Mathematical aspects of quantum field theories

CERN Document Server

Strobl, Thomas

2015-01-01

Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homolo...

It's about time elementary mathematical aspects of relativity

CERN Document Server

Cooke, Roger

2017-01-01

This book has three main goals. First, it explores a selection of topics from the early period of the theory of relativity, focusing on particular aspects that are interesting or unusual. These include the twin paradox relativistic mechanics and its interaction with Maxwell's laws the earliest triumphs of general relativity relating to the orbit of Mercury and the deflection of light passing near the sun and the surprising bizarre metric of Kurt Godel, in which time travel is possible. Second, it provides an exposition of the differential geometry needed to understand these topics on a level that is intended to be accessible to those with just two years of university-level mathematics as background. Third, it reflects on the historical development of the subject and its significance for our understanding of what reality is and how we can know about the physical universe. The book also takes note of historical prefigurations of relativity, such as Euler's 1744 result that a particle moving on a surface and sub...

Aspects of Mathematical Modelling of Pressure Retarded Osmosis

Science.gov (United States)

Anissimov, Yuri G.

2016-01-01

In power generating terms, a pressure retarded osmosis (PRO) energy generating plant, on a river entering a sea or ocean, is equivalent to a hydroelectric dam with a height of about 60 meters. Therefore, PRO can add significantly to existing renewable power generation capacity if economical constrains of the method are resolved. PRO energy generation relies on a semipermeable membrane that is permeable to water and impermeable to salt. Mathematical modelling plays an important part in understanding flows of water and salt near and across semipermeable membranes and helps to optimize PRO energy generation. Therefore, the modelling can help realizing PRO energy generation potential. In this work, a few aspects of mathematical modelling of the PRO process are reviewed and discussed. PMID:26848696

The ABCs of Math: A Genetic Analysis of Mathematics and Its Links With Reading Ability and General Cognitive Ability

Science.gov (United States)

Hart, Sara A.; Petrill, Stephen A.; Thompson, Lee A.; Plomin, Robert

2009-01-01

The goal of this first major report from the Western Reserve Reading Project Math component is to explore the etiology of the relationship among tester-administered measures of mathematics ability, reading ability, and general cognitive ability. Data are available on 314 pairs of monozygotic and same-sex dizygotic twins analyzed across 5 waves of assessment. Univariate analyses provide a range of estimates of genetic (h2 = .00 –.63) and shared (c2 = .15–.52) environmental influences across math calculation, fluency, and problem solving measures. Multivariate analyses indicate genetic overlap between math problem solving with general cognitive ability and reading decoding, whereas math fluency shares significant genetic overlap with reading fluency and general cognitive ability. Further, math fluency has unique genetic influences. In general, math ability has shared environmental overlap with general cognitive ability and decoding. These results indicate that aspects of math that include problem solving have different genetic and environmental influences than math calculation. Moreover, math fluency, a timed measure of calculation, is the only measured math ability with unique genetic influences. PMID:20157630

Mathematical biology

CERN Document Server

Murray, James D

1993-01-01

The book is a textbook (with many exercises) giving an in-depth account of the practical use of mathematical modelling in the biomedical sciences. The mathematical level required is generally not high and the emphasis is on what is required to solve the real biological problem. The subject matter is drawn, e.g. from population biology, reaction kinetics, biological oscillators and switches, Belousov-Zhabotinskii reaction, reaction-diffusion theory, biological wave phenomena, central pattern generators, neural models, spread of epidemics, mechanochemical theory of biological pattern formation and importance in evolution. Most of the models are based on real biological problems and the predictions and explanations offered as a direct result of mathematical analysis of the models are important aspects of the book. The aim is to provide a thorough training in practical mathematical biology and to show how exciting and novel mathematical challenges arise from a genuine interdisciplinary involvement with the biosci...

On an efficient general mathematical library

International Nuclear Information System (INIS)

Li Xiaomei; Yan Baoyong

1992-01-01

In this paper, the architecture of vector pipeline computer YH-1 is briefly described, and the characteristics of an efficient vector general mathematical library are discussed. Some approaches to vectorization, adopted in developing the vector mathematical library, are presented

Aspects of uncertainty analysis in accident consequence modeling

International Nuclear Information System (INIS)

Travis, C.C.; Hoffman, F.O.

1981-01-01

Mathematical models are frequently used to determine probable dose to man from an accidental release of radionuclides by a nuclear facility. With increased emphasis on the accuracy of these models, the incorporation of uncertainty analysis has become one of the most crucial and sensitive components in evaluating the significance of model predictions. In the present paper, we address three aspects of uncertainty in models used to assess the radiological impact to humans: uncertainties resulting from the natural variability in human biological parameters; the propagation of parameter variability by mathematical models; and comparison of model predictions to observational data

Working memory and language: skill-specific or domain-general relations to mathematics?

Science.gov (United States)

Purpura, David J; Ganley, Colleen M

2014-06-01

Children's early mathematics skills develop in a cumulative fashion; foundational skills form a basis for the acquisition of later skills. However, non-mathematical factors such as working memory and language skills have also been linked to mathematical development at a broad level. Unfortunately, little research has been conducted to evaluate the specific relations of these two non-mathematical factors to individual aspects of early mathematics. Thus, the focus of this study was to determine whether working memory and language were related to only individual aspects of early mathematics or related to many components of early mathematics skills. A total of 199 4- to 6-year-old preschool and kindergarten children were assessed on a battery of early mathematics tasks as well as measures of working memory and language. Results indicated that working memory has a specific relation to only a few-but critically important-early mathematics skills and language has a broad relation to nearly all early mathematics skills. Copyright © 2014 Elsevier Inc. All rights reserved.

Identifying Domain-General and Domain-Specific Predictors of Low Mathematics Performance: A Classification and Regression Tree Analysis

Directory of Open Access Journals (Sweden)

David J. Purpura

2017-12-01

Full Text Available Many children struggle to successfully acquire early mathematics skills. Theoretical and empirical evidence has pointed to deficits in domain-specific skills (e.g., non-symbolic mathematics skills or domain-general skills (e.g., executive functioning and language as underlying low mathematical performance. In the current study, we assessed a sample of 113 three- to five-year old preschool children on a battery of domain-specific and domain-general factors in the fall and spring of their preschool year to identify Time 1 (fall factors associated with low performance in mathematics knowledge at Time 2 (spring. We used the exploratory approach of classification and regression tree analyses, a strategy that uses step-wise partitioning to create subgroups from a larger sample using multiple predictors, to identify the factors that were the strongest classifiers of low performance for younger and older preschool children. Results indicated that the most consistent classifier of low mathematics performance at Time 2 was children’s Time 1 mathematical language skills. Further, other distinct classifiers of low performance emerged for younger and older children. These findings suggest that risk classification for low mathematics performance may differ depending on children’s age.

Mathematical theory of compressible viscous fluids analysis and numerics

CERN Document Server

Feireisl, Eduard; Pokorný, Milan

2016-01-01

This book offers an essential introduction to the mathematical theory of compressible viscous fluids. The main goal is to present analytical methods from the perspective of their numerical applications. Accordingly, we introduce the principal theoretical tools needed to handle well-posedness of the underlying Navier-Stokes system, study the problems of sequential stability, and, lastly, construct solutions by means of an implicit numerical scheme. Offering a unique contribution – by exploring in detail the “synergy” of analytical and numerical methods – the book offers a valuable resource for graduate students in mathematics and researchers working in mathematical fluid mechanics. Mathematical fluid mechanics concerns problems that are closely connected to real-world applications and is also an important part of the theory of partial differential equations and numerical analysis in general. This book highlights the fact that numerical and mathematical analysis are not two separate fields of mathematic...

SOME ASPECTS OF THE USE OF MATHEMATICAL-STATISTICAL METHODS IN THE ANALYSIS OF SOCIO-HUMANISTIC TEXTS Humanities and social text, mathematics, method, statistics, probability

Directory of Open Access Journals (Sweden)

Zaira M Alieva

2016-01-01

Full Text Available The article analyzes the application of mathematical and statistical methods in the analysis of socio-humanistic texts. The essence of mathematical and statistical methods, presents examples of their use in the study of Humanities and social phenomena. Considers the key issues faced by the expert in the application of mathematical-statistical methods in socio-humanitarian sphere, including the availability of sustainable contrasting socio-humanitarian Sciences and mathematics; the complexity of the allocation of the object that is the bearer of the problem; having the use of a probabilistic approach. The conclusion according to the results of the study.

Making mathematics and science integration happen: key aspects of practice

Science.gov (United States)

Ríordáin, Máire Ní; Johnston, Jennifer; Walshe, Gráinne

2016-02-01

The integration of mathematics and science teaching and learning facilitates student learning, engagement, motivation, problem-solving, criticality and real-life application. However, the actual implementation of an integrative approach to the teaching and learning of both subjects at classroom level, with in-service teachers working collaboratively, at second-level education, is under-researched due to the complexities of school-based research. This study reports on a year-long case study on the implementation of an integrated unit of learning on distance, speed and time, within three second-level schools in Ireland. This study employed a qualitative approach and examined the key aspects of practice that impact on the integration of mathematics and science teaching and learning. We argue that teacher perspective, teacher knowledge of the 'other subject' and of technological pedagogical content knowledge (TPACK), and teacher collaboration and support all impact on the implementation of an integrative approach to mathematics and science education.

Transform analysis of generalized functions

CERN Document Server

Misra, O P

1986-01-01

Transform Analysis of Generalized Functions concentrates on finite parts of integrals, generalized functions and distributions. It gives a unified treatment of the distributional setting with transform analysis, i.e. Fourier, Laplace, Stieltjes, Mellin, Hankel and Bessel Series.Included are accounts of applications of the theory of integral transforms in a distributional setting to the solution of problems arising in mathematical physics. Information on distributional solutions of differential, partial differential equations and integral equations is conveniently collected here.The volume will

General systems theory mathematical foundations

CERN Document Server

Mesarovic, Mihajlo D

1975-01-01

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

The 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

The Mathematical Aspects of Quantum Maps

International Nuclear Information System (INIS)

Berkolaiko, G

2003-01-01

The book represents the collected lectures given at the Summer School on Mathematical Aspects of Quantum Maps held at Bologna University in September 2001. Quantum maps gained their prominence as a testing ground for mathematical understanding of various concepts in quantum chaos, such as the spectral statistics, quantum ergodicity, scarring of the eigenfunctions and the connection to algebraic number theory. The book is nicely structured. It begins by reviewing the relevant concepts and results from dynamical systems (a contribution by A Knauf) and number theory (by Z Rudnick). A contribution by the editors, M Degli Esposti and S Graffi, explains the quantization procedure for the quantum maps and proceeds to discuss some properties of the quantized maps, such as ergodicity and scarring, and the number theoretical techniques involved in proving these properties. The contribution by A Baeacker discusses the numerical methods used to study quantum chaotic systems. It contains both the mathematical background and a detailed explanation of the numerical techniques, possible pitfalls at the implementation stage and how to avoid them. It even contains a computer program in Python used by the author to compute the eigenvalues of a perturbed cat map. The last contribution, by R Artuso, while very interesting in itself, feels somewhat disconnected from the rest of the book. It deals with deterministic transport in hyperbolic and weakly chaotic systems, where one can observe normal and anomalous diffusion respectively. Although being a collection of contributions from various authors, the book feels very much like a well-coordinated team effort, with frequent cross-contributional references underlying the connections between different facets of the discussed subjects. I consider it an invaluable reference for researchers in the field of quantum chaos and would recommend it as a first read for people just entering the field. It contains both the necessary background

A multidimensional approach to training mathematics students at a university: improving the efficiency through the unity of social, psychological and pedagogical aspects

Science.gov (United States)

Kuznetsova, Elena; Matytcina, Marina

2018-04-01

The article deals with social, psychological and pedagogical aspects of teaching mathematics students at universities. The sociological portrait and the factors influencing a career choice of a mathematician have been investigated through the survey results of 198 first-year students of applied mathematics major at 27 state universities (Russia). Then, psychological characteristics of mathematics students have been examined based on scientific publications. The obtained results have allowed us to reveal pedagogical conditions and specific ways of training mathematics students in the process of their education at university. The article also contains the analysis of approaches to the development of mathematics education both in Russia and in other countries. The results may be useful for teaching students whose training requires in-depth knowledge of mathematics.

The application of new mathematical structures to safety analysis

International Nuclear Information System (INIS)

Cooper, J.A.; Ross, T.J.

1997-10-01

Probabilistic safety analyses (PSAs) often depend on significant subjectivity. The recent successes of fuzzy logic and fuzzy and hybrid mathematics in portraying subjectivity is a reminder that a selection made from the most applicable mathematical tools is more important than forced adaptation of conventional tools. In this paper, the authors consider new approaches that enhance conventional and fuzzy PSA by improved handling of subjectivity. The most significant of the mathematical structures were have investigated (from a standpoint of safety analysis applications) will be described, and the general types of applications will be outlined

Visual Processing in Generally Gifted and Mathematically Excelling Adolescents

Science.gov (United States)

Paz-Baruch, Nurit; Leikin, Roza; Leikin, Mark

2016-01-01

Little empirical data are available concerning the cognitive abilities of gifted individuals in general and especially those who excel in mathematics. We examined visual processing abilities distinguishing between general giftedness (G) and excellence in mathematics (EM). The research population consisted of 190 students from four groups of 10th-…

Research Progress in Mathematical Analysis of Map Projection by Computer Algebra

Directory of Open Access Journals (Sweden)

BIAN Shaofeng

2017-10-01

Full Text Available Map projection is an important component of modern cartography, and involves many fussy mathematical analysis processes, such as the power series expansions of elliptical functions, differential of complex and implicit functions, elliptical integral and the operation of complex numbers. The derivation of these problems by hand not only consumes much time and energy but also makes mistake easily, and sometimes can not be realized at all because of the impossible complexity. The research achievements in mathematical analysis of map projection by computer algebra are systematically reviewed in five aspects, i.e., the symbolic expressions of forward and inverse solution of ellipsoidal latitudes, the direct transformations between map projections with different distortion properties, expressions of Gauss projection by complex function, mathematical analysis of oblique Mercator projection, polar chart projection with its transformation. Main problems that need to be further solved in this research field are analyzed. It will be helpful to promote the development of map projection.

Relationship of Mathematics Olympiad Performance of Gifted Students with IQ and Mathematics Achievement

Directory of Open Access Journals (Sweden)

Ali İhsan BORAN

2015-04-01

Full Text Available The purpose of this study is to investigate relationship of mathematics Olympiad (analysis-algebra and geometry scores of gifted students with IQ scores (verbal, performance and general and mathematics achievement scores of the gifted students. Study group of the study included 64 gifted students (27 girls and 37 boys who took courses from one Science and Art Center. Data of study involved scores of the participants on mathematics Olympiad exam, WISC-R test and school mathematics achievement. For analysis of the data Pearson correlation analysis, Spearman correlation analysis, independent groups’ t-test and Mann Whitney U test were utilized. The findings showed that there was no significant relationship between the Olympiad scores on analysis-algebra and geometry and IQ scores (general, performance and verbal. But the Olympiad scores on analysis-algebra and geometry factors were significantly related to school mathematics achievement. Comparing IQ scores of highest and lowest scorer groups on the Olympiad scores showed that there were no significant differences between IQ scores (general, performance and verbal of the groups. However school mathematics scores of the participants significantly differed in terms of groups determined based on analysis-algebra and geometry scores.

Mathematical aspects of vortex dynamics; Proceedings of the Workshop, Leesburg, VA, Apr. 25-27, 1988

International Nuclear Information System (INIS)

Caflisch, R.E.

1989-01-01

Various papers on the mathematical aspects of vortex dynamics are presented. Individual topics addressed include: mathematical analysis of vortex dynamics, improved vortex methods for three-dimensional flows, the relation between thin vortex layer and vortex sheets, computations of broadband instabilities in a class of closed-streamline flows, vortex-sheet dynamics and hyperfunction theory, free surface vortex method with weak viscous effects, iterative method for computing steady vortex flow systems, invariant measures for the two-dimensional Euler flow, similarity flows containing two-branched vortex sheets, strain-induced vortex stripping, convergence of the vortex method for vortex sheets, boundary conditions and deterministic vortex methods for the Navier-Stokes equations, vorticity creation boundary conditions, vortex dynamics of stratified flows, vortex breakdown, numerical studies of vortex reconnection, vortex lattices in theory and practice, dynamics of vortex structures in the wall region of a turbulent boundary layer, and energy of a vortex lattice configuration

Oral speech teaching to students of mathematic specialties: a grammatical aspect

Directory of Open Access Journals (Sweden)

Ibragimov I.I.

2016-08-01

Full Text Available the paper considers teaching features of English speech grammar aspects. The case studies include undergraduates of mathematical specialties. The content of students’ educational activity at the final stage of language teaching is pointed out. Besides the structure of grammar section, a special didactic training unit in which framework mastering grammar phenomena used in oral speech takes place is described.

Nuclear medicine and mathematics

Energy Technology Data Exchange (ETDEWEB)

Pedroso de Lima, J.J. [Dept. de Biofisica e Proc. de Imagem, IBILI - Faculdade de Medicina, Coimbra (Portugal)

1996-06-01

The purpose of this review is not to present a comprehensive description of all the mathematical tools used in nuclear medicine, but to emphasize the importance of the mathematical method in nuclear medicine and to elucidate some of the mathematical concepts currently used. We can distinguish three different areas in which mathematical support has been offered to nuclear medicine: Physiology, methodology and data processing. Nevertheless, the boundaries between these areas can be indistinct. It is impossible in a single article to give even an idea of the extent and complexity of the procedures currently usede in nuclear medicine, such as image processing, reconstruction from projections and artificial intelligence. These disciplines do not belong to nuclear medicine: They are already branches of engineering, and my interest will reside simply in revealing a little of the elegance and the fantastic potential of these new `allies` of nuclear medicine. In this review the mathematics of physiological interpretation and methodology are considered together in the same section. General aspects of data-processing methods, including image processing and artificial intelligence, are briefly analysed. The mathematical tools that are most often used to assist the interpretation of biological phenomena in nuclear medicine are considered; these include convolution and deconvolution methods, Fourier analysis, factorial analysis and neural networking. (orig.)

Nuclear medicine and mathematics

International Nuclear Information System (INIS)

Pedroso de Lima, J.J.

1996-01-01

The purpose of this review is not to present a comprehensive description of all the mathematical tools used in nuclear medicine, but to emphasize the importance of the mathematical method in nuclear medicine and to elucidate some of the mathematical concepts currently used. We can distinguish three different areas in which mathematical support has been offered to nuclear medicine: Physiology, methodology and data processing. Nevertheless, the boundaries between these areas can be indistinct. It is impossible in a single article to give even an idea of the extent and complexity of the procedures currently usede in nuclear medicine, such as image processing, reconstruction from projections and artificial intelligence. These disciplines do not belong to nuclear medicine: They are already branches of engineering, and my interest will reside simply in revealing a little of the elegance and the fantastic potential of these new 'allies' of nuclear medicine. In this review the mathematics of physiological interpretation and methodology are considered together in the same section. General aspects of data-processing methods, including image processing and artificial intelligence, are briefly analysed. The mathematical tools that are most often used to assist the interpretation of biological phenomena in nuclear medicine are considered; these include convolution and deconvolution methods, Fourier analysis, factorial analysis and neural networking. (orig.)

Mathematical aspects of finite element methods for incompressible viscous flows

Science.gov (United States)

Gunzburger, M. D.

1986-01-01

Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.

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.

Dyslexia, Dyspraxia and Mathematics.

Science.gov (United States)

Yeo, Dorian

This book explores how primary school children with dyslexia or dyspraxia and difficulty in math can learn math and provides practical support and detailed teaching suggestions. It considers cognitive features that underlie difficulty with mathematics generally or with specific aspects of mathematics. It outlines the ways in which children usually…

PhiMSAMP: philosophy of mathematics: sociological aspects and mathematical practice

NARCIS (Netherlands)

Löwe, B.; Müller, T.

2010-01-01

Philosophy of mathematics is moving in a new direction: away from a foundationalism in terms of formal logic and traditional ontology, and towards a broader range of approaches that are united by a focus on mathematical practice. The scientific research network PhiMSAMP (Philosophy of Mathematics:

The contribution of general cognitive abilities and approximate number system to early mathematics.

Science.gov (United States)

Passolunghi, Maria Chiara; Cargnelutti, Elisa; Pastore, Massimiliano

2014-12-01

Math learning is a complex process that entails a wide range of cognitive abilities to be fulfilled. There is sufficient evidence that both general and specific cognitive skills assume a fundamental role, despite the absence of shared consensus about the relative extent of their involvement. Moreover, regarding general abilities, there is no agreement about the recruitment of the different memory components or of intelligence. In relation to specific factors, great debate subsists regarding the role of the approximate number system (ANS). Starting from these considerations, we wanted to conduct a wide assessment of memory components and ANS, by controlling for the effects associated with intelligence and also exploring possible relationships between all precursors. To achieve this purpose, a sample of 157 children was tested at both beginning and end of their Grade 1. Both general (memory and intelligence) and specific (ANS) precursors were evaluated by a wide battery of tests and put in relation to concurrent and subsequent math skills. Memory was explored in passive and active aspects involving both verbal and visuo-spatial components. Path analysis results demonstrated that memory, and especially the more active processes, and intelligence were the strongest precursors in both assessment times. ANS had a milder role which lost significance by the end of the school year. Memory and ANS seemed to influence early mathematics almost independently. Both general and specific precursors seemed to have a crucial role in early math competences, despite the lower involvement of ANS. © 2014 The British Psychological Society.

