers as Related to Work with Tasks

Science.gov (United States)

Cannon, Tenille

2016-01-01

Mathematics can be conceptualized in different ways. Policy documents such as the National Council of Teachers of Mathematics (NCTM) (2000) and the Common Core State Standards Initiative (CCSSI) (2010), classify mathematics in terms of mathematical content (e.g., quadratic functions, Pythagorean theorem) and mathematical activity in the form of…

Acceptability of Functional Behavioral Assessment Procedures to Special Educators and School Psychologists

Science.gov (United States)

O'Neill, Robert E.; Bundock, Kaitlin; Kladis, Kristin; Hawken, Leanne S.

2015-01-01

This survey study assessed the acceptability of a variety of functional behavioral assessment (FBA) procedures (i.e., functional assessment interviews, rating scales/questionnaires, systematic direct observations, functional analysis manipulations) to a national sample of 123 special educators and a state sample of 140 school psychologists.…

A brief history of the most remarkable numbers e, i and γ in mathematical sciences with applications

Science.gov (United States)

Debnath, Lokenath

2015-08-01

This paper deals with a brief history of the most remarkable Euler numbers e, i and γ in mathematical sciences. Included are many properties of the constants e, i and γ and their applications in algebra, geometry, physics, chemistry, ecology, business and industry. Special attention is given to the growth and decay phenomena in many real-world problems including stability and instability of their solutions. Some specific and modern applications of logarithms, complex numbers and complex exponential functions to electrical circuits and mechanical systems are presented with examples. Included are the use of complex numbers and complex functions in the description and analysis of chaos and fractals with the aid of modern computer technology. In addition, the phasor method is described with examples of applications in engineering science. The major focus of this paper is to provide basic information through historical approach to mathematics teaching and learning of the fundamental knowledge and skills required for students and teachers at all levels so that they can understand the concepts of mathematics, and mathematics education in science and technology.

The conceptual basis of mathematics in cardiology: (I) algebra, functions and graphs.

Science.gov (United States)

Bates, Jason H T; Sobel, Burton E

2003-02-01

This is the first in a series of four articles developed for the readers of. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease, abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and

mathematical modelling of atmospheric dispersion of pollutants

International Nuclear Information System (INIS)

Mohamed, M.E.

2002-01-01

the main objectives of this thesis are dealing with environmental problems adopting mathematical techniques. in this respect, atmospheric dispersion processes have been investigated by improving the analytical models to realize the realistic physical phenomena. to achieve these aims, the skeleton of this work contained both mathematical and environmental topics,performed in six chapters. in chapter one we presented a comprehensive review study of most important informations related to our work such as thermal stability , plume rise, inversion, advection , dispersion of pollutants, gaussian plume models dealing with both radioactive and industrial contaminants. chapter two deals with estimating the decay distance as well as the decay time of either industrial or radioactive airborne pollutant. further, highly turbulent atmosphere has been investigated as a special case in the three main thermal stability classes namely, neutral, stable, and unstable atmosphere. chapter three is concerned with obtaining maximum ground level concentration of air pollutant. the variable effective height of pollutants has been considered throughout the mathematical treatment. as a special case the constancy of effective height has been derived mathematically and the maximum ground level concentration as well as its location have been established

Regional specialization within the human striatum for diverse psychological functions.

Science.gov (United States)

Pauli, Wolfgang M; O'Reilly, Randall C; Yarkoni, Tal; Wager, Tor D

2016-02-16

Decades of animal and human neuroimaging research have identified distinct, but overlapping, striatal zones, which are interconnected with separable corticostriatal circuits, and are crucial for the organization of functional systems. Despite continuous efforts to subdivide the human striatum based on anatomical and resting-state functional connectivity, characterizing the different psychological processes related to each zone remains a work in progress. Using an unbiased, data-driven approach, we analyzed large-scale coactivation data from 5,809 human imaging studies. We (i) identified five distinct striatal zones that exhibited discrete patterns of coactivation with cortical brain regions across distinct psychological processes and (ii) identified the different psychological processes associated with each zone. We found that the reported pattern of cortical activation reliably predicted which striatal zone was most strongly activated. Critically, activation in each functional zone could be associated with distinct psychological processes directly, rather than inferred indirectly from psychological functions attributed to associated cortices. Consistent with well-established findings, we found an association of the ventral striatum (VS) with reward processing. Confirming less well-established findings, the VS and adjacent anterior caudate were associated with evaluating the value of rewards and actions, respectively. Furthermore, our results confirmed a sometimes overlooked specialization of the posterior caudate nucleus for executive functions, often considered the exclusive domain of frontoparietal cortical circuits. Our findings provide a precise functional map of regional specialization within the human striatum, both in terms of the differential cortical regions and psychological functions associated with each striatal zone.

Mathematical models in radiogeochronology

International Nuclear Information System (INIS)

Abril, J.M.; Garcia Leon, M.

1991-01-01

The study of activity vs. depth profiles in sediment cores of some man-made and natural ocurring radionuclides have shown to be a poweful tool for dating purposes. Nevertheless, in most cases, an adecuate interpretation of such profiles requires mathematical models. In this paper, by considering the sediment as a continuum, a general equation for diffusion of radionuclides through it is obtained. Consequentely, some previously published dating models are found to be particular solutions of such general advenction-diffusion problem. Special emphasis is given to the mathematical treatment of compactation effect and time dependent problems. (author)

Philosophy of mathematics

CERN Document Server

Gabbay, Dov M; Woods, John

2009-01-01

One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mat

Mathematical methods of electromagnetic theory

CERN Document Server

Friedrichs, Kurt O

2014-01-01

This text provides a mathematically precise but intuitive introduction to classical electromagnetic theory and wave propagation, with a brief introduction to special relativity. While written in a distinctive, modern style, Friedrichs manages to convey the physical intuition and 19th century basis of the equations, with an emphasis on conservation laws. Particularly striking features of the book include: (a) a mathematically rigorous derivation of the interaction of electromagnetic waves with matter, (b) a straightforward explanation of how to use variational principles to solve problems in el

Specific descriptions of functional providing of the special endurance of boxers

Directory of Open Access Journals (Sweden)

S.B. Kiprich

2015-03-01

Full Text Available Purpose: to determine the specific characteristics of functional and metabolic support of special endurance of qualified boxers. Material: in research took part 16 boxers of high qualification at the age of 19-26 years. To estimate special endurance is used technique of detection the basic parameters of performance boxers "Spuderg-10." To estimate the response of cardiorespiratory system during the test "3x3" is used portable ergo-spirometry complex «Meta Max 3B» (Cortex, Germany. Results: It is shown that the range of individual distinctions of indexes of capacity and functional providing of the special endurance increased in every round under act of accumulation of fatigue. It is related to distinctions of kinetics of the cardiorespiratory system (by the increase of pulmonary ventilation in the first round, by the consumption of О 2 (by a capacity for the achievement of VO 2 max - in the second and by power of reaction of respiratory indemnification of metabolic acidosis - in the third. These distinctions are registered in default of reliable distinctions of quantitative descriptions of acidemic changes in an organism, increasing in the process of the test job processing. Conclusions: in different periods (rounds in boxers high grade found differences of manifestation and combinations of properties features of functional readiness.

Where mathematics come from how the embodied mind brings mathematics into being

CERN Document Server

Lakoff, George

2001-01-01

This book is about mathematical ideas, about what mathematics means-and why. Abstract ideas, for the most part, arise via conceptual metaphor-metaphorical ideas projecting from the way we function in the everyday physical world. Where Mathematics Comes From argues that conceptual metaphor plays a central role in mathematical ideas within the cognitive unconscious-from arithmetic and algebra to sets and logic to infinity in all of its forms.

A paradox in the electronic partition function or how to be cautious with mathematics

Energy Technology Data Exchange (ETDEWEB)

Miranda, E.N. [CRICYT - CONICET, Mendoza (Argentina); Departamento de Fisica, Universidad Nacional de San Luis, San Luis (Argentina)

2001-09-01

When the electronic partition functions of atoms or molecules are evaluated in textbooks, only the contribution of the ground state is considered. The excited states' contribution is argued to be negligible. However, a closer look shows that the partition function diverges if such states are taken into account. This paper shows that the blind use of mathematics is the reason behind this odd behaviour. (author)

A paradox in the electronic partition function or how to be cautious with mathematics

International Nuclear Information System (INIS)

Miranda, E.N.

2001-01-01

When the electronic partition functions of atoms or molecules are evaluated in textbooks, only the contribution of the ground state is considered. The excited states' contribution is argued to be negligible. However, a closer look shows that the partition function diverges if such states are taken into account. This paper shows that the blind use of mathematics is the reason behind this odd behaviour. (author)

Problems of Mathematical Finance by Stochastic Control Methods

Science.gov (United States)

Stettner, Łukasz

The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.

Training Public School Special Educators to Implement Two Functional Analysis Models

Science.gov (United States)

Rispoli, Mandy; Neely, Leslie; Healy, Olive; Gregori, Emily

2016-01-01

The purpose of this study was to investigate the efficacy and efficiency of a training package to teach public school special educators to conduct functional analyses of challenging behavior. Six public school educators were divided into two cohorts of three and were taught two models of functional analysis of challenging behavior: traditional and…

Generalization of Risch's algorithm to special functions

International Nuclear Information System (INIS)

Raab, Clemens G.

2013-05-01

Symbolic integration deals with the evaluation of integrals in closed form. We present an overview of Risch's algorithm including recent developments. The algorithms discussed are suited for both indefinite and definite integration. They can also be used to compute linear relations among integrals and to find identities for special functions given by parameter integrals. The aim of this presentation is twofold: to introduce the reader to some basic ideas of differential algebra in the context of integration and to raise awareness in the physics community of computer algebra algorithms for indefinite and definite integration.

Handbook of mathematics

CERN Document Server

Kuipers, L

1969-01-01

International Series of Monographs in Pure and Applied Mathematics, Volume 99: Handbook of Mathematics provides the fundamental mathematical knowledge needed for scientific and technological research. The book starts with the history of mathematics and the number systems. The text then progresses to discussions of linear algebra and analytical geometry including polar theories of conic sections and quadratic surfaces. The book then explains differential and integral calculus, covering topics, such as algebra of limits, the concept of continuity, the theorem of continuous functions (with examp

A Preservice Mathematics Teacher's Beliefs about Teaching Mathematics with Technology

Science.gov (United States)

Belbase, Shashidhar

2015-01-01

This paper analyzed a preservice mathematics teacher's beliefs about teaching mathematics with technology. The researcher used five semi-structured task-based interviews in the problematic contexts of teaching fraction multiplications with JavaBars, functions and limits, and geometric transformations with Geometer's Sketchpad, and statistical data…

Regaining the Edge in Urban Education: Mathematics and Sciences.

Science.gov (United States)

Gallon, Dennis P., Ed.

In order to remain competitive in the world economy, the United States must develop and improve mathematics and science education. Given that the future workforce in this country will be comprised largely of women and minorities, groups traditionally not entering mathematics and science careers, special recruitment and retention efforts must be…

Early Executive Function at Age Two Predicts Emergent Mathematics and Literacy at Age Five

NARCIS (Netherlands)

Mulder, Hanna; Verhagen, Josje; Van Der Ven, Sanne H. G.; Slot, Pauline L.; Leseman, Paul

2017-01-01

Previous work has shown that individual differences in executive function (EF) are predictive of academic skills in preschoolers, kindergartners, and older children. Across studies, EF is a stronger predictor of emergent mathematics than literacy. However, research on EF in children below age three

Dendritic cell maturation: functional specialization through signaling specificity and transcriptional programming.

Science.gov (United States)

Dalod, Marc; Chelbi, Rabie; Malissen, Bernard; Lawrence, Toby

2014-05-16

Dendritic cells (DC) are key regulators of both protective immune responses and tolerance to self-antigens. Soon after their discovery in lymphoid tissues by Steinman and Cohn, as cells with the unique ability to prime naïve antigen-specific T cells, it was realized that DC can exist in at least two distinctive states characterized by morphological, phenotypic and functional changes-this led to the description of DC maturation. It is now well appreciated that there are several subsets of DC in both lymphoid and non-lymphoid tissues of mammals, and these cells show remarkable functional specialization and specificity in their roles in tolerance and immunity. This review will focus on the specific characteristics of DC subsets and how their functional specialization may be regulated by distinctive gene expression programs and signaling responses in both steady-state and in the context of inflammation. In particular, we will highlight the common and distinctive genes and signaling pathways that are associated with the functional maturation of DC subsets. © 2014 The Authors.

Foreword to the Special Focus on Mathematics, Data and Knowledge

KAUST Repository

Chen, Xiaoyu; Wang, Dongming; Zhang, Xiangliang

2013-01-01

There is a growing interest in applying mathematical theories and methods from topology, computational geometry, differential equations, fluid dynamics, quantum statistics, etc. to describe and to analyze scientific regularities of diverse, massive

Special relativity a first encounter

CERN Document Server

Giulini, Domenico

2005-01-01

Special relativity provides the foundations of our knowledge of space and time. Without it, our understanding of the world, and its place in the universe, would be unthinkable. This book gives a concise, elementary, yet exceptionally modern, introduction to special relativity. It is a gentle yet serious 'first encounter', in that it conveys a true understanding rather than purely reports the basic facts. Only very elementary mathematical knowledge is needed to master it (basichigh-school maths), yet it will leave the reader with a sound understanding of the subject. Special Relativity: A First

Platonism, Naturalism, and Mathematical Knowledge

CERN Document Server

Brown, James Robert

2011-01-01

This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. Not only does this engaging book present the Platonist-Natural

Mathematical and physical theory of turbulence

CERN Document Server

Cannon, John

2006-01-01

Although the current dynamical system approach offers several important insights into the turbulence problem, issues still remain that present challenges to conventional methodologies and concepts. These challenges call for the advancement and application of new physical concepts, mathematical modeling, and analysis techniques. Bringing together experts from physics, applied mathematics, and engineering, Mathematical and Physical Theory of Turbulence discusses recent progress and some of the major unresolved issues in two- and three-dimensional turbulence as well as scalar compressible turbulence. Containing introductory overviews as well as more specialized sections, this book examines a variety of turbulence-related topics. The authors concentrate on theory, experiments, computational, and mathematical aspects of Navier-Stokes turbulence; geophysical flows; modeling; laboratory experiments; and compressible/magnetohydrodynamic effects. The topics discussed in these areas include finite-time singularities a...

Differences between quadratic equations and functions: Indonesian pre-service secondary mathematics teachers’ views

Science.gov (United States)

Aziz, T. A.; Pramudiani, P.; Purnomo, Y. W.

2018-01-01

Difference between quadratic equation and quadratic function as perceived by Indonesian pre-service secondary mathematics teachers (N = 55) who enrolled at one private university in Jakarta City was investigated. Analysis of participants’ written responses and interviews were conducted consecutively. Participants’ written responses highlighted differences between quadratic equation and function by referring to their general terms, main characteristics, processes, and geometrical aspects. However, they showed several obstacles in describing the differences such as inappropriate constraints and improper interpretations. Implications of the study are discussed.

Developing Students' Reflections on the Function and Status of Mathematical Modeling in Different Scientific Practices: History as a Provider of Cases

Science.gov (United States)

Kjeldsen, Tinne Hoff; Blomhøj, Morten

2013-01-01

Mathematical models and mathematical modeling play different roles in the different areas and problems in which they are used. The function and status of mathematical modeling and models in the different areas depend on the scientific practice as well as the underlying philosophical and theoretical position held by the modeler(s) and the…

Editorial: Special issue on education

OpenAIRE

Masal Ercan; Önder İsmail; Çalışkan Hüseyin; Beşoluk Şenol; Demirhan Eda

2017-01-01

This special issue consists of selected proceedings presented in ERPA International Congresses on Education 2017 which was held in Budapest / Hungary, 18-21 May 2017. Studies are related to educational sciences, science and mathematics education, social sciences education, health and sports science education, music and fine arts education, computer education and instructional technology, language education and management of education. There are eighty valuable studies in this special issue. I...

Multiscale mathematical modeling of the hypothalamo-pituitary-gonadal axis.

Science.gov (United States)

Clément, Frédérique

2016-07-01

Although the fields of systems and integrative biology are in full expansion, few teams are involved worldwide into the study of reproductive function from the mathematical modeling viewpoint. This may be due to the fact that the reproductive function is not compulsory for individual organism survival, even if it is for species survival. Alternatively, the complexity of reproductive physiology may be discouraging. Indeed, the hypothalamo-pituitary-gonadal (HPG) axis involves not only several organs and tissues but also intricate time (from the neuronal millisecond timescale to circannual rhythmicity) and space (from molecules to organs) scales. Yet, mathematical modeling, and especially multiscale modeling, can renew our approaches of the molecular, cellular, and physiological processes underlying the control of reproductive functions. In turn, the remarkable dynamic features exhibited by the HPG axis raise intriguing and challenging questions to modelers and applied mathematicians. In this article, we draw a panoramic review of some mathematical models designed in the framework of the female HPG, with a special focus on the gonadal and central control of follicular development. On the gonadal side, the modeling of follicular development calls to the generic formalism of structured cell populations, that allows one to make mechanistic links between the control of cell fate (proliferation, differentiation, or apoptosis) and that of the follicle fate (ovulation or degeneration) or to investigate how the functional interactions between the oocyte and its surrounding cells shape the follicle morphogenesis. On the central, mainly hypothalamic side, models based on dynamical systems with multiple timescales allow one to represent within a single framework both the pulsatile and surge patterns of the neurohormone GnRH. Beyond their interest in basic research investigations, mathematical models can also be at the source of useful tools to study the encoding and decoding of

Mathematical verification of a nuclear power plant protection system function with combined CPN and PVS

Energy Technology Data Exchange (ETDEWEB)

Koo, Seo Ryong; Son, Han Seong; Seong, Poong Hyun [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)

1999-12-31

In this work, an automatic software verification method for Nuclear Power Plant (NPP) protection system is developed. This method utilizes Colored Petri Net (CPN) for modeling and Prototype Verification System (PVS) for mathematical verification. In order to help flow-through from modeling by CPN to mathematical proof by PVS, a translator has been developed in this work. The combined method has been applied to a protection system function of Wolsong NPP SDS2(Steam Generator Low Level Trip) and found to be promising for further research and applications. 7 refs., 10 figs. (Author)

Mathematical verification of a nuclear power plant protection system function with combined CPN and PVS

Energy Technology Data Exchange (ETDEWEB)

Koo, Seo Ryong; Son, Han Seong; Seong, Poong Hyun [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)

1998-12-31

In this work, an automatic software verification method for Nuclear Power Plant (NPP) protection system is developed. This method utilizes Colored Petri Net (CPN) for modeling and Prototype Verification System (PVS) for mathematical verification. In order to help flow-through from modeling by CPN to mathematical proof by PVS, a translator has been developed in this work. The combined method has been applied to a protection system function of Wolsong NPP SDS2(Steam Generator Low Level Trip) and found to be promising for further research and applications. 7 refs., 10 figs. (Author)

Association of functional limitation with health care needs and experiences of children with special health care needs.

Science.gov (United States)

Nageswaran, Savithri; Silver, Ellen Johnson; Stein, Ruth E K

2008-05-01

The goal was to evaluate whether having a functional limitation was associated with health care needs and experiences of children with special health care needs. We used caregivers' responses in the National Survey of Children with Special Health Care Needs (2001). Functional limitation was categorized as severe, some, or no limitation. We performed analyses of the relationships of functional limitation to measures of health care needs and experiences. Children with special health care needs with severe functional limitation were more likely to have received specialized educational services, to have had physician visits, and to have needed health services, compared with those with no limitation. They had significantly greater odds of delayed care, unmet health care and care-coordination needs, referral problems, dissatisfaction, and difficulty using health services, compared with those without limitation. Caregivers of children with special health care needs with severe limitation were twice as likely as those with no limitation to report that providers did not spend enough time, listen carefully, provide needed information, and make family members partners in the child's care. Compared with children with special health care needs without limitation, those with severe limitation had worse health insurance experiences, in terms of insurance coverage, copayments, being able to see needed providers, and problems with health insurance. The impact on families (financial problems, need to provide home care, or need to stop or to cut work) of children with special health care needs with severe functional limitation was much greater than the impact on families of children with special health care needs without limitation. For most measures examined, results for some limitation were between those for severe limitation and no limitation. Functional limitation is significantly associated with the health care needs and experiences of children with special health care needs.

Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics

Science.gov (United States)

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-07-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit-reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.

Lectures on mathematical theory of extremum problems

CERN Document Server

1972-01-01

The author of this book, Igor' Vladimirovich Girsanov, was one of the first mathematicians to study general extremum problems and to realize the feasibility and desirability of a unified theory of extremal problems, based on a functional­ analytic approach. He actively advocated this view, and his special course, given at the Faculty of Mechanics and Mathematics of the Moscow State University in 1963 and 1964, was apparently the first systematic exposition of a unified approach to the theory of extremal problems. This approach was based on the ideas of Dubovitskii and Milyutin [1]. The general theory of extremal problems has developed so intensely during the past few years that its basic concepts may now be considered finalized. Nevertheless, as yet the basic results of this new field of mathematics have not been presented in a form accessible to a wide range of readers. (The profound paper of Dubovitskii and Milyutin [2] can hardly be recommended for a first study of the theory, since, in particular, it doe...

Interactive Apps Promote Learning of Basic Mathematics in Children With Special Educational Needs and Disabilities.

Science.gov (United States)

Pitchford, Nicola J; Kamchedzera, Elizabeth; Hubber, Paula J; Chigeda, Antonie L

2018-01-01

Interactive apps delivered on touch-screen tablets can be effective at supporting the acquisition of basic skills in mainstream primary school children. This technology may also be beneficial for children with Special Educational Needs and Disabilities (SEND) as it can promote high levels of engagement with the learning task and an inclusive learning environment. However, few studies have measured extent of learning for SEND pupils when using interactive apps, so it has yet to be determined if this technology is effective at raising attainment for these pupils. We report the first observational study of a group of 33 pupils with SEND from two primary schools in Malawi that are implementing a new digital technology intervention which uses touch-screen tablets to deliver interactive apps designed to teach basic mathematical skills. The apps contain topics that align to the national curriculum. To assess learning gains, rate of progress (minutes per topic) for each pupil was determined by calculating the average time taken to complete a topic. Progress rate was then correlated with teacher ratings of extent of disability and independent ratings of pupil engagement with the apps. Results showed SEND pupils could interact with the apps and all pupils passed at least one topic. Average progress rate for SEND pupils was twice as long as mainstream peers. Stepwise regression revealed extent of disability significantly predicted progress rate. Further exploratory correlations revealed pupils with moderate to severe difficulties with hearing and/or language made slower progress through the apps than those with greater functionality in these two domains because the use of verbal instructions within the apps limited their capacity to learn. This original quantitative analysis demonstrates that interactive apps can raise learning standards in pupils with SEND but may have limited utility for pupils with severe difficulties. Software modifications are needed to address specific

Mathematical models in biology bringing mathematics to life

CERN Document Server

Ferraro, Maria; Guarracino, Mario

2015-01-01

This book presents an exciting collection of contributions based on the workshop “Bringing Maths to Life” held October 27-29, 2014 in Naples, Italy.  The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content...