Visual Representations in Mathematics Teaching: An Experiment with Students

Science.gov (United States)

Debrenti, Edith

2015-01-01

General problem-solving skills are of central importance in school mathematics achievement. Word problems play an important role not just in mathematical education, but in general education as well. Meaningful learning and understanding are basic aspects of all kinds of learning and it is even more important in the case of learning mathematics. In…

Mathematical and Computational Aspects Related to Soil Modeling and Simulation

Science.gov (United States)

2017-09-26

and simulation challenges at the interface of applied math (homogenization, handling of discontinuous behavior, discrete vs. continuum representations...topics: a) Visco-elasto-plastic continuum models of geo-surface materials b) Discrete models of geo-surface materials (rocks/gravel/sand) c) Mixed...continuum- discrete representations. Coarse-graining and fine-graining mathematical formulations d) Multi-physics aspects related to the modeling of

70 years of the general theory of relativity

International Nuclear Information System (INIS)

Castro Diaz-Balart, F.; Cabezas Solorzano, R.

1986-06-01

In view of the 70th anniversary of the discovery of the General Theory of Relativity, an analysis was made of the special and general theories. The basic postulates, their consequences in the formulation of the theories, the main results, some aspects related to the experimental verification and its applications are presented, as are some elements of the mathematical formalism of the theories, to facilitate the logical interrelationships between its results and consequences. (author)

Elementary General and Special Education Teachers' Mathematics Skills and Efficacy

Science.gov (United States)

Flores, Margaret M.; Thornton, Jennifer; Franklin, Toni M.; Hinton, Vanessa M.; Strozier, Shaunita

2014-01-01

The purpose of this study was to extend the literature regarding elementary teachers' beliefs about mathematics instruction to include special education teachers by surveying special education and general education teachers' mathematics teaching efficacy. In addition, the researchers' surveyed teachers' mathematics skills. The participants (n =…

Mathematical methods in medicine: neuroscience, cardiology and pathology

Science.gov (United States)

Amigó, José M.

2017-01-01

The application of mathematics, natural sciences and engineering to medicine is gaining momentum as the mutual benefits of this collaboration become increasingly obvious. This theme issue is intended to highlight the trend in the case of mathematics. Specifically, the scope of this theme issue is to give a general view of the current research in the application of mathematical methods to medicine, as well as to show how mathematics can help in such important aspects as understanding, prediction, treatment and data processing. To this end, three representative specialties have been selected: neuroscience, cardiology and pathology. Concerning the topics, the 12 research papers and one review included in this issue cover biofluids, cardiac and virus dynamics, computational neuroscience, functional magnetic resonance imaging data processing, neural networks, optimization of treatment strategies, time-series analysis and tumour growth. In conclusion, this theme issue contains a collection of fine contributions at the intersection of mathematics and medicine, not as an exercise in applied mathematics but as a multidisciplinary research effort that interests both communities and our society in general. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’. PMID:28507240

Mathematical methods in medicine: neuroscience, cardiology and pathology.

Science.gov (United States)

Amigó, José M; Small, Michael

2017-06-28

The application of mathematics, natural sciences and engineering to medicine is gaining momentum as the mutual benefits of this collaboration become increasingly obvious. This theme issue is intended to highlight the trend in the case of mathematics. Specifically, the scope of this theme issue is to give a general view of the current research in the application of mathematical methods to medicine, as well as to show how mathematics can help in such important aspects as understanding, prediction, treatment and data processing. To this end, three representative specialties have been selected: neuroscience, cardiology and pathology. Concerning the topics, the 12 research papers and one review included in this issue cover biofluids, cardiac and virus dynamics, computational neuroscience, functional magnetic resonance imaging data processing, neural networks, optimization of treatment strategies, time-series analysis and tumour growth. In conclusion, this theme issue contains a collection of fine contributions at the intersection of mathematics and medicine, not as an exercise in applied mathematics but as a multidisciplinary research effort that interests both communities and our society in general.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'. © 2017 The Author(s).

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, ...

Episodes in the mathematics of medieval Islam

CERN Document Server

Berggren, J L

1986-01-01

From the reviews: The book is, in spite of the author's more modest claims, an introductory survey of main developments in those disciplines which were particularly important in Medieval Islamic mathematics...No knowledge of mathematics (or of the history of mathematics) beyond normal high-school level is presupposed, and everything required beyond that (be it Apollonian theory of conics or the definitions of celestial circles) is explained carefully and clearly. Scattered throughout the work are a number of lucid remarks on the character of Islamic mathematics or of mathematical work in general. The book will hence not only be an excellent textbook for the teaching of the history of mathematics but also for the liberal art aspect of mathematics teaching in general. - Jens Høyrup, Mathematical Reviews ...as a textbook, this work is highly commendable...It is definitely the product of a skillful mathematician who has collected over the years a reasonably large number of interesting problems from medieval Arab...

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 aspects of quantum field theory

CERN Document Server

de Faria, Edson

2010-01-01

Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.

Contemplating Symbolic Literacy of First Year Mathematics Students

Science.gov (United States)

Bardini, Caroline; Pierce, Robyn; Vincent, Jill

2015-01-01

Analysis of mathematical notations must consider both syntactical aspects of symbols and the underpinning mathematical concept(s) conveyed. We argue that the construct of "syntax template" provides a theoretical framework to analyse undergraduate mathematics students' written solutions, where we have identified several types of…

Combinatorial Aspects of the Generalized Euler's Totient

Directory of Open Access Journals (Sweden)

Nittiya Pabhapote

2010-01-01

Full Text Available A generalized Euler's totient is defined as a Dirichlet convolution of a power function and a product of the Souriau-Hsu-Möbius function with a completely multiplicative function. Two combinatorial aspects of the generalized Euler's totient, namely, its connections to other totients and its relations with counting formulae, are investigated.

Concepts of modern mathematics

CERN Document Server

Stewart, Ian

1995-01-01

Some years ago, ""new math"" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of ""new math"" have been eliminated and its positive elements assimilated into classroom instruction.In this charming volume, a noted English mathematician uses humor an

Values in the Mathematics Classroom: Supporting Cognitive and Affective Pedagogical Ideas

Science.gov (United States)

Seah, Wee Tiong

2016-01-01

Values are the personal convictions which one finds important. Three different aspects which are associated with mathematics education differently are identified, namely, values through mathematics education, values of mathematics education, and values for mathematics. These are paired with Bishop's (1996) conceptions of general educational,…

Analysis of students’ mathematical reasoning

Science.gov (United States)

Sukirwan; Darhim; Herman, T.

2018-01-01

The reasoning is one of the mathematical abilities that have very complex implications. This complexity causes reasoning including abilities that are not easily attainable by students. Similarly, studies dealing with reason are quite diverse, primarily concerned with the quality of mathematical reasoning. The objective of this study was to determine the quality of mathematical reasoning based perspective Lithner. Lithner looked at how the environment affects the mathematical reasoning. In this regard, Lithner made two perspectives, namely imitative reasoning and creative reasoning. Imitative reasoning can be memorized and algorithmic reasoning. The Result study shows that although the students generally still have problems in reasoning. Students tend to be on imitative reasoning which means that students tend to use a routine procedure when dealing with reasoning. It is also shown that the traditional approach still dominates on the situation of students’ daily learning.

CULTUROLOGICAL APPROACH AS METHODOLOGICAL BASIS OF MATHEMATICAL EDUCATION

Directory of Open Access Journals (Sweden)

Ye. A. Perminov

2017-01-01

Full Text Available Introduction. Today, in the era of a mathematization of science and total expansion of digital technologies, mass mathematical education becomes a necessary part of culture of every person. However, there are some serious obstacles to formation and development of general mathematical culture: insufficient understanding of its importance by society and the state; fragmentary-clipconsciousness, emerging among representatives of the younger generation under the influence of the Internet, and preventing formation of a complete picture of the modern world; traditional system of disjointed subjects and courses in school, secondary vocational and high school mathematics education; non-cognitive (automatic transferring of the approaches, principles, technologies and techniques into training which are not specific in order to master a course. Development of sociological, axiological and especially culturological aspects of mathematical methodology is required for the solution of the urgent problems of methodology in mathematical education.The aim of the publication is to discuss methodological aspects of culturological approach realization in mathematical education.Methodology and research methods. The theoretical scientific methods of the present article involve analysis and synthesis of the content of philosophical, mathematical, pedagogical, methodological literature and normative documents; comparative, culturological and logical types of analysis of mathematical education; systematic, competence-based, practice-oriented and personal-activity metho-dological approaches were used to understand the concept of mathematical education.Results and scientific novelty. The practicability and leading role of culturological approach to promoting mathematical knowledge is proved from historical, philosophical and pedagogical positions. It is stated that objective conceptualization of progressive ideas and new methods of mathematical science and mathematical

Mathematical and physical aspects of gauge theories

International Nuclear Information System (INIS)

Chatelet, G.; Paris-13 Univ., 93 - Saint-Denis

1981-01-01

We present here a survey of gauge theories, trying to relate the main mathematical and physical concepts. Part I is devoted to exhibiting parallel transport and connection as the adequate concepts for the constitution of the parametrized internal space of a particle. A covariant derivative provides the differential calculus, which is needed when one leaves the point-like description in microphysics. Part II deals with the so-called pure gauge theory and sketches the construction of the self-dual solutions of Yang-Mills equations. We briefly explain Guersey's method to get SU 2 self-dual potentials as quarternionic analytic maps from S 4 (first quarternionic projective space) into HPsub(n) (n-dimensional quarternionic projective space). Part III is devoted to the Goldstone's theorem and Higgs' mechanism used to provide a mass to gauge mesons. We describe a Salam-Weinberg model to illustrate these techniques. Part IV deals with the perturbative aspect. The Faddeev-Popov method, formerly conceived as a technique to get correct Feynmann rules, actually leads to a systematic study of the affine space of connections factored out by gauge transformations. (orig.)

General aspects of design and vessel nozzle analysis of nuclear power plants

International Nuclear Information System (INIS)

Back, N.

1980-01-01

Aspects of design and a procedure for nozzle tensile analysis under loads in project, normal and abnormal, emergency, failure and test conditions. For each condition, considerations about the tensile calculation methods, the tensile classification in corresponding categories and the comparison with admissible limits according to the norms. (M.C.K.) [pt

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.

Commognitive analysis of undergraduate mathematics students' first encounter with the subgroup test

Science.gov (United States)

Ioannou, Marios

2018-06-01

This study analyses learning aspects of undergraduate mathematics students' first encounter with the subgroup test, using the commognitive theoretical framework. It focuses on students' difficulties as these are related to the object-level and metalevel mathematical learning in group theory, and, when possible, highlights any commognitive conflicts. In the data analysis, one can identify three types of difficulties, relevant to object-level learning: namely regarding the frequently observed confusion between groups and sets, the object-level rules of visual mediators, and the object-level rules of contextual notions, such as permutations, exponentials, sets and matrices. In addition, data analysis suggests two types of difficulties, relevant to metalevel learning. The first refers to the actual proof that the three conditions of subgroup test hold, and the second is related to syntactic inaccuracies, incomplete argumentation and problematic use of visual mediators. Finally, this study suggests that there are clear links between object-level and metalevel learning, mainly due to the fact that objectification of the various relevant mathematical notions influences the endorsement of the governing metarules.

Mathematical aspects of surface water waves

International Nuclear Information System (INIS)

Craig, Walter; Wayne, Clarence E

2007-01-01

The theory of the motion of a free surface over a body of water is a fascinating subject, with a long history in both applied and pure mathematical research, and with a continuing relevance to the enterprises of mankind having to do with the sea. Despite the recent advances in the field (some of which we will hear about during this Workshop on Mathematical Hydrodynamics at the Steklov Institute), and the current focus of the mathematical community on the topic, many fundamental mathematical questions remain. These have to do with the evolution of surface water waves, their approximation by model equations and by computer simulations, the detailed dynamics of wave interactions, such as would produce rogue waves in an open ocean, and the theory (partially probabilistic) of approximating wave fields over large regions by averaged 'macroscopic' quantities which satisfy essentially kinetic equations of motion. In this note we would like to point out open problems and some of the directions of current research in the field. We believe that the introduction of new analytical techniques and novel points of view will play an important role in the future development of the area.

Enhanced Assessment Technology and Neurocognitive Aspects of Specific Learning Disorder with Impairment in Mathematics.

Directory of Open Access Journals (Sweden)

Marios A. Pappas

2018-02-01

Full Text Available Specific Learning Disorder with impairment in Mathematics (Developmental Dyscalculia is a complex learning disorder which affects arithmetic skills, symbolic magnitude processing, alertness, flexibility in problem solving and maintained attention. Neuro-cognitive studies revealed that such difficulties in children with DD could be related to poor Working Memory and attention deficits. Furthermore, neuroimaging studies indicate that brain structure differences in children with DD compared to typically developing children could affect mathematical performance. In this study we present the cognitive profile of Dyscalculia, as well as the neuropsychological aspects of the deficit, with special reference to the utilization of enhanced assessment technology such as computerized neuropsychological tools and neuroimaging techniques.

The Generalized Principle of the Golden Section and its applications in mathematics, science, and engineering

International Nuclear Information System (INIS)

Stakhov, A.P.

2005-01-01

The 'Dichotomy Principle' and the classical 'Golden Section Principle' are two of the most important principles of Nature, Science and also Art. The Generalized Principle of the Golden Section that follows from studying the diagonal sums of the Pascal triangle is a sweeping generalization of these important principles. This underlies the foundation of 'Harmony Mathematics', a new proposed mathematical direction. Harmony Mathematics includes a number of new mathematical theories: an algorithmic measurement theory, a new number theory, a new theory of hyperbolic functions based on Fibonacci and Lucas numbers, and a theory of the Fibonacci and 'Golden' matrices. These mathematical theories are the source of many new ideas in mathematics, philosophy, botanic and biology, electrical and computer science and engineering, communication systems, mathematical education as well as theoretical physics and physics of high energy particles

Richardson extrapolation practical aspects and applications

CERN Document Server

Zlatev, Zahari; Faragó, István; Havasi, Ágnes

2017-01-01

The series is devoted to the publication of high-level monographs and specialized graduate texts which cover the whole spectrum of applied mathematics, including its numerical aspects. The focus of the series is on the interplay between mathematical and numerical analysis, and also on its applications to mathematical models in the physical and life sciences.

The Generalized Principle of the Golden Section and its applications in mathematics, science, and engineering

Energy Technology Data Exchange (ETDEWEB)

Stakhov, A.P. [International Club of the Golden Section, 6 McCreary Trail, Bolton, ON, L7E 2C8 (Canada)] e-mail: goldenmuseum@rogers.com

2005-10-01

The 'Dichotomy Principle' and the classical 'Golden Section Principle' are two of the most important principles of Nature, Science and also Art. The Generalized Principle of the Golden Section that follows from studying the diagonal sums of the Pascal triangle is a sweeping generalization of these important principles. This underlies the foundation of 'Harmony Mathematics', a new proposed mathematical direction. Harmony Mathematics includes a number of new mathematical theories: an algorithmic measurement theory, a new number theory, a new theory of hyperbolic functions based on Fibonacci and Lucas numbers, and a theory of the Fibonacci and 'Golden' matrices. These mathematical theories are the source of many new ideas in mathematics, philosophy, botanic and biology, electrical and computer science and engineering, communication systems, mathematical education as well as theoretical physics and physics of high energy particles.

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.

Mathematical Creativity and Mathematical Aptitude: A Cross-Lagged Panel Analysis

Science.gov (United States)

Tyagi, Tarun Kumar

2016-01-01

Cross-lagged panel correlation (CLPC) analysis has been used to identify causal relationships between mathematical creativity and mathematical aptitude. For this study, 480 8th standard students were selected through a random cluster technique from 9 intermediate and high schools of Varanasi, India. Mathematical creativity and mathematical…

Generalized dynamics of soft-matter quasicrystals mathematical models and solutions

CERN Document Server

Fan, Tian-You

2017-01-01

The book systematically introduces the mathematical models and solutions of generalized hydrodynamics of soft-matter quasicrystals (SMQ). It provides methods for solving the initial-boundary value problems in these systems. The solutions obtained demonstrate the distribution, deformation and motion of the soft-matter quasicrystals, and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. Mathematical solutions for solid and soft-matter quasicrystals are compared, to help readers to better understand the featured properties of SMQ.

Attitude Determination Error Analysis System (ADEAS) mathematical specifications document

Science.gov (United States)

Nicholson, Mark; Markley, F.; Seidewitz, E.

1988-01-01

The mathematical specifications of Release 4.0 of the Attitude Determination Error Analysis System (ADEAS), which provides a general-purpose linear error analysis capability for various spacecraft attitude geometries and determination processes, are presented. The analytical basis of the system is presented. The analytical basis of the system is presented, and detailed equations are provided for both three-axis-stabilized and spin-stabilized attitude sensor models.

GENERAL MEETING OF OWNERS OF INVESTMENT SHARES: ORGANIZATIONAL ASPECTS

Directory of Open Access Journals (Sweden)

Olga A. Zhdanova

2014-01-01

Full Text Available General meeting of owners of the investment shares, possessing large powersof strategic character, needs continuous development of the substantial and organizational parties, with the subsequent entering of corresponding changes into acts.In article some organizational aspects ofcarrying out general meeting and possibility of their improvement are considered.

An Ecological Analysis of Mathematics Teachers' Noticing

Science.gov (United States)

Jazby, Dan

2016-01-01

Most studies which investigate mathematics teacher noticing cast perception into a passive role. This study develops an ecological analysis of mathematics teachers' noticing in order to investigate how teachers actively look for information in classroom environments. This method of analysis is applied to data collected as an experienced primary…

Mathematical foundations of image processing and analysis

CERN Document Server

Pinoli, Jean-Charles

2014-01-01

Mathematical Imaging is currently a rapidly growing field in applied mathematics, with an increasing need for theoretical mathematics. This book, the second of two volumes, emphasizes the role of mathematics as a rigorous basis for imaging sciences. It provides a comprehensive and convenient overview of the key mathematical concepts, notions, tools and frameworks involved in the various fields of gray-tone and binary image processing and analysis, by proposing a large, but coherent, set of symbols and notations, a complete list of subjects and a detailed bibliography. It establishes a bridg

Deepening Prospective Mathematics Teachers' Diagnostic Judgments: Interplay of Videos, Focus Questions and Didactic Categories

Science.gov (United States)

Prediger, Susanne; Zindel, Carina

2017-01-01

This article combines different conceptualizations of teachers' diagnostic competence in listening to students' mathematical thinking processes on the levels of general perspectives, noticed aspects and activated didactic categories. An empirical study of 159 prospective mathematics teachers' diagnostic judgments investigated how these levels are…

Foundations of mathematical analysis

CERN Document Server

Johnsonbaugh, Richard

2010-01-01

This classroom-tested volume offers a definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. Upper-level undergraduate students with a background in calculus will benefit from its teachings, along with beginning graduate students seeking a firm grounding in modern analysis. A self-contained text, it presents the necessary background on the limit concept, and the first seven chapters could constitute a one-semester introduction to limits. Subsequent chapters discuss

A note on stability of stationary points in mathematical programs with generalized complementarity constraints

Czech Academy of Sciences Publication Activity Database

Červinka, Michal

2016-01-01

Roč. 65, č. 5 (2016), s. 1049-1060 ISSN 0233-1934 R&D Projects: GA ČR GAP402/12/1309 Institutional support: RVO:67985556 Keywords : parameter-dependent mathematical programs with generalized equilibrium constraints * M-stationarity * C-stationarity * isolated calmness * Aubin property Subject RIV: BA - General Mathematics Impact factor: 0.943, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/cervinka-0461163.pdf

Specific Preschool Executive Functions Predict Unique Aspects of Mathematics Development: A 3-Year Longitudinal Study.

Science.gov (United States)

Simanowski, Stefanie; Krajewski, Kristin

2017-08-10

This study assessed the extent to which executive functions (EF), according to their factor structure in 5-year-olds (N = 244), influenced early quantity-number competencies, arithmetic fluency, and mathematics school achievement throughout first and second grades. A confirmatory factor analysis resulted in updating as a first, and inhibition and shifting as a combined second factor. In the structural equation model, updating significantly affected knowledge of the number word sequence, suggesting a facilitatory effect on basic encoding processes in numerical materials that can be learnt purely by rote. Shifting and inhibition significantly influenced quantity to number word linkages, indicating that these processes promote developing a profound understanding of numbers. These results show the supportive role of specific EF for specific aspects of a numerical foundation. © 2017 The Authors. Child Development © 2017 Society for Research in Child Development, Inc.

Mathematical foundations of time series analysis a concise introduction

CERN Document Server

Beran, Jan

2017-01-01

This book provides a concise introduction to the mathematical foundations of time series analysis, with an emphasis on mathematical clarity. The text is reduced to the essential logical core, mostly using the symbolic language of mathematics, thus enabling readers to very quickly grasp the essential reasoning behind time series analysis. It appeals to anybody wanting to understand time series in a precise, mathematical manner. It is suitable for graduate courses in time series analysis but is equally useful as a reference work for students and researchers alike.

Teacher's Guide to Secondary Mathematics.

Science.gov (United States)

Duval County Schools, Jacksonville, FL.

This is a teacher's guide to secondary school mathematics. Developed for use in the Duval County Public Schools, Jacksonville, Florida. Areas of mathematics covered are algebra, analysis, calculus, computer literacy, computer science, geometry, analytic geometry, general mathematics, consumer mathematics, pre-algebra, probability and statistics,…

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 aspects of superspace, volume 132

International Nuclear Information System (INIS)

Seifert, H.J.

1984-01-01

Through a continually increasing wave of activity in the physics community, super-gravity has come to be regarded as one of the most promising ways of unifying gravity with other particle interaction as a finite gauge theory to explain the particle-spectrum. Concurrently, important mathematical work on graded manifolds and superspace as proposed arenas of supergravity has been carried out. There remains a gap between the mathematical and physical approaches expressed by such unanswered questions as: Does there exist a superspace having the properties that physicists require. Does it make sense to perform a path-integral in such spaces. Does a sensible classical supergravity exist. It is hoped that this volume will stimulate the dialogue between mathematicians and physicists dealing with these questions

The Definition of Mathematics: Philosophical and Pedagogical Aspects

Science.gov (United States)

Khait, Alexander

There is a strange fact that many works written with the purpose to explain what is mathematics, somehow avoid the issue. This paper is aimed at filling this gap. After discussing various descriptions of mathematics as they appear in literature, it is suggested that mathematics is an essentially linguistic activity characterized by association of words with precise meanings. Educational implications of this idea are considered in the light of(1) a strong tendency of most humans to the fuzzy way of thought as described by the dual-process theory developed by researchers of human reasoning;

Dimensional analysis yields the general second-order differential equation underlying many natural phenomena: the mathematical properties of a phenomenon's data plot then specify a unique differential equation for it.

Science.gov (United States)

Kepner, Gordon R

2014-08-27

This study uses dimensional analysis to derive the general second-order differential equation that underlies numerous physical and natural phenomena described by common mathematical functions. It eschews assumptions about empirical constants and mechanisms. It relies only on the data plot's mathematical properties to provide the conditions and constraints needed to specify a second-order differential equation that is free of empirical constants for each phenomenon. A practical example of each function is analyzed using the general form of the underlying differential equation and the observable unique mathematical properties of each data plot, including boundary conditions. This yields a differential equation that describes the relationship among the physical variables governing the phenomenon's behavior. Complex phenomena such as the Standard Normal Distribution, the Logistic Growth Function, and Hill Ligand binding, which are characterized by data plots of distinctly different sigmoidal character, are readily analyzed by this approach. It provides an alternative, simple, unifying basis for analyzing each of these varied phenomena from a common perspective that ties them together and offers new insights into the appropriate empirical constants for describing each phenomenon.

Commognitive Analysis of Undergraduate Mathematics Students' First Encounter with the Subgroup Test

Science.gov (United States)

Ioannou, Marios

2018-01-01

This study analyses learning aspects of undergraduate mathematics students' first encounter with the subgroup test, using the commognitive theoretical framework. It focuses on students' difficulties as these are related to the object-level and metalevel mathematical learning in group theory, and, when possible, highlights any commognitive…

Integrating pedagogical content knowledge and pedagogical/psychological knowledge in mathematics

Science.gov (United States)

Harr, Nora; Eichler, Andreas; Renkl, Alexander

2014-01-01

In teacher education at universities, general pedagogical and psychological principles are often treated separately from subject matter knowledge and therefore run the risk of not being applied in the teaching subject. In an experimental study (N = 60 mathematics student teachers) we investigated the effects of providing aspects of general pedagogical/psychological knowledge (PPK) and pedagogical content knowledge (PCK) in an integrated or separated way. In both conditions (“integrated” vs. “separated”), participants individually worked on computer-based learning environments addressing the same topic: use and handling of multiple external representations, a central issue in mathematics. We experimentally varied whether PPK aspects and PCK aspects were treated integrated or apart from one another. As expected, the integrated condition led to greater application of pedagogical/psychological aspects and an increase in applying both knowledge types simultaneously compared to the separated condition. Overall, our findings indicate beneficial effects of an integrated design in teacher education. PMID:25191300

The estimation of patients' views on organizational aspects of a general dental practice by general dental practitioners: a survey study

Directory of Open Access Journals (Sweden)

Truin Gert-Jan

2011-10-01

Full Text Available Abstract Background Considering the changes in dental healthcare, such as the increasing assertiveness of patients, the introduction of new dental professionals, and regulated competition, it becomes more important that general dental practitioners (GDPs take patients' views into account. The aim of the study was to compare patients' views on organizational aspects of general dental practices with those of GDPs and with GDPs' estimation of patients' views. Methods In a survey study, patients and GDPs provided their views on organizational aspects of a general dental practice. In a second, separate survey, GDPs were invited to estimate patients' views on 22 organizational aspects of a general dental practice. Results For 4 of the 22 aspects, patients and GDPs had the same views, and GDPs estimated patients' views reasonably well: 'Dutch-speaking GDP', 'guarantee on treatment', 'treatment by the same GDP', and 'reminder of routine oral examination'. For 2 aspects ('quality assessment' and 'accessibility for disabled patients' patients and GDPs had the same standards, although the GDPs underestimated the patients' standards. Patients had higher standards than GDPs for 7 aspects and lower standards than GDPs for 8 aspects. Conclusion On most aspects GDPs and patient have different views, except for social desirable aspects. Given the increasing assertiveness of patients, it is startling the GDP's estimated only half of the patients' views correctly. The findings of the study can assist GDPs in adapting their organizational services to better meet the preferences of their patients and to improve the communication towards patients.

Math Self-Assessment, but Not Negative Feelings, Predicts Mathematics Performance of Elementary School Children

Directory of Open Access Journals (Sweden)

Vitor Geraldi Haase

2012-01-01

Full Text Available Mathematics anxiety has been associated to performance in school mathematics. The association between math anxiety and psychosocial competencies as well as their specific contribution to explain school mathematics performance are still unclear. In the present study, the impact of sociodemographic factors, psychosocial competencies, and math anxiety on mathematics and spelling performance was examined in school children with and without mathematics difficulties. The specific contributions of psychosocial competencies (i.e., general anxiety and attentional deficits with hyperactivity and math anxiety (i.e., self-assessment in mathematics to school mathematics performance were found to be statistically independent from each other. Moreover, psychosocial competencies—but not math anxiety—were related also to spelling performance. These results suggest that psychosocial competencies are more related to general mechanisms of emotional regulation and emotional response towards academic performance, while mathematics anxiety is related to the specific cognitive aspect of self-assessment in mathematics.

The physical and mathematical model of dynamic economic analysis and assessment for NPP

International Nuclear Information System (INIS)

Xu Jiming

1992-01-01

A set physical and mathematical model of dynamic economic analysis referring to international general sub-item and account of investment and constant money levelized model and combining current economic analysis method in China for nuclear power plant was established. The model can be used in economic analysis not only for nuclear power plant but also for coal-fired power plant and can satisfy demand of doing economic analysis and assessment for nuclear power plant and conventional power plant

Students’ Perceptions of Learning Mathematics With Cellular Phones and Applets

Directory of Open Access Journals (Sweden)

Wajeeh M. Daher

2009-03-01

Full Text Available This paper describes the perceptions of middle school students regarding learning mathematics with cellular phones and web applets, their perceptions regarding the differences between these two electronic devices and their preferences regarding using the devices in learning mathematics. To analyze these perceptions I used the grounded theory approach which involves: open coding, axial coding, and selective coding, where the unit of analysis was the sentence in each of the interviews. The research findings imply that the participants perceived different aspects of both of the electronic devices: the availability of the device, the collaboration aspect, the communication aspect, the size of the device, and the swiftness of working with the device. These aspects influenced the participants’ decisions when, where and how to use each of the devices for the learning of mathematics. More participants preferred the cellular phone over the applet primarily for its small size which makes easy its portability as well as for its communication facilities.

Ratio Analysis: Where Investments Meet Mathematics.

Science.gov (United States)

Barton, Susan D.; Woodbury, Denise

2002-01-01

Discusses ratio analysis by which investments may be evaluated. Requires the use of fundamental mathematics, problem solving, and a comparison of the mathematical results within the framework of industry. (Author/NB)

The Cold War in the Soviet School: A Case Study of Mathematics Education

Science.gov (United States)

Karp, Alexander

2007-01-01

This article is devoted to certain aspects of the cold war reflected in the teaching of mathematics in the Soviet Union. The author deals specifically with direct manifestations of the cold war, not with the teaching of mathematics during the cold war in general. His aim is not to present a comprehensive examination of school programs in…

An Aristotelian realist philosophy of mathematics mathematics as the science of quantity and structure

CERN Document Server

Franklin, J

2014-01-01

Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.

Enhancing Mathematics Communication using Critical Aspects and Dimensions of Variation

Science.gov (United States)

Olteanu, Constanta; Olteanu, Lucian

2013-01-01

This article deals with two prominent topics in the field of mathematics education: the communication in mathematics and its teaching and learning and the continuous professional development of mathematics teachers. In this article, a framework is proposed for analysing the effectiveness of communication in mathematics classrooms. The presentation…

SOME ASPECTS OF USING MATHEMATICS IN MEDICAL SCIENCES

Directory of Open Access Journals (Sweden)

Ivana Ilic

2008-01-01

Full Text Available The aim of the paper was to present some new possibilities of using mathematicsin medical sciences and medical practice. The so-called mathematical way of thinkingis presented, which is, basically, the starting point of usual way of thinking, and alsothe essence of scientific and technological literacy, necessary for the development oftheoretical and practical modern medicine. The aim of the paper was to show that it isreasonable to choose certain mathematical points of view, present them to thestudents of medicine, and thus, help them to use that knowledge in their futurestudies in order to be more successful in their professions. Modern mathematical andstatistical methods are important in professional and scientific work in clinical andlaboratory environment.

Aspects That Arise in the Transition from the Montessori Method to a Traditional Method: A Fourth Grade Mathematics View

Science.gov (United States)

Hurdle, Zachariah B.

2017-01-01

The purpose of the dissertation is to investigate three particular aspects that may affect the transition between a third grade Montessori system and a fourth grade non-Montessori system, specifically within the context of teaching and learning mathematics. These aspects are 1) the change in pacing and structure of the classroom, 2) the removal of…

Analysis of creative mathematic thinking ability in problem based learning model based on self-regulation learning

Science.gov (United States)

Munahefi, D. N.; Waluya, S. B.; Rochmad

2018-03-01

The purpose of this research identified the effectiveness of Problem Based Learning (PBL) models based on Self Regulation Leaning (SRL) on the ability of mathematical creative thinking and analyzed the ability of mathematical creative thinking of high school students in solving mathematical problems. The population of this study was students of grade X SMA N 3 Klaten. The research method used in this research was sequential explanatory. Quantitative stages with simple random sampling technique, where two classes were selected randomly as experimental class was taught with the PBL model based on SRL and control class was taught with expository model. The selection of samples at the qualitative stage was non-probability sampling technique in which each selected 3 students were high, medium, and low academic levels. PBL model with SRL approach effectived to students’ mathematical creative thinking ability. The ability of mathematical creative thinking of low academic level students with PBL model approach of SRL were achieving the aspect of fluency and flexibility. Students of academic level were achieving fluency and flexibility aspects well. But the originality of students at the academic level was not yet well structured. Students of high academic level could reach the aspect of originality.

Handbook of mathematical analysis in mechanics of viscous fluids

CERN Document Server

Novotný, Antonín

2018-01-01

Mathematics has always played a key role for researches in fluid mechanics. The purpose of this handbook is to give an overview of items that are key to handling problems in fluid mechanics. Since the field of fluid mechanics is huge, it is almost impossible to cover many topics. In this handbook, we focus on mathematical analysis on viscous Newtonian fluid. The first part is devoted to mathematical analysis on incompressible fluids while part 2 is devoted to compressible fluids.

Some aspects of the dynamic analysis of piping systems

International Nuclear Information System (INIS)

Galeao, A.C.N.R.

1981-04-01

Some aspects of vibration and dynamic response of piping systems are presented. The following subjects were analysed: sources of dynamic excitation; steady-state response-periodic excitation; resonance; flow induced vibrations; transient response - seismic excitations; non-linear transient response - pipe - whip. For each of these topics, the mathematical models, the governing equations and the approximate methods of solution, showing some numerical results obtained from the literature. (Author) [pt

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.

What field school teachers say about the teaching of mathematics: A study in the Northeast of Brazil

Directory of Open Access Journals (Sweden)

Carlos Monteiro

2014-04-01

Full Text Available The majority of research in mathematics education in Brazil focuses on aspects related to urban schools. Although there has been a discussion for decades about the need for a curriculum in schools located in rural areas that considers the importance of the local culture and the concept of context-based knowledge, there is still precarious teaching of mathematics in these schools. This paper discusses research data that addresses the teaching of mathematics in rural schools located in Pernambuco, Brazil. The method used is a qualitative research method based on interviews and discourse analysis. We focus on the discourse of teachers who participated in the empirical study by analyzing their views on rural education, the conceptualization of resources, and on their performance in mathematics teaching. Although most teachers positively evaluate their performance when they teach mathematics, they do not identify differences between teaching in the city and in rural areas. Generally, the teachers were unaware of the field schools' specificities. The results lead us to reflect on the possibilities of teaching mathematics to empower rural communities.

Corresponding Habits of Mind and Mathematical Ability

Science.gov (United States)

Dwirahayu, G.; Kustiawati, D.; Bidari, I.

2017-09-01

Objective of learning process regarding system of Indonesia government should be consist of knowledge, attitudes, and skills, or in general we call cognitive, affective and psychomotor. These objective are apply to mathematics education also. Attitude in mathematics known as habits of mind. The teacher should create a learning objective which including all, cognitive, affective and psychomotor. In general, math teachers in Indonesia pay attention to aspects of knowledge, and they ignore other aspects. Habits of mind is term which means the tendency to behave intellectually or intelligently when faced with problems which is immediately known solution. This article examines the math teacher’s attention to students’ habits of mind. The research done by survey method to 38 students at Islamic School 32 Jakarta academic year 2015/2016 from April to May 2016. Habits of mind are observed in this research restricted to persisting, thinking about thinking, thinking flexible and applying past knowledge to new situation. Based on survey, conclude that teacher, without realizing, they have to improve students’ habits of mind, as long as teaching and learning only persisting and thinking about thinking are already well developed, while flexible thinking and applying past knowledge to new situation has not well developed. We hope, math teacher can pay attention not only cognitive aspect but habits of mind also.

Pedagogical Applications from Real Analysis for Secondary Mathematics Teachers

Science.gov (United States)

Wasserman, Nicholas; Weber, Keith

2017-01-01

In this article, we consider the potential influences of the study of proofs in advanced mathematics on secondary mathematics teaching. Thus far, the literature has highlighted the benefits of applying the conclusions of particular proofs to secondary content and of developing a more general sense of disciplinary practices in mathematics in…

Photoelectric effect from observer's mathematics point of view

Science.gov (United States)

Khots, Boris; Khots, Dmitriy

2014-12-01

When we consider and analyze physical events with the purpose of creating corresponding models we often assume that the mathematical apparatus used in modeling is infallible. In particular, this relates to the use of infinity in various aspects and the use of Newton's definition of a limit in analysis. We believe that is where the main problem lies in contemporary study of nature. This work considers Physical aspects in a setting of arithmetic, algebra, geometry, analysis, topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided. In particular, we prove the following Theorems, which give Observer's Mathematics point of view on Einstein photoelectric effect theory and Lamb-Scully and Hanbury-Brown-Twiss experiments: Theorem 1. There are some values of light intensity where anticorrelation parameter A ∈ [0,1). Theorem 2. There are some values of light intensity where anticorrelation parameter A = 1. Theorem 3. There are some values of light intensity where anticorrelation parameter A > 1.

Observerʼs mathematics applications to quantum mechanics

Science.gov (United States)

Khots, B.; Khots, D.

2014-12-01

When we consider and analyze physical events with the purpose of creating corresponding models we often assume that the mathematical apparatus used in modeling is infallible. In particular, this relates to the use of infinity in various aspects and the use of Newton's definition of a limit in analysis. We believe that is where the main problem lies in the contemporary study of nature. This work considers physical aspects in a setting of arithmetic, algebra, geometry, analysis, and topology provided by Observer's Mathematics (see www.mathrelativity.com). In this paper, we consider Dirac equations for free electrons. Certain results and communications pertaining to solutions of these problems are provided.

Mathematical principles of signal processing Fourier and wavelet analysis

CERN Document Server

Brémaud, Pierre

2002-01-01

Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicates that in spite of its long history and well-established applications, the field is still one of active research. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals. The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing - sampling, filtering, digital signal proc...

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...

Mathematical Analysis of Evolution, Information, and Complexity

CERN Document Server

Arendt, Wolfgang

2009-01-01

Mathematical Analysis of Evolution, Information, and Complexity deals with the analysis of evolution, information and complexity. The time evolution of systems or processes is a central question in science, this text covers a broad range of problems including diffusion processes, neuronal networks, quantum theory and cosmology. Bringing together a wide collection of research in mathematics, information theory, physics and other scientific and technical areas, this new title offers elementary and thus easily accessible introductions to the various fields of research addressed in the book.

Methodological aspects of fuel performance system analysis at raw hydrocarbon processing plants

Science.gov (United States)

Kulbjakina, A. V.; Dolotovskij, I. V.

2018-01-01

The article discusses the methodological aspects of fuel performance system analysis at raw hydrocarbon (RH) processing plants. Modern RH processing facilities are the major consumers of energy resources (ER) for their own needs. To reduce ER, including fuel consumption, and to develop rational fuel system structure are complex and relevant scientific tasks that can only be done using system analysis and complex system synthesis. In accordance with the principles of system analysis, the hierarchical structure of the fuel system, the block scheme for the synthesis of the most efficient alternative of the fuel system using mathematical models and the set of performance criteria have been developed on the main stages of the study. The results from the introduction of specific engineering solutions to develop their own energy supply sources for RH processing facilities have been provided.

Human evaluation in association to the mathematical analysis of arch forms: Two-dimensional study.

Science.gov (United States)

Zabidin, Nurwahidah; Mohamed, Alizae Marny; Zaharim, Azami; Marizan Nor, Murshida; Rosli, Tanti Irawati

2018-03-01

To evaluate the relationship between human evaluation of the dental-arch form, to complete a mathematical analysis via two different methods in quantifying the arch form, and to establish agreement with the fourth-order polynomial equation. This study included 64 sets of digitised maxilla and mandible dental casts obtained from a sample of dental arch with normal occlusion. For human evaluation, a convenient sample of orthodontic practitioners ranked the photo images of dental cast from the most tapered to the less tapered (square). In the mathematical analysis, dental arches were interpolated using the fourth-order polynomial equation with millimetric acetate paper and AutoCAD software. Finally, the relations between human evaluation and mathematical objective analyses were evaluated. Human evaluations were found to be generally in agreement, but only at the extremes of tapered and square arch forms; this indicated general human error and observer bias. The two methods used to plot the arch form were comparable. The use of fourth-order polynomial equation may be facilitative in obtaining a smooth curve, which can produce a template for individual arch that represents all potential tooth positions for the dental arch. Copyright © 2018 CEO. Published by Elsevier Masson SAS. All rights reserved.

Modelling Mathematical Reasoning in Physics Education

Science.gov (United States)

Uhden, Olaf; Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche

2012-04-01

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

Mathematical Methods in Survival Analysis, Reliability and Quality of Life

CERN Document Server

Huber, Catherine; Mesbah, Mounir

2008-01-01

Reliability and survival analysis are important applications of stochastic mathematics (probability, statistics and stochastic processes) that are usually covered separately in spite of the similarity of the involved mathematical theory. This title aims to redress this situation: it includes 21 chapters divided into four parts: Survival analysis, Reliability, Quality of life, and Related topics. Many of these chapters were presented at the European Seminar on Mathematical Methods for Survival Analysis, Reliability and Quality of Life in 2006.

Lectures on the mathematics of quantum mechanics I

CERN Document Server

Dell'Antonio, Gianfausto

2015-01-01

The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving th...

Complementing Mathematics Teachers’ Horizon Content Knowledge with an Elementary-on-Advanced Aspect

Directory of Open Access Journals (Sweden)

Yi-An Cho

2018-02-01

Full Text Available Although Ball and her colleagues provided empirical evidence to support the existence of the six sub-domains in mathematical knowledge for teaching (MKT and further explained or defined the majority of these sub-domains, there were few explanations of what horizon content knowledge (HCK embedded in MKT meant and they merely provided ideas about HCK. Many researchers attempted to provide some teaching incidents and exemplification to interpret the construct of HCK. Moreover, they thought teachers’ studies of tertiary mathematics are useful for classroom teaching practice. Their discourse and instantiation of HCK was correspondent with a higher perspective on elementary mathematics mentioned by Felix Klein (1924, but was not entirely coincide with a kind of elementary perspective on advanced knowledge introduced by Ball and Bass (2009. This study lasted 1 years, and data collection included in-depth interviews, classroom observation and video analysis. We provide a shared classroom teaching incidence and illustrations to explain and to describe the construct of HCK. HCK not only is a kind of elementary perspective on advanced mathematical knowledge, but also complements to a higher perspective on elementary mathematics. Furthermore, HCK could be seen as a reciprocal pathway between the elementary and advanced mathematical knowledge.