International Summer School on Mathematical Systems Theory and Economics

CERN Document Server

Szegö, G

1969-01-01

The International Summer School on Mathematical Systems Theory and Economics was held at the Villa Monastero in Varenna, Italy, from June 1 through June 12, 1967. The objective of this Summer School was to review the state of the art and the prospects for the application of the mathematical theory of systems to the study and the solution of economic problems. Particular emphasis was given to the use of the mathematical theory of control for the solution of problems in economics. It was felt that the publication of a volume collecting most of the lectures given at the school would show the current status of the application of these methods. The papers are organized into four sections arranged into two volumes: basic theories and optimal control of economic systems which appear in the first volume, and special mathematical problems and special applications which are contained in the second volume. Within each section the papers follow in alphabetical order by author. The seven papers on basic theories are a rat...

Mathematics 2

CERN Document Server

Kodaira, Kunihiko

1996-01-01

This is the translation from the Japanese textbook for the grade 11 course, "General Mathematics". It is part of the easier of the three elective courses in mathematics offered at this level and is taken by about 40% of students. The book covers basic notions of probability and statistics, vectors, exponential, logarithmic, and trigonometric functions, and an introduction to differentiation and integration.

Prospective Teachers' Understandings: Function and Composite Function.

Science.gov (United States)

Meel, David E.

2003-01-01

The current education reform efforts place greater emphasis on conceptual understanding and focus attention on teacher preparation, especially on the adequacy of teachers' mathematical knowledge of the material they will be teaching. This paper discusses the responses of 20 prospective elementary and special education mathematics specialists to…

Every Day Is Mathematical

Science.gov (United States)

Barger, Rita H.; Jarrah, Adeeb M.

2012-01-01

March 14 is special because it is Pi Day. Mathematics is celebrated on that day because the date, 3-14, replicates the first three digits of pi. Pi-related songs, websites, trivia facts, and more are at the fingertips of interested teachers and students. Less celebrated, but still fairly well known, is National Metric Day, which falls on October…

The CP-based electrochemical biosensors with autocatalytic stage in their function and the mathematical description of their work

Directory of Open Access Journals (Sweden)

Volodymyr Valentynovych Tkach

2012-07-01

Full Text Available The electroanalytic process of the detection of biosubstances, realized by the biosensor, based in conducting polyheterocyclic compounds, the function of which contained autocatalytic stage, was mathematically described. The correspondent mathematical model was analyzed by linear stability theory and bifurcational analysis. The electrochemical instabilities, capable to succeed in this process, were explained in the terms of this model.

METHOD OF GREEN FUNCTIONS IN MATHEMATICAL MODELLING FOR TWO-POINT BOUNDARY-VALUE PROBLEMS

Directory of Open Access Journals (Sweden)

E. V. Dikareva

2015-01-01

Full Text Available Summary. In many applied problems of control, optimization, system theory, theoretical and construction mechanics, for problems with strings and nods structures, oscillation theory, theory of elasticity and plasticity, mechanical problems connected with fracture dynamics and shock waves, the main instrument for study these problems is a theory of high order ordinary differential equations. This methodology is also applied for studying mathematical models in graph theory with different partitioning based on differential equations. Such equations are used for theoretical foundation of mathematical models but also for constructing numerical methods and computer algorithms. These models are studied with use of Green function method. In the paper first necessary theoretical information is included on Green function method for multi point boundary-value problems. The main equation is discussed, notions of multi-point boundary conditions, boundary functionals, degenerate and non-degenerate problems, fundamental matrix of solutions are introduced. In the main part the problem to study is formulated in terms of shocks and deformations in boundary conditions. After that the main results are formulated. In theorem 1 conditions for existence and uniqueness of solutions are proved. In theorem 2 conditions are proved for strict positivity and equal measureness for a pair of solutions. In theorem 3 existence and estimates are proved for the least eigenvalue, spectral properties and positivity of eigenfunctions. In theorem 4 the weighted positivity is proved for the Green function. Some possible applications are considered for a signal theory and transmutation operators.

Mathematical analysis II

CERN Document Server

Canuto, Claudio

2015-01-01

The purpose of the volume is to provide a support textbook for a second lecture course on Mathematical Analysis. The contents are organised to suit, in particular, students of Engineering, Computer Science and Physics, all areas in which mathematical tools play a crucial role. The basic notions and methods concerning integral and differential calculus for multivariable functions, series of functions and ordinary differential equations are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The pedagogical layout echoes the one used in the companion text Mathematical Analysis I. The book’s structure has a specifically-designed modular nature, which allows for great flexibility in the preparation of a lecture course on Mathematical Analysis. The style privileges clarity in the exposition and a linear progression through the theory. The material is organised on two levels. The first, reflected in this book, allows students to grasp the essential ideas, ...

Mathematics learning on geometry for children with autism

Science.gov (United States)

Widayati, F. E.; Usodo, B.; Pamudya, I.

2017-12-01

The purpose of this research is to describe: (1) the mathematics learning process in an inclusion class and (2) the obstacle during the process of mathematics learning in the inclusion class. This research is a descriptive qualitative research. The subjects were a mathematics teacher, children with autism, and a teacher assistant. Method of collecting data was observation and interview. Data validation technique is triangulation technique. The results of this research are : (1) There is a modification of lesson plan for children with autism. This modification such as the indicator of success, material, time, and assessment. Lesson plan for children with autism is arranged by mathematics teacher and teacher assistant. There is no special media for children with autism used by mathematics teacher. (2) The obstacle of children with autism is that they are difficult to understand mathematics concept. Besides, children with autism are easy to lose their focus.

Mathematical modelling of metabolism

DEFF Research Database (Denmark)

Gombert, Andreas Karoly; Nielsen, Jens

2000-01-01

Mathematical models of the cellular metabolism have a special interest within biotechnology. Many different kinds of commercially important products are derived from the cell factory, and metabolic engineering can be applied to improve existing production processes, as well as to make new processes...... availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology....... available. Both stoichiometric and kinetic models have been used to investigate the metabolism, which has resulted in defining the optimal fermentation conditions, as well as in directing the genetic changes to be introduced in order to obtain a good producer strain or cell line. With the increasing...

Mechanisms of interactive specialization and emergence of functional brain circuits supporting cognitive development in children

Science.gov (United States)

Battista, Christian; Evans, Tanya M.; Ngoon, Tricia J.; Chen, Tianwen; Chen, Lang; Kochalka, John; Menon, Vinod

2018-01-01

Cognitive development is thought to depend on the refinement and specialization of functional circuits over time, yet little is known about how this process unfolds over the course of childhood. Here we investigated growth trajectories of functional brain circuits and tested an interactive specialization model of neurocognitive development which posits that the refinement of task-related functional networks is driven by a shared history of co-activation between cortical regions. We tested this model in a longitudinal cohort of 30 children with behavioral and task-related functional brain imaging data at multiple time points spanning childhood and adolescence, focusing on the maturation of parietal circuits associated with numerical problem solving and learning. Hierarchical linear modeling revealed selective strengthening as well as weakening of functional brain circuits. Connectivity between parietal and prefrontal cortex decreased over time, while connectivity within posterior brain regions, including intra-hemispheric and inter-hemispheric parietal connectivity, as well as parietal connectivity with ventral temporal occipital cortex regions implicated in quantity manipulation and numerical symbol recognition, increased over time. Our study provides insights into the longitudinal maturation of functional circuits in the human brain and the mechanisms by which interactive specialization shapes children's cognitive development and learning.

Teach the Mathematics of Mathematicians

Directory of Open Access Journals (Sweden)

Peter Taylor

2018-04-01

Full Text Available The secondary-school mathematics curriculum is narrow in scope and technical in character; this is quite different from the nature of the discipline itself. As a result, it offers little inspiration to both students and teachers, and provides students with poor preparation for university mathematics courses and indeed for life. Over the past century, recently more than ever, there have been calls for change, for a curriculum that is true to the subject of mathematics as the creation and study of patterns and structures. While there are hopeful responses to this at the elementary level, there is almost nothing at the secondary level. Ironically, it is felt that in order to prepare students for university calculus, the secondary curriculum simply has to be what it is. This is a special case of a myth that needs to be destroyed.

Students' Competencies in Working with Functions in Secondary Mathematics Education-Empirical Examination of a Competence Structure Model

Science.gov (United States)

Nitsch, Renate; Fredebohm, Anneke; Bruder, Regina; Kelava, Augustin; Naccarella, Dominik; Leuders, Timo; Wirtz, Markus

2015-01-01

In the subject matter of functional relationships, a student's ability to translate from one form of representation to another is seen as a central competence. In the course of the HEUREKO project (heuristic work with representations of functional relationships and the diagnosis of mathematical competencies of students), a theoretical competence…

A course of higher mathematics

CERN Document Server

Smirnov, Vladimir Ivanovich; Lohwater, A J

1964-01-01

A Course of Higher Mathematics, I: Elementary Calculus is a five-volume course of higher mathematics used by mathematicians, physicists, and engineers in the U.S.S.R. This volume deals with calculus and principles of mathematical analysis including topics on functions of single and multiple variables. The functional relationships, theory of limits, and the concept of differentiation, whether as theories and applications, are discussed. This book also examines the applications of differential calculus to geometry. For example, the equations to determine the differential of arc or the parameter

Guide to mathematical tables supplement no 1

CERN Document Server

Burunova, N M; Fedorova, R M

1960-01-01

A Guide to Mathematical Tables is a supplement to the Guide to Mathematical Tables published by the U.S.S.R. Academy of Sciences in 1956. The tables contain information on subjects such as powers, rational and algebraic functions, and trigonometric functions, as well as logarithms and polynomials and Legendre functions. An index listing all functions included in both the Guide and the Supplement is included.Comprised of 15 chapters, this supplement first describes mathematical tables in the following order: the accuracy of the table (that is, the number of decimal places or significant

Attitude toward mathematics among the students at Nazarbayev University Foundation Year Programme

Science.gov (United States)

Karjanto, N.

2017-08-01

This article investigates the attitude toward mathematics among the students enrolled in the Foundation Year Programme at Nazarbayev University. The study is conducted quantitatively and an inventory developed by Tapia and Marsh II is adopted in this research. The inventory consists of 40 statements on the five-point Likert scale. Gender, specialization and final high school score in mathematics are collected. The number of valid returned questionnaires is 108. There are 55 males, 53 females, 73 Mathematical-Physics (MP), 22 Biology-Chemistry (BC) and 13 International Relations-Economics (IRE) students. Generally, they have a positive attitude toward mathematics, with the score mean and standard deviation are 3.999 and 0.531 out of five, respectively. We confirm a hypothesis on a positive correlation between previous high achievement in mathematics and favorable attitude toward it. The correlation value is r = 0.300, its effect size is medium and it is extremely significant (p-value = 0.0008 0.05). There is a very significant difference between students who specialize in IRE and MP in terms of their attitude toward mathematics (F(2, 105) = 5.6848, p-value = 0.0045 < 0.01).

Editorial: Special issue on education

Directory of Open Access Journals (Sweden)

Masal Ercan

2017-01-01

Full Text Available This special issue consists of selected proceedings presented in ERPA International Congresses on Education 2017 which was held in Budapest / Hungary, 18-21 May 2017. Studies are related to educational sciences, science and mathematics education, social sciences education, health and sports science education, music and fine arts education, computer education and instructional technology, language education and management of education. There are eighty valuable studies in this special issue. In sum the results of studies will contribute to the field.

Portugal's special education law: implementing the International Classification of Functioning, Disability and Health in policy and practice.

Science.gov (United States)

Sanches-Ferreira, Manuela; Simeonsson, Rune J; Silveira-Maia, Mónica; Alves, Sílvia; Tavares, Ana; Pinheiro, Sara

2013-05-01

The International Classification of Functioning, Disability and Health (ICF) was introduced in Portuguese education law as the compulsory system to guide eligibility policy and practice in special education. This paper describes the implementation of the ICF and its utility in the assessment process and eligibility determination of students for special education. A study to evaluate the utility of the ICF was commissioned by the Portuguese Ministry of Education and carried out by an external evaluation team. A document analysis was made of the assessment and eligibility processes of 237 students, selected from a nationally representative sample. The results provided support for the use of the ICF in student assessment and in the multidimensional approach of generating student functioning profiles as the basis for determining eligibility. The use of the ICF contributed to the differentiation of eligible and non eligible students based on their functioning profiles. The findings demonstrate the applicability of the ICF framework and classification system for determining eligibility for special education services on the basis of student functioning rather than medical or psychological diagnose. The use of the International Classification of Functioning, Disability and Health (ICF) framework in special education policy is as follows: • The functional perspective of the ICF offers a more comprehensive, holistic assessment of student needs than medical diagnoses. • ICF-based assessment of the nature and severity of functioning can serve as the basis for determining eligibility for special education and habilitation. • Profiles of functioning can support decision making in designing appropriate educational interventions for students.

A Mathematical Approach to Establishing Constitutive Models for Geomaterials

Directory of Open Access Journals (Sweden)

Guang-hua Yang

2013-01-01

Full Text Available The mathematical foundation of the traditional elastoplastic constitutive theory for geomaterials is presented from the mathematical point of view, that is, the expression of stress-strain relationship in principal stress/strain space being transformed to the expression in six-dimensional space. A new framework is then established according to the mathematical theory of vectors and tensors, which is applicable to establishing elastoplastic models both in strain space and in stress space. Traditional constitutive theories can be considered as its special cases. The framework also enables modification of traditional constitutive models.

Applications of zeta functions and other spectral functions in mathematics and physics: a special issue in honour of Stuart Dowker's 75th birthday Applications of zeta functions and other spectral functions in mathematics and physics: a special issue in honour of Stuart Dowker's 75th birthday

Science.gov (United States)

Dowker, Fay; Elizalde, Emilio; Kirsten, Klaus

2012-09-01

. Chapter 5 is devoted to the image and inversion methods and I must have read this closely as there are lots of marginal notes...' The second principle can be read off from the following quote: 'After reading Eddington circa 1960 it was clear to me (and others of course) there is a strong analogy (at least) between gravitation and electromagnetism ... (His work has very strongly influenced me.) So I played a game of asking for the gravitational analogues of existing electromagnetic concepts. The basic analogue is between field strength/charge and curvature/spin... [in that] ...spin, in general relativity, plays the passive role that charge plays in electromagnetism in the sense that it is the spin-curvature coupling that knocks a particle off a geodesic.' It is quite amazing how much of Stuart's work can be traced back to these principles. This is briefly explained in the following by describing some of his most important works. His most cited work [7] fits this bill and can be seen as doing what Julian Schwinger did in [8], for a constant electromagnetic field in the gravitational setting. In more detail he noticed Schulman's work on propagators on the three sphere [9], which he extended to Lie groups; see [10, 11]. He then noticed that having exact propagators, work like Schwinger's could be done and de Sitter space was a natural 'curved' candidate. The paper is best known for the mathematical technique introduced, namely for the zeta function method much used since for the computation of singular quantum field theoretic quantities like effective actions and the Casimir energy. The motivation for introducing this scheme goes back to reading an article of I M Gel'fand about some number theory problem involving zeta functions, image sums, propagators etc. How could an object occurring with other objects physicists were using all the time not be useful? It turned out to be very useful, although in this paper the method was only introduced but actually not used! This is

A National Study of Mathematics Requirements for Scientists and Engineers. Final Report.

Science.gov (United States)

Miller, G. H.

The National Study of Mathematics Requirements for Scientists and Engineers is concerned with establishing the mathematics experiences desired for the many specializations in science and engineering, such as microbiology, organic chemistry, electrical engineering, and molecular physics. An instruction and course content sheet and a course…

Solar thermal energy as a topic in secondary mathematics classrooms

Energy Technology Data Exchange (ETDEWEB)

Brinkmann, A.; Brinkmann, K. [EnviPro Environmental Process Engineering Prof. Dr. Klaus Brinkmann, Iserlohn (Germany)

2004-07-01

One of the most effective methods to achieve a sustainable change of our momentary existing power supply system to a system mainly based on renewable energy conversion is the education of our children. For this purpose the compulsory school subject mathematics appears to be suitable. In order to promote renewable energy issues in mathematics classrooms, the authors have developed a special didactical concept to open this field for students, as well as for their teachers. The aim of this paper is to present firstly an overview of our concept and secondly examples of problems to the special topic of solar thermal energy, developed on the basis of our concept. (orig.)

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Special issue devoted to advances in specific areas of mathematics and proceedings of selected high quality conferences are also published. ... Editorial Manager is a user-friendly online submission and review management system. Authors ...

Recent software developments for special functions in the Santander-Amsterdam project

NARCIS (Netherlands)

A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)

2014-01-01

textabstractWe give an overview of published algorithms by our group and of current activities and future plans. In particular we give details on methods for computing special functions and discuss in detail two current lines of research. Firstly, we describe the recent developments for the

Optimization and mathematical modeling in computer architecture

CERN Document Server

Sankaralingam, Karu; Nowatzki, Tony

2013-01-01

In this book we give an overview of modeling techniques used to describe computer systems to mathematical optimization tools. We give a brief introduction to various classes of mathematical optimization frameworks with special focus on mixed integer linear programming which provides a good balance between solver time and expressiveness. We present four detailed case studies -- instruction set customization, data center resource management, spatial architecture scheduling, and resource allocation in tiled architectures -- showing how MILP can be used and quantifying by how much it outperforms t

The History of Mathematics and Mathematical Education

Science.gov (United States)

Grattan-Guinness, I.

1977-01-01

Answers to questions which were asked after the author's various lectures in Australia are gathered here. Topics touched upon include "new" mathematics, unknown constants and free variables, propositional functions, linear algebra, arithmetic and geometry, and student assessment. (MN)

Scaffolding and Dialogic Teaching in Mathematics Education: Introduction and Review

Science.gov (United States)

Bakker, Arthur; Smit, Jantien; Wegerif, Rupert

2015-01-01

This article has two purposes: firstly to introduce this special issue on scaffolding and dialogic teaching in mathematics education and secondly to review the recent literature on these topics as well as the articles in this special issue. First we define and characterise scaffolding and dialogic teaching and provide a brief historical overview…

Elementary Students' Spontaneous Metacognitive Functions in Different Types of Mathematical Problems

Science.gov (United States)

Mokos, Evagelos; Kafoussi, Sonia

2013-01-01

Metacognition is the mind's ability to monitor and control itself or, in other words, the ability to know about our knowing (Dunlosky & Bjork, 2008). In mathematics education, the importance of the investigation of students' metacognition during their mathematical activity has been focused on the area of mathematics problem solving. This study…

Examination of Pre-Service Mathematics Teachers' Knowledge of Teaching Function Concept

Science.gov (United States)

Tasdan, Berna Tataroglu; Koyunkaya, Melike Yigit

2017-01-01

Teaching of mathematics could be improved with teachers who have a strong mathematical knowledge and have an ability to reflect this knowledge on their teaching. Therefore, it is important to develop mathematics teachers' theoretical and pedagogical knowledge. This study was designed to examine pre-service secondary mathematics teachers' (PSMT)…

Reflections from the Application of Different Type of Activities: Special Training Methods Course

Science.gov (United States)

Karadeniz, Mihriban Hacisalihoglu

2017-01-01

The aim of this study is to reveal the benefits gained from "Special Training Methods II" course and the problems prospective mathematics teachers encountered with it. The case study method was used in the study. The participants in the study were 34 prospective mathematics teachers studying at a Primary School Mathematics Education…

Influence of short-term memory on achievement of pupils in special schools

OpenAIRE

Podrazilová, Jana

2010-01-01

a klíčová slova diplomové práce v anglickém jazyce Key words: Memory - short - term memory - learning Pedagogy - special pedagogy Game - didactic game - mathematic - geometrical pexeso - arithmetic environment of stepping Annotation My master thesis is focused on the analysis of influence of motivation on short-term memory and in consequence on long-term memory in education of mathematics in second and third class of practical and special elementary schools. I have considered the influence of...

Generalized zeta function representation of groups and 2-dimensional topological Yang-Mills theory: The example of GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q})

Energy Technology Data Exchange (ETDEWEB)

Roche, Ph., E-mail: philippe.roche@univ-montp2.fr [Université Montpellier 2, CNRS, L2C, IMAG, Montpellier (France)

2016-03-15

We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of zeta function representations of groups. We compute some of these functions in the case of the finite group GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q}). We recall the table characters of these groups for any q, compute the Frobenius-Schur indicator of their irreducible representations, and give the explicit structure of their fusion rings.

Focus on the use of language in the multicultural mathematics classroom

DEFF Research Database (Denmark)

Johansen, Lene Østergaard

. understanding the meaning of the words "in front of") when they enter first grade in primary school (Nyborg and Nyborg, 1990). Students who lack these abilities either with regard to mathematics or language are from the beginning of schooling limited in their mathematical performance and in a "risk zone......" of developing learning difficulties in mathematics. Teaching the teachers a consciousness for the use of language in mathematics teaching as well as educating them to have a special focus on developing the vocabulary of the students can render the mathematics teaching more inclusive. Furthermore, it may help......Learning mathematics can be seen as learning a foreign language or learning a particular mathematical discourse.  Nolte (2004) calls mathematics the students' first second language. The use of language in mathematics teaching, hence the way we talk and the way we write, differ from the way the same...

Ideation in mathematical writing

DEFF Research Database (Denmark)

Misfeldt, Morten

2007-01-01

This paper considers idea generation during the mathematical writing process. Two contrasting explanations of the creative potential in connection to writing is presented; writing as a process of setting and obtaining rhetorical goals and writing as a process of discovery. These views...... are then related to two empirically found categories of functions that writing serves researchers in the field of mathematics, concluding that both views contributes to understanding the creative potential in relation to mathematical writing....