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

The role of mathematics in physical sciences interdisciplinary and philosophical aspects

CERN Document Server

Boniolo, Giovanni; Trobok, Majda

2005-01-01

Even though mathematics and physics have been related for centuries and this relation appears to be unproblematic, there are many questions still open: Is mathematics really necessary for physics, or could physics exist without mathematics? Should we think physically and then add the mathematics apt to formalise our physical intuition, or should we think mathematically and then interpret physically the obtained results? Do we get mathematical objects by abstraction from real objects, or vice versa? Why is mathematics effective into physics? These are all relevant questions, whose answers are necessary to fully understand the status of physics, particularly of contemporary physics. The aim of this book is to offer plausible answers to such questions through both historical analyses of relevant cases, and philosophical analyses of the relations between mathematics and physics.

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.

Mathematics in narratives of Geodetic expeditions.

Science.gov (United States)

Terrall, Mary

2006-12-01

In eighteenth-century France, geodesy (the measure of the earth's shape) became an arena where mathematics and narrative intersected productively. Mathematics played a crucial role not only in the measurements and analysis necessary to geodesy but also in the narrative accounts that presented the results of elaborate and expensive expeditions to the reading public. When they returned to France to write these accounts after their travels, mathematician-observers developed a variety of ways to display numbers and mathematical arguments and techniques. The numbers, equations, and diagrams they produced could not be separated from the story of their acquisition. Reading these accounts for the interplay of these two aspects--the mathematical and the narrative--shows how travelers articulated the intellectual and physical difficulties of their work to enhance the value of their results for specialist and lay readers alike.

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…

Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

Science.gov (United States)

Wasserman, Nicholas H.

2016-01-01

This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…

Time-frequency analysis : mathematical analysis of the empirical mode decomposition.

Science.gov (United States)

2009-01-01

Invented over 10 years ago, empirical mode : decomposition (EMD) provides a nonlinear : time-frequency analysis with the ability to successfully : analyze nonstationary signals. Mathematical : Analysis of the Empirical Mode Decomposition : is a...

The Origins of Diverse Domains of Mathematics: Generalist Genes but Specialist Environments

OpenAIRE

Kovas, Y.; Petrill, S. A.; Plomin, R.

2007-01-01

The authors assessed 2,502 ten-year-old children, members of 1,251 pairs of twins, on a Web-based battery of problems from 5 diverse aspects of mathematics assessed as part of the U.K. national curriculum. This 1st genetic study into the etiology of variation in different domains of mathematics showed that the heritability estimates were moderate and highly similar across domains and that these genetic influences were mostly general. Environmental factors unique to each twin in a family (rath...

La Meme Chose: How Mathematics Can Explain the Thinking of Children and the Thinking of Children Can Illuminate Mathematical Philosophy

Science.gov (United States)

Cable, John

2014-01-01

This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which has been formally enunciated in mathematical philosophy but has universal application. It becomes necessary to identity fluid objects (both configured and unconfigured) and configured and unconfigured sets-of-objects. Issues emerge regarding the conflict between philosophic realism and anti-realism, including constructivism. Questions are asked concerning mathematics and mathematical philosophy, particularly over the nature of sets, the wisdom of the axiomatic method and aspects of the abstraction principle itself.

General aspects of metal toxicity.

Science.gov (United States)

Kozlowski, H; Kolkowska, P; Watly, J; Krzywoszynska, K; Potocki, S

2014-01-01

This review is focused on the general mechanisms of metal toxicity in humans. The possible and mainly confirmed mechanisms of their action are discussed. The metals are divided into four groups due to their toxic effects. First group comprises of metal ions acting as Fenton reaction catalyst mainly iron and copper. These types of metal ions participate in generation of the reactive oxygen species. Metals such as nickel, cadmium and chromium are considered as carcinogenic agents. Aluminum, lead and tin are involved in neurotoxicity. The representative of the last group is mercury, which may be considered as a generally toxic metal. Fenton reaction is a naturally occurring process producing most active oxygen species, hydroxyl radical: Fe(2+) + He2O2 ↔ Fe(3+) + OH(-) + OH(•) It is able to oxidize most of the biomolecules including DNA, proteins, lipids etc. The effect of toxicity depends on the damage of molecules i.e. production site of the hydroxyl radical. Chromium toxicity depends critically on its oxidation state. The most hazardous seems to be Cr(6+) (chromates) which are one of the strongest inorganic carcinogenic agents. Cr(6+) species act also as oxidative agents damaging among other nucleic acids. Redox inactive Al(3+), Cd(2+) or Hg(2+) may interfere with biology of other metal ions e.g. by occupying metal binding sites in biomolecules. All these aspects will be discussed in the review.

Kant's Schematism and the Foundations of Mathematics

DEFF Research Database (Denmark)

Jørgensen, Klaus Frovin

The theory of schematism was initiated by I. Kant, who, however, was never precise with respect to what he understood under this theory. I give---based on the theoretical works of Kant---an interpretation of the most important aspects of Kant's theory of schematism. In doing this I show how...... show that, contrary to Kant's own intentions, he was not up-to-date on mathematics. And in fact, it was because of this that it was possible for him to formulate his rather rigid theory concerning the unique characterizations of intuition and understanding. I show how phenomena in the mathematics...... of the time of Kant should have had an effect on him. He should have remained more critical towards his formulation and demarcation of intuition, understanding and reason. Finally I show how D. Hilbert in fact gives the necessary generalization of Kant's philosophy. This generalization provides us...

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

Mathematical foundations of biomechanics.

Science.gov (United States)

Niederer, Peter F

2010-01-01

The aim of biomechanics is the analysis of the structure and function of humans, animals, and plants by means of the methods of mechanics. Its foundations are in particular embedded in mathematics, physics, and informatics. Due to the inherent multidisciplinary character deriving from its aim, biomechanics has numerous connections and overlapping areas with biology, biochemistry, physiology, and pathophysiology, along with clinical medicine, so its range is enormously wide. This treatise is mainly meant to serve as an introduction and overview for readers and students who intend to acquire a basic understanding of the mathematical principles and mechanics that constitute the foundation of biomechanics; accordingly, its contents are limited to basic theoretical principles of general validity and long-range significance. Selected examples are included that are representative for the problems treated in biomechanics. Although ultimate mathematical generality is not in the foreground, an attempt is made to derive the theory from basic principles. A concise and systematic formulation is thereby intended with the aim that the reader is provided with a working knowledge. It is assumed that he or she is familiar with the principles of calculus, vector analysis, and linear algebra.

A Meta-Analysis of Mathematics and Working Memory: Moderating Effects of Working Memory Domain, Type of Mathematics Skill, and Sample Characteristics

Science.gov (United States)

Peng, Peng; Namkung, Jessica; Barnes, Marcia; Sun, Congying

2016-01-01

The purpose of this meta-analysis was to determine the relation between mathematics and working memory (WM) and to identify possible moderators of this relation including domains of WM, types of mathematics skills, and sample type. A meta-analysis of 110 studies with 829 effect sizes found a significant medium correlation of mathematics and WM, r…

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.

A General Contact Force Analysis of an Under-Actuated Finger in Robot Hand Grasping

Directory of Open Access Journals (Sweden)

Xuan Vinh Ha

2016-02-01

Full Text Available This paper develops a mathematical analysis of contact forces for the under-actuated finger in a general under-actuated robotic hand during grasping. The concept of under-actuation in robotic grasping with fewer actuators than degrees of freedom (DOF, through the use of springs and mechanical limits, allows the hand to adjust itself to an irregularly shaped object without complex control strategies and sensors. Here the main concern is the contact forces, which are important elements in grasping tasks, based on the proposed mathematical analysis of their distributions of the n-DOF under-actuated finger. The simulation results, along with the 3-DOF finger from the ADAMS model, show the effectiveness of the mathematical analysis method, while comparing them with the measured results. The system can find magnitudes of the contact forces at the contact positions between the phalanges and the object.

Spatial Skill Profile of Mathematics Pre-Service Teachers

Science.gov (United States)

Putri, R. O. E.

2018-01-01

This study is aimed to investigate the spatial intelligence of mathematics pre-service teachers and find the best instructional strategy that facilitates this aspect. Data were collected from 35 mathematics pre-service teachers. The Purdue Spatial Visualization Test (PSVT) was used to identify the spatial skill of mathematics pre-service teachers. Statistical analysis indicate that more than 50% of the participants possessed spatial skill in intermediate level, whereas the other were in high and low level of spatial skill. The result also shows that there is a positive correlation between spatial skill and mathematics ability, especially in geometrical problem solving. High spatial skill students tend to have better mathematical performance compare to those in two other levels. Furthermore, qualitative analysis reveals that most students have difficulty in manipulating geometrical objects mentally. This problem mostly appears in intermediate and low-level spatial skill students. The observation revealed that 3-D geometrical figures is the best method that can overcome the mentally manipulation problem and develop the spatial visualization. Computer application can also be used to improve students’ spatial skill.

Mathematical and numerical aspects of low mach number flows

Energy Technology Data Exchange (ETDEWEB)

Schochet, St.; Bresch, D.; Grenier, E.; Alazard, T.; Gordner, A.; Sankaran, V.; Massot, M.; Sery, R.; Pebay, P.; Lunch, O.; Mazhorova, O.; Turkel, O.E.; Faille, I.; Danchin, R.; Allain, O.; Birken, P.; Lafitte, O.; Kloczko, T.; Frick, W.; Bui, T.; Dellacherie, S.; Klein, R.; Roe, Ph.; Accary, G.; Braack, M.; Picano, F.; Cadiou, A.; Dinescu, C.; Lesage, A.C.; Wesseling, P.; Heuveline, V.; Jobelin, M.; Weisman, C.; Merkle, C.

2004-07-01

Low Mach number flows represent a significant part of the various flows encountered in geophysics, industry or every day life. Paradoxically, the mathematical analysis of the equations governing these flows is difficult and on the practical side, the research of numerical algorithms valid for all flow speeds is continuing to be a challenge. However, in the last decade, both from the theoretical and the numerical sides, significant progresses were made in the understanding and analysis of the equations governing these flows. This conference intends to provide an up-to-date inventory of recent mathematical and numerical results in the analysis of these flows by bringing together both mathematicians and numericists active in this area. In the framework of the conference, a numerical workshop is organized which proposes to compute several challenging low Mach number flows: liquid flow around non-cavitating and cavitating NACA0015 hydrofoil, natural convection with large temperature differences, free convection, free surface flow, vessel pressurization. This document brings together the descriptions of the test cases of the numerical workshop and the abstracts of the conference papers: A 3D high order finite volume method for the prediction of near-critical fluid flows (G. ACCARY, I. RASPO, P. BONTOUX, B. ZAPPOLI); low Mach number limit of the non-isentropic Navier-Stokes equations (T. ALAZARD); simulation of cavitation rolls past a forward step with a bubble model (O. ALLAIN, N. BLASKA, C. LECA); flux preconditioning methods and fire events (P. BIRKEN, A. MEISTER); an adaptive finite element solver for compressible flows: application to heat-driven cavity benchmarks in 2D and 3D (M. BRAACK); comparison of various implicit, explicit, centered and upwind schemes for the simulation of compressed flows on moving mesh (A. CADIOU, M. BUFFAT, L. Le PENVEN, C. Le RIBAULT); low Mach number limit for viscous compressible flows (R. DANCHIN); some Properties of the low Mach number

Mathematics of the 19th century mathematical logic, algebra, number theory, probability theory

CERN Document Server

Yushkevich, A

1992-01-01

This multi-authored effort, Mathematics of the nineteenth century (to be fol­ lowed by Mathematics of the twentieth century), is a sequel to the History of mathematics fram antiquity to the early nineteenth century, published in three 1 volumes from 1970 to 1972. For reasons explained below, our discussion of twentieth-century mathematics ends with the 1930s. Our general objectives are identical with those stated in the preface to the three-volume edition, i. e. , we consider the development of mathematics not simply as the process of perfecting concepts and techniques for studying real-world spatial forms and quantitative relationships but as a social process as weIl. Mathematical structures, once established, are capable of a certain degree of autonomous development. In the final analysis, however, such immanent mathematical evolution is conditioned by practical activity and is either self-directed or, as is most often the case, is determined by the needs of society. Proceeding from this premise, we intend...

The Contributions of Domain-General and Numerical Factors to Third-Grade Arithmetic Skills and Mathematical Learning Disability

Science.gov (United States)

Cowan, Richard; Powell, Daisy

2014-01-01

Explanations of the marked individual differences in elementary school mathematical achievement and mathematical learning disability (MLD or dyscalculia) have involved domain-general factors (working memory, reasoning, processing speed, and oral language) and numerical factors that include single-digit processing efficiency and multidigit skills…

Mathematical theory of sedimentation analysis

CERN Document Server

Fujita, Hiroshi; Van Rysselberghe, P

1962-01-01

Mathematical Theory of Sedimentation Analysis presents the flow equations for the ultracentrifuge. This book is organized into two parts encompassing six chapters that evaluate the systems of reacting components, the differential equations for the ultracentrifuge, and the case of negligible diffusion. The first chapters consider the Archibald method for molecular weight determination; pressure-dependent sedimentation; expressions for the refractive index and its gradient; relation between refractive index and concentration; and the analysis of Gaussian distribution. Other chapters deal with th

Mathematics Teaching Today

Science.gov (United States)

Martin, Tami S.; Speer, William R.

2009-01-01

This article describes features, consistent messages, and new components of "Mathematics Teaching Today: Improving Practice, Improving Student Learning" (NCTM 2007), an updated edition of "Professional Standards for Teaching Mathematics" (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing,…

A Spoonful of Math Helps the Medicine Go Down: An Illustration of How Healthcare can Benefit from Mathematical Modeling and Analysis

Directory of Open Access Journals (Sweden)

Ziya Serhan

2010-06-01

Full Text Available Abstract Objectives A recent joint report from the Institute of Medicine and the National Academy of Engineering, highlights the benefits of--indeed, the need for--mathematical analysis of healthcare delivery. Tools for such analysis have been developed over decades by researchers in Operations Research (OR. An OR perspective typically frames a complex problem in terms of its essential mathematical structure. This article illustrates the use and value of the tools of operations research in healthcare. It reviews one OR tool, queueing theory, and provides an illustration involving a hypothetical drug treatment facility. Method Queueing Theory (QT is the study of waiting lines. The theory is useful in that it provides solutions to problems of waiting and its relationship to key characteristics of healthcare systems. More generally, it illustrates the strengths of modeling in healthcare and service delivery. Queueing theory offers insights that initially may be hidden. For example, a queueing model allows one to incorporate randomness, which is inherent in the actual system, into the mathematical analysis. As a result of this randomness, these systems often perform much worse than one might have guessed based on deterministic conditions. Poor performance is reflected in longer lines, longer waits, and lower levels of server utilization. As an illustration, we specify a queueing model of a representative drug treatment facility. The analysis of this model provides mathematical expressions for some of the key performance measures, such as average waiting time for admission. Results We calculate average occupancy in the facility and its relationship to system characteristics. For example, when the facility has 28 beds, the average wait for admission is 4 days. We also explore the relationship between arrival rate at the facility, the capacity of the facility, and waiting times. Conclusions One key aspect of the healthcare system is its complexity, and

Mathematical aspects of reacting and diffusing systems

CERN Document Server

Fife, Paul C

1979-01-01

Modeling and analyzing the dynamics of chemical mixtures by means of differ- tial equations is one of the prime concerns of chemical engineering theorists. These equations often take the form of systems of nonlinear parabolic partial d- ferential equations, or reaction-diffusion equations, when there is diffusion of chemical substances involved. A good overview of this endeavor can be had by re- ing the two volumes by R. Aris (1975), who himself was one of the main contributors to the theory. Enthusiasm for the models developed has been shared by parts of the mathematical community, and these models have, in fact, provided motivation for some beautiful mathematical results. There are analogies between chemical reactors and certain biological systems. One such analogy is rather obvious: a single living organism is a dynamic structure built of molecules and ions, many of which react and diffuse. Other analogies are less obvious; for example, the electric potential of a membrane can diffuse like a chemical, and ...

Using Visualization to Generalize on Quadratic Patterning Tasks

Science.gov (United States)

Kirwan, J. Vince

2017-01-01

Patterning tasks engage students in a core aspect of algebraic thinking-generalization (Kaput 2008). The National Council of Teachers of Mathematics (NCTM) Algebra Standard states that students in grades 9-12 should "generalize patterns using explicitly defined and recursively defined functions" (NCTM 2000, p. 296). Although educators…

Mathematical and theoretical neuroscience cell, network and data analysis

CERN Document Server

Nieus, Thierry

2017-01-01

This volume gathers contributions from theoretical, experimental and computational researchers who are working on various topics in theoretical/computational/mathematical neuroscience. The focus is on mathematical modeling, analytical and numerical topics, and statistical analysis in neuroscience with applications. The following subjects are considered: mathematical modelling in Neuroscience, analytical  and numerical topics;  statistical analysis in Neuroscience; Neural Networks; Theoretical Neuroscience. The book is addressed to researchers involved in mathematical models applied to neuroscience.

Aspects of Mathematical Modelling Applications in Science, Medicine, Economics and Management

CERN Document Server

Hosking, Roger J

2008-01-01

The construction of mathematical models is an essential scientific activity. Mathematics has long been associated with developments in the exact sciences and engineering, but more recently mathematical modelling has been used to investigate complex systems that arise in many other fields. The contributors to this book demonstrate the application of mathematics to modern research topics in ecology and environmental science, health and medicine, phylogenetics and neural networks, theoretical chemistry, economics and management.

A course in mathematical analysis

CERN Document Server

Garling, D J H

The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in the first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. Volume 1 focuses on the analysis of real-valued functions of a real variable. Volume 2 goes on to consider metric and topological spaces. This third volume develops the classical theory of functions of a complex variable. It carefully establishes the properties of the complex plane, including a proof of the Jordan curve theorem. Lebesgue measure is introduced, and is used as a model for other measure spaces, where the theory of integration is developed. The RadonÐNikodym theorem is proved, and the differentiation of measures discussed.

Mathematical analysis of complex cellular activity

CERN Document Server

Bertram, Richard; Teka, Wondimu; Vo, Theodore; Wechselberger, Martin; Kirk, Vivien; Sneyd, James

2015-01-01

This book contains two review articles on mathematical physiology that deal with closely related topics but were written and can be read independently. The first article reviews the basic theory of calcium oscillations (common to almost all cell types), including spatio-temporal behaviors such as waves. The second article uses, and expands on, much of this basic theory to show how the interaction of cytosolic calcium oscillators with membrane ion channels can result in highly complex patterns of electrical spiking. Through these examples one can see clearly how multiple oscillatory processes interact within a cell, and how mathematical methods can be used to understand such interactions better. The two reviews provide excellent examples of how mathematics and physiology can learn from each other, and work jointly towards a better understanding of complex cellular processes. Review 1: Richard Bertram, Joel Tabak, Wondimu Teka, Theodore Vo, Martin Wechselberger: Geometric Singular Perturbation Analysis of Burst...

Contributions to sensitivity analysis and generalized discriminant analysis

International Nuclear Information System (INIS)

Jacques, J.

2005-12-01

Two topics are studied in this thesis: sensitivity analysis and generalized discriminant analysis. Global sensitivity analysis of a mathematical model studies how the output variables of this last react to variations of its inputs. The methods based on the study of the variance quantify the part of variance of the response of the model due to each input variable and each subset of input variables. The first subject of this thesis is the impact of a model uncertainty on results of a sensitivity analysis. Two particular forms of uncertainty are studied: that due to a change of the model of reference, and that due to the use of a simplified model with the place of the model of reference. A second problem was studied during this thesis, that of models with correlated inputs. Indeed, classical sensitivity indices not having significance (from an interpretation point of view) in the presence of correlation of the inputs, we propose a multidimensional approach consisting in expressing the sensitivity of the output of the model to groups of correlated variables. Applications in the field of nuclear engineering illustrate this work. Generalized discriminant analysis consists in classifying the individuals of a test sample in groups, by using information contained in a training sample, when these two samples do not come from the same population. This work extends existing methods in a Gaussian context to the case of binary data. An application in public health illustrates the utility of generalized discrimination models thus defined. (author)

Conference on "Mathematical Technology of Networks"

CERN Document Server

2015-01-01

Bringing together leading researchers in the fields of functional analysis, mathematical physics and graph theory, as well as natural scientists using networks as a tool in their own research fields, such as neuroscience and machine learning, this volume presents recent advances in functional, analytical, probabilistic, and spectral aspects in the study of graphs, quantum graphs, and complex networks. The contributors to this volume explore the interplay between theoretical and applied aspects of discrete and continuous graphs. Their work helps to close the gap between different avenues of research on graphs, including metric graphs and ramified structures. All papers were presented at the conference "Mathematical Technology of Networks," held December 4–7, 2013 at the Zentrum für interdisziplinäre Forschung (ZiF) in Bielefeld, Germany, and are supplemented with detailed figures illustrating both abstract concepts as well as their real-world applications. Dynamical models on graphs or random graphs a...