The clinical value of the special functions of DSA in interventional embolization for uterine fibroids

International Nuclear Information System (INIS)

He Yushen; Lu Dong; Lv Weifu; Zhang Jingsong

2009-01-01

Objective: To evaluate the special functions of DSA in interventional embolization therapy for uterine fibroids. Methods: The special functions of DSA, including 3D-DSA, the optimal working position and road-mapping technique, were utilized in performing interventional embolization therapy for uterine fibroids in twenty-six cases (experimental group). Routine DSA angiography was employed in twenty cases(control group). The volume of contrast media used, the time of completing the interventional procedure and the total fluoroscopic time in two groups were compared and the results were analyzed. Results: The difference in the volume of contrast agent used and in the total fluoroscopic time between two groups was statistically significant (P 0.05). Conclusion: In treating uterine fibroids with interventional embolization, the use of the special functions of DSA can reduce the manipulation time and lower the operation risk. Moreover, the technique of visible 3D reconstruction image is of great significance in guiding the procedure. (authors)

Interactive Apps Promote Learning of Basic Mathematics in Children With Special Educational Needs and Disabilities

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Nicola J. Pitchford

2018-03-01

Full Text Available Interactive apps delivered on touch-screen tablets can be effective at supporting the acquisition of basic skills in mainstream primary school children. This technology may also be beneficial for children with Special Educational Needs and Disabilities (SEND as it can promote high levels of engagement with the learning task and an inclusive learning environment. However, few studies have measured extent of learning for SEND pupils when using interactive apps, so it has yet to be determined if this technology is effective at raising attainment for these pupils. We report the first observational study of a group of 33 pupils with SEND from two primary schools in Malawi that are implementing a new digital technology intervention which uses touch-screen tablets to deliver interactive apps designed to teach basic mathematical skills. The apps contain topics that align to the national curriculum. To assess learning gains, rate of progress (minutes per topic for each pupil was determined by calculating the average time taken to complete a topic. Progress rate was then correlated with teacher ratings of extent of disability and independent ratings of pupil engagement with the apps. Results showed SEND pupils could interact with the apps and all pupils passed at least one topic. Average progress rate for SEND pupils was twice as long as mainstream peers. Stepwise regression revealed extent of disability significantly predicted progress rate. Further exploratory correlations revealed pupils with moderate to severe difficulties with hearing and/or language made slower progress through the apps than those with greater functionality in these two domains because the use of verbal instructions within the apps limited their capacity to learn. This original quantitative analysis demonstrates that interactive apps can raise learning standards in pupils with SEND but may have limited utility for pupils with severe difficulties. Software modifications are needed to

9th and 10th Asian Symposium on Computer Mathematics

CERN Document Server

Lee, Wen-shin; Sato, Yosuke

2014-01-01

This book covers original research and the latest advances in symbolic, algebraic and geometric computation; computational methods for differential and difference equations, symbolic-numerical computation; mathematics software design and implementation; and scientific and engineering applications based on features, invited talks, special sessions and contributed papers presented at the 9th (in Fukuoka, Japan in 2009) and 10th (in Beijing China in 2012) Asian Symposium on Computer Mathematics (ASCM). Thirty selected and refereed articles in the book present the conference participants’ ideas and views on researching mathematics using computers.

Gifted Education in Korea: Three Korean High Schools for the Mathematically Gifted

Science.gov (United States)

Choi, Kyong Mi; Hon, Dae Sik

2009-01-01

This article presents a brief history of three Korean high schools for mathematically gifted students. It describes how these schools operate, how their mathematics curricula differ compared to those of regular high schools, the admissions criteria, curriculum offered, and the student and teacher population. This review of specialized, science,…

Early Executive Function at Age Two Predicts Emergent Mathematics and Literacy at Age Five.

Science.gov (United States)

Mulder, Hanna; Verhagen, Josje; Van der Ven, Sanne H G; Slot, Pauline L; Leseman, Paul P M

2017-01-01

Previous work has shown that individual differences in executive function (EF) are predictive of academic skills in preschoolers, kindergartners, and older children. Across studies, EF is a stronger predictor of emergent mathematics than literacy. However, research on EF in children below age three is scarce, and it is currently unknown whether EF, as assessed in toddlerhood, predicts emergent academic skills a few years later. This longitudinal study investigates whether early EF, assessed at two years, predicts (emergent) academic skills, at five years. It examines, furthermore, whether early EF is a significantly stronger predictor of emergent mathematics than of emergent literacy, as has been found in previous work on older children. A sample of 552 children was assessed on various EF and EF-precursor tasks at two years. At age five, these children performed several emergent mathematics and literacy tasks. Structural Equation Modeling was used to investigate the relationships between early EF and academic skills, modeled as latent factors. Results showed that early EF at age two was a significant and relatively strong predictor of both emergent mathematics and literacy at age five, after controlling for receptive vocabulary, parental education, and home language. Predictive relations were significantly stronger for mathematics than literacy, but only when a verbal short-term memory measure was left out as an indicator to the latent early EF construct. These findings show that individual differences in emergent academic skills just prior to entry into the formal education system can be traced back to individual differences in early EF in toddlerhood. In addition, these results highlight the importance of task selection when assessing early EF as a predictor of later outcomes, and call for further studies to elucidate the mechanisms through which individual differences in early EF and precursors to EF come about.

Early Executive Function at Age Two Predicts Emergent Mathematics and Literacy at Age Five

Directory of Open Access Journals (Sweden)

Hanna Mulder

2017-10-01

Full Text Available Previous work has shown that individual differences in executive function (EF are predictive of academic skills in preschoolers, kindergartners, and older children. Across studies, EF is a stronger predictor of emergent mathematics than literacy. However, research on EF in children below age three is scarce, and it is currently unknown whether EF, as assessed in toddlerhood, predicts emergent academic skills a few years later. This longitudinal study investigates whether early EF, assessed at two years, predicts (emergent academic skills, at five years. It examines, furthermore, whether early EF is a significantly stronger predictor of emergent mathematics than of emergent literacy, as has been found in previous work on older children. A sample of 552 children was assessed on various EF and EF-precursor tasks at two years. At age five, these children performed several emergent mathematics and literacy tasks. Structural Equation Modeling was used to investigate the relationships between early EF and academic skills, modeled as latent factors. Results showed that early EF at age two was a significant and relatively strong predictor of both emergent mathematics and literacy at age five, after controlling for receptive vocabulary, parental education, and home language. Predictive relations were significantly stronger for mathematics than literacy, but only when a verbal short-term memory measure was left out as an indicator to the latent early EF construct. These findings show that individual differences in emergent academic skills just prior to entry into the formal education system can be traced back to individual differences in early EF in toddlerhood. In addition, these results highlight the importance of task selection when assessing early EF as a predictor of later outcomes, and call for further studies to elucidate the mechanisms through which individual differences in early EF and precursors to EF come about.

A Mathematical Model, Implementation and Study of a Swarm System

OpenAIRE

Varghese, Blesson; McKee, Gerard

2013-01-01

The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model comprises two general methods for pattern transformation, namely a macroscopic transformation and mathematical transformation method. The problem of transformation is formally expressed and four special cases of transformation are considered. Simulations to conf...

An Effect of the Environmental Pollution via Mathematical Model Involving the Mittag-Leffler Function

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Anjali Goswami

2017-08-01

Full Text Available In the existing condition estimation of pollution effect on environment is big change for all of us. In this study we develop a new approach to estimate the effect of pollution on environment via mathematical model which involves the generalized Mittag-Leffler function of one variable $E_{\\alpha_{2},\\delta_{1};\\alpha_{3},\\delta_{2}}^{\\gamma_{1},\\alpha_{1}} (z$ which we introduced here.

A bridge to advanced mathematics

CERN Document Server

Sentilles, Dennis

2011-01-01

This helpful workbook-style ""bridge"" book introduces students to the foundations of advanced mathematics, spanning the gap between a practically oriented calculus sequence and subsequent courses in algebra and analysis with a more theoretical slant. Part 1 focuses on logic and number systems, providing the most basic tools, examples, and motivation for the manner, method, and concerns of higher mathematics. Part 2 covers sets, relations, functions, infinite sets, and mathematical proofs and reasoning. Author Dennis Sentilles also discusses the history and development of mathematics as well a

Mathematical verification of a nuclear power plant protection system function with combined CPN and PVS

International Nuclear Information System (INIS)

Koo, Seo Ryong; Son, Han Seong; Seong, Poong Hyun

1999-01-01

In this work, an automatic software verification method for Nuclear Power Plant (NPP) protection system is developed. This method utilizes Colored Petri Net (CPN) for system modeling and Prototype Verification System (PVS) for mathematical verification. In order to help flow-through from modeling by CPN to mathematical proof by PVS, an information extractor from CPN models has been developed in this work. In order to convert the extracted information to the PVS specification language, a translator also has been developed. ML that is a higher-order functional language programs the information extractor and translator. This combined method has been applied to a protection system function of Wolsung NPP SDS2 (Steam Generator Low Level Trip). As a result of this application, we could prove completeness and consistency of the requirement logically. Through this work, in short, an axiom or lemma based-analysis method for CPN models is newly suggested in order to complement CPN analysis methods and a guideline for the use of formal methods is proposed in order to apply them to NPP software verification and validation. (author). 9 refs., 15 figs

Construction and modification of the autonomy of school mathematical knowledge in Portugal

Directory of Open Access Journals (Sweden)

José Manuel Matos

2016-01-01

Full Text Available During the second half of the nineteenth century and early twentieth century the discipline of secondary mathematics was gradually built in Portugal and certified teachers, textbooks, programs, special teaching techniques emerge. This consolidation process ends with the emergency of school subjects that develop some kind of autonomy as Chervel puts it. This article discusses how the school discipline of mathematics in secondary education in Portugal was set. This process is inseparable from teacher training and so we will observe professional legitimation processes paying special attention to ways in which autonomy has been building and modifying over time.

Mathematical foundations of elasticity

CERN Document Server

Marsden, Jerrold E

1994-01-01

This advanced-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is directed to mathematicians, engineers and physicists who wish to see this classical subject in a modern setting with examples of newer mathematical contributions. Prerequisites include a solid background in advanced calculus and the basics of geometry and functional analysis.The first two chapters cover the background geometry ― developed as needed ― and use this discussion to obtain the basic results on kinematics and dynamics of con

A short course in discrete mathematics

CERN Document Server

Bender, Edward A

2004-01-01

What sort of mathematics do I need for computer science? In response to this frequently asked question, a pair of professors at the University of California at San Diego created this text. Its sources are two of the university's most basic courses: Discrete Mathematics, and Mathematics for Algorithm and System Analysis. Intended for use by sophomores in the first of a two-quarter sequence, the text assumes some familiarity with calculus. Topics include Boolean functions and computer arithmetic; logic; number theory and cryptography; sets and functions; equivalence and order; and induction, seq

Features of Functioning the Integrated Building Thermal Model

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Morozov Maxim N.

2017-01-01

Full Text Available A model of the building heating system, consisting of energy source, a distributed automatic control system, elements of individual heating unit and heating system is designed. Application Simulink of mathematical package Matlab is selected as a platform for the model. There are the specialized application Simscape libraries in aggregate with a wide range of Matlab mathematical tools allow to apply the “acausal” modeling concept. Implementation the “physical” representation of the object model gave improving the accuracy of the models. Principle of operation and features of the functioning of the thermal model is described. The investigations of building cooling dynamics were carried out.

Mathematical competencies and the role of mathematics in physics education: A trend analysis of TIMSS Advanced 1995 and 2008

Directory of Open Access Journals (Sweden)

Trude Nilsen

2013-10-01

Full Text Available As students advance in their learning of physics over the course of their education, the requirement of mathematical applications in physics-related tasks increases, especially so in upper secondary school and in higher education. Yet there is little empirical work (particularly large-scale or longitudinal on the application of mathematics in physics education compared with the research related to the conceptual knowledge of physics. In order to clarify the nature of mathematics in physics education, we developed a theoretical framework for mathematical competencies pertinent to various physics tasks based on theoretical frameworks from mathematics and physics education. We used this synthesis of frameworks as a basis to create a model for physics competence. The framework also served as a tool for analyzing and categorizing trend items from the international large-scale survey, TIMSS Advanced 1995 and 2008. TIMSS Advanced assessed students in upper secondary school with special preparation in advanced physics and mathematics. We then investigated the changes in achievements on these categorized items across time for nations who participated in both surveys. The results from our analysis indicate that students whose overall physics achievement declined struggled the most with items requiring mathematics, especially items requiring them to handle symbols, such as manipulating equations. This finding suggests the importance of collaboration between mathematics and physics education as well as the importance of traditional algebra for physics education.

A mathematical framework for functional mapping of complex phenotypes using delay differential equations.

Science.gov (United States)

Fu, Guifang; Wang, Zhong; Li, Jiahan; Wu, Rongling

2011-11-21

All biological phenomena occurring at different levels of organization from cells to organisms can be modeled as a dynamic system, in which the underlying components interact dynamically to comprehend its biological function. Such a systems modeling approach facilitates the use of biochemically and biophysically detailed mathematical models to describe and quantify "living cells," leading to an in-depth and precise understanding of the behavior, development and function of a biological system. Here, we illustrate how this approach can be used to map genes or quantitative trait loci (QTLs) that control a complex trait using the example of the circadian rhythm system which has been at the forefront of analytical mathematical modeling for many years. We integrate a system of biologically meaningful delay differential equations (DDEs) into functional mapping, a statistical model designed to map dynamic QTLs involved in biological processes. The DDEs model the ability of circadian rhythm to generate autonomously sustained oscillations with a period close to 24h, in terms of time-varying mRNA and protein abundances. By incorporating the Runge-Kutta fourth order algorithm within the likelihood-based context of functional mapping, we estimated the genetic parameters that define the periodic pattern of QTL effects on time-varying mRNA and protein abundances and their dynamic association as well as the linkage disequilibrium of the QTL and a marker. We prove theorems about how to choose appropriate parameters to guarantee periodic oscillations. We further used simulation studies to investigate how a QTL influences the period and the amplitude of circadian oscillations through changing model parameters. The model provides a quantitative framework for assessing the interplay between genetic effects of QTLs and rhythmic responses. Copyright © 2011 Elsevier Ltd. All rights reserved.

Special metrics and group actions in geometry

CERN Document Server

Fino, Anna; Musso, Emilio; Podestà, Fabio; Vezzoni, Luigi

2017-01-01

The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.

Solving applied mathematical problems with Matlab

CERN Document Server

Xue, Dingyu

2008-01-01

Computer Mathematics Language-An Overview. Fundamentals of MATLAB Programming. Calculus Problems. MATLAB Computations of Linear Algebra Problems. Integral Transforms and Complex Variable Functions. Solutions to Nonlinear Equations and Optimization Problems. MATLAB Solutions to Differential Equation Problems. Solving Interpolations and Approximations Problems. Solving Probability and Mathematical Statistics Problems. Nontraditional Solution Methods for Mathematical Problems.

SPECIAL EDUCATION COURSES OF STUDY. COURSE OF STUDY, GRADES 9 THROUGH 11, FOR SPECIAL EDUCATION.

Science.gov (United States)

Phoenix Union High School District, AZ.

THIS GUIDE FOR GRADES 9 TO 11 WAS DEVELOPED FROM MANY SOURCES BUT WITH MAJOR CONTRIBUTIONS FROM TEACHERS WHO USE IT IN A SPECIAL EDUCATION PROGRAM TO PARTIALLY MEET DIPLOMA REQUIREMENTS. UNITS ARE IN ENGLISH, MATHEMATICS, SCIENCE, SOCIAL STUDIES, AMERICAN HISTORY AND GOVERNMENT, ECONOMICS, HOME ECONOMICS, FOOD SERVICE, AND SHOP. EACH COURSE PLAN…

Basic mathematics for the biological and social sciences

CERN Document Server

Marriott, F H C

2013-01-01

Basic Mathematics for the Biological and Social Sciences deals with the applications of basic mathematics in the biological and social sciences. Mathematical concepts that are discussed in this book include graphical methods, differentiation, trigonometrical or circular functions, limits and convergence, integration, vectors, and differential equations. The exponential function and related functions are also considered. This monograph is comprised of 11 chapters and begins with an overview of basic algebra, followed by an introduction to infinitesimal calculus, scalar and vector quantities, co

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Proceedings – Mathematical Sciences. Current Issue : Vol. 128, Issue 1. Current Issue Volume 128 | Issue 1. March 2018. Home · Volumes & Issues · Special Issues · Forthcoming Articles · Search · Editorial Board · Information for Authors · Subscription ...

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Proceedings – Mathematical Sciences. Current Issue : Vol. 128, Issue 2. Current Issue Volume 128 | Issue 2. April 2018. Home · Volumes & Issues · Special Issues · Forthcoming Articles · Search · Editorial Board · Information for Authors · Subscription ...

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Proceedings – Mathematical Sciences. Current Issue : Vol. 128, Issue 1 · Current Issue Volume 128 | Issue 1. March 2018. Home · Volumes & Issues · Special Issues · Forthcoming Articles · Search · Editorial Board · Information for Authors · Subscription ...

The fundamentals of mathematical analysis

CERN Document Server

Fikhtengol'ts, G M

1965-01-01

The Fundamentals of Mathematical Analysis, Volume 1 is a textbook that provides a systematic and rigorous treatment of the fundamentals of mathematical analysis. Emphasis is placed on the concept of limit which plays a principal role in mathematical analysis. Examples of the application of mathematical analysis to geometry, mechanics, physics, and engineering are given. This volume is comprised of 14 chapters and begins with a discussion on real numbers, their properties and applications, and arithmetical operations over real numbers. The reader is then introduced to the concept of function, i

Mapping Functional Brain Development: Building a Social Brain through Interactive Specialization

Science.gov (United States)

Johnson, Mark H.; Grossmann, Tobias; Kadosh, Kathrin Cohen

2009-01-01

The authors review a viewpoint on human functional brain development, interactive specialization (IS), and its application to the emerging network of cortical regions referred to as the "social brain." They advance the IS view in 2 new ways. First, they extend IS into a domain to which it has not previously been applied--the emergence of social…

Developing Student-Centered Learning Model to Improve High Order Mathematical Thinking Ability

Science.gov (United States)

Saragih, Sahat; Napitupulu, Elvis

2015-01-01

The purpose of this research was to develop student-centered learning model aiming to improve high order mathematical thinking ability of junior high school students of based on curriculum 2013 in North Sumatera, Indonesia. The special purpose of this research was to analyze and to formulate the purpose of mathematics lesson in high order…

Historiography of mathematics in the 19th and 20th centuries

CERN Document Server

Schneider, Martina; Sørensen, Henrik

2016-01-01

This book addresses the historiography of mathematics as it was practiced during the 19th and 20th centuries by paying special attention to the cultural contexts in which the history of mathematics was written. In the 19th century, the history of mathematics was recorded by a diverse range of people trained in various fields and driven by different motivations and aims. These backgrounds often shaped not only their writing on the history of mathematics, but, in some instances, were also influential in their subsequent reception. During the period from roughly 1880-1940, mathematics modernized in important ways, with regard to its content, its conditions for cultivation, and its identity; and the writing of the history of mathematics played into the last part in particular. Parallel to the modernization of mathematics, the history of mathematics gradually evolved into a field of research with its own journals, societies and academic positions. Reflecting both a new professional identity and changes in its prim...

What can atypical language hemispheric specialization tell us about cognitive functions?

Science.gov (United States)

Cai, Qing; Van der Haegen, Lise

2015-04-01

Recent studies have made substantial progress in understanding the interactions between cognitive functions, from language to cognitive control, attention, and memory. However, dissociating these functions has been hampered by the close proximity of regions involved, as in the case in the prefrontal and parietal cortex. In this article, we review a series of studies that investigated the relationship between language and other cognitive functions in an alternative way - by examining their functional (co-)lateralization. We argue that research on the hemispheric lateralization of language and its link with handedness can offer an appropriate starting-point to shed light on the relationships between different functions. Besides functional interactions, anatomical asymmetries in non-human primates and those underlying language in humans can provide unique information about cortical organization. Finally, some open questions and criteria are raised for an ideal theoretical model of the cortex based on hemispheric specialization.

General existence principles for Stieltjes differential equations with applications to mathematical biology

Science.gov (United States)

López Pouso, Rodrigo; Márquez Albés, Ignacio

2018-04-01

Stieltjes differential equations, which contain equations with impulses and equations on time scales as particular cases, simply consist on replacing usual derivatives by derivatives with respect to a nondecreasing function. In this paper we prove new existence results for functional and discontinuous Stieltjes differential equations and we show that such general results have real world applications. Specifically, we show that Stieltjes differential equations are specially suitable to study populations which exhibit dormant states and/or very short (impulsive) periods of reproduction. In particular, we construct two mathematical models for the evolution of a silkworm population. Our first model can be explicitly solved, as it consists on a linear Stieltjes equation. Our second model, more realistic, is nonlinear, discontinuous and functional, and we deduce the existence of solutions by means of a result proven in this paper.

Mathematical Sciences Institute Workshop

CERN Document Server

Scott, Philip

1990-01-01

A so-called "effective" algorithm may require arbitrarily large finite amounts of time and space resources, and hence may not be practical in the real world. A "feasible" algorithm is one which only requires a limited amount of space and/or time for execution; the general idea is that a feasible algorithm is one which may be practical on today's or at least tomorrow's computers. There is no definitive analogue of Church's thesis giving a mathematical definition of feasibility; however, the most widely studied mathematical model of feasible computability is polynomial-time computability. Feasible Mathematics includes both the study of feasible computation from a mathematical and logical point of view and the reworking of traditional mathematics from the point of view of feasible computation. The diversity of Feasible Mathematics is illustrated by the. contents of this volume which includes papers on weak fragments of arithmetic, on higher type functionals, on bounded linear logic, on sub recursive definitions ...

A history of mathematics

CERN Document Server

Boyer, Carl B

1989-01-01

"Boyer and Merzbach distill thousands of years of mathematics into this fascinating chronicle. From the Greeks to Godel, the mathematics is brilliant; the cast of characters is distinguished; the ebb and flow of ideas is everywhere evident. And, while tracing the development of European mathematics, the authors do not overlook the contributions of Chinese, Indian, and Arabic civilizations. Without doubt, this is--and will long remain--a classic one-volume history of mathematics and mathematicians who create it." --William Dunham Author, Journey Through Genius, The Great Theorems of Mathematics "When we read a book like A History of Mathematics, we get the picture of a mounting structure, ever taller and broader and more beautiful and magnificent--and with a foundation, moreover, that is as untainted and as functional now as it was when Thales worked out the first geometrical theorems nearly 26 centuries ago." --From the Foreword by Isaac Asimov "One of the most useful and comprehensive general introductions t...

The thumb carpometacarpal joint: curvature morphology of the articulating surfaces, mathematical description and mechanical functioning.

Science.gov (United States)

Dathe, Henning; Dumont, Clemens; Perplies, Rainer; Fanghänel, Jochen; Kubein-Meesenburg, Dietmar; Nägerl, Hans; Wachowski, Martin M

2016-01-01

The purpose is to present a mathematical model of the function of the thumb carpometacarpal joint (TCMCJ) based on measurements of human joints. In the TCMCJ both articulating surfaces are saddle-shaped. The aim was to geometrically survey the shapes of the articulating surfaces using precise replicas of 28 TCMCJs. None of these 56 articulating surfaces did mathematically extend the differential geometrical neighbourhood around the main saddle point so that each surface could be characterised by three main parameters: the two extreme radii of curvature in the main saddle point and the angle between the saddles' asymptotics (straight lines). The articulating surfaces, when contacting at the respective main saddle points, are incongruent. Hence, the TCMCJ has functionally five kinematical degrees of freedom (DOF); two DOF belong to flexion/extension, two to ab-/adduction. These four DOF are controlled by the muscular apparatus. The fifth DOF, axial rotation, cannot be adjusted but stabilized by the muscular apparatus so that physiologically under compressive load axial rotation does not exceed an angle of approximately ±3°. The TCMCJ can be stimulated by the muscular apparatus to circumduct. The mechanisms are traced back to the curvature incongruity of the saddle surfaces. Hence we mathematically proved that none of the individual saddle surfaces can be described by a quadratic saddle surface as is often assumed in literature. We derived an algebraic formula with which the articulating surfaces in the TCMCJ can be quantitatively described. This formula can be used to shape the articulating surfaces in physiologically equivalent TCMCJ-prostheses.

Mapping Mathematics in Classroom Discourse

Science.gov (United States)

Herbel-Eisenmann, Beth A.; Otten, Samuel

2011-01-01

This article offers a particular analytic method from systemic functional linguistics, "thematic analysis," which reveals the mathematical meaning potentials construed in discourse. Addressing concerns that discourse analysis is too often content-free, thematic analysis provides a way to represent semantic structures of mathematical content,…

Essentials engineering mathematics

CERN Document Server

Jeffrey, Alan

2004-01-01

Real numbers, inequalities and intervalsFunction, domain and rangeBasic coordinate geometryPolar coordinatesMathematical inductionBinomial theoremCombination of functionsSymmetry in functions and graphsInverse functionsComplex numbers; real and imaginary formsGeometry of complex analysisModulus-argument form of a complex numberRoots of complex numbersLimitsOne-sided limitsDerivativesLeibniz's formulaDifferentialsDifferentiation of inverse trigonometric functionsImplicit differentiationParametrically defined curves and parametric differentiationThe exponential functionThe logarithmic functionHy

Tables of generalized Airy functions for the asymptotic solution of the differential equation

CERN Document Server

Nosova, L N

1965-01-01

Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equations contains tables of the special functions, namely, the generalized Airy functions, and their first derivatives, for real and pure imaginary values. The tables are useful for calculations on toroidal shells, laminae, rode, and for the solution of certain other problems of mathematical physics. The values of the functions were computed on the ""Strela"" highspeed electronic computer.This book will be of great value to mathematicians, researchers, and students.

Mathematical theory of elasticity of quasicrystals and its applications

CERN Document Server

Fan, Tian-You

2016-01-01

This interdisciplinary work on condensed matter physics, the continuum mechanics of novel materials, and partial differential equations, discusses the mathematical theory of elasticity and hydrodynamics of quasicrystals, as well as its applications. By establishing new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions, the theories developed here dramatically simplify the solution of complex elasticity problems. Comprehensive and detailed mathematical derivations guide readers through the work. By combining theoretical analysis and experimental data, mathematical studies and practical applications, readers will gain a systematic, comprehensive and in-depth understanding of condensed matter physics, new continuum mechanics and applied mathematics. This new edition covers the latest developments in quasicrystal studies. In particular, it pays special attention to the hydrodynamics, soft-matter quasicrystals, and the Poisson bracket m...

Fundamentals of university mathematics

CERN Document Server

McGregor, C M; Stothers, W W

2010-01-01

The third edition of this popular and effective textbook provides in one volume a unified treatment of topics essential for first year university students studying for degrees in mathematics. Students of computer science, physics and statistics will also find this book a helpful guide to all the basic mathematics they require. It clearly and comprehensively covers much of the material that other textbooks tend to assume, assisting students in the transition to university-level mathematics.Expertly revised and updated, the chapters cover topics such as number systems, set and functions, differe

Methods and models in mathematical biology deterministic and stochastic approaches

CERN Document Server

Müller, Johannes

2015-01-01

This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models, and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks, and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and  branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.

Families with special needs children: family health, functioning, and care burden.

Science.gov (United States)

Caicedo, Carmen

2014-01-01

There are 11.2 million children with special health care needs in the United States or one in five households caring for a special needs child. A small group of children who need continuous medical, nursing, therapeutic services that enable them to survive is growing in numbers. This study examined physical health (physical functioning), mental health (emotional, social, and cognitive functioning; communication; and worry), family functioning (daily activities, family relationships), and care burden (caregiver employment, caregiving time, travel time, health-related out-of-pocket expenditures) of parent caregivers for medically complex, medical technology-dependent children. Data were collected once a month for 5 months on 84 parents recruited in South Florida using the Pediatric Quality of Life Family Impact Module. Physically, parents were tired when they woke up: too tired to do the things they liked to do and with little energy for chores or social activities. Mentally, they were frustrated, anxious, and angry; felt helpless and hopeless; had cognitive problems remembering and focusing on tasks; were worried about the child's medications, treatments, side effects; and were anxious about child's future and effect of the child's condition on other family members. Socially, they felt isolated and that people did not understand their family situation; they found it hard to talk with others including physicians and nurses. Average weekly hours of direct care was 33.0 (SD = 30.4 hours); average monthly out-of-pocket expenditures was $348.78 (SD = $623.34). It is essential to assess parents' physical and mental health and functioning and to provide interventions to improve health and functioning for both the parents and the children for whom they are caring. © The Author(s) 2014.

REVIEW OF MATHEMATICAL METHODS AND ALGORITHMS OF MEDICAL IMAGE PROCESSING ON THE EXAMPLE OF TECHNOLOGY OF MEDICAL IMAGE PROCESSING FROM WOLFRAM MATHEMATICS

Directory of Open Access Journals (Sweden)

O. Ye. Prokopchenko

2015-10-01

Full Text Available The article analyzes the basic methods and algorithms of mathematical processing of medical images as objects of computer mathematics. The presented methods and computer algorithms of mathematics relevant and may find application in the field of medical imaging - automated processing of images; as a tool for measurement and determination the optical parameters; identification and formation of medical images database. Methods and computer algorithms presented in the article and based on Wolfram Mathematica are also relevant to the problem of modern medical education. As an example of Wolfram Mathematics may be considered appropriate demonstration, such as recognition of special radiographs and morphological imaging. These methods are used to improve  the diagnostic significance and value of medical (clinical research and can serve as an educational interactive demonstration. Implementation submitted individual methods and algorithms of computer Wolfram Mathematics contributes, in general, the optimization process of practical processing and presentation of medical images.

The geometry of special relativity

International Nuclear Information System (INIS)

Parizet, Jean

2008-01-01

This book for students in mathematics or physics shows the interest of geometry to understand special relativity as a consequence of invariance of Maxwell equations and of constancy of the speed of light. Space-time is actually provided with a geometrical structure and a physical interpretation: at each observer are associated his own time and his own physical space in which occur events he is concerned with. This leads to a natural approach to special relativity. The Lorentz group and its algebra are then studied by using matrices and the Pauli algebra. Quaternions are also addressed

Fundamentals of scientific mathematics

CERN Document Server

Owen, George E

2003-01-01

Offering undergraduates a solid mathematical background (and functioning equally well for independent study), this rewarding, beautifully illustrated text covers geometry and matrices, vector algebra, analytic geometry, functions, and differential and integral calculus. 1961 edition.

Discrete mathematics using a computer

CERN Document Server

Hall, Cordelia

2000-01-01

Several areas of mathematics find application throughout computer science, and all students of computer science need a practical working understanding of them. These core subjects are centred on logic, sets, recursion, induction, relations and functions. The material is often called discrete mathematics, to distinguish it from the traditional topics of continuous mathematics such as integration and differential equations. The central theme of this book is the connection between computing and discrete mathematics. This connection is useful in both directions: • Mathematics is used in many branches of computer science, in applica­ tions including program specification, datastructures,design and analysis of algorithms, database systems, hardware design, reasoning about the correctness of implementations, and much more; • Computers can help to make the mathematics easier to learn and use, by making mathematical terms executable, making abstract concepts more concrete, and through the use of software tools su...

Matrix Mathematics Theory, Facts, and Formulas (Second Edition)

CERN Document Server

Bernstein, Dennis S

2011-01-01

When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices. Each chapter describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly and rigorously with cross references, citations to the literature, and illuminat

Certain properties of some special functions of two variables and two indices

International Nuclear Information System (INIS)

Khan, Subuhi

2002-07-01

In this paper, we derive a result concerning eigenvector and eigenvalue for a quadratic combination of four operators defined on a Lie algebra of endomorphisms of a vector space. Further, using this result, we deduce certain properties of some special functions of two variables and two indices. (author)

mathematical model of thermal explosion, the dual variational formulation of nonlinear problem, alternative functional

Directory of Open Access Journals (Sweden)

V. S. Zarubin

2016-01-01

in its plane, and in the circular cylinder unlimited in length.An approximate numerical solution of the differential equation that is included in a nonlinear mathematical model of the thermal explosion enables us to obtain quantitative estimates of combination of determining parameters at which the limit state occurs in areas of not only canonical form. A capability to study of the thermal explosion state can be extended in the context of development of mathematical modeling methods, including methods of model analysis to describe the thermal state of solids.To analyse a mathematical model of the thermal explosion in a homogeneous solid the paper uses a variational approach based on the dual variational formulation of the appropriate nonlinear stationary problem of heat conduction in such a body. This formulation contains two alternative functional reaching the matching values in their stationary points corresponding to the true temperature distribution. This functional feature allows you to not only get an approximate quantitative estimate of the combination of parameters that determine the thermal explosion state, but also to find the greatest possible error in such estimation.

Participation of Faculty of Mathematics and Physics, Charles University in Prague, in training of personnel for nuclear power

International Nuclear Information System (INIS)

Sterba, F.

1983-01-01

Graduates of application oriented fields of all mathematics and physics specializations of Solid state physics and Nuclear physics work successfully in nuclear power. In the mathematics fields great attention is devoted to optimization, control, process modeling, etc. The subject Solid state physics is subdivided into the following specializations: physics of metals, magnetic properties of the solid state and structural analysis. These specializations educate specialists with a good knowledge of the structure and properties of metal materials. Great attention is devoted to the causes and development of defects, materials creep and the radiation damage of crystal lattices. The nuclear physics specialization Applied nuclear physics deals with the use of nuclear methods in diverse fields and provides basic knowledge in nuclear power generation and the operation of nuclear reactors. The Faculty of Mathematics and Physics of the Charles University in Prague also runs postgraduate study courses in nuclear physics measurement methods, solid state physics, etc. (E.S.)

Examining mathematical discourse to understand in-service teachers’ mathematical activities

Directory of Open Access Journals (Sweden)

Margot Berger

2013-04-01

Full Text Available In this article I use Sfard’s theory of commognition to examine the surprising activities of a pair of in-service mathematics teachers in South Africa as they engaged in a particular mathematical task which allowed for, but did not prescribe, the use of GeoGebra. The (pre-calculus task required students to examine a function at an undefined point and to decide whether a vertical asymptote is associated with this point or not. Using the different characteristics of mathematical discourse, I argue that the words that students use really matter and show how a change in one participant’s use of the term ‘vertical asymptote’ constituted and reflected her learning. I also show how the other participant used imitation in a ritualised routine to get through the task. Furthermore I demonstrate how digital immigrants may resist the use of technology as the generator of legitimate mathematical objects.

On Approximation of Hyper-geometric Function Values of a Special Class

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P. L. Ivankov

2017-01-01

Full Text Available Investigations of arithmetic properties of the hyper-geometric function values make it possible to single out two trends, namely, Siegel’s method and methods based on the effective construction of a linear approximating form. There are also methods combining both approaches mentioned.  The Siegel’s method allows obtaining the most general results concerning the abovementioned problems. In many cases it was used to establish the algebraic independence of the values of corresponding functions. Although the effective methods do not allow obtaining propositions of such generality they have nevertheless some advantages. Among these advantages one can distinguish at least two: a higher precision of the quantitative results obtained by effective methods and a possibility to study the hyper-geometric functions with irrational parameters.In this paper we apply the effective construction to estimate a measure of the linear independence of the hyper-geometric function values over the imaginary quadratic field. The functions themselves were chosen by a special way so that it could be possible to demonstrate a new approach to the effective construction of a linear approximating form. This approach makes it possible also to extend the well-known effective construction methods of the linear approximating forms for poly-logarithms to the functions of more general type.To obtain the arithmetic result we had to establish a linear independence of the functions under consideration over the field of rational functions. It is apparently impossible to apply directly known theorems containing sufficient (and in some cases needful and sufficient conditions for the system of functions appearing in the theorems mentioned. For this reason, a special technique has been developed to solve this problem.The paper presents the obtained arithmetic results concerning the values of integral functions, but, with appropriate alterations, the theorems proved can be adapted to

DOE Fundamentals Handbook: Mathematics, Volume 1

International Nuclear Information System (INIS)

1992-06-01

The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclear facility operations

DOE Fundamentals Handbook: Mathematics, Volume 2

International Nuclear Information System (INIS)

1992-06-01

The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclear facility operations

Rethinking logic logic in relation to mathematics, evolution, and method

CERN Document Server

Cellucci, Carlo

2014-01-01

This book examines the limitations of mathematical logic and proposes a new approach intended to overcome them. Formulates new rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition and diagrams.

A quest towards a mathematical theory of living systems

CERN Document Server

Bellomo, Nicola; Gibelli, Livio; Outada, Nisrine

2017-01-01

This monograph aims to lay the groundwork for the design of a unified mathematical approach to the modeling and analysis of large, complex systems composed of interacting living things. Drawing on twenty years of research in various scientific fields, it explores how mathematical kinetic theory and evolutionary game theory can be used to understand the complex interplay between mathematical sciences and the dynamics of living systems. The authors hope this will contribute to the development of new tools and strategies, if not a new mathematical theory. The first chapter discusses the main features of living systems and outlines a strategy for their modeling. The following chapters then explore some of the methods needed to potentially achieve this in practice. Chapter Two provides a brief introduction to the mathematical kinetic theory of classical particles, with special emphasis on the Boltzmann equation; the Enskog equation, mean field models, and Monte Carlo methods are also briefly covered. Chapter Three...

Exposing the Mathematical Wizard: Approximating Trigonometric Functions

Science.gov (United States)

Gordon, Sheldon P.

2011-01-01

For almost all students, what happens when they push buttons on their calculators is essentially magic, and the techniques used are seemingly pure wizardry. In this article, the author draws back the curtain to expose some of the mathematics behind computational wizardry and introduces some fundamental ideas that are accessible to precalculus…

Twenty years of functional near-infrared spectroscopy: introduction for the special issue.

Science.gov (United States)

Boas, David A; Elwell, Clare E; Ferrari, Marco; Taga, Gentaro

2014-01-15

Papers from four different groups were published in 1993 demonstrating the ability of functional near infrared spectroscopy (fNIRS) to non-invasively measure hemoglobin concentration responses to brain function in humans. This special issue commemorates the first 20years of fNIRS research. The 9 reviews and 49 contributed papers provide a comprehensive survey of the exciting advances driving the field forward and of the myriad of applications that will benefit from fNIRS. Copyright © 2013 Elsevier Inc. All rights reserved.

Applied geometry and discrete mathematics

CERN Document Server

Sturm; Gritzmann, Peter; Sturmfels, Bernd

1991-01-01

This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's sixty-fifth birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honor of Klee's achievements, this volume presents more than forty papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, th...

The Holey Grail : a special score function for non-binary traitor tracing

NARCIS (Netherlands)

Skoric, B.; Oosterwijk, J.; Doumen, J.M.

2013-01-01

We study collusion-resistant traitor tracing in the simple decoder approach, i.e. assignment of scores for each user separately. We introduce a new score function for non-binary bias-based traitor tracing. It has three special properties that have long been sought after: (i) The expected score of an

Further development of mathematical description for combined toxicity: A case study of lead–fluoride combination

Directory of Open Access Journals (Sweden)

Vladimir G. Panov

2015-01-01

Full Text Available In this article, we check and develop further some postulates of the theory and mathematical modeling of combined toxic effect that we proposed earlier [1]. To this end, we have analyzed the results of an experiment on rats exposed during 6 weeks to repeated intraperitoneal injections of lead acetate, sodium fluoride or both. The development of intoxication was estimated quantitatively with 54 functional, biochemical and morphometric indices. For mathematical description of the effect that lead and fluorine doses produced alone or in combination, we used a response surface regression model containing linear and cross terms (hyperbolic paraboloid. It is shown that the combination of lead and fluoride features the same 10 types of combined effect that we found previously for the lead and cadmium combination. Special attention is given to indices on which lead and fluorine produce an opposite effect.

Variational functionals which admit discontinuous trial functions

International Nuclear Information System (INIS)

Nelson, P. Jr.

1975-01-01

It is argued that variational synthesis with discontinuous trial functions requires variational principles applicable to equations involving operators acting between distinct Hilbert spaces. A description is given of a Roussopoulos-type variational principle generalized to cover this situation. This principle is suggested as the basis for a unified approach to the derivation of variational functionals. In addition to esthetics, this approach has the advantage that the mathematical details increase the understanding of the derived functional, particularly the sense in which a synthesized solution should be regarded as an approximation to the true solution. By way of illustration, the generalized Roussopoulos principle is applied to derive a class of first-order diffusion functionals which admit trial functions containing approximations at an interface. These ''asymptotic'' interface quantities are independent of the limiting approximations from either side and permit use of different trial spectra at and on either side of an interface. The class of functionals derived contains as special cases both the Lagrange multiplier method of Buslik and two functionals of Lambropoulos and Luco. Some numerical results for a simple two-group model confirm that the ''multipliers'' can closely approximate the appropriate quantity in the region near an interface. (U.S.)

A MATLAB-Aided Method for Teaching Calculus-Based Business Mathematics

Science.gov (United States)

Liang, Jiajuan; Pan, William S. Y.

2009-01-01

MATLAB is a powerful package for numerical computation. MATLAB contains a rich pool of mathematical functions and provides flexible plotting functions for illustrating mathematical solutions. The course of calculus-based business mathematics consists of two major topics: 1) derivative and its applications in business; and 2) integration and its…

Biodiversity, ecosystem functions and services in environmental risk assessment: introduction to the special issue.

Science.gov (United States)

Schäfer, Ralf B

2012-01-15

This Special Issue focuses on the questions if and how biodiversity, ecosystem functions and resulting services could be incorporated into the Ecological Risk Assessment (ERA). Therefore, three articles provide a framework for the integration of ecosystem services into ERA of soils, sediments and pesticides. Further articles demonstrate ways how stakeholders can be integrated into an ecosystem service-based ERA for soils and describe how the current monitoring could be adapted to new assessment endpoints that are directly linked to ecosystem services. Case studies show that the current ERA may not be protective for biodiversity, ecosystem functions and resulting services and that both pesticides and salinity currently adversely affect ecosystem functions in the field. Moreover, ecological models can be used for prediction of new protection goals and could finally support their implementation into the ERA. Overall, the Special Issue stresses the urgent need to enhance current procedures of ERA if biodiversity, ecosystem functions and resulting services are to be protected. Copyright © 2011 Elsevier B.V. All rights reserved.

Friend Influence and Susceptibility to Influence: Changes in Mathematical Reasoning as a Function of Relative Peer Acceptance and Interest in Mathematics

Science.gov (United States)

DeLay, Dawn; Laursen, Brett; Kiuru, Noona; Poikkeus, Anna-Maija; Aunola, Kaisa

2016-01-01

This study investigated friend influence over mathematics achievement in 202 same-sex friendship dyads (106 girl dyads). Participants were in the third grade (around age 9) at the outset. Each friend completed a questionnaire describing interest in mathematics and a standardized mathematical reasoning assessment. Peer nominations provided a…

Evidence of two distinct functionally specialized fibroblast lineages in breast stroma

DEFF Research Database (Denmark)

Morsing, Mikkel; Klitgaard, Marie Christine; Jafari Kermani, Abbas

2016-01-01

Background The terminal duct lobular unit (TDLU) is the most dynamic structure in the human breast and the putative site of origin of human breast cancer. Although stromal cells contribute to a specialized microenvironment in many organs, this component remains largely understudied in the human...... conditions followed by analysis of adipogenic and osteogenic differentiation. To test whether the two fibroblast lineages are functionally imprinted by their site of origin, single cell sorted CD271low/MUC1high normal breast luminal epithelial cells are plated on fibroblast feeders for the observation...... fibroblast lineages exist in the normal human breast, of which the lobular fibroblasts have properties in common with mesenchymal stem cells and support epithelial growth and morphogenesis. We propose that lobular fibroblasts constitute a specialized microenvironment for human breast luminal epithelial...

Preface for the special issue of Mathematical Biosciences and Engineering, BIOCOMP 2012.

Science.gov (United States)

Buonocore, Aniello; Di Crescenzo, Antonio; Hastings, Alan

2014-04-01

The International Conference "BIOCOMP2012 - Mathematical Modeling and Computational Topics in Biosciences'', was held in Vietri sul Mare (Italy), June 4-8, 2012. It was dedicated to the Memory of Professor Luigi M. Ricciardi (1942-2011), who was a visionary and tireless promoter of the 3 previous editions of the BIOCOMP conference series. We thought that the best way to honor his memory was to continue the BIOCOMP program. Over the years, this conference promoted scientific activities related to his wide interests and scientific expertise, which ranged in various areas of applications of mathematics, probability and statistics to biosciences and cybernetics, also with emphasis on computational problems. We are pleased that many of his friends and colleagues, as well as many other scientists, were attracted by the goals of this recent event and offered to contribute to its success.

Einstein in matrix form. Exact derivation of the theory of special and general relativity without tensors

Energy Technology Data Exchange (ETDEWEB)

Ludyk, Guenter [Bremen Univ. (Germany). Physics and Electrical Engineering

2013-11-01

Derives the fundamental equations of Einstein's theory of special and general relativity using matrix calculus, without the help of tensors. Provides necessary mathematical tools in a user-friendly way, either directly in the text or in the appendices. Appendices contain an introduction to classical dynamics as a refresher of known fundamental physics. Rehearses vector and matrix calculus, differential geometry, and some special solutions of general relativity in the appendices. This book is an introduction to the theories of Special and General Relativity. The target audience are physicists, engineers and applied scientists who are looking for an understandable introduction to the topic - without too much new mathematics. The fundamental equations of Einsteins theory of Special and General Relativity are derived using matrix calculus, without the help of tensors. This feature makes the book special and a valuable tool for scientists and engineers with no experience in the field of tensor calculus. In part I the foundations of Special Relativity are developed, part II describes the structure and principle of General Relativity. Part III explains the Schwarzschild solution of spherical body gravity and examines the ''Black Hole'' phenomenon. Any necessary mathematical tools are user friendly provided, either directly in the text or in the appendices.

Einstein in matrix form. Exact derivation of the theory of special and general relativity without tensors

International Nuclear Information System (INIS)

Ludyk, Guenter

2013-01-01

Derives the fundamental equations of Einstein's theory of special and general relativity using matrix calculus, without the help of tensors. Provides necessary mathematical tools in a user-friendly way, either directly in the text or in the appendices. Appendices contain an introduction to classical dynamics as a refresher of known fundamental physics. Rehearses vector and matrix calculus, differential geometry, and some special solutions of general relativity in the appendices. This book is an introduction to the theories of Special and General Relativity. The target audience are physicists, engineers and applied scientists who are looking for an understandable introduction to the topic - without too much new mathematics. The fundamental equations of Einsteins theory of Special and General Relativity are derived using matrix calculus, without the help of tensors. This feature makes the book special and a valuable tool for scientists and engineers with no experience in the field of tensor calculus. In part I the foundations of Special Relativity are developed, part II describes the structure and principle of General Relativity. Part III explains the Schwarzschild solution of spherical body gravity and examines the ''Black Hole'' phenomenon. Any necessary mathematical tools are user friendly provided, either directly in the text or in the appendices.

A Special Assignment from NASA: Understanding Earth's Atmosphere through the Integration of Science and Mathematics

Science.gov (United States)

Fox, Justine E.; Glen, Nicole J.