Mathematical aspects of Feynman integrals

International Nuclear Information System (INIS)

Bogner, Christian

2009-08-01

In the present dissertation we consider Feynman integrals in the framework of dimensional regularization. As all such integrals can be expressed in terms of scalar integrals, we focus on this latter kind of integrals in their Feynman parametric representation and study their mathematical properties, partially applying graph theory, algebraic geometry and number theory. The three main topics are the graph theoretic properties of the Symanzik polynomials, the termination of the sector decomposition algorithm of Binoth and Heinrich and the arithmetic nature of the Laurent coefficients of Feynman integrals. The integrand of an arbitrary dimensionally regularised, scalar Feynman integral can be expressed in terms of the two well-known Symanzik polynomials. We give a detailed review on the graph theoretic properties of these polynomials. Due to the matrix-tree-theorem the first of these polynomials can be constructed from the determinant of a minor of the generic Laplacian matrix of a graph. By use of a generalization of this theorem, the all-minors-matrix-tree theorem, we derive a new relation which furthermore relates the second Symanzik polynomial to the Laplacian matrix of a graph. Starting from the Feynman parametric parameterization, the sector decomposition algorithm of Binoth and Heinrich serves for the numerical evaluation of the Laurent coefficients of an arbitrary Feynman integral in the Euclidean momentum region. This widely used algorithm contains an iterated step, consisting of an appropriate decomposition of the domain of integration and the deformation of the resulting pieces. This procedure leads to a disentanglement of the overlapping singularities of the integral. By giving a counter-example we exhibit the problem, that this iterative step of the algorithm does not terminate for every possible case. We solve this problem by presenting an appropriate extension of the algorithm, which is guaranteed to terminate. This is achieved by mapping the iterative

Mathematical aspects of Feynman integrals

Energy Technology Data Exchange (ETDEWEB)

Bogner, Christian

2009-08-15

In the present dissertation we consider Feynman integrals in the framework of dimensional regularization. As all such integrals can be expressed in terms of scalar integrals, we focus on this latter kind of integrals in their Feynman parametric representation and study their mathematical properties, partially applying graph theory, algebraic geometry and number theory. The three main topics are the graph theoretic properties of the Symanzik polynomials, the termination of the sector decomposition algorithm of Binoth and Heinrich and the arithmetic nature of the Laurent coefficients of Feynman integrals. The integrand of an arbitrary dimensionally regularised, scalar Feynman integral can be expressed in terms of the two well-known Symanzik polynomials. We give a detailed review on the graph theoretic properties of these polynomials. Due to the matrix-tree-theorem the first of these polynomials can be constructed from the determinant of a minor of the generic Laplacian matrix of a graph. By use of a generalization of this theorem, the all-minors-matrix-tree theorem, we derive a new relation which furthermore relates the second Symanzik polynomial to the Laplacian matrix of a graph. Starting from the Feynman parametric parameterization, the sector decomposition algorithm of Binoth and Heinrich serves for the numerical evaluation of the Laurent coefficients of an arbitrary Feynman integral in the Euclidean momentum region. This widely used algorithm contains an iterated step, consisting of an appropriate decomposition of the domain of integration and the deformation of the resulting pieces. This procedure leads to a disentanglement of the overlapping singularities of the integral. By giving a counter-example we exhibit the problem, that this iterative step of the algorithm does not terminate for every possible case. We solve this problem by presenting an appropriate extension of the algorithm, which is guaranteed to terminate. This is achieved by mapping the iterative

Introduction to the discrete Fourier series considering both mathematical and engineering aspects - A linear-algebra approach

Directory of Open Access Journals (Sweden)

Ludwig Kohaupt

2015-12-01

Full Text Available The discrete Fourier series is a valuable tool developed and used by mathematicians and engineers alike. One of the most prominent applications is signal processing. Usually, it is important that the signals be transmitted fast, for example, when transmitting images over large distances such as between the moon and the earth or when generating images in computer tomography. In order to achieve this, appropriate algorithms are necessary. In this context, the fast Fourier transform (FFT plays a key role which is an algorithm for calculating the discrete Fourier transform (DFT; this, in turn, is tightly connected with the discrete Fourier series. The last one itself is the discrete analog of the common (continuous-time Fourier series and is usually learned by mathematics students from a theoretical point of view. The aim of this expository/pedagogical paper is to give an introduction to the discrete Fourier series for both mathematics and engineering students. It is intended to expand the purely mathematical view; the engineering aspect is taken into account by applying the FFT to an example from signal processing that is small enough to be used in class-room teaching and elementary enough to be understood also by mathematics students. The MATLAB program is employed to do the computations.

Lectures on the mathematics of quantum mechanics II selected topics

CERN Document Server

Dell'Antonio, Gianfausto

2016-01-01

The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving th...

To What Extent Is Mathematical Ability Predictive of Performance in a Methodology and Statistics Course? Can an Action Research Approach Be Used to Understand the Relevance of Mathematical Ability in Psychology Undergraduates?

Science.gov (United States)

Bourne, Victoria J.

2014-01-01

Research methods and statistical analysis is typically the least liked and most anxiety provoking aspect of a psychology undergraduate degree, in large part due to the mathematical component of the content. In this first cycle of a piece of action research, students' mathematical ability is examined in relation to their performance across…

Mathematics Teaching Anxiety and Self-Efficacy Beliefs toward Mathematics Teaching: A Path Analysis

Science.gov (United States)

Peker, Murat

2016-01-01

The purpose of this study was to investigate the relationship between pre-service primary school teachers' mathematics teaching anxiety and their self-efficacy beliefs toward mathematics teaching through path analysis. There were a total of 250 pre-service primary school teachers involved in this study. Of the total, 202 were female and 48 were…

The physics and mathematics of microstates in string theory: And a monstrous Farey tail

NARCIS (Netherlands)

de Lange, P.

2016-01-01

A dissertation that delves into physical and mathematical aspects of string theory. In the first part of this work, microscopic properties string theoretic black holes are investigated. The second part is concerned with the moonshine phenomenon. The theory of generalized umbral moonshine is

Freeform surface descriptions. Part I: Mathematical representations

Science.gov (United States)

Broemel, Anika; Lippmann, Uwe; Gross, Herbert

2017-10-01

Optical systems can benefit strongly from freeform surfaces; however, the choice of the right surface representation is not trivial and many aspects must be considered. In this work, we discuss the general approach classical globally defined representations, as well as the basic mathematics and properties of the most commonly used descriptions and present a new description developed by us for describing freeform surfaces.

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.

Modeling hazardous mass flows Geoflows09: Mathematical and computational aspects of modeling hazardous geophysical mass flows; Seattle, Washington, 9–11 March 2009

Science.gov (United States)

Iverson, Richard M.; LeVeque, Randall J.

2009-01-01

A recent workshop at the University of Washington focused on mathematical and computational aspects of modeling the dynamics of dense, gravity-driven mass movements such as rock avalanches and debris flows. About 30 participants came from seven countries and brought diverse backgrounds in geophysics; geology; physics; applied and computational mathematics; and civil, mechanical, and geotechnical engineering. The workshop was cosponsored by the U.S. Geological Survey Volcano Hazards Program, by the U.S. National Science Foundation through a Vertical Integration of Research and Education (VIGRE) in the Mathematical Sciences grant to the University of Washington, and by the Pacific Institute for the Mathematical Sciences. It began with a day of lectures open to the academic community at large and concluded with 2 days of focused discussions and collaborative work among the participants.

TEACHING MATHEMATICAL DISCIPLINES AT THE MEDICAL UNIVERSITY

Directory of Open Access Journals (Sweden)

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

Mathematical aspects of Rietveld refinement and crystal structure ...

Indian Academy of Sciences (India)

Administrator

The core mathematics, goodness-of-fit parameters of Rietveld refinement technique is introduced for structural ... transducers in medical and solar applications (Obmann ..... Prince 1985 in Structure and statistics in crystallography (ed.).

Mathematical Interventions for Secondary Students with Learning Disabilities and Mathematics Difficulties: A Meta-Analysis

Science.gov (United States)

Jitendra, Asha K.; Lein, Amy E.; Im, Soo-hyun; Alghamdi, Ahmed A.; Hefte, Scott B.; Mouanoutoua, John

2018-01-01

This meta-analysis is the first to provide a quantitative synthesis of empirical evaluations of mathematical intervention programs implemented in secondary schools for students with learning disabilities and mathematics difficulties. Included studies used a treatment-control group design. A total of 19 experimental and quasi-experimental studies…

THE LARGE ASPECT RATIO LIMIT OF NEOCLASSICAL TRANSPORT THEORY

Energy Technology Data Exchange (ETDEWEB)

WONG,SK; CHAN,VS

2002-11-01

OAK B202 THE LARGE ASPECT RATIO LIMIT OF NEOCLASSICAL TRANSPORT THEORY. This article presents a comprehensive description of neoclassical transport theory in the banana regime for large aspect ratio flux surfaces of arbitrary shapes. The method of matched asymptotic expansions is used to obtain analytical solutions for plasma distribution functions and to compute transport coefficients. The method provides justification for retaining only the part of the Fokker-Planck operator that involves the second derivative with respect to the cosine of the pitch angle for the trapped and barely circulating particles. It leads to a simple equation for the freely circulating particles with boundary conditions that embody a discontinuity separating particles moving in opposite directions. Corrections to the transport coefficients are obtained by generalizing an existing boundary layer analysis. The system of moment and field equations is consistently taken in the cylinder limit, which facilitates discussion of the treatment of dynamical constraints. it is shown that the nonlocal nature of Ohm's law in neoclassical theory renders the mathematical problem of plasma transport with changing flux surfaces nonstandard.

THE LARGE ASPECT RATIO LIMIT OF NEOCLASSICAL TRANSPORT THEORY

International Nuclear Information System (INIS)

WONG, S.K.; CHAN, V.S.

2002-01-01

OAK B202 THE LARGE ASPECT RATIO LIMIT OF NEOCLASSICAL TRANSPORT THEORY. This article presents a comprehensive description of neoclassical transport theory in the banana regime for large aspect ratio flux surfaces of arbitrary shapes. The method of matched asymptotic expansions is used to obtain analytical solutions for plasma distribution functions and to compute transport coefficients. The method provides justification for retaining only the part of the Fokker-Planck operator that involves the second derivative with respect to the cosine of the pitch angle for the trapped and barely circulating particles. It leads to a simple equation for the freely circulating particles with boundary conditions that embody a discontinuity separating particles moving in opposite directions. Corrections to the transport coefficients are obtained by generalizing an existing boundary layer analysis. The system of moment and field equations is consistently taken in the cylinder limit, which facilitates discussion of the treatment of dynamical constraints. it is shown that the nonlocal nature of Ohm's law in neoclassical theory renders the mathematical problem of plasma transport with changing flux surfaces nonstandard

Mathematical aspects of subsonic and transonic gas dynamics

CERN Document Server

Bers, Lipman

2016-01-01

Concise treatment by prominent mathematician covers differential equations of potential gas flow, mathematical background of subsonic flow theory, behavior of flow at infinity, flows in channels and with free boundary, more. 1958 edition.

A REVIEW AND CONTENT ANALYSIS OF MATHEMATICS TEXTBOOKS IN EDUCATIONAL RESEARCH

Directory of Open Access Journals (Sweden)

Cheng Chieh Chang

2017-06-01

Full Text Available Research collected and reviewed a number of empirical studies in the field of educational research regarding the analysis of mathematics textbooks to provide summary and overview the information there in. The questions were identified via Google Scholar and collected from different data sources. A total of 44 papers published from 1953 to 2015 were selected based specific criteria, with 24 articles include in the SSCI database. Descriptive statistics were used to evaluate and interpret the results. A perspective on the learning analysis methods was used to collect studies and showed the mathematics textbooks analyzed were investigated under four themes: The analysis of standards, distributive property, language in mathematics, and others. School’s level which is investigated textbooks: Kindergarten, elementary, junior school, and senior school. Subjects covered in the mathematics textbooks included algebra and arithmetic, geometry, measurement, data analysis and probability, number and operations, among others. Research found the most frequently discussed in perspective on learning was the analysis of the standards and the distributive property (15 studies, the most common subject was number and operations (16 studies, and the highest number in school’s level was elementary school (18 studies. Nevertheless, fewer studies have been found to analyzing mathematics textbooks. Future research can pay attention for the relevant theoretical issues and collaborate studies in more perspective learning analysis.

Teaching general problem-solving skills is not a substitute for, or a viable addition to, teaching mathematics

NARCIS (Netherlands)

Sweller, John; Clark, Richard; Kirschner, Paul A.

2010-01-01

Sweller, J., Clark, R., & Kirschner, P. A. (2010). Teaching general problem-solving skills is not a substitute for, or a viable addition to, teaching mathematics. Notices of the American Mathematical Society, 57, 1303-1304.

Diffusion, quantum theory, and radically elementary mathematics (MN-47)

CERN Document Server

Faris, William G

2014-01-01

Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein''s work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book''s inspiration is Princeton University mathematics professor Edward Nelson''s influential work in

International Conference on Recent Advances in Mathematical Biology, Analysis and Applications

CERN Document Server

Saleem, M; Srivastava, H; Khan, Mumtaz; Merajuddin, M

2016-01-01

The book contains recent developments and contemporary research in mathematical analysis and in its application to problems arising from the biological and physical sciences. The book is of interest to readers who wish to learn of new research in such topics as linear and nonlinear analysis, mathematical biology and ecology, dynamical systems, graph theory, variational analysis and inequalities, functional analysis, differential and difference equations, partial differential equations, approximation theory, and chaos. All papers were prepared by participants at the International Conference on Recent Advances in Mathematical Biology, Analysis and Applications (ICMBAA-2015) held during 4–6 June 2015 in Aligarh, India. A focal theme of the conference was the application of mathematics to the biological sciences and on current research in areas of theoretical mathematical analysis that can be used as sophisticated tools for the study of scientific problems. The conference provided researchers, academicians and ...

How do open-ended problems promote mathematical creativity? A reflection of bare mathematics problem and contextual problem

Science.gov (United States)

Wijaya, A.

2018-03-01

Creativity is often seen as one of the fundamental aspects of character education. As one of the 21st century skills, creativity has also been considered as an important goal of education across the world. This paper reports a study on promoting mathematical creativity through the use of open-ended mathematics problems. A total of 53 undergraduate students participated in the study. These students worked on open-ended problems in two types, i.e. bare mathematics problem and contextual problem. The contextual problem was presented in the form of paper-based and Geogebra-based. The students’ works were analysed qualitatively in order to describe how students’ mathematical creativity developed. It was found that the open-ended problems successfully promote students’ creativity as indicated by various solutions or strategies that were used by students to solve the problems. The analysis of students’ works show that students’ creativity developed through three kinds of exploration, i. e. (1) exploration of contexts, (2) exploration of software features, and (3) exploration of mathematics concepts. The use of metacognitive questioning was found to be helpful to develop the first two explorations into mathematical exploration.

Multilingualism in indigenous mathematics education: an epistemic matter

Science.gov (United States)

Parra, Aldo; Trinick, Tony

2017-12-01

An investigation into an aspect of indigenous education provides the opportunity to forefront an epistemological discussion about mathematical knowledge. This paper analyses indigenous peoples' educational experiences in Colombia and Aotearoa/New Zealand of mathematics education, focusing on, among other things, sociolinguistic issues such as language planning. In these experiences, researchers, teachers and local communities, working together, elaborated their respective languages to create a corpus of lexicon that has enabled the teaching of Western mathematics. An analysis using decolonial theory is made, showing how this corpus development works to enable the teaching of [Western] mathematics resulted in investigations into culture, language and mathematics that revealed an interplay among knowledge and power. Such analysis raises issues about the epistemology of mathematics and the politics of knowledge, analogous with current discussions on multilingualism in mathematics education and in ethnomathematics. The paper concludes that mathematics educators can explore and take advantage of the sociolinguistic and epistemological issues that arise when an indigenous language is elaborated in a short period of time in comparison to other languages which have been developed incrementally over hundreds of years and thus much more difficult to critique.

A case study of pedagogy of mathematics support tutors without a background in mathematics education

Science.gov (United States)

Walsh, Richard

2017-01-01

This study investigates the pedagogical skills and knowledge of three tertiary-level mathematics support tutors in a large group classroom setting. This is achieved through the use of video analysis and a theoretical framework comprising Rowland's Knowledge Quartet and general pedagogical knowledge. The study reports on the findings in relation to these tutors' provision of mathematics support to first and second year undergraduate engineering students and second year undergraduate science students. It was found that tutors are lacking in various pedagogical skills which are needed for high-quality learning amongst service mathematics students (e.g. engineering/science/technology students), a demographic which have low levels of mathematics upon entering university. Tutors teach their support classes in a very fast didactic way with minimal opportunities for students to ask questions or to attempt problems. It was also found that this teaching method is even more so exaggerated in mandatory departmental mathematics tutorials that students take as part of their mathematics studies at tertiary level. The implications of the findings on mathematics tutor training at tertiary level are also discussed.

Mathematical visualization process of junior high school students in solving a contextual problem based on cognitive style

Science.gov (United States)

Utomo, Edy Setiyo; Juniati, Dwi; Siswono, Tatag Yuli Eko

2017-08-01

The aim of this research was to describe the mathematical visualization process of Junior High School students in solving contextual problems based on cognitive style. Mathematical visualization process in this research was seen from aspects of image generation, image inspection, image scanning, and image transformation. The research subject was the students in the eighth grade based on GEFT test (Group Embedded Figures Test) adopted from Within to determining the category of cognitive style owned by the students namely field independent or field dependent and communicative. The data collection was through visualization test in contextual problem and interview. The validity was seen through time triangulation. The data analysis referred to the aspect of mathematical visualization through steps of categorization, reduction, discussion, and conclusion. The results showed that field-independent and field-dependent subjects were difference in responding to contextual problems. The field-independent subject presented in the form of 2D and 3D, while the field-dependent subject presented in the form of 3D. Both of the subjects had different perception to see the swimming pool. The field-independent subject saw from the top, while the field-dependent subject from the side. The field-independent subject chose to use partition-object strategy, while the field-dependent subject chose to use general-object strategy. Both the subjects did transformation in an object rotation to get the solution. This research is reference to mathematical curriculum developers of Junior High School in Indonesia. Besides, teacher could develop the students' mathematical visualization by using technology media or software, such as geogebra, portable cabri in learning.

Mathematical tapas

CERN Document Server

Hiriart-Urruty, Jean-Baptiste

This book contains a collection of exercises (called “tapas”) at undergraduate level, mainly from the fields of real analysis, calculus, matrices, convexity, and optimization. Most of the problems presented here are non-standard and some require broad knowledge of different mathematical subjects in order to be solved. The author provides some hints and (partial) answers and also puts these carefully chosen exercises into context, presents information on their origins, and comments on possible extensions. With stars marking the levels of difficulty, these tapas show or prove something interesting, challenge the reader to solve and learn, and may have surprising results. This first volume of Mathematical Tapas will appeal to mathematicians, motivated undergraduate students from science-based areas, and those generally interested in mathematics.

The image of mathematics held by Irish post-primary students

Science.gov (United States)

Lane, Ciara; Stynes, Martin; O'Donoghue, John

2014-08-01

The image of mathematics held by Irish post-primary students was examined and a model for the image found was constructed. Initially, a definition for 'image of mathematics' was adopted with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. Research focused on students studying ordinary level mathematics for the Irish Leaving Certificate examination - the final examination for students in second-level or post-primary education. Students were aged between 15 and 18 years. A questionnaire was constructed with both quantitative and qualitative aspects. The questionnaire survey was completed by 356 post-primary students. Responses were analysed quantitatively using Statistical Package for the Social Sciences (SPSS) and qualitatively using the constant comparative method of analysis and by reviewing individual responses. Findings provide an insight into Irish post-primary students' images of mathematics and offer a means for constructing a theoretical model of image of mathematics which could be beneficial for future research.

Tools of the trade introduction to advanced mathematics

CERN Document Server

Sally, Jr, Paul J

2008-01-01

This book provides a transition from the formula-full aspects of the beginning study of college level mathematics to the rich and creative world of more advanced topics. It is designed to assist the student in mastering the techniques of analysis and proof that are required to do mathematics. Along with the standard material such as linear algebra, construction of the real numbers via Cauchy sequences, metric spaces and complete metric spaces, there are three projects at the end of each chapter that form an integral part of the text. These projects include a detailed discussion of topics such

Mathematical Methods of Game and Economic Theory

CERN Document Server

Aubin, J-P

1982-01-01

This book presents a unified treatment of optimization theory, game theory and a general equilibrium theory in economics in the framework of nonlinear functional analysis. It not only provides powerful and versatile tools for solving specific problems in economics and the social sciences but also serves as a unifying theme in the mathematical theory of these subjects as well as in pure mathematics itself.