2012-01-01

Have your students ever wondered what NASA scientists do? Have they asked you what their science and mathematics lessons have to do with the real world? This unit about Earth's atmosphere can help to answer both of those questions. The unit described here showcases "content specific integration" of science and mathematics in that the lessons meet…

Basic Phage Mathematics.

Science.gov (United States)

Abedon, Stephen T; Katsaounis, Tena I

2018-01-01

Basic mathematical descriptions are useful in phage ecology, applied phage ecology such as in the course of phage therapy, and also toward keeping track of expected phage-bacterial interactions as seen during laboratory manipulation of phages. The most basic mathematical descriptor of phages is their titer, that is, their concentration within stocks, experimental vessels, or other environments. Various phenomena can serve to modify phage titers, and indeed phage titers can vary as a function of how they are measured. An important aspect of how changes in titers can occur results from phage interactions with bacteria. These changes tend to vary in degree as a function of bacterial densities within environments, and particularly densities of those bacteria that are susceptible to or at least adsorbable by a given phage type. Using simple mathematical models one can describe phage-bacterial interactions that give rise particularly to phage adsorption events. With elaboration one can consider changes in both phage and bacterial densities as a function of both time and these interactions. In addition, phages along with their impact on bacteria can be considered as spatially constrained processes. In this chapter we consider the simpler of these concepts, providing in particular detailed verbal explanations toward facile mathematical insight. The primary goal is to stimulate a more informed use and manipulation of phages and phage populations within the laboratory as well as toward more effective phage application outside of the laboratory, such as during phage therapy. More generally, numerous issues and approaches to the quantification of phages are considered along with the quantification of individual, ecological, and applied properties of phages.

Success and failure in school mathematics: effects of instruction and school environment.

Science.gov (United States)

Reusser, K

2000-01-01

Given the stubborn phenomenon of many children's serious difficulties and failure in mathematical learning, the hypothesis of developmental delay, or neurocognitively based deficiency should be complemented by further explanantions of children's weaknesses and substandard performance in mathematics. One obvious explanantion is that schooling and instruction for low ability children and for children with special needs is often inadequate. The present contribution examines selected research on mathematics learning under a cognitive instructional (didactical) perspective. Constructivist learning theory, the rooting of meaningful learning in concrete modeling activities, the balancing of understanding and practice in mathematics instruction, diagnostic and adaptive teaching, computer-assisted instruction, and the role of nonmathematical stumbling-blocks are discussed as principles and factors of effective mathematics learning and teaching.

Training to develop sense of numbers and quantities for preschool children with special needs

OpenAIRE

Kuplenk, Petra

2017-01-01

Children as well as adults have to cope with mathematics every day either at nursery school, at work or at home. Mathematics has a great impact on our lives and work. When I was working with children with special needs I noticed that they found it very difficult to understand numbers and numbers relations. That is why I devoted my diploma work to preparing a complete training for developing a feeling of number sense with children with special needs. I believe that it is of great importan...

Modeling interdisciplinary activities involving Mathematics

DEFF Research Database (Denmark)

Iversen, Steffen Møllegaard

2006-01-01

In this paper a didactical model is presented. The goal of the model is to work as a didactical tool, or conceptual frame, for developing, carrying through and evaluating interdisciplinary activities involving the subject of mathematics and philosophy in the high schools. Through the terms...... of Horizontal Intertwining, Vertical Structuring and Horizontal Propagation the model consists of three phases, each considering different aspects of the nature of interdisciplinary activities. The theoretical modelling is inspired by work which focuses on the students abilities to concept formation in expanded...... domains (Michelsen, 2001, 2005a, 2005b). Furthermore the theoretical description rest on a series of qualitative interviews with teachers from the Danish high school (grades 9-11) conducted recently. The special case of concrete interdisciplinary activities between mathematics and philosophy is also...

Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

Science.gov (United States)

Mumcu, Hayal Yavuz

2016-01-01

The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

Mathematical simulation of point defect interaction with grain boundaries

International Nuclear Information System (INIS)

Bojko, V.S.

1987-01-01

Published works, where the interaction of point defects and grain boundaries was studied by mathematical simulation methods, have been analysed. Energetics of the vacancy formation both in nuclei of large-angle special grain boundaries and in lattice regions adjoining them has been considered. The data obtained permit to explain specific features of grain-boundary diffusion processes. Results of mathematical simulation of the interaction of impurity atoms and boundaries have been considered. Specific features of the helium atom interaction with large-angle grain boundaries are analysed as well

Functional specialization and phenotypic generalization in the pollination system of an epiphytic cactus

Directory of Open Access Journals (Sweden)

Cristiane Martins

2018-03-01

Full Text Available ABSTRACT Plant-pollinator interactions range from obligatory specialists to facultative generalists, and floral morphology and pollination system may not match completely. The floral biology, reproductive system and floral visitors of a species of the tribe Rhipsalideae were investigated with a focus on the consistency between the pollination system and the floral phenotype. Rhipsalis neves-armondii is an obligate xenogamous species, due to self-sterility. Its flowers are white, small and diurnal, and radially symmetrical. These features, along with their small amount of nectar, characterize the flowers as phenotypic generalists. The most frequent pollinators were a solitary oligolectic species of Andrenidae (Rhophitulus solani, two species of Meliponinae (Trigona spinipes and T. braueri and Apis mellifera. Despite the generalist floral phenotype, the pollination system is functionally specialized, since only small bees performed effective visits. Flowers of R. neves-armondii may represent a case of cryptic floral specialization in which attributes other than morphology act as filters, restricting them to a single functional group of pollinators. Moreover, the four most frequent species of pollinators cover a spectrum ranging from solitary oligolectic to social polylectic bees, including an exotic species. These results illustrate the distinct dimensions of specialization-generalization that may occur in the pollination process of a single species.

Rings Related to Special Atoms | France-Jackson | Quaestiones ...

African Journals Online (AJOL)

Abstract unavailable at this time... Mathematics Subject Classification (1991): 16A21, 16A12 Keywords: ring, special atoms, atoms, *k-ring, prime ring, *-ring, Jacobson, artinia, essential extension, homomorphic image, ideals. Quaestiones Mathematicae 24(1) 2001, 105–109 ...

Mathematical Footprints Discovering Mathematics Everywhere

CERN Document Server

Pappas, Theoni

1999-01-01

MATHEMATICAL FOOTPRINTS takes a creative look at the role mathematics has played since prehistoric times, and will play in the future, and uncovers mathematics where you least expect to find it from its many uses in medicine, the sciences, and its appearance in art to its patterns in nature and its central role in the development of computers. Pappas presents mathematical ideas in a readable non-threatening manner. MATHEMATICAL FOOTPRINTS is another gem by the creator of THE MATHEMATICS CALENDAR and author of THE JOY OF MATHEMATICS. "Pappas's books have been gold mines of mathematical ent

Functional analysis in modern applied mathematics

CERN Document Server

Curtain, Ruth F

1977-01-01

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat

Wronski's Foundations of Mathematics.

Science.gov (United States)

Wagner, Roi

2016-09-01

Argument This paper reconstructs Wronski's philosophical foundations of mathematics. It uses his critique of Lagrange's algebraic analysis as a vignette to introduce the problems that he raised, and argues that these problems have not been properly appreciated by his contemporaries and subsequent commentators. The paper goes on to reconstruct Wronski's mathematical law of creation and his notions of theory and techne, in order to put his objections to Lagrange in their philosophical context. Finally, Wronski's proof of his universal law (the expansion of a given function by any series of functions) is reviewed in terms of the above reconstruction. I argue that Wronski's philosophical approach poses an alternative to the views of his contemporary mainstream mathematicians, which brings up the contingency of their choices, and bridges the foundational concerns of early modernity with those of the twentieth-century foundations crisis. I also argue that Wronski's views may be useful to contemporary philosophy of mathematical practice, if they are read against their metaphysical grain.

The effect of special health care needs and health status on school functioning.

Science.gov (United States)

Reuben, Cynthia A; Pastor, Patricia N

2013-10-01

Past studies have shown that specific child conditions are associated with poor school outcomes. A national health survey with noncategorical measures of health and indicators of school functioning offers the opportunity to examine this association. To compare links between two health measures (children with special health care needs and general health status) and multiple school outcomes. The analysis was based on 59,440 children aged 6-17 years from the 2007 National Survey of Children's Health. Child health was assessed using the Children with Special Health Care Needs (CSHCN) screener and a question on general health status. CSHCN were classified by the complexity of their health care needs. Indicators of school functioning included special education use, many problem reports, repeated a grade, lack of school engagement, and many missed school days. Overall 22% of children were identified as CSHCN: 13% with more complex needs (C-CSHCN) and 9% with medication use only (CSHCN-RX). Approximately 17% of children were in less than optimal health. After controlling for a child's sociodemographic characteristics C-CSHCN had an increased risk of all of the negative school outcomes compared to children without SHCN, while CSHCN-RX had an increased risk of only one school outcome (many missed school days). Children in less than optimal health were at an increased risk of all negative school outcomes compared to children in optimal health. The CSHCN screener and health status question identify related, but distinct, groups of children with worse outcomes on the indicators of school functioning. Published by Elsevier Inc.

Preface to the Special Issue on the International Workshop on Applied Mathematics Errachidia (IWAM’2017

Directory of Open Access Journals (Sweden)

M. R. Sidi Ammi

2017-04-01

Full Text Available The International Workshop on Applied Mathematics, Errachidia (IWAM’2017 took place in Errachidia, Morocco at the Faculty of Sciences and Technics during March 13, 2017 (https://iwam2017.sciencesconf.org/. The workshop was held with the support of FST Errachidia, the University Moulay Isma¨ıl. It is aimed at celebrating the collaborative research in applied mathematics by the mathematicians of the FST Errachidia, the Systems and Control Group of CIDMA, University of Aveiro, and with the MIA Lab, University of La Rochelle. It was attended by about 100 Mathematicians and Ph.D. and M.S. students, coming from universities from different countries, such as Algeria, Egypt, France, Portugal, and Morocco. The aim of IWAM’2017 is to bring researchers and professionals to discuss recent developments in both theoretical and applied mathematics, to create the knowledge exchange platform between mathematicians. The workshop is broad-based that covers several branches of engineering sciences, mathematics and interdisciplinary researches mainly in the fields of optimization and variational analysis, theoretical, asymptotic and numerical analysis of ordinary, partial and fractional differential equations

Brain correlates of mathematical competence in processing mathematical representations

Directory of Open Access Journals (Sweden)

Roland H. Grabner

2011-11-01

Full Text Available The ability to extract numerical information from different representation formats (e.g., equations, tables, or diagrams is a key component of mathematical competence but little is known about its neural correlate. Previous studies comparing mathematically less and more competent adults have focused on mental arithmetic and reported differences in left angular gyrus activity which were interpreted to reflect differential reliance on arithmetic fact retrieval during problem solving. The aim of the present functional magnetic resonance imaging (fMRI study was to investigate the brain correlates of mathematical competence in a task requiring the processing of typical mathematical representations. Twenty-eight adults of lower and higher mathematical competence worked on a representation matching task in which they had to evaluate whether the numerical information of a symbolic equation matches that of a bar chart. Two task conditions without and one condition with arithmetic demands were administered. Both competence groups performed equally well in the non-arithmetic conditions and only differed in accuracy in the condition requiring calculation. Activation contrasts between the groups revealed consistently stronger left angular gyrus activation in the more competent individuals across all three task conditions. The finding of competence-related activation differences independently of arithmetic demands suggests that more and less competent individuals differ in a cognitive process other than arithmetic fact retrieval. Specifically, it is argued that the stronger left angular gyrus activity in the more competent adults may reflect their higher proficiency in processing mathematical symbols. Moreover, the study demonstrates competence-related parietal activation differences that were not accompanied by differential experimental performance.

EULER - A Real Virtual Library for Mathematics

CERN Document Server

Jost, Michael

2004-01-01

The EULER project completed its work in November 2002. It forms the last part of a very successful project in the specialized but global discipline of mathematics. After a successful RTD project had created the technology, a take-up project has effectively exploited it to the point where its future is assured through a not-for-profit consortium. EULER is a European based, world class, real virtual library for mathematics with up-to-date technological solutions, well accepted by users. In particular, EULER provides a world reference and delivery service, transparent to the end user and offering full coverage of the mathematics literature world-wide, including bibliographic data, peer reviews and/or abstracts, indexing, classification and search, transparent access to library services, co-operation with commercial information providers (publishers, bookstores). The EULER services provide a gateway to the electronic catalogues and repositories of participating institutions, while the latter retain complete respo...

Solutions manual to accompany finite mathematics models and applications

CERN Document Server

Morris, Carla C

2015-01-01

A solutions manual to accompany Finite Mathematics: Models and Applications In order to emphasize the main concepts of each chapter, Finite Mathematics: Models and Applications features plentiful pedagogical elements throughout such as special exercises, end notes, hints, select solutions, biographies of key mathematicians, boxed key principles, a glossary of important terms and topics, and an overview of use of technology. The book encourages the modeling of linear programs and their solutions and uses common computer software programs such as LINDO. In addition to extensive chapters on pr

ON THE FOUNDATIONS OF MATHEMATICAL ECONOMICS

OpenAIRE

J. BARKLEY ROSSER

2012-01-01

Kumaraswamy Vela Velupillai74 presents a constructivist perspective on the foundations of mathematical economics, praising the views of Feynman in developing path integrals and Dirac in developing the delta function. He sees their approach as consistent with the Bishop constructive mathematics and considers its view on the Bolzano-Weierstrass, Hahn-Banach, and intermediate value theorems, and then the implications of these arguments for such "crown jewels" of mathematical economics as the exi...

MATHEMATICAL MODELLING OF PREFERED SOLUTIONS CHOICE FUNCTION FOR TUBULAR GAS HEATERS BY EXPERIMENTAL INFORMATIONS

Directory of Open Access Journals (Sweden)

BARSUK R. V.

2016-08-01

Full Text Available Annotation. Problems formulation. The article deals with choice functions building of preferred solutions by experimental information for tubular gas heater working on fuel granules - pellets.Further choice functions using for making technical solutions by tubular gas heaters construction and designing. Recently research analysis. There are works about choice functions construction by separate presents are examined. But full chose functions building by separate presents are not examined. Aims and tasks. There are setting aim to develop full choice functions mathematical model on separate presents by authors. The expert are connect to primary experimental data’s evaluation that estimates separate results by output functions (criteria. Its evaluations issue in experimental points paired comparison’s table form. Thus, there are necessary construct binary choice relations presents on experimental “points” set by expert that then using for full choice function’s constructing. Conclusions. There are choice function’s construction’s sequence are sets. There are posed point comparison results that characterized tubular gas heater’s condition with expert’s evaluation using. Also posed output functions comparisons by which can be characterized improving tubular gas heater’s performance or vice versa.

Engineering Play: Exploring Associations with Executive Function, Mathematical Ability, and Spatial Ability in Preschool

Science.gov (United States)

Gold, Zachary Samuel

Engineering play is a new perspective on preschool education that views constructive play as an engineering design process that parallels the way engineers think and work when they develop engineered solutions to human problems (Bairaktarova, Evangelou, Bagiati, & Brophy, 2011). Early research from this perspective supports its use in framing play as a key learning context. However, no research to date has examined associations between engineering play and other factors linked with early school success, such as executive function, mathematical ability, and spatial ability. Additionally, more research is needed to further validate a new engineering play observational measure. This study had two main goals: (1) to gather early validity data on the engineering play measure as a potentially useful instrument for documenting the occurrence of children's engineering play behaviors in educational contexts, such as block play. This was done by testing the factor structure of the engineering play behaviors in this sample and their association with preschoolers' planning, a key aspect of the engineering design process; (2) to explore associations between preschoolers' engineering play and executive function, mathematical ability, and spatial ability. Participants included 110 preschoolers (62 girls; 48 boys; M = 58.47 months) from 10 classrooms in the Midwest United States coded for their frequency of engagement in each of the nine engineering play behaviors. A confirmatory factor analysis resulted in one engineering play factor including six of the engineering play behaviors. A series of marginal regression models revealed that the engineering play factor was significantly and positively associated with the spatial horizontal rotation transformation. However, engineering play was not significantly related to planning ability, executive function, informal mathematical abilities, or other spatial transformation skills. Follow-up analyses revealed significant positive

Core-Plus Mathematics. What Works Clearinghouse Intervention Report

Science.gov (United States)

What Works Clearinghouse, 2010

2010-01-01

"Core-Plus Mathematics" is a four-year curriculum that replaces the traditional sequence with courses that each feature interwoven strands of algebra and functions, statistics and probability, geometry and trigonometry, and discrete mathematics. The first three courses in the series provide a common core of broadly useful mathematics,…

Academic Supports, Cognitive Disability and Mathematics Acheivement for Visually Imparied Youth: A Multilevel Modeling Approach

Science.gov (United States)

Giesen, J. Martin; Cavenaugh, Brenda S.; McDonnall, Michele Capella

2012-01-01

Elementary and middle school students who are blind or visually impaired (VI) lag up to three years behind non-disabled peers in mathematics achievement. We investigated the impact of academic supports in the school on mathematics achievement, controlling grade, gender, cognitive disability, and family SES. Data were from SEELS (Special Education…

The Mathematical Theory of Multifocal Lenses

Institute of Scientific and Technical Information of China (English)

Jacob RUBINSTEIN

2017-01-01

This paper presents the fundamental optical concepts of designing multifocal ophthalmic lenses and the mathematical methods associated with them.In particular,it is shown that the design methodology is heavily based on differential geometric ideas such as Willmore surfaces.A key role is played by Hamilton's eikonal functions.It is shown that these functions capture all the information on the local blur and distortion created by the lenses.Along the way,formulas for computing the eikonal functions are derived.Finally,the author lists a few intriguing mathematical problems and novel concepts in optics as future projects.

Mathematical analysis fundamentals

CERN Document Server

Bashirov, Agamirza

2014-01-01

The author's goal is a rigorous presentation of the fundamentals of analysis, starting from elementary level and moving to the advanced coursework. The curriculum of all mathematics (pure or applied) and physics programs include a compulsory course in mathematical analysis. This book will serve as can serve a main textbook of such (one semester) courses. The book can also serve as additional reading for such courses as real analysis, functional analysis, harmonic analysis etc. For non-math major students requiring math beyond calculus, this is a more friendly approach than many math-centric o

Mathematical models for plant-herbivore interactions

Science.gov (United States)

Feng, Zhilan; DeAngelis, Donald L.

2017-01-01

Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology.

Stealing from Physics: Modeling with Mathematical Functions in Data-Rich Contexts

Science.gov (United States)

Erickson, Tim

2006-01-01

In the course of a project to create physics education materials for secondary schools in the USA we have, not surprisingly, had insights into how students develop certain mathematical understandings. Some of these translate directly into the mathematics classroom. With our materials, students get data from a variety of sources, data that arise in…

Applications of Functional Near-Infrared Spectroscopy (fNIRS) in Studying Cognitive Development: The Case of Mathematics and Language.

Science.gov (United States)

Soltanlou, Mojtaba; Sitnikova, Maria A; Nuerk, Hans-Christoph; Dresler, Thomas

2018-01-01

In this review, we aim to highlight the application of functional near-infrared spectroscopy (fNIRS) as a useful neuroimaging technique for the investigation of cognitive development. We focus on brain activation changes during the development of mathematics and language skills in schoolchildren. We discuss how technical limitations of common neuroimaging techniques such as functional magnetic resonance imaging (fMRI) have resulted in our limited understanding of neural changes during development, while fNIRS would be a suitable and child-friendly method to examine cognitive development. Moreover, this technique enables us to go to schools to collect large samples of data from children in ecologically valid settings. Furthermore, we report findings of fNIRS studies in the fields of mathematics and language, followed by a discussion of the outlook of fNIRS in these fields. We suggest fNIRS as an additional technique to track brain activation changes in the field of educational neuroscience.

Functional specialization and evolution of leader proteinases in the family Closteroviridae.

Science.gov (United States)

Peng, C W; Peremyslov, V V; Mushegian, A R; Dawson, W O; Dolja, V V

2001-12-01

Members of the Closteroviridae and Potyviridae families of the plant positive-strand RNA viruses encode one or two papain-like leader proteinases. In addition to a C-terminal proteolytic domain, each of these proteinases possesses a nonproteolytic N-terminal domain. We compared functions of the several leader proteinases using a gene swapping approach. The leader proteinase (L-Pro) of Beet yellows virus (BYV; a closterovirus) was replaced with L1 or L2 proteinases of Citrus tristeza virus (CTV; another closterovirus), P-Pro proteinase of Lettuce infectious yellows virus (LIYV; a crinivirus), and HC-Pro proteinase of Tobacco etch virus (a potyvirus). Each foreign proteinase efficiently processed the chimeric BYV polyprotein in vitro. However, only L1 and P-Pro, not L2 and HC-Pro, were able to rescue the amplification of the chimeric BYV variants. The combined expression of L1 and L2 resulted in an increased RNA accumulation compared to that of the parental BYV. Remarkably, this L1-L2 chimera exhibited reduced invasiveness and inability to move from cell to cell. Similar analyses of the BYV hybrids, in which only the papain-like domain of L-Pro was replaced with those derived from L1, L2, P-Pro, and HC-Pro, also revealed functional specialization of these domains. In subcellular-localization experiments, distinct patterns were observed for the leader proteinases of BYV, CTV, and LIYV. Taken together, these results demonstrated that, in addition to a common proteolytic activity, the leader proteinases of closteroviruses possess specialized functions in virus RNA amplification, virus invasion, and cell-to-cell movement. The phylogenetic analysis suggested that functionally distinct L1 and L2 of CTV originated by a gene duplication event.

Problem of mathematical deduction of the existence of black holes

Directory of Open Access Journals (Sweden)

Yuan-Shun Chin

1990-01-01

Full Text Available The mathematical proof of existence of Black Hole is based on the assumption of mass being independent of speed. Considering the effect of special relativity of the dependence of mass with speed there is no Black hole.

Assessment of Primary 5 Students' Mathematical Modelling Competencies

Science.gov (United States)

Chan, Chun Ming Eric; Ng, Kit Ee Dawn; Widjaja, Wanty; Seto, Cynthia

2012-01-01

Mathematical modelling is increasingly becoming part of an instructional approach deemed to develop students with competencies to function as 21st century learners and problem solvers. As mathematical modelling is a relatively new domain in the Singapore primary school mathematics curriculum, many teachers may not be aware of the learning outcomes…

Mathematical statistics and limit theorems Festschrift in honour of Paul Deheuvels

CERN Document Server

Mason, David; Pfeifer, Dietmar; Steinebach, Josef

2015-01-01

This Festschrift in honour of Paul Deheuvels’ 65th birthday compiles recent research results in the area between mathematical statistics and probability theory with a special emphasis on limit theorems. The book brings together contributions from invited international experts to provide an up-to-date survey of the field. Written in textbook style, this collection of original material addresses researchers, PhD and advanced Master students with a solid grasp of mathematical statistics and probability theory.  

[Executive functioning and motivation in preschool children at risk for learning difficulties in mathematics].