Electromagnetic ion-cyclotron instability in the presence of a parallel electric field with general loss-cone distribution function - particle aspect analysis

Directory of Open Access Journals (Sweden)

G. Ahirwar

2006-08-01

Full Text Available The effect of parallel electric field on the growth rate, parallel and perpendicular resonant energy and marginal stability of the electromagnetic ion-cyclotron (EMIC wave with general loss-cone distribution function in a low β homogeneous plasma is investigated by particle aspect approach. The effect of the steepness of the loss-cone distribution is investigated on the electromagnetic ion-cyclotron wave. The whole plasma is considered to consist of resonant and non-resonant particles. It is assumed that resonant particles participate in the energy exchange with the wave, whereas non-resonant particles support the oscillatory motion of the wave. The wave is assumed to propagate parallel to the static magnetic field. The effect of the parallel electric field with the general distribution function is to control the growth rate of the EMIC waves, whereas the effect of steep loss-cone distribution is to enhance the growth rate and perpendicular heating of the ions. This study is relevant to the analysis of ion conics in the presence of an EMIC wave in the auroral acceleration region of the Earth's magnetoplasma.

Analyzing Mathematics Beliefs of Pre-Service Teachers Using Confirmatory Factor Analysis

Directory of Open Access Journals (Sweden)

Mazlini Adnan

2011-12-01

Full Text Available Mathematics beliefs play an important role in enhancing the quality and the effectiveness of teaching and learning. This study analyzes the mathematics beliefs of 317 pre-service teachers from six Higher Education Institutions (HEIs (Government Public Universities who were randomly selected to participate in this study. Questionnaires consisting of twenty three items were given to the respondents during the data collection process. The validation of the items was done by using confirmatory factor analysis (CFA. In order to obtain a model fit for the measurement model of mathematics beliefs, several fit index tests such as CMINDF, GFI, AGFI, IFI, NFI, CFI, TLI and RMSEA were used. Constructivist beliefs and traditional beliefs were identified as the contributing factors in the model. The analysis also revealed that mathematics beliefs consist of structures of two hidden variables. The correlation between the two variables (constructivist beliefs and traditional beliefs is at a moderate level. Hence, pre-service teachers should be able to recognize their type of mathematics beliefs in order to become effective mathematics teachers.

SYSTEM OF COMPUTER MODELING OBJECTS AND PROCESSES AND FEATURES OF ITS USE IN THE EDUCATIONAL PROCESS OF GENERAL SECONDARY EDUCATION

Directory of Open Access Journals (Sweden)

Svitlana G. Lytvynova

2018-04-01

Full Text Available The article analyzes the historical aspect of the formation of computer modeling as one of the perspective directions of educational process development. The notion of “system of computer modeling”, conceptual model of system of computer modeling (SCMod, its components (mathematical, animation, graphic, strategic, functions, principles and purposes of use are grounded. The features of the organization of students work using SCMod, individual and group work, the formation of subject competencies are described; the aspect of students’ motivation to learning is considered. It is established that educational institutions can use SCMod at different levels and stages of training and in different contexts, which consist of interrelated physical, social, cultural and technological aspects. It is determined that the use of SCMod in general secondary school would increase the capacity of teachers to improve the training of students in natural and mathematical subjects and contribute to the individualization of the learning process, in order to meet the pace, educational interests and capabilities of each particular student. It is substantiated that the use of SCMod in the study of natural-mathematical subjects contributes to the formation of subject competencies, develops the skills of analysis and decision-making, increases the level of digital communication, develops vigilance, raises the level of knowledge, increases the duration of attention of students. Further research requires the justification of the process of forming students’ competencies in natural-mathematical subjects and designing cognitive tasks using SCMod.

The 1989 progress report: Applied Mathematics

International Nuclear Information System (INIS)

Nedelec, J.C.

1989-01-01

The 1989 progress report of the laboratory of Applied Mathematics of the Polytechnic School (France) is presented. The investigations reported were performed in the following fields: mathematical and numerical aspects of wave propagation, nonlinear hyperbolic fluid mechanics, numerical simulations and mathematical aspects of semiconductors and electron beams, mechanics of solids, plasticity, viscoelasticity, stochastic, automatic and statistic calculations, synthesis and image processing. The published papers, the conferences and the Laboratory staff are listed [fr

On the mathematical theory of classical fields and general relativity

CERN Document Server

Klainerman, S

1993-01-01

From the perspective of an analyst, like myself, the General Theory of Relativity provides an extrordinary rich and vastly virgin territory. It is the aim of my lecture to provide, first, an account of those aspects of the theory which attract me most and second a perspective of what has been accomplished so far in that respect. In trying to state our main objectives it helps to view General Relativity in the broader context of Classical Field Theory. EinsteiniVacuum equations, or shortly E—V, is already sufficiently complicated. I will thus restrict my attention to them.

An Invitation to Mathematics

CERN Document Server

Schleicher, Dierk

2011-01-01

This "Invitation to Mathematics" consists of 14 contributions, many from the world's leading mathematicians, which introduce the readers to exciting aspects of current mathematical research. The contributions are as varied as the personalities of active mathematicians, but together they show mathematics as a rich and lively field of research. The contributions are written for interested students at the age of transition between high school and university who know high school mathematics and perhaps competition mathematics and who want to find out what current research mathematics is

Mathematical models of electrical network systems theory and applications : an introduction

CERN Document Server

Kłos, Andrzej

2017-01-01

This book is for all those who are looking for a non-conventional mathematical model of electrical network systems. It presents a modern approach using linear algebra and derives various commonly unknown quantities and interrelations of network analysis. It also explores some applications of algebraic network model of and solves some examples of previously unsolved network problems in planning and operation of network systems. Complex mathematical aspects are illustrated and described in a way that is understandable for non-mathematicians. Discussing interesting concepts and practically useful methods of network analysis, it is a valuable resource for lecturers, students, engineers and research workers. .

Mathematical analysis of the boundary-integral based electrostatics estimation approximation for molecular solvation: exact results for spherical inclusions.

Science.gov (United States)

Bardhan, Jaydeep P; Knepley, Matthew G

2011-09-28

We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBε theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements. © 2011 American Institute of Physics

Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance

OpenAIRE

Motsepa, Tanki; Khalique, Chaudry Masood; Molati, Motlatsi

2014-01-01

We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant so...

Domain General Mediators of the Relation between Kindergarten Number Sense and First-Grade Mathematics Achievement

Science.gov (United States)

Hassinger-Das, Brenna; Jordan, Nancy C.; Glutting, Joseph; Irwin, Casey; Dyson, Nancy

2013-01-01

Domain general skills that mediate the relation between kindergarten number sense and first-grade mathematics skills were investigated. Participants were 107 children who displayed low number sense in the fall of kindergarten. Controlling for background variables, multiple regression analyses showed that attention problems and executive functioning both were unique predictors of mathematics outcomes. Attention problems were more important for predicting first-grade calculation performance while executive functioning was more important for predicting first-grade performance on applied problems. Moreover, both executive functioning and attention problems were unique partial mediators of the relationship between kindergarten and first-grade mathematics skills. The results provide empirical support for developing interventions that target executive functioning and attention problems in addition to instruction in number skills for kindergartners with initial low number sense. PMID:24237789

Mathematical supply-chain modelling: Product analysis of cost and time

International Nuclear Information System (INIS)

Easters, D J

2014-01-01

Establishing a mathematical supply-chain model is a proposition that has received attention due to its inherent benefits of evolving global supply-chain efficiencies. This paper discusses the prevailing relationships found within apparel supply-chain environments, and contemplates the complex issues indicated for constituting a mathematical model. Principal results identified within the data suggest, that the multifarious nature of global supply-chain activities require a degree of simplification in order to fully dilate the necessary factors which affect, each sub-section of the chain. Subsequently, the research findings allowed the division of supply-chain components into sub-sections, which amassed a coherent method of product development activity. Concurrently, the supply-chain model was found to allow systematic mathematical formulae analysis, of cost and time, within the multiple contexts of each subsection encountered. The paper indicates the supply-chain model structure, the mathematics, and considers how product analysis of cost and time can improve the comprehension of product lifecycle management

Mathematical supply-chain modelling: Product analysis of cost and time

Science.gov (United States)

Easters, D. J.

2014-03-01

Establishing a mathematical supply-chain model is a proposition that has received attention due to its inherent benefits of evolving global supply-chain efficiencies. This paper discusses the prevailing relationships found within apparel supply-chain environments, and contemplates the complex issues indicated for constituting a mathematical model. Principal results identified within the data suggest, that the multifarious nature of global supply-chain activities require a degree of simplification in order to fully dilate the necessary factors which affect, each sub-section of the chain. Subsequently, the research findings allowed the division of supply-chain components into sub-sections, which amassed a coherent method of product development activity. Concurrently, the supply-chain model was found to allow systematic mathematical formulae analysis, of cost and time, within the multiple contexts of each subsection encountered. The paper indicates the supply-chain model structure, the mathematics, and considers how product analysis of cost and time can improve the comprehension of product lifecycle management.

General aspects of radiological protection to consider for the licensing a hospital cyclotron

International Nuclear Information System (INIS)

Andrada Contardi, F.A.; Fruttero, N.H.; Bozzo, R.H.; Moschella, E.G.

2010-01-01

The use of PET/PET-CT studies for a variety of diagnoses has increased significantly on a global scale. Modern medical cyclotrons must be placed in or near hospitals on account of the short radioactive half-life of the pharmaceuticals used in such studies. Many countries in Latin America are now licensing cyclotrons and laboratories for the production of radio-pharmaceuticals for the first time, and most are expected to have installations within the near future. This report outlines the general aspects of radiological protection important to consideration during the licensing of these facilities, and includes the following: general operation of the cyclotron and laboratory for the production of radiopharmaceuticals, safety systems (shielding, interlocks, ventilation, manual safety systems, alarms and monitors), and general aspects for licensing an installation (monitoring, accidental and incidental events, activation of components, etc.) and personnel. (authors) [es

Bio mathematical aspects of chronic cardiac electric stimulation

International Nuclear Information System (INIS)

Suarez Antola, R

1984-01-01

In the framework a mathematical model of the electrode-tissue system new several concepts are introduced(global versus local threshold variables,critical region for electric stimulation,mechanical hysteresis amongst others) several well known facts are explained,and some guidelines for electrode design are derived

Survey of meshless and generalized finite element methods: A unified approach

Science.gov (United States)

Babuška, Ivo; Banerjee, Uday; Osborn, John E.

In the past few years meshless methods for numerically solving partial differential equations have come into the focus of interest, especially in the engineering community. This class of methods was essentially stimulated by difficulties related to mesh generation. Mesh generation is delicate in many situations, for instance, when the domain has complicated geometry; when the mesh changes with time, as in crack propagation, and remeshing is required at each time step; when a Lagrangian formulation is employed, especially with nonlinear PDEs. In addition, the need for flexibility in the selection of approximating functions (e.g., the flexibility to use non-polynomial approximating functions), has played a significant role in the development of meshless methods. There are many recent papers, and two books, on meshless methods; most of them are of an engineering character, without any mathematical analysis.In this paper we address meshless methods and the closely related generalized finite element methods for solving linear elliptic equations, using variational principles. We give a unified mathematical theory with proofs, briefly address implementational aspects, present illustrative numerical examples, and provide a list of references to the current literature.The aim of the paper is to provide a survey of a part of this new field, with emphasis on mathematics. We present proofs of essential theorems because we feel these proofs are essential for the understanding of the mathematical aspects of meshless methods, which has approximation theory as a major ingredient. As always, any new field is stimulated by and related to older ideas. This will be visible in our paper.

Analytic, Algebraic and Geometric Aspects of Differential Equations

CERN Document Server

Haraoka, Yoshishige; Michalik, Sławomir

2017-01-01

This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of i...

Mathematical model of combined parametrical analysis of indicator process and thermal loading on the Diesel engine piston

Directory of Open Access Journals (Sweden)

G. Lebedeva

2004-06-01

Full Text Available In the publication the methodical aspects of a mathematical model of the combined parametrical analysis of an indicator process and thermal loading on the diesel engine piston have been considered. A thermodynamic model of a diesel engine cycle is developed. The executed development is intended for use during researches and on the initial stages of design work. Its realization for high revolution diesel engines of perspective type CHN15/15 allowed to choose rational variants for the organization of an indicator process and to prove power ranges of application for not cooled and created cooled oil welded pistons.

Mathematical modelling in solid mechanics

CERN Document Server

Sofonea, Mircea; Steigmann, David

2017-01-01

This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling a...

Mathematical structures of natural intelligence

CERN Document Server

Neuman, Yair

2017-01-01

This book uncovers mathematical structures underlying natural intelligence and applies category theory as a modeling language for understanding human cognition, giving readers new insights into the nature of human thought. In this context, the book explores various topics and questions, such as the human representation of the number system, why our counting ability is different from that which is evident among non-human organisms, and why the idea of zero is so difficult to grasp. The book is organized into three parts: the first introduces the general reason for studying general structures underlying the human mind; the second part introduces category theory as a modeling language and use it for exposing the deep and fascinating structures underlying human cognition; and the third applies the general principles and ideas of the first two parts to reaching a better understanding of challenging aspects of the human mind such as our understanding of the number system, the metaphorical nature of our thinking and...

Examining the Interactions between Mathematical Content and Pedagogical Form: Notes on the Structure of the Lesson

Science.gov (United States)

Karp, Alexander

2004-01-01

Research conducted during the Trends in International Mathematics and Science Study (TIMSS) and later (Stigler et al. 1999; Stigler and Hiebert 1999) undertook a thorough analysis of lessons in the United States, Japan, and Germany. This article focuses on certain aspects of mathematics lessons in Russia. Specifically, the attempt is made to…

Mathematical modelling and analysis for a three-tiered microbial food web in a chemostat

Directory of Open Access Journals (Sweden)

Miled El hajji

2017-10-01

Full Text Available In this article, we present a mathematical six-dimensional dynamical system involving a three-tiered microbial food web without maintenance. We give a qualitative analysis of the model, and an analysis of the local stability of equilibrium points. Under general assumptions of monotonicity, we prove the uniqueness and the local stability of the positive equilibrium point corresponding to the persistence of the three bacteria. Possibilities of periodic orbits are not excluded and asymptotic coexistence is satisfied.

Some statistical design and analysis aspects for NAEG studies

International Nuclear Information System (INIS)

Gilbert, R.O.; Eberhardt, L.L.

1975-01-01

Some of the design and analysis aspects of the NAEG studies at safety-shot sites are reviewed in conjunction with discussions of possible new approaches. The use of double sampling to estimate inventories is suggested as a means of obtaining data for estimating the geographical distribution of plutonium using computer contouring programs. The lack of estimates of error for plutonium contours is noted and a regression approach discussed for obtaining such estimates. The kinds of new data that are now available for analysis from A site of Area 11 and the four Tonopah Test Range (TTR) sites are outlined, and the need for a closer look at methods for analyzing ratio-type data is pointed out. The necessity for thorough planning of environmental sampling programs is emphasized in order to obtain the maximum amount of information for fixed cost. Some general planning aspects of new studies at nuclear sites and experimental clean-up plots are discussed, as is the planning of interlaboratory comparisons. (U.S.)

The Origins of Diverse Domains of Mathematics: Generalist Genes but Specialist Environments.

Science.gov (United States)

Kovas, Y; Petrill, S A; Plomin, R

2007-02-01

The authors assessed 2,502 ten-year-old children, members of 1,251 pairs of twins, on a Web-based battery of problems from 5 diverse aspects of mathematics assessed as part of the U.K. national curriculum. This 1st genetic study into the etiology of variation in different domains of mathematics showed that the heritability estimates were moderate and highly similar across domains and that these genetic influences were mostly general. Environmental factors unique to each twin in a family (rather than shared by the 2 twins) explained most of the remaining variance, and these factors were mostly specific to each domain.

The Origins of Diverse Domains of Mathematics: Generalist Genes but Specialist Environments

Science.gov (United States)

Kovas, Y.; Petrill, S. A.; Plomin, R.

2009-01-01

The authors assessed 2,502 ten-year-old children, members of 1,251 pairs of twins, on a Web-based battery of problems from 5 diverse aspects of mathematics assessed as part of the U.K. national curriculum. This 1st genetic study into the etiology of variation in different domains of mathematics showed that the heritability estimates were moderate and highly similar across domains and that these genetic influences were mostly general. Environmental factors unique to each twin in a family (rather than shared by the 2 twins) explained most of the remaining variance, and these factors were mostly specific to each domain. PMID:19756208

On the stability analysis of a general discrete-time population model involving predation and Allee effects

International Nuclear Information System (INIS)

Merdan, H.; Duman, O.

2009-01-01

This paper presents the stability analysis of equilibrium points of a general discrete-time population dynamics involving predation with and without Allee effects which occur at low population density. The mathematical analysis and numerical simulations show that the Allee effect has a stabilizing role on the local stability of the positive equilibrium points of this model.

Mathematical modelling

DEFF Research Database (Denmark)

Blomhøj, Morten

2004-01-01

Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...

Mathematical models of ABE fermentation: review and analysis.

Science.gov (United States)

Mayank, Rahul; Ranjan, Amrita; Moholkar, Vijayanand S

2013-12-01

Among different liquid biofuels that have emerged in the recent past, biobutanol produced via fermentation processes is of special interest due to very similar properties to that of gasoline. For an effective design, scale-up, and optimization of the acetone-butanol-ethanol (ABE) fermentation process, it is necessary to have insight into the micro- and macro-mechanisms of the process. The mathematical models for ABE fermentation are efficient tools for this purpose, which have evolved from simple stoichiometric fermentation equations in the 1980s to the recent sophisticated and elaborate kinetic models based on metabolic pathways. In this article, we have reviewed the literature published in the area of mathematical modeling of the ABE fermentation. We have tried to present an analysis of these models in terms of their potency in describing the overall physiology of the process, design features, mode of operation along with comparison and validation with experimental results. In addition, we have also highlighted important facets of these models such as metabolic pathways, basic kinetics of different metabolites, biomass growth, inhibition modeling and other additional features such as cell retention and immobilized cultures. Our review also covers the mathematical modeling of the downstream processing of ABE fermentation, i.e. recovery and purification of solvents through flash distillation, liquid-liquid extraction, and pervaporation. We believe that this review will be a useful source of information and analysis on mathematical models for ABE fermentation for both the appropriate scientific and engineering communities.

Real mathematical analysis

CERN Document Server

Pugh, Charles C

2015-01-01

Based on an honors course taught by the author at UC Berkeley, this introduction to undergraduate real analysis gives a different emphasis by stressing the importance of pictures and hard problems. Topics include: a natural construction of the real numbers, four-dimensional visualization, basic point-set topology, function spaces, multivariable calculus via differential forms (leading to a simple proof of the Brouwer Fixed Point Theorem), and a pictorial treatment of Lebesgue theory. Over 150 detailed illustrations elucidate abstract concepts and salient points in proofs. The exposition is informal and relaxed, with many helpful asides, examples, some jokes, and occasional comments from mathematicians, such as Littlewood, Dieudonné, and Osserman. This book thus succeeds in being more comprehensive, more comprehensible, and more enjoyable, than standard introductions to analysis. New to the second edition of Real Mathematical Analysis is a presentation of Lebesgue integration done almost entirely using the un...

European Conference on Numerical Mathematics and Advanced Applications

CERN Document Server

Manguoğlu, Murat; Tezer-Sezgin, Münevver; Göktepe, Serdar; Uğur, Ömür

2016-01-01

The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), held every 2 years, provides a forum for discussing recent advances in and aspects of numerical mathematics and scientific and industrial applications. The previous ENUMATH meetings took place in Paris (1995), Heidelberg (1997), Jyvaskyla (1999), Ischia (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011) and Lausanne (2013). This book presents a selection of invited and contributed lectures from the ENUMATH 2015 conference, which was organised by the Institute of Applied Mathematics (IAM), Middle East Technical University, Ankara, Turkey, from September 14 to 18, 2015. It offers an overview of central recent developments in numerical analysis, computational mathematics, and applications in the form of contributions by leading experts in the field.

Domain-general mediators of the relation between kindergarten number sense and first-grade mathematics achievement.

Science.gov (United States)

Hassinger-Das, Brenna; Jordan, Nancy C; Glutting, Joseph; Irwin, Casey; Dyson, Nancy

2014-02-01

Domain-general skills that mediate the relation between kindergarten number sense and first-grade mathematics skills were investigated. Participants were 107 children who displayed low number sense in the fall of kindergarten. Controlling for background variables, multiple regression analyses showed that both attention problems and executive functioning were unique predictors of mathematics outcomes. Attention problems were more important for predicting first-grade calculation performance, whereas executive functioning was more important for predicting first-grade performance on applied problems. Moreover, both executive functioning and attention problems were unique partial mediators of the relationship between kindergarten and first-grade mathematics skills. The results provide empirical support for developing interventions that target executive functioning and attention problems in addition to instruction in number skills for kindergartners with initial low number sense. Copyright © 2013 Elsevier Inc. All rights reserved.