Science.gov (United States)

Presentación-Herrero, M Jesús; Mercader-Ruiz, Jessica; Siegenthaler-Hierro, Rebeca; Fernández-Andrés, Inmaculada; Miranda-Casas, Ana

2015-02-25

Early identification of the factors involved in the development of learning difficulties in mathematics is essential to be able to understand their origin and implement successful interventions. This study analyses the capacity of executive functioning and of variables from the motivational belief system to differentiate and classify preschool children with and without risk of having difficulties in mathematics. A total of 146 subjects from the third year of preschool education took part in the study, divided into risk/no risk according to the score obtained on the operations subtest of the TEDI-MATH test. Working memory (verbal and visuospatial) and inhibition (with auditory and visual stimuli) neuropsychological tasks were applied. Teachers filled in a questionnaire on the children's motivation with regard to learning. Significant differences were found between the two groups on the working memory and inhibition-auditory factors, as well as on all the motivation variables. The results also show a similar power of classification, with percentages above 80%, for both groups of variables. The implications of these findings for educational practice are discussed.

SLATEC-4.1, Subroutine Library for Solution of Mathematical Problems

International Nuclear Information System (INIS)

Boland, W.R.

1999-01-01

1 - Description of problem or function: SLATEC4.1 is a large collection of FORTRAN mathematical subprograms brought together in a joint effort by the Air Force Phillips Laboratory, Lawrence Livermore National Laboratory, Los Alamos National Laboratory, Magnetic Fusion Energy Computing Center, National Institute of Standards and Technology, Sandia National Laboratories (Albuquerque and Livermore), and Oak Ridge National Laboratory. SLATEC is characterized by portability, good numerical technology, good documentation, robustness, and quality assurance. The library can be divided into the following subsections following the lines of the GAMS classification system: Error Analysis, Elementary and Special Functions, Elementary Vector Operations, Solutions of Systems of Linear Equations, Eigen analysis, QR Decomposition, Singular Value Decomposition, Overdetermined or Underdetermined Systems, Interpolation, Solution of Nonlinear Equations, Optimization, Quadrature, Ordinary Differential Equations, Partial Differential Equations, Fast Fourier Transforms, Approximation, Pseudo-random Number Generation, Sorting, Machine Constants, and Diagnostics and Error Handling. 2 - Method of solution: This information is provided by comments within the individual library subroutines

Explorations in Mathematical Physics The Concepts Behind an Elegant Language

CERN Document Server

Koks, Don

2006-01-01

Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You'll see how the accelerated frames of special relativity tell us about gravity. On the journey, you'll discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis buil...

Einstein in matrix form exact derivation of the theory of special and general relativity without tensors

CERN Document Server

Ludyk, Günter

2013-01-01

This book is an introduction to the theories of Special and General Relativity. The target audience are physicists, engineers and applied scientists who are looking for an understandable introduction to the topic - without too much new mathematics. The fundamental equations of Einsteins theory of Special and General Relativity are derived using matrix calculus, without the help of tensors. This feature makes the book special and a valuable tool for scientists and engineers with no experience in the field of tensor calculus. In part I the foundations of Special Relativity are developed, part II describes the structure and principle of General Relativity. Part III explains the Schwarzschild solution of spherical body gravity and examines the "Black Hole" phenomenon. Any necessary mathematical tools are user friendly provided, either directly in the text or in the appendices.

A review of mathematical models for the formation of vascular networks

KAUST Repository

Scianna, M.; Bell, C.G.; Preziosi, L.

2013-01-01

process generally called lymphangiogenesis. A number of mathematical approaches have been used to analyze these phenomena. In this paper, we review the different types of models, with special emphasis on their ability to reproduce different biological

Features functional activity kinesthetic and visual sensory systems in athletes of different specializations

Directory of Open Access Journals (Sweden)

Anatoliy Rovnyy

2015-02-01

Full Text Available Purpose: to establish specific effects of different sports on functional status and co mood kinesthetic and visual analyzers skilled athletes. Materials and Methods: the study was conducted on athletes qualified five sports: modern pentathlon, volleyball, basketball, handball and fencing. We used methods of difference sensometry and mathematical statistics. Results revealed that the sensitivity of sensor systems depend on the specifics of sports activities and sports equipment. Conclusions: the complex is set internally sensor and between sensory bonds that are formed on the basis of the specific sports activity.

Co-operation Between Science Teachers and Mathematics Teachers. Volumes 1-6.

Science.gov (United States)

Rogerson, Alan, Ed.

This document contains six separate works, titled: (1) Functions and Physics; (2) Links Between Geography and Mathematics; (3) Our Inheritance: Common Ground for the Mathematics and Biology Teacher; (4) Mathematics and Chemistry: The Classroom Interface; (5) Mathematical Modeling; and (6) Mathematical Modeling with Calculus. This series of…

Views of Elementary School Pre-Service Teachers About the Use of Educational Mathematics Games in Mathematics Teaching

Directory of Open Access Journals (Sweden)

Hasan Topçu

2014-08-01

Full Text Available The aim of this study was to reveal the opinions of elementary school pre-service teachers about the usage of educational mathematics games in elementary mathematics teaching. In this study, case study that, one of qualitative research methods, was used. Data were collected by utilizing a semi-structured interview form to these elementary school pre-service teachers and analyzed using by content analysis method. A total of 10 junior pre-service teachers enrolled in undergraduate programs of elementary teaching attended to this research. In conclusion, these pre-service teachers indicated that educational computer games would provide benefits such as making students’ learning more permanent, visualizing concepts, making students love mathematics, learning by entertaining, reinforcing what has been learnt and developing thinking skills. Nevertheless, these elementary school pre-service teachers stated the limitations about educational computer games such as causing addiction and physical damages, being time-consuming, requiring special equipment and software and making class management difficult. Besides, it was revealed that the pre-service teachers demonstrated positive attitudes towards the use of games in courses while that they did not feel themselves competent in terms of application.Key Words:    Educational computer games, mathematics teaching, elementary school pre-service teachers

Using mathematical software to design power electronic converters

Science.gov (United States)

Hinov, Nikolay; Hranov, Tsveti

2017-12-01

In the paper is presented mathematical software, which was used for design of power electronic devices. Examined to different example, which are applied to designing electronic converters. In this way, it is possible to play different combinations of the circuit elements by simple means, thus optimizing according to certain criteria and limitations. Free software with a simple and intuitive interface is selected. No special user training is required to work with it and no further training is required. The use of mathematical software greatly facilitates the design, assists and makes it attractive and accessible to a wider range of students and specialists in power electronics training.

Mathematical modeling of flow-injection techniques and their applications for environmental monitoring

International Nuclear Information System (INIS)

Begum, N.N.; Ahmed, J.

2006-01-01

A classification of the existing mathematical models of flow-injection (FI) manifolds based on the main principles on which they are built, have been proposed. Numerous mathematical models of FI systems employing ideas from different scientific areas (e.g. mathematical statistics, chemical engineering, chromatography) have been developed so far. The models have been compared with respect to their predictive power, the complexity of their mathematical treatment, and the requirements for computation time when applied to single-line, multi-channel and conjugated two-line FI systems. It is concluded that the axially dispersed plug flow model deserves special attention because it offers an acceptable compromise between the conflicting requirements for maximal possible mathematical simplicity and maximal possible precision. Applicability of these existing flow-injection models to single-line, multi-channel and conjugated two-line systems for environmental monitoring have been discussed. (author)

Communicating Mathematics on the Internet: Synchronous and Asynchronous Tools

Science.gov (United States)

Hodges, Charles B.; Hunger, Gail M.

2011-01-01

Communicating and collaborating online are becoming common requirements in education. The specialized notations and symbols necessary for some content areas where mathematical expressions are part of the conversation require that users select appropriate communication tools. The purpose of this article is to describe tools that can be used for…

Measuring and factors influencing mathematics teachers' technological pedagogical and content knowledge (TPACK) in three southernmost provinces, Thailand

Science.gov (United States)

Adulyasas, Lilla

2017-08-01

Technology becomes an important role in teaching and learning mathematics nowadays. Integrating technology in the classroom helps students have better understanding in many of mathematics concepts. One of the major framework for assessing the knowledge of integrating technology with the pedagogy and content in the classroom is Technological Pedagogical and Content Knowledge (TPACK) framework. This study aimed to measure mathematics teachers' TPACK in three southernmost provinces, Thailand and to study on factors influencing their TPACK. A quantitative study was carried out with 210 secondary level mathematics teachers in the three southernmost provinces, Thailand which were random by two stage sampling technique. Data were collected by using a questionnaire to identify the level of mathematics teachers' TPACK and the factors influencing their TPACK. Descriptive statistics, Pearson product moment correlation and multiple regression analysis were used for analysing data. Findings reveal that the mean score of mathematics teachers' TPACK is 3.33 which is in the medium level and the three factors which have positive correlation at .05 level of significant with the level of TPACK are teaching experience factor, individual specialization factor and personal & organization factor. However, there are only two factors influencing mathematics teachers' TPACK. The two factors are individual specialization factor and personal & organization factors. These give better understanding on mathematics teachers' knowledge in integrating technology with the pedagogy and content which will be the important information for improving mathematics teachers' TPACK.

The tools of mathematical reasoning

CERN Document Server

Lakins, Tamara J

2016-01-01

This accessible textbook gives beginning undergraduate mathematics students a first exposure to introductory logic, proofs, sets, functions, number theory, relations, finite and infinite sets, and the foundations of analysis. The book provides students with a quick path to writing proofs and a practical collection of tools that they can use in later mathematics courses such as abstract algebra and analysis. The importance of the logical structure of a mathematical statement as a framework for finding a proof of that statement, and the proper use of variables, is an early and consistent theme used throughout the book.

Teachers Perspective of Using English as a Medium of Instruction in Mathematics and Science Subjects

Science.gov (United States)

Mansor, Norudin; Badarudin, Mohamed Ishak; Mat, Azman Che

2011-01-01

The policy of changing the medium of instruction in the teaching of mathematics and science from Bahasa Melayu to English is an important innovation affecting teachers of mathematics and science. It poses special challenges not only for teachers who have been trained in the Malay medium but also for those trained in English. This investigation…

Physical Consequences of Mathematical Principles

Directory of Open Access Journals (Sweden)

Comay E.

2009-10-01

Full Text Available Physical consequences are derived from the following mathematical structures: the variational principle, Wigner’s classifications of the irreducible representations of the Poincar ́ e group and the duality invariance of the homogeneous Maxwell equations. The analysis is carried out within the validity domain of special relativity. Hierarchical re- lations between physical theories are used. Some new results are pointed out together with their comparison with experimental data. It is also predicted that a genuine Higgs particle will not be detected.

Special issue on quantum physics with non-Hermitian operators Special issue on quantum physics with non-Hermitian operators

Science.gov (United States)

Bender, Carl M.; Fring, Andreas; Guenther, Uwe; Jones, Hugh F.

2012-01-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to quantum physics with non-Hermitian operators. The main motivation behind this special issue is to gather together recent results, developments and open problems in this rapidly evolving field of research in a single comprehensive volume. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will be open to all contributions containing new results on non-Hermitian theories which are explicitly PT-symmetric and/or pseudo-Hermitian or quasi-Hermitian. The main novelties in the past years in this area have been many experimental observations, realizations, and applications of PT symmetric Hamiltonians in optics and microwave cavities. We especially invite contributions on the theoretical interpretations of these recent PT-symmetric experiments and on theoretical proposals for new experiments. Editorial policy The Guest Editors for this issue are Carl Bender, Andreas Fring, Uwe Guenther and Hugh Jones. The areas and topics for this issue include, but are not limited to: spectral problems novel properties of complex optical potentials PT-symmetry related threshold lasers and spectral singularities construction of metric operators scattering theory supersymmetric theories Lie algebraic and Krein-space methods random matrix models classical and semi-classical models exceptional points in model systems operator theoretic approaches microwave cavities aspects of integrability and exact solvability field theories with indefinite metric All contributions will be refereed and processed according to the usual procedure of the journal. Papers should report original and significant research that has not already been published. Guidelines for preparation of contributions The deadline for contributed papers will be 31 March 2012. This deadline will allow the

The growth of mathematical knowledge --- introduction of convex bodies

DEFF Research Database (Denmark)

Carter, Jessica M H Grund; Hoff Kjeldsen, Tinne

2012-01-01

The article addresses the topic of the growth of mathematicalknowledge with a special focus on the question: How are mathematical objects introduced to mathematical practice? It takes as starting point a proposal made in a previous paper which is based on a case study on the introduction of Riemann......, which makes new definitions possible. This proposal is tested on a case study on Minkowski’s introduction of convexbodies. The conclusion is that the proposal holds also for this example. In both cases we notice that in a first stage is a close connection between the new object and the objects...

The discursive production of classroom mathematics

Science.gov (United States)

Smith, Kim; Hodson, Elaine; Brown, Tony

2013-09-01

School mathematics is a function of its discursive environment where the language being used formats mathematical activity. The paper explores this theme through an extended example in which the conduct of mathematical teaching and learning is restricted by regulative educational policies. It considers how mathematics is discursively produced by student teachers within an employment-based model of teacher education in England where there is a low university input. It is argued that teacher reflections on mathematical learning and teaching within the course are patterned discursively in line with formal curriculum framings, assessment requirements and the local demands of their placement school. Both teachers and students are subject to regulative discourses that shape their actions and as a consequence this regulation influences the forms of mathematical activity that can take place. It is shown how university sessions can provide a limited critical platform from which to interrogate these restrictions and renegotiate them.

NATO Advanced Research Workshop on Exploiting Mental Imagery with Computers in Mathematics Education

CERN Document Server

Mason, John

1995-01-01

The advent of fast and sophisticated computer graphics has brought dynamic and interactive images under the control of professional mathematicians and mathematics teachers. This volume in the NATO Special Programme on Advanced Educational Technology takes a comprehensive and critical look at how the computer can support the use of visual images in mathematical problem solving. The contributions are written by researchers and teachers from a variety of disciplines including computer science, mathematics, mathematics education, psychology, and design. Some focus on the use of external visual images and others on the development of individual mental imagery. The book is the first collected volume in a research area that is developing rapidly, and the authors pose some challenging new questions.

75 FR 50853 - Special Conditions: Cirrus Design Corporation Model SF50 Airplane; Function and Reliability Testing

Science.gov (United States)

2010-08-18

... airplanes. 1. Function and Reliability Testing. Flight tests: In place of 14 CFR 21.35(b)(2), the following...; Function and Reliability Testing AGENCY: Federal Aviation Administration (FAA), DOT. ACTION: Final special... to CAR part 3 became effective January 15, 1951, and deleted the service test requirements in Section...

Mathematics of epidemics on networks from exact to approximate models

CERN Document Server

Kiss, István Z; Simon, Péter L

2017-01-01

This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate...

Pre-Employment Training Handbook for Secondary Special Education.

Science.gov (United States)

Pine Bluff School District 3, AR.

Presented is a curriculum guide on job skills for special education secondary students. Listed are tasks, skills and related academic concepts (including reading, mathematics, and vocabulary) for the following 10 units: housekeeping, floor care, laundry worker, food service worker, grocery store worker, general shop worker, clerical aide, nurse's…

INFORMATIVE SYSTEM OF EDUCATIONAL PURPOSE FROM MATHEMATICS AS A WAY OF PROFESSIONAL ORIENTATION OF TEACHING STUDENTS IT SPECIALTIES

Directory of Open Access Journals (Sweden)

Lyudmyla Shishko

2016-01-01

Full Text Available The current state of formation of mathematical knowledge in universities insufficiently focused on their further use in professional activities. Students not formed the ability to apply mathematical knowledge to study general professional and special disciplines. In this article: –\tconsidered features of formation of a professional orientation of teaching mathematics using structured content multimedia information system for educational purposes (MISEP; –\tfound psychologo-pedagogical features of teaching mathematics of students IT specialties; –\tconsidered methodical aspects of MISEP in teaching the course "Discrete Mathematics" for students of IT specialties

Special Relativity: Will it Survive the Next 101 Years?

International Nuclear Information System (INIS)

Altschul, Brett D

2007-01-01

All the physics we observe in our world is underlain by special relativity, a theory that has survived for more than a hundred years, in many respects completely intact. Yet despite its status as the most stringently tested theory in all of physics, special relativity is still frequently questioned. In the last decade and a half, many scientists have come to believe that special relativity, as Einstein formulated it, will need to be modified to accommodate a quantum theory of gravity. {/it Special Relativity: Will it Survive the Next 101 Years?} is a volume intended to introduce the reader to this new and still slightly controversial area of research. The book is divided into four parts. The first part is essentially historical. It consists of an essay discussing Einstein's work in the context of contemporary technological developments and a amusing note by R W P Drever on a precision Lorentz test that he performed literally in his backyard. These set the stage for the more modern material that follows. Part II discusses the theory of relativity and its mathematical foundations, from completely modern perspectives. There is much here that may be new even for experts on special relativity, and a significant level of mathematical sophistication on the part of the reader is assumed. A number of the lectures delve into the crucial question of how special relativity and its generalizations can be combined with quantum mechanics. The third part discusses theoretical models of Lorentz violation, and all the important paradigms that appear in the current literature are considered. These include the standard model extension (an effective field theory), modified dispersion relations and 'double special relativity', and noncommutative geometry. These lectures generally delve into less detail than those in part II; the focus is on helping the reader digest the new principles that must arise in theories without Lorentz symmetry. The final part of the volume covers current

Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-efficacy Beliefs towards Mathematics and Mathematics Teaching

OpenAIRE

Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

2017-01-01

The purpose of the research is to investigate the relationships betweenself-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacybeliefs toward mathematics teaching, mathematics teaching anxiety variables andtesting the relationships between these variables with structural equationmodel. The sample of the research, which was conducted in accordance withrelational survey model, consists of 380 university students, who studied atthe department of Elementary Mathematics Educ...

19th European Conference on Mathematics for Industry

CERN Document Server

Barral, Patricia; Gómez, Dolores; Pena, Francisco; Rodríguez, Jerónimo; Salgado, Pilar; Vázquez-Méndez, Miguel; ECMI 2016; Progress in industrial mathematics

2017-01-01

This book addresses mathematics in a wide variety of applications, ranging from problems in electronics, energy and the environment, to mechanics and mechatronics. Using the classification system defined in the EU Framework Programme for Research and Innovation H2020, several of the topics covered belong to the challenge climate action, environment, resource efficiency and raw materials; and some to health, demographic change and wellbeing; while others belong to Europe in a changing world – inclusive, innovative and reflective societies. The 19th European Conference on Mathematics for Industry, ECMI2016, was held in Santiago de Compostela, Spain in June 2016. The proceedings of this conference include the plenary lectures, ECMI awards and special lectures, mini-symposia (including the description of each mini-symposium) and contributed talks. The ECMI conferences are organized by the European Consortium for Mathematics in Industry with the aim of promoting interaction between academy and industry, leading...

Theoretical Basics of Teaching Discrete Mathematics

Directory of Open Access Journals (Sweden)

Y. A. Perminov

2012-01-01

Full Text Available  The paper deals with the research findings concerning the process of mastering the theoretical basics of discrete mathematics by the students of vocational pedagogic profile. The methodological analysis is based on the subject and functions of the modern discrete mathematics and its role in mathematical modeling and computing. The modern discrete mathematics (i.e. mathematics of the finite type structures plays the important role in modernization of vocational training. It is especially rele- vant to training students for vocational pedagogic qualifications, as in the future they will be responsible for training the middle and the senior level specialists in engineer- ing and technical spheres. Nowadays in different industries, there arise the problems which require for their solving both continual – based on the classical mathematical methods – and discrete modeling. The teaching course of discrete mathematics for the future vocational teachers should be relevant to the target qualification and aimed at mastering the mathematical modeling, systems of computer mathematics and computer technologies. The author emphasizes the fundamental role of mastering the language of algebraic and serial structures, as well as the logical, algorithmic, combinatory schemes dominating in dis- crete mathematics. The guidelines for selecting the content of the course in discrete mathematics are specified. The theoretical findings of the research can be put into practice whilst developing curricula and working programs for bachelors and masters’ training. 

The semantic system is involved in mathematical problem solving.

Science.gov (United States)

Zhou, Xinlin; Li, Mengyi; Li, Leinian; Zhang, Yiyun; Cui, Jiaxin; Liu, Jie; Chen, Chuansheng

2018-02-01

Numerous studies have shown that the brain regions around bilateral intraparietal cortex are critical for number processing and arithmetical computation. However, the neural circuits for more advanced mathematics such as mathematical problem solving (with little routine arithmetical computation) remain unclear. Using functional magnetic resonance imaging (fMRI), this study (N = 24 undergraduate students) compared neural bases of mathematical problem solving (i.e., number series completion, mathematical word problem solving, and geometric problem solving) and arithmetical computation. Direct subject- and item-wise comparisons revealed that mathematical problem solving typically had greater activation than arithmetical computation in all 7 regions of the semantic system (which was based on a meta-analysis of 120 functional neuroimaging studies on semantic processing). Arithmetical computation typically had greater activation in the supplementary motor area and left precentral gyrus. The results suggest that the semantic system in the brain supports mathematical problem solving. Copyright © 2017 Elsevier Inc. All rights reserved.

A brief history of partitions of numbers, partition functions and their modern applications

Science.gov (United States)

Debnath, Lokenath

2016-04-01

'Number rules the universe.' The Pythagoras 'If you wish to forsee the future of mathematics our course is to study the history and present conditions of the science.' Henri Poincaré 'The primary source (Urqell) of all mathematics are integers.' Hermann Minkowski This paper is written to commemorate the centennial anniversary of the Mathematical Association of America. It deals with a short history of different kinds of natural numbers including triangular, square, pentagonal, hexagonal and k-gonal numbers, and their simple properties and their geometrical representations. Included are Euclid's and Pythagorean's main contributions to elementary number theory with the main contents of the Euclid Elements of the 13-volume masterpiece of mathematical work. This is followed by Euler's new discovery of the additive number theory based on partitions of numbers. Special attention is given to many examples, Euler's theorems on partitions of numbers with geometrical representations of Ferrers' graphs, Young's diagrams, Lagrange's four-square theorem and the celebrated Waring problem. Included are Euler's generating functions for the partitions of numbers, Euler's pentagonal number theorem, Gauss' triangular and square number theorems and the Jacobi triple product identity. Applications of the theory of partitions of numbers to different statistics such as the Bose- Einstein, Fermi- Dirac, Gentile, and Maxwell- Boltzmann statistics are briefly discussed. Special attention is given to pedagogical information through historical approach to number theory so that students and teachers at the school, college and university levels can become familiar with the basic concepts of partitions of numbers, partition functions and their modern applications, and can pursue advanced study and research in analytical and computational number theory.

Special functions & their applications

CERN Document Server

Lebedev, N N

1972-01-01

Famous Russian work discusses the application of cylinder functions and spherical harmonics; gamma function; probability integral and related functions; Airy functions; hyper-geometric functions; more. Translated by Richard Silverman.

The Relationship between Neuropsychological and Ecological Measurements of Executive Functioning in Childhood and the Prediction of Mathematics Performance. A Pilot Study

Science.gov (United States)

Zorrilla-Silvestre, Lorena; Presentación-Herrero, María Jesús; Gil-Gómez, Jesús

2016-01-01

Introduction: This study explored the variables of executive functioning (EF) that permitted the evaluation of EF both at home and at school. The objective was to compare the results of the evaluations of these functions in children aged 5 to 6 years, and see to what extent these variables predicted mathematics performance best. Method: Sixty-six…

Students discussing their mathematical ideas: Group-tests and mind-maps

NARCIS (Netherlands)

Pijls, M.; de Kramer, D.; Maj, B.; Pytlak, M.; Swoboda, E.

2008-01-01

In an explorative research project, teachers experimented with new ideas to make their students discuss (i.e. show, explain, justify and reconstruct their work) their mathematical ideas with each other. Two kind of special tasks were developed: group tests and mind maps. Also, the role of the

Comparisons of Mathematics Intervention Effects in Resource and Inclusive Classrooms

Science.gov (United States)

Bottge, Brian A.; Cohen, Allan S.; Choi, Hye-Jeong

2018-01-01

In this article, we describe results of a reanalysis of two randomized studies that tested the effects of enhanced anchored instruction (EAI) on the fractions computation performance of students in special education resource rooms and inclusive mathematics classrooms. Latent class analysis and latent transition analysis classified students…

Mathematical Modeling Approaches in Plant Metabolomics.

Science.gov (United States)

Fürtauer, Lisa; Weiszmann, Jakob; Weckwerth, Wolfram; Nägele, Thomas

2018-01-01

The experimental analysis of a plant metabolome typically results in a comprehensive and multidimensional data set. To interpret metabolomics data in the context of biochemical regulation and environmental fluctuation, various approaches of mathematical modeling have been developed and have proven useful. In this chapter, a general introduction to mathematical modeling is presented and discussed in context of plant metabolism. A particular focus is laid on the suitability of mathematical approaches to functionally integrate plant metabolomics data in a metabolic network and combine it with other biochemical or physiological parameters.

Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-Efficacy Beliefs towards Mathematics and Mathematics Teaching

Science.gov (United States)

Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

2017-01-01

The purpose of the research is to investigate the relationships between self-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacy beliefs toward mathematics teaching, mathematics teaching anxiety variables and testing the relationships between these variables with structural equation model. The sample of the research, which…

Mathematical Sense-Making in Quantum Mechanics: An Initial Peek

Science.gov (United States)

Dreyfus, Benjamin W.; Elby, Andrew; Gupta, Ayush; Sohr, Erin Ronayne

2017-01-01

Mathematical sense-making--looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world--is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and…

TEACHING MATHEMATICAL DISCIPLINES AT THE MEDICAL UNIVERSITY

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V. Ya. Gelman

2018-01-01

Full Text Available Introduction.In programs of training of students of medical specialties, Mathematics is a subject of basic education, i.e. non-core discipline. However, studying Mathematics is extremely important for future physicians, as recently there has been an impetuous development of mathematization in the field of health care. Today, a set of the new medical devices, the equipment and high technologies are being developed based on the mathematical modeling, analysis and forecasting. Mathematical methods are widely applied to diagnostics, development of life-support systems and the description of various biological processes both at the molecular level,  and at the level of a whole organism, its systems, bodies and tissues. The solution of many medical tasks in the field of taxonomy, genetics, and organization of medical service is impossible without knowledge of mathematics. Unfortunately, along with the evident importance of mathematical preparation for a medical profession, its need is poorly realized not only by junior students, but even by some teachers of specialized departments of medical schools.The aim of the publication is to discuss the problems that arise in the teaching of mathematical disciplines to students at a medical school and to suggest possible solutions to these problems.Methodology and research methods. The study is based on the use of modeling of the educational process. The methods of analysis, generalization and the method of expert assessments were applied in the course of the research.Results and scientific novelty. The aspects of mathematical preparation at the university are considered on the basis of the application of the multiplicative model of training quality. It is shown that the main students’ learning difficulties in Mathematics are connected with the following factors: the initial level of mathematical preparation of students and their motivation; outdated methods of Mathematics teaching and academic content

Special Features In Turbulent Mixing. Comparison between Periodic and Non Periodic Case

Directory of Open Access Journals (Sweden)

Mihai Costescu

2006-12-01

Full Text Available After hundreds of years of stability study, the problems of flow kinematics are far from complete solving. A modern theory appears in this field: the mixing theory. Its mathematical methods and techniques developed the significant relation between turbulence and chaos. The turbulence is an important feature of dynamic systems with few freedom degrees, the so-called far from equilibrium systems. These are widespread between the models of excitable media.Studying a mixing for a flow implies the analysis of successive stretching and folding phenomena for its particles, the influence of parameters and initial conditions. In the previous works, the study of the 3D non-periodic models exhibited a quite complicated behavior, involving some significant events - the so-called rare events. The variation of parameters had a great influence on the length and surface deformations. The 2D (periodic case is simpler, but significant events can also issue for irrational values of the length and surface versors, as was the situation in 3D case.The comparison between 2D and 3D case revealed interesting properties; therefore a modified 2D (periodic model is tested. The numerical simulations were realized in MapleVI, for searching special mathematical events. Continuing this work both from analytical and numeric standpoint would relieve useful properties for the turbulent mixing. A proximal target is to test some special functions for the periodic model, and to study the behavior of the structures realized by the model.

Generalized harmonic, cyclotomic, and binomial sums, their polylogarithms and special numbers

Energy Technology Data Exchange (ETDEWEB)

Ablinger, J.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, J. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2013-10-15

A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of special numbers. Starting with harmonic sums and polylogarithms we discuss recent extensions of these quantities as cyclotomic, generalized (cyclotomic), and binomially weighted sums, associated iterated integrals and special constants and their relations.

Generalized harmonic, cyclotomic, and binomial sums, their polylogarithms and special numbers

International Nuclear Information System (INIS)

Ablinger, J.; Schneider, C.; Bluemlein, J.

2013-10-01

A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of special numbers. Starting with harmonic sums and polylogarithms we discuss recent extensions of these quantities as cyclotomic, generalized (cyclotomic), and binomially weighted sums, associated iterated integrals and special constants and their relations.

Mathematical determination of image quality

Energy Technology Data Exchange (ETDEWEB)

Barrett, H H

1982-01-01

The subjective term ''image quality'' is generally not easy to define and to measure. If, however, we limit ourselves, to determine certain anomalies in blurred images, then the task can be done more easily. The efficiency can in fact be measured and the results can be presented as ROC-characteristics (receiver operating characteristics). One can determine a relation between the characteristic and the noise distance of the imaging system, and this way the efficiency of an hypothetical ideal observer can be predicted. Furthermore one can compute noise distance and other statistical parameters of X-ray images distorted by quantum interference by special techniques that are founded on the so-called ''blur core''. The technique proved to be very successful in nuclear medicine, but is also valid in computerized tomography and X-ray diagnostics. The technique is explained without mathematical details. The question will be answered concerning the role mathematical analysis will play in the determination and optimization of the quality of diagnostic exposures.

Is special relativity logically inconsistent

International Nuclear Information System (INIS)

Prokhovnik, S.J.

1980-01-01

The author gives his view that Special Relativity is logically and mathematically consistent, as well as physically comprehensible if, and only if, it is firmly based on the single assumption of a unique fundamental reference frame for light propagation. The theory and all its results are derivable from this assumption; the Relativity and Light Principles become intelligible consequences of this assumption; the physical significance and source of time dilation and length contraction are made manifest thereby. (Auth.)

Lectures on Selected Topics in Mathematical Physics: Elliptic Functions and Elliptic Integrals

Science.gov (United States)

Schwalm, William A.

2015-12-01

This volume is a basic introduction to certain aspects of elliptic functions and elliptic integrals. Primarily, the elliptic functions stand out as closed solutions to a class of physical and geometrical problems giving rise to nonlinear differential equations. While these nonlinear equations may not be the types of greatest interest currently, the fact that they are solvable exactly in terms of functions about which much is known makes up for this. The elliptic functions of Jacobi, or equivalently the Weierstrass elliptic functions, inhabit the literature on current problems in condensed matter and statistical physics, on solitons and conformal representations, and all sorts of famous problems in classical mechanics. The lectures on elliptic functions have evolved as part of the first semester of a course on theoretical and mathematical methods given to first- and second-year graduate students in physics and chemistry at the University of North Dakota. They are for graduate students or for researchers who want an elementary introduction to the subject that nevertheless leaves them with enough of the details to address real problems. The style is supposed to be informal. The intention is to introduce the subject as a moderate extension of ordinary trigonometry in which the reference circle is replaced by an ellipse. This entre depends upon fewer tools and has seemed less intimidating that other typical introductions to the subject that depend on some knowledge of complex variables. The first three lectures assume only calculus, including the chain rule and elementary knowledge of differential equations. In the later lectures, the complex analytic properties are introduced naturally so that a more complete study becomes possible.

Pedagogical Content Knowledge: Teacher’s Knowledge of Students in Learning Mathematics on Limit of Function Subject

Science.gov (United States)

Ma'rufi; Ketut Budayasa, I.; Juniati, Dwi

2018-01-01

This research aims at describing the profile of high school teacher’s Pedagogical Content Knowledge in learning mathematics from the perspective of teaching experience. Pedagogical Content Knowledge (PCK) covers teacher’s knowledge of subject matter, knowledge of pedagogy, and knowledge of students. The subject of this research was two high school mathematics teachers who have different teaching experience. The data were obtained through interview and observation then analyzed qualitatively. The focus of this research is the novice teacher’s PCK deals with knowledge of students. Knowledge of Student is defined as teacher’s knowledge about the students’ conception and misconception on limit of function material and teacher’s ability to cope with students’ difficulty, mistake, and misconception. The result of this research shows that novice teacher’s ability in analyzing the cause of students’ difficulty, mistake, and misconception was limited. Novice teacher tended to overcome the students’ difficulty, mistake, and misconception by re-explaining the procedure of question completion which is not understood by the students.

Mathematical analogies in physics. Thin-layer wave theory

Directory of Open Access Journals (Sweden)

José M. Carcione

2014-03-01

Full Text Available Field theory applies to elastodynamics, electromagnetism, quantum mechanics, gravitation and other similar fields of physics, where the basic equations describing the phenomenon are based on constitutive relations and balance equations. For instance, in elastodynamics, these are the stress-strain relations and the equations of momentum conservation (Euler-Newton law. In these cases, the same mathematical theory can be used, by establishing appropriate mathematical equivalences (or analogies between material properties and field variables. For instance, the wave equation and the related mathematical developments can be used to describe anelastic and electromagnetic wave propagation, and are extensively used in quantum mechanics. In this work, we obtain the mathematical analogy for the reflection/refraction (transmission problem of a thin layer embedded between dissimilar media, considering the presence of anisotropy and attenuation/viscosity in the viscoelastic case, conductivity in the electromagnetic case and a potential barrier in quantum physics (the tunnel effect. The analogy is mainly illustrated with geophysical examples of propagation of S (shear, P (compressional, TM (transverse-magnetic and TE (transverse-electric waves. The tunnel effect is obtained as a special case of viscoelastic waves at normal incidence.

Mathematics related anxiety: Mathematics bogeyman or not?

Directory of Open Access Journals (Sweden)

Videnović Marina

2011-01-01

Full Text Available Data of the PISA 2003 survey indicate high levels of mathematics anxiety of students in Serbia. More than half of our students worry whether they will have difficulties in mathematics class or whether they will earn poor marks. Aims of this study therefore are: examining relationship between math anxiety and achievement at mathematics literacy scale; establishing possible predictors of math anxiety and identification of students' groups in relations to their relationship towards mathematics as a subject. Mathematics anxiety is statistically negatively correlated with school achievement and achievement at mathematics literacy scale. Socio-demographic factors, motivational and cognitive aspects related to learning mathematics, perception of school and classroom climate explain 40% variance of mathematics anxiety. Based on students' relationship towards mathematics they cam be divided into three groups; while dimensions that apart them are uninterested-interested in mathematics and presence-absence of anxiety. The group displaying anxiety scores lowest among the three. Applying qualitative analysis students' and teachers' attitudes on specific issues related to teaching and learning mathematics was examined.

The (Mathematical) Modeling Process in Biosciences.

Science.gov (United States)

Torres, Nestor V; Santos, Guido

2015-01-01

In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology.

Tools for Teaching Mathematical Functions and Geometric Figures to Tactile Visualization through a Braille Printer for Visual Impairment People

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Lorena León

2016-04-01

Full Text Available In this article, we showed the features and facilities offered by two new computer programs developed for the treatment and generation of geometric figures and math functions, through a Braille printer designed for visually impaired people. The programs have complete accessible features, in which users with full visual impairments can communicate with the systems via short-keys, and the speech synthesizer. The system sends sound messages that will accompanying the user during all the process to generate geometrical figures or to do a mathematical treatment. Finally, a tactile visualization displays as the results to the person with visual impairment, thus they will can complete their geometry and mathematical studies.

Interactions Between Mathematics and Physics

DEFF Research Database (Denmark)

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-01-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a var......In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined...... it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction...... of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student...

3rd International Conference on Applied Mathematics and Approximation Theory

CERN Document Server

Duman, Oktay

2016-01-01

This special volume is a collection of outstanding theoretical articles presented at the conference AMAT 2015, held in Ankara, Turkey from May 28-31, 2015, at TOBB University of Economics and Technology. The collection is suitable for a range of applications: from researchers and practitioners of applied and computational mathematics, to students in graduate-level seminars. Furthermore it will be a useful resource for all science libraries. This book includes 27 self-contained and expertly-refereed chapters that provide numerous insights into the latest developments at the intersection of applied and computational mathematics, engineering, and statistics.

Implementation of the - Constraint Method in Special Class of Multi-objective Fuzzy Bi-Level Nonlinear Problems

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Azza Hassan Amer

2017-12-01

Full Text Available Geometric programming problem is a powerful tool for solving some special type nonlinear programming problems. In the last few years we have seen a very rapid development on solving multiobjective geometric programming problem. A few mathematical programming methods namely fuzzy programming, goal programming and weighting methods have been applied in the recent past to find the compromise solution. In this paper, -constraint method has been applied in bi-level multiobjective geometric programming problem to find the Pareto optimal solution at each level. The equivalent mathematical programming problems are formulated to find their corresponding value of the objective function based on the duality theorem at eash level. Here, we have developed a new algorithm for fuzzy programming technique to solve bi-level multiobjective geometric programming problems to find an optimal compromise solution. Finally the solution procedure of the fuzzy technique is illustrated by a numerical example

Meaningful Statistics in Professional Practices as a Bridge between Mathematics and Science: An Evaluation of a Design Research Project

Science.gov (United States)

Dierdorp, Adri; Bakker, Arthur; van Maanen, Jan A.; Eijkelhof, Harrie M. C.

2014-01-01

Background: Creating coherence between school subjects mathematics and science and making these school subjects meaningful are still topical challenges. This study investigates how students make meaningful connections between mathematics, statistics, science and applications when they engage in a specially developed unit that is based on…

Factors involved in making post-performance judgments in mathematics problem-solving.

Science.gov (United States)

García Fernández, Trinidad; Kroesbergen, Evelyn; Rodríguez Pérez, Celestino; González-Castro, Paloma; González-Pienda, Julio A

2015-01-01

This study examines the impact of executive functions, affective-motivational variables related to mathematics, mathematics achievement and task characteristics on fifth and sixth graders’ calibration accuracy after completing two mathematical problems. A sample of 188 students took part in the study. They were divided into two groups as function of their judgment accuracy after completing the two tasks (accurate= 79, inaccurate= 109). Differences between these groups were examined. The discriminative value of these variables to predict group membership was analyzed, as well as the effect of age, gender, and grade level. The results indicated that accurate students showed better levels of executive functioning, and more positive feelings, beliefs, and motivation related to mathematics. They also spent more time on the tasks. Mathematics achievement, perceived usefulness of mathematics, and time spent on Task 1 significantly predicted group membership, classifying 71.3% of the sample correctly. These results support the relationship between academic achievement and calibration accuracy, suggesting the need to consider a wide range of factors when explaining performance judgments.

Teachers' Mathematics as Mathematics-at-Work

Science.gov (United States)

Bednarz, Nadine; Proulx, Jérôme

2017-01-01

Through recognising mathematics teachers as professionals who use mathematics in their workplace, this article traces a parallel between the mathematics enacted by teachers in their practice and the mathematics used in workplaces found in studies of professionals (e.g. nurses, engineers, bankers). This parallel is developed through the five…

The Study of the Relationship between Mother's Studies with Study Skills and Mathematics Performance of Students

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Behnoush Taheri

2015-07-01

Full Text Available Certainly teaching study skills of mathematics has special importance and plays important role in mathematics performance of students. As mothers spend more times with self-children then they can be effect on study and their mathematics performance. Present research implements to study of the relationship between mothers' studies with study skills and mathematics performance of their children. Population of this research is all girl students of first grade in high school at zone one of Tehran and sample is 97 people. For collecting data of this research through standard questionnaire of mathematics studies skills is used for measuring of study skill of mathematics and questions for studying information related to mothers' studies and a math exam for getting information of mathematics performance of students are used. The results indicated that there is not significant relationship between mothers' studies and study skill of mathematics among students. Also, it is indicated that there is positive significant relationship between mothers' studies and mathematic performance of students.

Savant Syndrome: Case Studies, Hypotheses, and Implications for Special Education.

Science.gov (United States)

Cheatham, Susan Klug; And Others

1995-01-01

The concept of savant syndrome, encompassing those individuals historically known as "idiot savants," is reviewed. Case studies demonstrating special abilities in the areas of calendar calculating, musical ability, artistic talent, memorization, mathematical skills, mechanical achievement, and fine sensory discrimination are discussed,…

The infinite well and Dirac delta function potentials as pedagogical, mathematical and physical models in quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Belloni, M., E-mail: mabelloni@davidson.edu [Physics Department, Davidson College, Davidson, NC 28035 (United States); Robinett, R.W., E-mail: rick@phys.psu.edu [Department of Physics, The Pennsylvania State University, University Park, PA 16802 (United States)

2014-07-01

The infinite square well and the attractive Dirac delta function potentials are arguably two of the most widely used models of one-dimensional bound-state systems in quantum mechanics. These models frequently appear in the research literature and are staples in the teaching of quantum theory on all levels. We review the history, mathematical properties, and visualization of these models, their many variations, and their applications to physical systems.

Does Computer Use Promote the Mathematical Proficiency of ELL Students?

Science.gov (United States)

Kim, Sunha; Chang, Mido

2010-01-01

The study explored the effects of computer use on the mathematical performance of students with special attention to ELL students. To achieve a high generalizability of findings, the study used a U.S. nationally representative database, the Early Childhood Longitudinal Survey Kindergarten Cohort (ECLS-K), and adopted proper weights. The study…

On algebraically special perturbations of black holes

International Nuclear Information System (INIS)

Chandrasekhar, S.

1984-01-01

Algebraically special perturbations of black holes excite gravitational waves that are either purely ingoing or purely outgoing. Solutions, appropriate to such perturbations of the Kerr, the Schwarzschild, and the Reissner-Nordstroem black-holes, are obtained in explicit forms by different methods. The different methods illustrate the remarkable inner relations among different facets of the mathematical theory. In the context of the Kerr black-hole they derive from the different ways in which the explicit value of the Starobinsky constant emerges, and in the context of the Schwarzschild and the Reissner-Nordstroem black-holes they derive from the potential barriers surrounding them belonging to a special class. (author)

Exploring Mathematics Teachers' Pedagogical Content Knowledge in the Context of Knowledge of Students

Science.gov (United States)

Aksu, Zeki; Kul, Ümit

2016-01-01

Functions are one of the basic topics taught in mathematics curriculum at Secondary school level requiring knowledge from the students' past, and uniting mathematical topics. Mathematics teachers have both their own learning experience of functions, as well as their own teaching experience, leading to the question of what level of student…

VMEXT: A Visualization Tool for Mathematical Expression Trees

OpenAIRE

Schubotz, Moritz; Meuschke, Norman; Hepp, Thomas; Cohl, Howard S.; Gipp, Bela

2017-01-01

Mathematical expressions can be represented as a tree consisting of terminal symbols, such as identifiers or numbers (leaf nodes), and functions or operators (non-leaf nodes). Expression trees are an important mechanism for storing and processing mathematical expressions as well as the most frequently used visualization of the structure of mathematical expressions. Typically, researchers and practitioners manually visualize expression trees using general-purpose tools. This approach is labori...

Examining Fourth-Grade Mathematics Writing: Features of Organization, Mathematics Vocabulary, and Mathematical Representations

Science.gov (United States)

Hebert, Michael A.; Powell, Sarah R.

2016-01-01

Increasingly, students are expected to write about mathematics. Mathematics writing may be informal (e.g., journals, exit slips) or formal (e.g., writing prompts on high-stakes mathematics assessments). In order to develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and…

Mathematical Properties Relevant to Geomagnetic Field Modeling

DEFF Research Database (Denmark)

Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils

2010-01-01

be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focussed. Time can be dealt with as an independent variable and is not explicitly considered......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations.The set of numerical coefficients defining this linear combination is then what one refers.......The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...

Mathematical Properties Relevant to Geomagnetic Field Modeling

DEFF Research Database (Denmark)

Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils

2014-01-01

be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focused. Time can be dealt with as an independent variable and is not explicitly considered......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations. The set of numerical coefficients defining this linear combination is then what one refers....... The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...

An introduction to the mathematics of biology with computer algebra models

CERN Document Server

Yeargers, Edward K; Herod, James V

1996-01-01

Biology is a source of fascination for most scientists, whether their training is in the life sciences or not. In particular, there is a special satisfaction in discovering an understanding of biology in the context of another science like mathematics. Fortunately there are plenty of interesting (and fun) problems in biology, and virtually all scientific disciplines have become the richer for it. For example, two major journals, Mathematical Biosciences and Journal of Mathematical Biology, have tripled in size since their inceptions 20-25 years ago. The various sciences have a great deal to give to one another, but there are still too many fences separating them. In writing this book we have adopted the philosophy that mathematical biology is not merely the intrusion of one science into another, but has a unity of its own, in which both the biology and the math­ ematics should be equal and complete, and should flow smoothly into and out of one another. We have taught mathematical biology with this philosophy...

[On the founders of the Institute of Mathematics and Physics, University of Bahia].

Science.gov (United States)

Dias, A L

The reduced number of female students of mathematics at the University of Bahia School of Philosophy (Faculdade de Filosofia, Universidade da Bahia - FF/UBa) is quite surprising. To date, they are concentrated in areas traditionally viewed as feminine whereas men predominate in the mathematical fields. I have examined interview data from a few women who graduated in mathematics and went on to teach at the University of Bahia School of Mathematics (Faculdade de Filosofia - FF) and at the Institute of Mathematics and Physics (Instituto de Matemática e Física - IMF), where they were soon to outnumber men and constitute the majority of the mathematics teaching staff. In this study, I have investigated the course of their careers over time: from their early student days, through their time as teaching assistants and professors, and finally as founders of the Institute of Mathematics and Physics, in 1960. Special reference is made to Martha Maria de Souza Dantas, organizer of the I Brazilian Conference on Mathematics Teaching, an event which has provided the groundwork for what was to become the Institute (IMF); and to Arlete Cerqueira Lima, the mastermind behind its creation.