An epistemic framing analysis of upper level physics students' use of mathematics

Science.gov (United States)

Bing, Thomas Joseph

Mathematics is central to a professional physicist's work and, by extension, to a physics student's studies. It provides a language for abstraction, definition, computation, and connection to physical reality. This power of mathematics in physics is also the source of many of the difficulties it presents students. Simply put, many different activities could all be described as "using math in physics". Expertise entails a complicated coordination of these various activities. This work examines the many different kinds of thinking that are all facets of the use of mathematics in physics. It uses an epistemological lens, one that looks at the type of explanation a student presently sees as appropriate, to analyze the mathematical thinking of upper level physics undergraduates. Sometimes a student will turn to a detailed calculation to produce or justify an answer. Other times a physical argument is explicitly connected to the mathematics at hand. Still other times quoting a definition is seen as sufficient, and so on. Local coherencies evolve in students' thought around these various types of mathematical justifications. We use the cognitive process of framing to model students' navigation of these various facets of math use in physics. We first demonstrate several common framings observed in our students' mathematical thought and give several examples of each. Armed with this analysis tool, we then give several examples of how this framing analysis can be used to address a research question. We consider what effects, if any, a powerful symbolic calculator has on students' thinking. We also consider how to characterize growing expertise among physics students. Framing offers a lens for analysis that is a natural fit for these sample research questions. To active physics education researchers, the framing analysis presented in this dissertation can provide a useful tool for addressing other research questions. To physics teachers, we present this analysis so that it

General safety aspects

International Nuclear Information System (INIS)

1998-01-01

In this part next aspects are described: (1) Priority to safety; (2) Financial and human resources;; (3) Human factor; (4) Operator's quality assurance system; (5) Safety assessment and Verification; (6) Radiation protection and (7) Emergency preparedness

[Mathematical exploration of essence of herbal properties based on "Three-Elements" theory].

Science.gov (United States)

Jin, Rui; Zhao, Qian; Zhang, Bing

2014-10-01

Herbal property theory of traditional Chinese medicines is the theoretical guidance on authentication of medicinal plants, herborization, preparation of herbal medicines for decoction and clinical application, with important theoretical value and prac- tical significance. Our research team proposed the "three-element" theory for herbal properties for the first time, conducted a study by using combined methods of philology, chemistry, pharmacology and mathematics, and then drew the research conclusion that herbal properties are defined as the chemical compositions-based comprehensive expression with complex and multi-level (positive/negative) biological effects in specific organism state. In this paper, researchers made a systematic mathematical analysis in four aspects--the correlation between herbal properties and chemical component factors, the correlation between herbal properties and organism state fac- tor, the correlation between herbal properties and biological effect factor and the integration study of the three elements, proposed future outlook, and provided reference to mathematical studies and mathematical analysis of herbal properties.

Mathematics in India

CERN Document Server

Plofker, Kim

2009-01-01

Based on extensive research in Sanskrit sources, Mathematics in India chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic sc

CIME Summer School on Mathematical Thermodynamics of Complex Fluids

CERN Document Server

Rocca, Elisabetta

2017-01-01

The main goal of this book is to provide an overview of the state of the art in the mathematical modeling of complex fluids, with particular emphasis on its thermodynamical aspects. The central topics of the text, the modeling, analysis and numerical simulation of complex fluids, are of great interest and importance both for the understanding of various aspects of fluid dynamics and for its applications to special real-world problems.  New emerging trends in the subject are highlighted with the intent to inspire and motivate young researchers and PhD students.

The Mathematics of Medical Imaging in the Classroom.

Science.gov (United States)

Funkhouser, Charles P.; Jafari, Farhad; Eubank, William B.

2002-01-01

Presents an integrated exposition of aspects of secondary school mathematics and a medical science specialty. Reviews clinical medical practice and theoretical and empirical literature in mathematics education and radiology to develop and pilot model integrative classroom topics and activities. Suggests mathematical applications in numeration and…

Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance

Directory of Open Access Journals (Sweden)

Tanki Motsepa

2014-01-01

Full Text Available We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant solutions are constructed for some cases.

Parallelization of mathematical library for generalized eigenvalue problem for real band matrices

International Nuclear Information System (INIS)

Tanaka, Yasuhisa.

1997-05-01

This research has focused on a parallelization of the mathematical library for a generalized eigenvalue problem for real band matrices on IBM SP and Hitachi SR2201. The origin of the library is LASO (Lanczos Algorithm with Selective Orthogonalization), which was developed on the basis of Block Lanczos method for standard eigenvalue problem for real band matrices at Texas University. We adopted D.O.F. (Degree Of Freedom) decomposition method for a parallelization of this library, and evaluated its parallel performance. (author)

Neutron activation analysis with k0-standardisation : general formalism and procedure

International Nuclear Information System (INIS)

Pomme, S.; Hardeman, F.; Robouch, P.; Etxebarria, N.; Arana, G.

1997-09-01

Instrumental neutron activation analysis (INAA) with k 0 -standardisation is a powerful tool for multi-element analysis at a broad range of trace element concentrations. An overview is given of the basic principles, fundamental equations, and general procedure of this method. Different aspects of the description of the neutron activation reaction rate are discussed, applying the Hogdahl convention. A general activation-decay formula is derived and its application to INAA is demonstrated. Relevant k 0 -definitions for different activation decay schemes are summarised and upgraded to cases of extremely high fluxes. The main standardisation techniques for INAA are discussed, emphasizing the k 0 -standardisation. Some general aspects of the basic equipment and its calibration are discussed, such as the characterisation of the neutron field and the tuning of the spectrometry part. A method for the prediction and optimisation of the analytical performance of INAA is presented

Adversity Quotient in Mathematics Learning (Quantitative Study on Students Boarding School in Pekanbaru

Directory of Open Access Journals (Sweden)

Zubaidah Amir MZ

2017-08-01

Full Text Available The aim of this study is to analyze students’ Adversity Quotient (AQ in mathematics learning viewed from gender aspect. This study is quantitative survey study on students in MTs Al-Munawarah Boarding School, Pekanbaru. The subjects of study are 8th grade students consisting of  75 girls and 63 boys. Data are collected by AQ scale and analyzed with statistic descriptive and inferential (test-t. The indicator of AQ consist of control, origin, ownership, reach and endurance.  The result of descriptive analysis shows that there is difference in mean of each indicator for two groups, but analysis of test-t  shows that there is no difference in students’ mathematical AQ for two group of gender. Through variance test, students’ mathematical AQ in two groups is homogeneous. The indicator of AQ in boys which is categorized as high are endurance and reach. While, the indicator in girls is aspect of control. This study contributes to literature study in identifying students’ AQ and the effort done to enhance students’ AQ in mathematics learning.

Some aspects of analogical reasoning in mathematical creativity

OpenAIRE

Pease, Alison; Guhe, Markus; Smaill, Alan

2010-01-01

Analogical reasoning can shed light on both of the two key processes of creativity– generation and evaluation. Hence, it is a powerful tool for creativity. We illustrate this with three historical case studies of creative mathematical conjectures which were either found or evaluated via analogies. We conclude by describing our ongoing efforts to build computational realisations of these ideas.

International seminar series on mathematics and applied mathematics and a series of three focused international research workshops on engineering mathematics organised by the Research Environment in Mathematics and Applied Mathematics at Mälardalen University from autumn 2014 to autumn 2015: the International Workshop on Engineering Mathematics for Electromagnetics and Health Technology; the International Workshop on Engineering Mathematics, Algebra, Analysis and Electromagnetics; and the 1st Swedish-Estonian International Workshop on Engineering Mathematics, Algebra, Analysis and Applications

CERN Document Server

Rancic, Milica

2016-01-01

This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most relevant for applications in modern technologies and engineering. It addresses mathematical methods of algebra, applied matrix analysis, operator analysis, probability theory and stochastic processes, geometry and computational methods in network analysis, data classification, ranking and optimisation. The individual chapters cover both theory and applications, and include a wealth of figures, schemes, algorithms, tables and results of data analysis and simulation. Presenting new methods and results, reviews of cutting-edge research, and open problems for future research, they equip readers to develop new mathematical methods and concepts of their own, and to further compare and analyse the methods and results discussed. The book consists of contributed chapters covering research developed as a result of a focused interna...

Aspects of Mathematical Logic

CERN Document Server

Casari, Ettore

2011-01-01

H. Hermes: Basic notions and applications of the theory of decidability.- D. Kurepa: On several continuum hypotheses.- A. Mostowski: Models of set theory.- A. Robinson: Problems and methods of model theory.- S. Sochor, B. Balcar: The general theory of semisets. Syntactic models of the set theory.

A Comparative Analysis of Quadratics Unit in Singaporean, Turkish and IBDP Mathematics Textbooks

Directory of Open Access Journals (Sweden)

Reyhan Sağlam

2012-12-01

Full Text Available The purpose of this study was to analyze and compare the contents of the chapters on quadratics in three mathematics textbooks selected from Turkey, Singapore, and the International Baccalaureate Diploma Program (IBDP through content analysis. The analysis of mathematical content showed that the three textbooks have different approaches and priorities in terms of the positions of chapters and weights of the quadratics units, and the time allocated to them within the respective curricular programs. It was also found that the Turkish textbook covers a greater number of learning outcomes targeted for quadratics among the three mathematics syllabi, showing a detailed treatment of the topic compared to the other two textbooks.Key Words: Content analysis, international comparative studies, mathematics textbooks

Aspects of Accounting and Financial Analysis Service Outsourcing: a Romanian Approach

Directory of Open Access Journals (Sweden)

Vasile-Daniel W. Păvăloaia

2011-06-01

Full Text Available In January 2010, Forbes magazine published an article with an attractive title: Romania –became an accounting outsourcing destination. The article states that our country has fully enteredthe market of accounting service outsourcing. Also, the results of a study ordered byPricewaterhouseCoopers in 2010 confirm that outsourcing has encountered a revival in the last sixmonths and the trend is ascending. The director of PricewaterhouseCoopers says that companies stillresort to service outsourcing primarily to reduce costs but at the same level, customers began to alsoappreciate other aspects such as high efficiency, high quality services and, of course, access to highleveltalent and expertise. In the above mentioned context, in author’s opinion, the theme of thecurrent research seems appropriate as it proposes and emphasize of the fundamental aspects ofoutsourcing in general and specific issues related to outsourcing the services of accounting andfinancial analysis. This study illustrates novel aspects related to the requirements for outsourcingaccounting services in our country and captures the authors' opinion on the possibilities ofoutsourcing the financial and economic analysis services, since these belong to a quite sensitivecategory. If this information comes across foreign hands, the financial and accounting informationcan be used for destructive purposes.

Some applications of mathematics in golf.

Science.gov (United States)

Otto, S R

2017-08-01

At its core, like many other sports, golf is a game of integers. The minimization of the number of strokes played is generally what determines the winner, whether each of these are associated with the shortest of putts or the longest of drives. The outcomes of these shots are influenced by very slight changes, but hopefully in a deterministic sense. Understanding the mechanics of golf necessitates the development of models and this is coupled more often than not to the use of statistics. In essence, the individual aspects of the sport can be modelled adequately via fairly simplistic models, but the presence of a human at one end of the kinematic chain has a significant impact on the variability of the entire process. In this paper, we will review some of the ways that mathematics has been used to develop the understanding of the physical processes involved in the sport, including some of the analysis which is exploited within the Equipment Rules. We will also discuss some of the future challenges.

Large-aspect-ratio limit of neoclassical transport theory

International Nuclear Information System (INIS)

Wong, S K.; Chan, V.S.

2003-01-01

This paper presents a comprehensive description of neoclassical transport theory in the banana regime for large-aspect-ratio flux surfaces of arbitrary shapes. The method of matched-asymptotic expansions is used to obtain analytical solutions for plasma distribution functions and to compute transport coefficients. The method provides justification for retaining only the part of the Fokker-Planck operator that involves the second derivative with respect to the cosine of the pitch angle for the trapped and barely circulating particles. It leads to a simple equation for the freely circulating particles with boundary conditions that embody a discontinuity separating particles moving in opposite directions. Corrections to the transport coefficients are obtained by generalizing an existing boundary layer analysis. The system of moment and field equations is consistently taken in the cylinder limit, which facilitates the discussion of the treatment of dynamical constraints. It is shown that the nonlocal nature of Ohm's law in neoclassical theory renders the mathematical problem of plasma transport with changing flux surfaces nonstandard

Large-aspect-ratio limit of neoclassical transport theory.

Science.gov (United States)

Wong, S K; Chan, V S

2003-06-01

This paper presents a comprehensive description of neoclassical transport theory in the banana regime for large-aspect-ratio flux surfaces of arbitrary shapes. The method of matched-asymptotic expansions is used to obtain analytical solutions for plasma distribution functions and to compute transport coefficients. The method provides justification for retaining only the part of the Fokker-Planck operator that involves the second derivative with respect to the cosine of the pitch angle for the trapped and barely circulating particles. It leads to a simple equation for the freely circulating particles with boundary conditions that embody a discontinuity separating particles moving in opposite directions. Corrections to the transport coefficients are obtained by generalizing an existing boundary layer analysis. The system of moment and field equations is consistently taken in the cylinder limit, which facilitates the discussion of the treatment of dynamical constraints. It is shown that the nonlocal nature of Ohm's law in neoclassical theory renders the mathematical problem of plasma transport with changing flux surfaces nonstandard.

Application and the Identity of Mathematics

DEFF Research Database (Denmark)

Jensen, Kasper Bjering Søby

In the paper a conceptual framework for discussing the identity of mathematics as a school subject is constructed with particular emphasize on application of mathematics. The framework is used to analyze the identity of mathematics, as it appears on two different kinds of domains: the political s...... system and the teachers. At the end it is discussed whether this frameworks gives us new insights into mathematics teaching. It is concluded that the framework can articulates important aspects.......In the paper a conceptual framework for discussing the identity of mathematics as a school subject is constructed with particular emphasize on application of mathematics. The framework is used to analyze the identity of mathematics, as it appears on two different kinds of domains: the political...

Developing self-concept instrument for pre-service mathematics teachers

Science.gov (United States)

Afgani, M. W.; Suryadi, D.; Dahlan, J. A.

2018-01-01

This study aimed to develop self-concept instrument for undergraduate students of mathematics education in Palembang, Indonesia. Type of this study was development research of non-test instrument in questionnaire form. A Validity test of the instrument was performed with construct validity test by using Pearson product moment and factor analysis, while reliability test used Cronbach’s alpha. The instrument was tested by 65 undergraduate students of mathematics education in one of the universities at Palembang, Indonesia. The instrument consisted of 43 items with 7 aspects of self-concept, that were the individual concern, social identity, individual personality, view of the future, the influence of others who become role models, the influence of the environment inside or outside the classroom, and view of the mathematics. The result of validity test showed there was one invalid item because the value of Pearson’s r was 0.107 less than the critical value (0.244; α = 0.05). The item was included in social identity aspect. After the invalid item was removed, Construct validity test with factor analysis generated only one factor. The Kaiser-Meyer-Olkin (KMO) coefficient was 0.846 and reliability coefficient was 0.91. From that result, we concluded that the self-concept instrument for undergraduate students of mathematics education in Palembang, Indonesia was valid and reliable with 42 items.

Generalized direct Lyapunov method for the analysis of stability and attraction in general time systems

International Nuclear Information System (INIS)

Druzhinina, O V; Shestakov, A A

2002-01-01

A generalized direct Lyapunov method is put forward for the study of stability and attraction in general time systems of the following types: the classical dynamical system in the sense of Birkhoff, the general system in the sense of Zubov, the general system in the sense of Seibert, the general system with delay, and the general 'input-output' system. For such systems, with the help of generalized Lyapunov functions with respect to two filters, two quasifilters, or two filter bases, necessary and sufficient conditions for stability and attraction are obtained under minimal assumptions about the mathematical structure of the general system

Using Covariation Reasoning to Support Mathematical Modeling

Science.gov (United States)

Jacobson, Erik

2014-01-01

For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…

Mathematical methods in quantum and statistical mechanics

International Nuclear Information System (INIS)

Fishman, L.

1977-01-01

The mathematical structure and closed-form solutions pertaining to several physical problems in quantum and statistical mechanics are examined in some detail. The J-matrix method, introduced previously for s-wave scattering and based upon well-established Hilbert Space theory and related generalized integral transformation techniques, is extended to treat the lth partial wave kinetic energy and Coulomb Hamiltonians within the context of square integrable (L 2 ), Laguerre (Slater), and oscillator (Gaussian) basis sets. The theory of relaxation in statistical mechanics within the context of the theory of linear integro-differential equations of the Master Equation type and their corresponding Markov processes is examined. Several topics of a mathematical nature concerning various computational aspects of the L 2 approach to quantum scattering theory are discussed

Relationships of Mathematics Anxiety, Mathematics Self-Efficacy and Mathematics Performance of Adult Basic Education Students

Science.gov (United States)

Watts, Beverly Kinsey

2011-01-01

Competent mathematical skills are needed in the workplace as well as in the college setting. Adults in Adult Basic Education classes and programs generally perform below high school level competency, but very few studies have been performed investigating the predictors of mathematical success for adults. The current study contributes to the…

Innovation in mathematics education: beyond the technology

Directory of Open Access Journals (Sweden)

Salvador Llinares

2013-06-01

Full Text Available Relationships between mathematical competence and mathematics teaching innovation do emerge the need for new practices of mathematics teaching. One of the aspects of this new practice is the interaction patterns in the classroom characterizing the mathematical discourse. From these perspectives, the relation between innovation and new mathematics practices defines different contexts for professional development of mathematics teacher.

The quest for a new modelling framework in mathematical biology. Comment on "On the interplay between mathematics and biology: Hallmarks towards a new systems biology" by N. Bellomo et al.

Science.gov (United States)

Eftimie, Raluca

2015-03-01

One of the main unsolved problems of modern physics is finding a "theory of everything" - a theory that can explain, with the help of mathematics, all physical aspects of the universe. While the laws of physics could explain some aspects of the biology of living systems (e.g., the phenomenological interpretation of movement of cells and animals), there are other aspects specific to biology that cannot be captured by physics models. For example, it is generally accepted that the evolution of a cell-based system is influenced by the activation state of cells (e.g., only activated and functional immune cells can fight diseases); on the other hand, the evolution of an animal-based system can be influenced by the psychological state (e.g., distress) of animals. Therefore, the last 10-20 years have seen also a quest for a "theory of everything"-approach extended to biology, with researchers trying to propose mathematical modelling frameworks that can explain various biological phenomena ranging from ecology to developmental biology and medicine [1,2,6]. The basic idea behind this approach can be found in a few reviews on ecology and cell biology [6,7,9-11], where researchers suggested that due to the parallel between the micro-scale dynamics and the emerging macro-scale phenomena in both cell biology and in ecology, many mathematical methods used for ecological processes could be adapted to cancer modelling [7,9] or to modelling in immunology [11]. However, this approach generally involved the use of different models to describe different biological aspects (e.g., models for cell and animal movement, models for competition between cells or animals, etc.).

Error analysis of mathematical problems on TIMSS: A case of Indonesian secondary students

Science.gov (United States)

Priyani, H. A.; Ekawati, R.

2018-01-01

Indonesian students’ competence in solving mathematical problems is still considered as weak. It was pointed out by the results of international assessment such as TIMSS. This might be caused by various types of errors made. Hence, this study aimed at identifying students’ errors in solving mathematical problems in TIMSS in the topic of numbers that considered as the fundamental concept in Mathematics. This study applied descriptive qualitative analysis. The subject was three students with most errors in the test indicators who were taken from 34 students of 8th graders. Data was obtained through paper and pencil test and student’s’ interview. The error analysis indicated that in solving Applying level problem, the type of error that students made was operational errors. In addition, for reasoning level problem, there are three types of errors made such as conceptual errors, operational errors and principal errors. Meanwhile, analysis of the causes of students’ errors showed that students did not comprehend the mathematical problems given.

Student comprehension of mathematics through astronomy

Science.gov (United States)

Search, Robert

The purpose of this study is to examine how knowledge of astronomy can enhance college-level learning situations involving mathematics. The fundamental symbiosis between mathematics and astronomy was established early in the 17th century when Johannes Kepler deduced the 3 basic laws of planetary motion. This mutually harmonious relationship between these sciences has been reinforced repeatedly in history. In the early 20th century, for example, astronomer Arthur Eddington used photographic evidence from a 1919 solar eclipse to verify Einstein's mathematical theory of relativity. This study was conducted in 5 undergraduate mathematics classes over the course of 2 years. An introductory course in ordinary differential equations, taught in Spring Semester 2013, involved 4 students. A similar course in Spring Semester 2014 involved 6 students, a Summer Semester 2014 Calculus II course involved 2 students, and a Summer 2015 Astronomy course involved 8 students. The students were asked to use Kepler's astronomical evidence to deduce mathematical laws normally encountered on an undergraduate level. They were also asked to examine the elementary mathematical aspects involved in a theoretical trajectory to the planet Neptune. The summer astronomy class was asked to draw mathematical conclusions about large numbers from the recent discoveries concerning the dwarf planet Pluto. The evidence consists primarily of videotaped PowerPoint presentations conducted by the students in both differential equations classes, along with interviews and tests given in all the classes. All presentations were transcribed and examined to determine the effect of astronomy as a generator of student understanding of mathematics. An analysis of the data indicated two findings: definite student interest in a subject previously unknown to most of them and a desire to make the mathematical connection to celestial phenomena.

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.