An Out-of-Math Experience: Einstein, Relativity, and the Developmental Mathematics Student.

Science.gov (United States)

Fiore, Greg

2000-01-01

Discusses Einstein's special relativity theory and some of the developmental mathematics involved. Presents motivational classroom materials used in discussing relative-motion problems, evaluating a radical expression, graphing with asymptotes, interpreting a graph, studying variation, and solving literal and radical equations. (KHR)

Avoiding Misinterpretations of Piaget and Vygotsky: Mathematical Teaching without Learning, Learning without Teaching, or Helpful Learning-Path Teaching?

Science.gov (United States)

Fuson, Karen C.

2009-01-01

This article provides an overview of some perspectives about special issues in classroom mathematical teaching and learning that have stemmed from the huge explosion of research in children's mathematical thinking stimulated by Piaget. It concentrates on issues that are particularly important for less-advanced learners and for those who might be…

School-Age Test Proficiency and Special Education After Congenital Heart Disease Surgery in Infancy.

Science.gov (United States)

Mulkey, Sarah B; Bai, Shasha; Luo, Chunqiao; Cleavenger, Jordyn E; Gibson, Neal; Holland, Greg; Mosley, Bridget S; Kaiser, Jeffrey R; Bhutta, Adnan T

2016-11-01

To evaluate test proficiency and the receipt of special education services in school-age children who had undergone surgery for congenital heart disease (CHD) at age Education longitudinal database containing achievement test scores in literacy and mathematics for grades 3-4 and special education codes. The primary negative outcome was not achieving grade-level proficiency on achievement tests. Logistic regression accounting for repeated measures was used to evaluate for associations between achieving proficiency and demographic data, maternal education, and clinical factors. A total of 362 of 458 (79%) children who underwent surgery for CHD were matched to the Arkansas Department of Education database, 285 of whom had grade 3 and/or 4 achievement tests scores. Fewer students with CHD achieved proficiency in literacy and mathematics (P education predicted proficiency in literacy (P special education services (26.9% vs 11.6%; P special education services than all state students. Results from this study support the need for neurodevelopmental evaluations as standard practice in children with CHD. Copyright © 2016 Elsevier Inc. All rights reserved.

Relationships between the generalized functional method and other methods of nonimaging optical design.

Science.gov (United States)

Bortz, John; Shatz, Narkis

2011-04-01

The recently developed generalized functional method provides a means of designing nonimaging concentrators and luminaires for use with extended sources and receivers. We explore the mathematical relationships between optical designs produced using the generalized functional method and edge-ray, aplanatic, and simultaneous multiple surface (SMS) designs. Edge-ray and dual-surface aplanatic designs are shown to be special cases of generalized functional designs. In addition, it is shown that dual-surface SMS designs are closely related to generalized functional designs and that certain computational advantages accrue when the two design methods are combined. A number of examples are provided. © 2011 Optical Society of America

Teaching Mathematical Modeling in Mathematics Education

Science.gov (United States)

Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

2016-01-01

Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…

The Effectiveness of Brain Based Teaching on the Executive Functions of the Students with Mathematics Learning Disability

Directory of Open Access Journals (Sweden)

Salar Faramarzi

2014-04-01

Full Text Available Target: With advances in cognitive neuroscience and the developing connection between neuroscience and education in recent years, new windows has been opened in the realm of teaching and learning for the education experts. So education has vastly benefited from the results of researches in neuroscience to improve learning. The study strived to investigate the effectiveness of “brain based teaching” on the executive functions of the students with mathematics learning disability in Isfahan city. Method: To this end, three students with mathematical learning disability were selected using purposeful sampling. In this investing used a single subject with A-B design. Intervention was started after determining the base-line. The “brain based teaching” package was taught to each single participant for 26 intervention sessions. And 1 month after the intervention period follow-up test was performed. The instruments used, included, Raven intelligence test, The Iran key math diagnostic arithmetic and Conner’s questionnaire neuropsychological. The gathered data was analyzed using descriptive statistics and visual analysis. Results: Based on that, Results revealed that during the visual analysis of data graphs for executive function deficits, the study intervention was significantly effective for all 3 participants. Conclusions: This study showed that brain based teaching improves the executive functions of the students and thus, could be used in educating children with learning disabilities.

Mathematical models of hysteresis

International Nuclear Information System (INIS)

1998-01-01

The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above

Mathematical models of hysteresis

Energy Technology Data Exchange (ETDEWEB)

NONE

1998-08-01

The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above.

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences; Forthcoming articles. Forthcoming articles. Proceedings – Mathematical Sciences. PMSC-D-14-00136. Combinatorics of tenth order mock theta functions. J K SAREEN M RANA. Abstract. In this paper we are providing the combinatorial interpretations of two tenth ...

A Mathematical Account of the NEGF Formalism

DEFF Research Database (Denmark)

Cornean, Decebal Horia; Moldoveanu, Valeriu; Pillet, Claude-Alain

2018-01-01

The main goal of this paper is to put on solid mathematical grounds the so-called non-equilibrium Green’s function transport formalism for open systems. In particular, we derive the Jauho–Meir–Wingreen formula for the time-dependent current through an interacting sample coupled to non-interacting......The main goal of this paper is to put on solid mathematical grounds the so-called non-equilibrium Green’s function transport formalism for open systems. In particular, we derive the Jauho–Meir–Wingreen formula for the time-dependent current through an interacting sample coupled to non...

TUTOR SUPPORT OF TEACHING MATHEMATICS WITH INFORMATION AND COMMUNICATION TECHNOLOGIES

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Kateryna P. Osadcha

2017-10-01

Full Text Available The paper describes the tutor activity in the process of mathematics teaching support on the basis of the use of information and communication technologies (ICT. The author has analysed the available Internet resources and mobile applications in mathematics, which are classified according to their functional purposes into groups: systems of mass open courses, platforms for adaptive learning, video channels, mathematical online simulators, online tasks, mathematical games, mathematical portals, online platforms, mathematical sites, mathematical online platforms, mathematical services, mobile applications in mathematics (simulators, games, generators of example, assistant programs, training complexes, calculators. In accordance with the student age categories mathematical information and communication technologies are divided into three groups: for elementary school students, secondary school students and high school students. The basic ICT tools for teaching mathematics are outlined. The algorithm for constructing tutorial classes with their application is presented.

Morphology and function of the forelimb in arboreal frogs: specializations for grasping ability?

Science.gov (United States)

Manzano, Adriana S; Abdala, Virginia; Herrel, Anthony

2008-09-01

Frogs are characterized by a unique morphology associated with their saltatory lifestyle. Although variation in the form and function of the pelvic girdle and associated appendicular system related to specialized locomotor modes such as swimming or burrowing has been documented, the forelimbs have typically been viewed as relatively unspecialized. Yet, previous authors have noted versatility in forelimb function among arboreal frogs associated with feeding. Here we study the morphology and function of the forelimb and hand during locomotion in two species of arboreal frogs (Litoria caerulea and Phyllomedusa bicolor). Our data show a complex arrangement of the distal forelimb and hand musculature with some notable differences between species. Analyses of high-speed video and video fluoroscopy recordings show that forelimbs are used in alternating fashion in a diagonal sequence footfall pattern and that the position of the hand is adjusted when walking on substrates of different diameters. Electromyographic recordings show that the flexors of the hand are active during substrate contact, suggesting the use of gripping to generate a stabilizing torque. Measurements of grasping forces in vivo and during stimulation experiments show that both species, are capable of executing a so-called power grip but also indicates marked differences between species, in the magnitude of forces generated. Stimulation experiments showed an increased control of digit flexion in the more specialized of the two species, allowing it to execute a precision grip paralleled only by that seen in primates.

Theological Underpinnings of the Modern Philosophy of Mathematics.

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Shaposhnikov Vladislav

2016-03-01

Full Text Available The study is focused on the relation between theology and mathematics in the situation of increasing secularization. My main concern in the second part of this paper is the early-twentieth-century foundational crisis of mathematics. The hypothesis that pure mathematics partially fulfilled the functions of theology at that time is tested on the views of the leading figures of the three main foundationalist programs: Russell, Hilbert and Brouwer.

Mathematical methods linear algebra normed spaces distributions integration

CERN Document Server

Korevaar, Jacob

1968-01-01

Mathematical Methods, Volume I: Linear Algebra, Normed Spaces, Distributions, Integration focuses on advanced mathematical tools used in applications and the basic concepts of algebra, normed spaces, integration, and distributions.The publication first offers information on algebraic theory of vector spaces and introduction to functional analysis. Discussions focus on linear transformations and functionals, rectangular matrices, systems of linear equations, eigenvalue problems, use of eigenvectors and generalized eigenvectors in the representation of linear operators, metric and normed vector

Cognitive Neuroscience and Mathematics Learning: How Far Have We Come? Where Do We Need to Go?

Science.gov (United States)

Ansari, Daniel; Lyons, Ian M.

2016-01-01

In this commentary on the ZDM special issue: "Cognitive neuroscience and mathematics learning--revisited after 5 years," we explore the progress that has been made since ZDM published a similar special issue in 2010. We consider the extent to which future frontiers and methodological concerns raised in the commentary on the 2010 issue by…

Linking Preservice Teachers' Mathematics Self-Efficacy and Mathematics Teaching Efficacy to Their Mathematical Performance

Science.gov (United States)

Bates, Alan B.; Latham, Nancy; Kim, Jin-ah

2011-01-01

This study examined preservice teachers' mathematics self-efficacy and mathematics teaching efficacy and compared them to their mathematical performance. Participants included 89 early childhood preservice teachers at a Midwestern university. Instruments included the Mathematics Self-Efficacy Scale (MSES), Mathematics Teaching Efficacy Beliefs…

Assessment of dentally related functional competency for older adults with cognitive impairment--a survey for special-care dental professionals.

Science.gov (United States)

Chen, Xi; Clark, Jennifer J J

2013-01-01

This survey was to study whether and how dental professional assess dental-related function in older adults with cognitive impairment (OACI). An invitation was sent to 525 special-care dental professionals, followed by a reminder in 2 weeks. Thirteen percent of the targeted participants completed the survey. Among them, 88% completed a hospital dentistry, geriatric dentistry, or other postgraduate training program. Nearly 70% of the respondents considered somewhat to very difficult to assess dentally related function; 45% did not ever or did not regularly assess dental-related function for OACI. Dental-related functional assessments were often based on a subjective, unstructured approach. Only 6% of the respondents routinely used standard instruments to assess the patients' function. These results indicate that an objective functional assessment based on a standardized instrument has not been routinely incorporated into dental care for OACI, raising concerns for quality of care in this vulnerable population. ©2012 Special Care Dentistry Association and Wiley Periodicals, Inc.

Mathematics and Computer Science: Exploring a Symbiotic Relationship

Science.gov (United States)

Bravaco, Ralph; Simonson, Shai

2004-01-01

This paper describes a "learning community" designed for sophomore computer science majors who are simultaneously studying discrete mathematics. The learning community consists of three courses: Discrete Mathematics, Data Structures and an Integrative Seminar/Lab. The seminar functions as a link that integrates the two disciplines. Participation…

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

Home; Journals; Proceedings – Mathematical Sciences; Volume 127; Issue 2. Nonfiniteness of Hilbert–Kunz functions. V TRIVEDI. Research Article Volume 127 Issue 2 April 2017 ... Author Affiliations. V TRIVEDI1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India ...

Contrasts in Mathematical Challenges in A-Level Mathematics and Further Mathematics, and Undergraduate Mathematics Examinations

Science.gov (United States)

Darlington, Ellie

2014-01-01

This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…

DEVELOPMENT OF COORDINATION ABILITIES OF SPECIAL MEDICAL GROUPS STUDENTS IN PHYSICAL EDUCATION PROCESS

Directory of Open Access Journals (Sweden)

E. N. Dotsenko

2013-08-01

kinesthesia was introduced for the first time. The effect of the experimental program to the level of development and the relationship of coordination abilities and criteria of spare capacities in exact motions system control were determined. Practical value. To develop the content of training in special medical groups using the coordination exercises and elements to enhance the motor abilities of female students. Organizational and methodological aspects of holding trainings in special medical group with a load for students with different variations in health status were improved. The mathematical model describing the movements, including coordi nating students abilities in special medical group was developed. On the basis of developed indicators one can take into account the functional and physical fitness of students and form optimal regimes of motor activity for each nosologic group. It is especially important for the organization of educational process in universities physical education.

Mathematical Knowledge and Skills Expected by Higher Education in Engineering and the Social Sciences: Implications for High School Mathematics Curriculum

Science.gov (United States)

Basaran, Mehmet; Özalp, Gülümser; Kalender, Ilker; Alacaci, Cengiz

2015-01-01

One important function of school mathematics curriculum is to prepare high school students with the knowledge and skills needed for university education. Identifying them empirically will help making sound decisions about the contents of high school mathematics curriculum. It will also help students to make informed choices in course selection at…

Improving Early Numeracy of Young Children with Special Education Needs.

Science.gov (United States)

Van Luit, Johannes E. H.; Schopman, Esther A.

2000-01-01

Sixty-two students from special needs kindergartens were given early mathematics intervention. The early numeracy program was developed for children with disabilities and early numeracy difficulties by basing instruction on perceptual gestalt theory. Children performed better at posttest than controls but failed to transfer their knowledge to…

String partition functions, Hilbert schemes and affine Lie algebra representations on homology groups

International Nuclear Information System (INIS)

Bonora, Loriano; Bytsenko, Andrey; Elizalde, Emilio

2012-01-01

This review paper contains a concise introduction to highest weight representations of infinite-dimensional Lie algebras, vertex operator algebras and Hilbert schemes of points, together with their physical applications to elliptic genera of superconformal quantum mechanics and superstring models. The common link of all these concepts and of the many examples considered in this paper is to be found in a very important feature of the theory of infinite-dimensional Lie algebras: the modular properties of the characters (generating functions) of certain representations. The characters of the highest weight modules represent the holomorphic parts of the partition functions on the torus for the corresponding conformal field theories. We discuss the role of the unimodular (and modular) groups and the (Selberg-type) Ruelle spectral functions of hyperbolic geometry in the calculation of elliptic genera and associated q-series. For mathematicians, elliptic genera are commonly associated with new mathematical invariants for spaces, while for physicists elliptic genera are one-loop string partition function. (Therefore, they are applicable, for instance, to topological Casimir effect calculations.) We show that elliptic genera can be conveniently transformed into product expressions, which can then inherit the homology properties of appropriate polygraded Lie algebras. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (review)

A statistical mechanical approach to restricted integer partition functions

Science.gov (United States)

Zhou, Chi-Chun; Dai, Wu-Sheng

2018-05-01

The main aim of this paper is twofold: (1) suggesting a statistical mechanical approach to the calculation of the generating function of restricted integer partition functions which count the number of partitions—a way of writing an integer as a sum of other integers under certain restrictions. In this approach, the generating function of restricted integer partition functions is constructed from the canonical partition functions of various quantum gases. (2) Introducing a new type of restricted integer partition functions corresponding to general statistics which is a generalization of Gentile statistics in statistical mechanics; many kinds of restricted integer partition functions are special cases of this restricted integer partition function. Moreover, with statistical mechanics as a bridge, we reveal a mathematical fact: the generating function of restricted integer partition function is just the symmetric function which is a class of functions being invariant under the action of permutation groups. Using this approach, we provide some expressions of restricted integer partition functions as examples.

Contradictions and shifts in teaching with a new curriculum: The role of mathematics

DEFF Research Database (Denmark)

Stouraitis, Konstantinos; Potari, Despina; Skott, Jeppe

2015-01-01

In the framework of Cultural Historical Activity Theory (AT) contradictions are sources of change and development. Borrowing concepts from AT we attempt an interpretation of identified contradictions in a collaborative context where teachers plan and evaluate their teaching in the process...... of enacting a new mathematics curriculum. We examine the connection between contradictions and shifts in teaching activity, with a special focus on the mathematical character of these contradictions. We claim that dialectical oppositions lying in the background of these contradictions promote teachers...

Barriers to Medical Compassion as a Function of Experience and Specialization: Psychiatry, Pediatrics, Internal Medicine, Surgery, and General Practice.

Science.gov (United States)

Fernando, Antonio T; Consedine, Nathan S

2017-06-01

Compassion is an expectation of patients, regulatory bodies, and physicians themselves. Most research has, however, studied compassion fatigue rather than compassion itself and has concentrated on the role of the physician. The Transactional Model of Physician Compassion suggests that physician, patient, external environment, and clinical factors are all relevant. Because these factors vary both across different specialities and among physicians with differing degrees of experience, barriers to compassion are also likely to vary. We describe barriers to physician compassion as a function of specialization (psychiatry, general practice, surgery, internal medicine, and pediatrics) and physician experience. We used a cross-sectional study using demographic data, specialization, practice parameters, and the Barriers to Physician Compassion Questionnaire. Nonrandom convenience sampling was used to recruit 580 doctors, of whom 444 belonged to the targeted speciality groups. The sample was characterized before conducting a factorial Multivariate Analysis of Covariance and further post hoc analyses. A 5 (speciality grouping) × 2 (more vs. less physician experience) Multivariate Analysis of Covariance showed that the barriers varied as a function of both speciality and experience. In general, psychiatrists reported lower barriers, whereas general practitioners and internal medicine specialists generally reported greater barriers. Barriers were generally greater among less experienced doctors. Documenting and investigating barriers to compassion in different speciality groups have the potential to broaden current foci beyond the physician and inform interventions aimed at enhancing medical compassion. In addition, certain aspects of the training or practice of psychiatry that enhance compassion may mitigate barriers to compassion in other specialities. Copyright © 2017 American Academy of Hospice and Palliative Medicine. Published by Elsevier Inc. All rights reserved.

Improving the Graduate School Experience for Women in Mathematics: the Edge Program

Science.gov (United States)

Bozeman, Sylvia T.; Hughes, Rhonda J.

For over a decade, Spelman College and Bryn Mawr College have collaborated on initiatives designed to increase the presence of women, with a special focus on women of color, in the upper ranks of mathematical science. The most recent initiative is the EDGE Program (Enhancing Diversity in Graduate Education), which addresses this challenge by attempting to decrease the loss of talent from U.S. graduate programs. To this end, the program provides structures that help women make successful transitions from undergraduate into graduate mathematics programs, redirect or refocus their ambitions when programs are inappropriate or unsuitable, and, ultimately, enable them to "accumulate advantages" that will empower them and foster success in their careers. A broader goal of this program is to diversify the mathematics community by creating models for mathematics programs that allow people from all backgrounds and cultures to thrive, advance, and contribute to the profession.

A Cp-theory problem book special features of function spaces

CERN Document Server

Tkachuk, Vladimir V

2014-01-01

The books in Vladimir Tkachuk’s A Cp-Theory Problem Book series will be the ‘go to’ texts for basic reference to Cp-theory. This second volume, Special Features of Function Spaces, gives a reasonably complete coverage of Cp-theory, systematically introducing each of the major topics and providing  500 carefully selected problems and exercises with complete solutions. Bonus results and open problems are also given. The text is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research covering a wide variety of topics in Cp-theory and general topology at the professional level. The first volume, Topological and Function Spaces © 2011, provided an introduction from scratch to Cp-theory and general topology, preparing the reader for a professional understanding of Cp-theory in the last section of its main text. This second volume continues from the first, and can be used as a textbook for courses in both Cp-theory and general topology as well as a referenc...

Special Relativity: Will it Survive the Next 101 Years?

Energy Technology Data Exchange (ETDEWEB)

Altschul, Brett D [Department of Physics, Indiana University, Bloomington, IN 47405 (United States)

2007-06-18

All the physics we observe in our world is underlain by special relativity, a theory that has survived for more than a hundred years, in many respects completely intact. Yet despite its status as the most stringently tested theory in all of physics, special relativity is still frequently questioned. In the last decade and a half, many scientists have come to believe that special relativity, as Einstein formulated it, will need to be modified to accommodate a quantum theory of gravity. {l_brace}/it Special Relativity: Will it Survive the Next 101 Years?{r_brace} is a volume intended to introduce the reader to this new and still slightly controversial area of research. The book is divided into four parts. The first part is essentially historical. It consists of an essay discussing Einstein's work in the context of contemporary technological developments and a amusing note by R W P Drever on a precision Lorentz test that he performed literally in his backyard. These set the stage for the more modern material that follows. Part II discusses the theory of relativity and its mathematical foundations, from completely modern perspectives. There is much here that may be new even for experts on special relativity, and a significant level of mathematical sophistication on the part of the reader is assumed. A number of the lectures delve into the crucial question of how special relativity and its generalizations can be combined with quantum mechanics. The third part discusses theoretical models of Lorentz violation, and all the important paradigms that appear in the current literature are considered. These include the standard model extension (an effective field theory), modified dispersion relations and 'double special relativity', and noncommutative geometry. These lectures generally delve into less detail than those in part II; the focus is on helping the reader digest the new principles that must arise in theories without Lorentz symmetry. The final part of

Breaking the Mathematics Phobia of Secondary School Students ...

African Journals Online (AJOL)

kofimereku

functional knowledge of the world and their mastery of school subjects. Teaching ... the use of behaviour method of teaching mathematics to alleviate the Mathematics ... space for demonstrations and self-learning activities to make an educated man. .... activities, he or she may not be able to concentrate on their studies.

Progress in Industrial Mathematics at ECMI 2000

CERN Document Server

Capasso, Vincenzo; Greco, Antonio

2002-01-01

The European Consortium for Mathematics in Industry (ECMI) was founded in 1986 by leading groups of mathematicians in Europe for the following scopes: i) direct involvement of mathematicians in R&D activities; ii) international cooperation at a European scale; iii) education of industrial mathematicians to meet the growing demand for such experts. ECMI 2000 shows that ECMI has offered a unique example of effective international cooperation thanks to the financial support of the European Framework programmes. In particular they have helped ECMI establishing a set of Special Interest Groups to favour interaction with industry . This volume includes minisymposia about their activities, in particular microelectronics, glass, polymers, finance, traffic, and textiles. Applied mathematicians and other professionals working in academia or industry will find the book to be a useful and stimulating source of mathematical applications related to industrial problems.

Einstein's Theory A Rigorous Introduction for the Mathematically Untrained

CERN Document Server

Grøn, Øyvind

2011-01-01

This book provides an introduction to the theory of relativity and the mathematics used in its processes. Three elements of the book make it stand apart from previously published books on the theory of relativity. First, the book starts at a lower mathematical level than standard books with tensor calculus of sufficient maturity to make it possible to give detailed calculations of relativistic predictions of practical experiments. Self-contained introductions are given, for example vector calculus, differential calculus and integrations. Second, in-between calculations have been included, making it possible for the non-technical reader to follow step-by-step calculations. Thirdly, the conceptual development is gradual and rigorous in order to provide the inexperienced reader with a philosophically satisfying understanding of the theory.  Einstein's Theory: A Rigorous Introduction for the Mathematically Untrained aims to provide the reader with a sound conceptual understanding of both the special and genera...

An excursion through elementary mathematics, volume iii discrete mathematics and polynomial algebra