General aspects of nuclear power, radiation and environmental effects. Chapter 3

International Nuclear Information System (INIS)

1978-01-01

A general introduction to the principles of the functioning of a nuclear reactor and of power plants based on the reactor types at present in use, and likely to be used in the near future (PWR,BWR,FBR,HTGR and CANDU) is given. The general principles of a thermonuclear power plant are also briefly presented, and general safety aspects discussed. The physics of ionising radiations is briefly presented and natural and artificial sources of radiation are discussed. The fuel cycle, from mining to reprocessing and waste disposal and transport, is presented. The behaviour and effects of radioactive substances in the biosphere, radiation doses, and biological effects of ionising radiation are discussed. In conclusion there is an appendix in which the main characteristics of a number of elements which have important radioactive isotopes are presented. (JIW)

The integration of DVH-based planning aspects into a convex intensity modulated radiation therapy optimization framework

International Nuclear Information System (INIS)

Kratt, Karin; Scherrer, Alexander

2009-01-01

The formulation of intensity modulated radiation therapy (IMRT) planning aspects frequently uses the dose-volume histogram (DVH), whereas plan computations often happen in the more desirable convex IMRT optimization framework. Inspired by a recent publication of Zinchenko et al (2008 Phys. Med. Biol. 53 3231-50), this work addresses the integration of DVH-based planning aspects into this framework from a general point of view. It first provides the basic mathematical requirements on the evaluation functions in order to support such an incorporation. Then it introduces the condition number as a description for how precisely DVH-based planning aspects can be reformulated in terms of evaluation functions. Exemplary numerical studies for the generalized equivalent uniform dose and a physical constraint function show the influence of function parameter values and DVH approximation on the condition number. The work concludes by formulating the aspects that should be taken into account for an appropriate integration of DVH-based planning aspects. (note)

The integration of DVH-based planning aspects into a convex intensity modulated radiation therapy optimization framework

Energy Technology Data Exchange (ETDEWEB)

Kratt, Karin [Faculty of Mathematics, Technical University of Kaiserslautern, Kaiserslautern (Germany); Scherrer, Alexander [Department of Optimization, Fraunhofer Institute for Industrial Mathematics (ITWM), Kaiserslautern (Germany)], E-mail: alexander.scherrer@itwm.fraunhofer.de

2009-06-21

The formulation of intensity modulated radiation therapy (IMRT) planning aspects frequently uses the dose-volume histogram (DVH), whereas plan computations often happen in the more desirable convex IMRT optimization framework. Inspired by a recent publication of Zinchenko et al (2008 Phys. Med. Biol. 53 3231-50), this work addresses the integration of DVH-based planning aspects into this framework from a general point of view. It first provides the basic mathematical requirements on the evaluation functions in order to support such an incorporation. Then it introduces the condition number as a description for how precisely DVH-based planning aspects can be reformulated in terms of evaluation functions. Exemplary numerical studies for the generalized equivalent uniform dose and a physical constraint function show the influence of function parameter values and DVH approximation on the condition number. The work concludes by formulating the aspects that should be taken into account for an appropriate integration of DVH-based planning aspects. (note)

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.

New Avenues for History in Mathematics Education: Mathematical Competencies and Anchoring

DEFF Research Database (Denmark)

Jankvist, U. T.; Kjeldsen, T. H.

2011-01-01

. The first scenario occurs when history is used as a ‘tool’ for the learning and teaching of mathematics, the second when history of mathematics as a ‘goal’ is pursued as an integral part of mathematics education. We introduce a multiple-perspective approach to history, and suggest that research on history......The paper addresses the apparent lack of impact of ‘history in mathematics education’ in mathematics education research in general, and proposes new avenues for research. We identify two general scenarios of integrating history in mathematics education that each gives rise to different problems...... in mathematics education follows one of two different avenues in dealing with these scenarios. The first is to focus on students’ development of mathematical competencies when history is used a tool for the learning of curriculum-dictated mathematical in-issues. A framework for this is described. Secondly, when...

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...

Mathematical Methods in Tomography

CERN Document Server

Louis, Alfred; Natterer, Frank

1991-01-01

The conference was devoted to the discussion of present and future techniques in medical imaging, including 3D x-ray CT, ultrasound and diffraction tomography, and biomagnetic ima- ging. The mathematical models, their theoretical aspects and the development of algorithms were treated. The proceedings contains surveys on reconstruction in inverse obstacle scat- tering, inversion in 3D, and constrained least squares pro- blems.Research papers include besides the mentioned imaging techniques presentations on image reconstruction in Hilbert spaces, singular value decompositions, 3D cone beam recon- struction, diffuse tomography, regularization of ill-posed problems, evaluation reconstruction algorithms and applica- tions in non-medical fields. Contents: Theoretical Aspects: J.Boman: Helgason' s support theorem for Radon transforms-a newproof and a generalization -P.Maass: Singular value de- compositions for Radon transforms- W.R.Madych: Image recon- struction in Hilbert space -R.G.Mukhometov: A problem of in- teg...

DETERMINATION ALGORITHM OF OPTIMAL GEOMETRICAL PARAMETERS FOR COMPONENTS OF FREIGHT CARS ON THE BASIS OF GENERALIZED MATHEMATICAL MODELS

Directory of Open Access Journals (Sweden)

O. V. Fomin

2013-10-01

Full Text Available Purpose. Presentation of features and example of the use of the offered determination algorithm of optimum geometrical parameters for the components of freight cars on the basis of the generalized mathematical models, which is realized using computer. Methodology. The developed approach to search for optimal geometrical parameters can be described as the determination of optimal decision of the selected set of possible variants. Findings. The presented application example of the offered algorithm proved its operation capacity and efficiency of use. Originality. The determination procedure of optimal geometrical parameters for freight car components on the basis of the generalized mathematical models was formalized in the paper. Practical value. Practical introduction of the research results for universal open cars allows one to reduce container of their design and accordingly to increase the carrying capacity almost by100 kg with the improvement of strength characteristics. Taking into account the mass of their park this will provide a considerable economic effect when producing and operating. The offered approach is oriented to the distribution of the software packages (for example Microsoft Excel, which are used by technical services of the most enterprises, and does not require additional capital investments (acquisitions of the specialized programs and proper technical staff training. This proves the correctness of the research direction. The offered algorithm can be used for the solution of other optimization tasks on the basis of the generalized mathematical models.

A unified MGF-based capacity analysis of diversity combiners over generalized fading channels

KAUST Repository

Yilmaz, Ferkan

2012-03-01

Unified exact ergodic capacity results for L-branch coherent diversity combiners including equal-gain combining (EGC) and maximal-ratio combining (MRC) are not known. This paper develops a novel generic framework for the capacity analysis of L-branch EGC/MRC over generalized fading channels. The framework is used to derive new results for the gamma-shadowed generalized Nakagami-m fading model which can be a suitable model for the fading environments encountered by high frequency (60 GHz and above) communications. The mathematical formalism is illustrated with some selected numerical and simulation results confirming the correctness of our newly proposed framework. © 2012 IEEE.

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.

Problems in mathematical analysis III integration

CERN Document Server

Kaczor, W J

2003-01-01

We learn by doing. We learn mathematics by doing problems. This is the third volume of Problems in Mathematical Analysis. The topic here is integration for real functions of one real variable. The first chapter is devoted to the Riemann and the Riemann-Stieltjes integrals. Chapter 2 deals with Lebesgue measure and integration. The authors include some famous, and some not so famous, integral inequalities related to Riemann integration. Many of the problems for Lebesgue integration concern convergence theorems and the interchange of limits and integrals. The book closes with a section on Fourier series, with a concentration on Fourier coefficients of functions from particular classes and on basic theorems for convergence of Fourier series. The book is primarily geared toward students in analysis, as a study aid, for problem-solving seminars, or for tutorials. It is also an excellent resource for instructors who wish to incorporate problems into their lectures. Solutions for the problems are provided in the boo...

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.

Mathematical methods for physical and analytical chemistry

CERN Document Server

Goodson, David Z

2011-01-01

Mathematical Methods for Physical and Analytical Chemistry presents mathematical and statistical methods to students of chemistry at the intermediate, post-calculus level. The content includes a review of general calculus; a review of numerical techniques often omitted from calculus courses, such as cubic splines and Newton's method; a detailed treatment of statistical methods for experimental data analysis; complex numbers; extrapolation; linear algebra; and differential equations. With numerous example problems and helpful anecdotes, this text gives chemistry students the mathematical

Neutron activation analysis with k{sub 0}-standardisation : general formalism and procedure

Energy Technology Data Exchange (ETDEWEB)

Pomme, S.; Hardeman, F. [Centre de l`Etude de l`Energie Nucleaire, Mol (Belgium); Robouch, P.; Etxebarria, N.; Arana, G. [European Commission, Joint Research Centre, Institute for Reference Materials and Measurements, Geel (Belgium)

1997-09-01

Instrumental neutron activation analysis (INAA) with k{sub 0}-standardisation is a powerful tool for multi-element analysis at a broad range of trace element concentrations. An overview is given of the basic principles, fundamental equations, and general procedure of this method. Different aspects of the description of the neutron activation reaction rate are discussed, applying the Hogdahl convention. A general activation-decay formula is derived and its application to INAA is demonstrated. Relevant k{sub 0}-definitions for different activation decay schemes are summarised and upgraded to cases of extremely high fluxes. The main standardisation techniques for INAA are discussed, emphasizing the k{sub 0}-standardisation. Some general aspects of the basic equipment and its calibration are discussed, such as the characterisation of the neutron field and the tuning of the spectrometry part. A method for the prediction and optimisation of the analytical performance of INAA is presented.

Third international handbook of mathematics education

CERN Document Server

Bishop, Alan; Keitel, Christine; Kilpatrick, Jeremy; Leung, Frederick

2013-01-01

This entirely new Third International Handbook of Mathematics Education comprises 31 chapters which have been written by a total of 84 different authors representing 26 nations, each a recognized expert in the field.   Comprised of four sections: Social, Political and Cultural Dimensions in Mathematics Education; Mathematics Education as a Field of Study; Technology in the Mathematics Curriculum; and International Perspectives on Mathematics Education, this Third Handbook offers essential reading for all persons interested in the future of mathematics education. The authors present challenging international perspectives on the history of mathematics education, current issues, and future directions.   What makes this Handbook unique is its structure. Each section covers past, present and future aspects of mathematics education.   The first chapter in each section identifies and analyzes historical antecedents The “middle” chapters draw attention to present-day key issues and themes The final chapter in ...

Mathematical Modelling Research in Turkey: A Content Analysis Study

Science.gov (United States)

Çelik, H. Coskun

2017-01-01

The aim of the present study was to examine the mathematical modelling studies done between 2004 and 2015 in Turkey and to reveal their tendencies. Forty-nine studies were selected using purposeful sampling based on the term, "mathematical modelling" with Higher Education Academic Search Engine. They were analyzed with content analysis.…

The analysis of mathematics literacy on PMRI learning with media schoology of junior high school students

Science.gov (United States)

Wardono; Mariani, S.

2018-03-01

Indonesia as a developing country in the future will have high competitiveness if its students have high mathematics literacy ability. The current reality from year to year rankings of PISA mathematics literacy Indonesian students are still not good. This research is motivated by the importance and low ability of the mathematics literacy. The purpose of this study is to: (1) analyze the effectiveness of PMRI learning with media Schoology, (2) describe the ability of students' mathematics literacy on PMRI learning with media Schoology which is reviewed based on seven components of mathematics literacy, namely communication, mathematizing, representation, reasoning, devising strategies, using symbols, and using mathematics tool. The method used in this research is the method of sequential design method mix. Techniques of data collection using observation, interviews, tests, and documentation. Data analysis techniques use proportion test, appellate test, and use descriptive analysis. Based on the data analysis, it can be concluded; (1) PMRI learning with media Schoology effectively improve the ability of mathematics literacy because of the achievement of classical completeness, students' mathematics literacy ability in PMRI learning with media Schoology is higher than expository learning, and there is increasing ability of mathematics literacy in PMRI learning with media Schoology of 30%. (2) Highly capable students attain excellent mathematics literacy skills, can work using broad thinking with appropriate resolution strategies. Students who are capable of achieving good mathematics literacy skills can summarize information, present problem-solving processes, and interpret solutions. low-ability students have reached the level of ability of mathematics literacy good enough that can solve the problem in a simple way.

INTERSUBJECT CONNECTIONS OF COURSE OF MATHEMATICAL LOGIC AND OTHER MATHEMATICAL COURSES AT PREPARATION OF FUTURE TEACHER OF MATHEMATICS

Directory of Open Access Journals (Sweden)

Yu.I. Sinko

2012-03-01

Full Text Available In this article the interconnections of course of mathematical logic with other mathematical courses – geometry, algebra and theory of numbers, mathematical analysis, and also with the courses of mathematics teaching methodology, history of mathematics in the system of preparation of teachers of mathematics in pedagogical Institute of higher education are analyzed. The presence of connections between the elements of the system and their quality is the important description of the pedagogical system.

New SUSYQM coherent states for Pöschl-Teller potentials: a detailed mathematical analysis

Science.gov (United States)

Bergeron, H.; Siegl, P.; Youssef, A.

2012-06-01

In a recent short note (Bergeron et al 2010 Europhys. Lett. 92 60003), we have presented the good properties of a new family of semi-classical states for Pöschl-Teller potentials. These states are built from a supersymmetric quantum mechanics (SUSYQM) approach and the parameters of these ‘coherent’ states are points in the classical phase space. In this paper, we develop all the mathematical aspects that have been left out of the previous paper (proof of the resolution of unity, detailed calculations of the quantized version of classical observables and mathematical study of the resulting operators: problems of domains, self-adjointness or self-adjoint extensions). Some additional questions such as asymptotic behavior are also studied. Moreover, the framework is extended to a larger class of Pöschl-Teller potentials. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.

New SUSYQM coherent states for Pöschl–Teller potentials: a detailed mathematical analysis

International Nuclear Information System (INIS)

Bergeron, H; Siegl, P; Youssef, A

2012-01-01

In a recent short note (Bergeron et al 2010 Europhys. Lett. 92 60003), we have presented the good properties of a new family of semi-classical states for Pöschl–Teller potentials. These states are built from a supersymmetric quantum mechanics (SUSYQM) approach and the parameters of these ‘coherent’ states are points in the classical phase space. In this paper, we develop all the mathematical aspects that have been left out of the previous paper (proof of the resolution of unity, detailed calculations of the quantized version of classical observables and mathematical study of the resulting operators: problems of domains, self-adjointness or self-adjoint extensions). Some additional questions such as asymptotic behavior are also studied. Moreover, the framework is extended to a larger class of Pöschl–Teller potentials. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)

Mathematical analysis II

CERN Document Server

Zorich, Vladimir A

2016-01-01

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, and fresh applications to areas seldom touched on in textbooks on real analysis. The main difference between the second and first English editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different go...

The materiality of mathematics: presenting mathematics at the blackboard.

Science.gov (United States)

Greiffenhagen, Christian

2014-09-01

Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body. As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of 'mind' and 'body'. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics. The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an 'architecture' visualizing the overall structure of the proof). The paper argues that doing mathematics really is 'thinking with eyes and hands' (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics. © London School of Economics and Political Science 2014.

The written mathematical communication profile of prospective math teacher in mathematical proving

Science.gov (United States)

Pantaleon, K. V.; Juniati, D.; Lukito, A.; Mandur, K.

2018-01-01

Written mathematical communication is the process of expressing mathematical ideas and understanding in writing. It is one of the important aspects that must be mastered by the prospective math teacher as tool of knowledge transfer. This research was a qualitative research that aimed to describe the mathematical communication profile of the prospective mathematics teacher in mathematical proving. This research involved 48 students of Mathematics Education Study Program; one of them with moderate math skills was chosen as the main subject. Data were collected through tests, assignments, and task-based interviews. The results of this study point out that in the proof of geometry, the subject explains what is understood, presents the idea in the form of drawing and symbols, and explains the content/meaning of a representation accurately and clearly, but the subject can not convey the argument systematically and logically. Whereas in the proof of algebra, the subject describes what is understood, explains the method used, and describes the content/meaning of a symbolic representation accurately, systematically, logically, but the argument presented is not clear because it is insufficient detailed and complete.

Amazing and aesthetic aspects of analysis

CERN Document Server

Loya, Paul

2017-01-01

Lively prose and imaginative exercises draw the reader into this unique introductory real analysis textbook. Motivating the fundamental ideas and theorems that underpin real analysis with historical remarks and well-chosen quotes, the author shares his enthusiasm for the subject throughout. A student reading this book is invited not only to acquire proficiency in the fundamentals of analysis, but to develop an appreciation for abstraction and the language of its expression. In studying this book, students will encounter: the interconnections between set theory and mathematical statements and proofs; the fundamental axioms of the natural, integer, and real numbers; rigorous ε-N and ε-δ definitions; convergence and properties of an infinite series, product, or continued fraction; series, product, and continued fraction formulæ for the various elementary functions and constants. Instructors will appreciate this engaging perspective, showcasing the beauty of these fundamental results.

Word problems and make-believe: Using frame analysis and ethnomethodology to explore aspects of the culture of schooling

Directory of Open Access Journals (Sweden)

Benincasa Luciana

2017-12-01

Full Text Available The paper applies Goffman’s frame analysis and ethnomethodology to student performance on mathematical word problems. In educational research, frame analysis has usually been limited to primary frames. Instead, in this paper I focus on the kind of secondary frame that Goffman calls ‘utilitarian make-believe’. The data consist of a fragment of verbal interaction between a teacher and a 12-year-old pupil during an oral mathematics exam. By evoking the idea of ‘as-ifness’, word problems introduce pupils to a make-believe world. The text consists only of ‘filler words’ because what really matters are the figures. Word problems and possibly other aspects of schooling can be interpreted in terms of a utilitarian make-believe key. Readiness to adopt this make-believe frame when required may be the difference between school success and failure. I argue that maths achievement takes more than just ‘being good with numbers’. It is a joint enterprise of people interacting within a culturally-shaped setting, organized so as to make some phenomena stand out rather than others. Finally, I argue that ‘word problems and possibly other ‘school genres’ could be added to the list of utilitarian make-believe frames provided by Goffman.

Mathematics-for-teaching: Insights from the case of annuities

Directory of Open Access Journals (Sweden)

Craig Pournara

2014-11-01

Full Text Available Shulman’s notations of subject matter knowledge (SMK and pedagogical content knowledge (PCK have been very influential in education research on teachers’ knowledge for teaching. However, there is little empirical evidence in support of these as separate analytical constructs. Furthermore, attempts to distinguish SMK and PCK highlight the complex and multidimensional nature of teachers’ knowledge and hence the difficulty of separating SMK and PCK. The author adopts the notion of mathematics-for-teaching (MfT and argues that teachers’ knowledge for teaching annuities comprises knowledge of mathematical aspects, knowledge of pedagogical aspects and contextual knowledge of finance. Drawing from a larger study in which the author taught a financial mathematics course to pre-service secondary mathematics teachers, four examples of teachers’ knowledge for teaching annuities are identified, each of which illustrates how knowledge of mathematics, knowledge of pedagogy and contextual knowledge of finance are intertwined.

Study orientation and knowledge of basic vocabulary in Mathematics in the primary school

Directory of Open Access Journals (Sweden)

Marthie van der Walt

2009-09-01

mathematics on secondary and tertiary levels. The aim of this research was to investigate the extent to which the performance in study orientation (Study Orientation questionnaire in Mathematics (Primary and knowledge of basic vocabulary/terminology in mathematics (Mathematics Vocabulary (Primary (vocabulary as one aspect of language in Mathematics of Grade 4 to 7 learners predict performance in mathematics (Basic Mathematics (Primary. Three standardised questionnaires were administered, namely the Study Orientation questionnaire in Mathematics (Primary, or SOM(P, Mathematics Vocabulary (Primary or (MV(P, and Basic Mathematics (Primary or BM(P. The participants consisted of learners in Grade 4 to 7 (n = 1 103 in North-West Province with respectively Afrikaans, English and Tswana as their home language. Results from the data, by calculating intercorrelations and stepwise regression, confirmed that learners’ performance in mathematics (BM(P can be predicted through their performance in the knowledge of basic vocabulary in mathematics (MV(P, their “maths” anxiety, study attitude towards and study habits in mathematics (SOM(P. The results can be implemented to improve learners’ performance in mathematics when teachers identify inadequate knowledge of basic vocabulary in mathematics as well as study orientation (for example, “maths” anxiety, study attitude towards and study habits in mathematics in the early years of schooling. Learners’ scores can be checked to identify those requiring aid, support, remediation and/or counselling. An analysis of individual answers (particularly those where learner’s replies differ significantly in respect of the answers usually given by good achievers in mathematics could be extremely useful. Enculturing learners to the vocabulary of mathematical language is an aspect of instruction that needs specific attention. The three questionnaires, which are administered in this research, provide mathematics teachers with standardised

PROGRAMMING FUNDAMENTALS TEACHING TO THE STUDENTS OF PHYSICO-MATHEMATICAL PROFILE

Directory of Open Access Journals (Sweden)

Vdovychyn Tatiana

2017-05-01

Full Text Available The article provides methodical recommendations on studying of the discipline "Informatics" for the specialists preparation of the first (Bachelor level of higher education of the field of knowledge 01 "Education" of the specialty 014.04 "Secondary education (mathematics", 014.08 "Secondary education (physics". This discipline plays a particularly important role in the higher education establishments physical and mathematical field specialists training, since it combines both the fundamental concepts and principles of various mathematical and informatics disciplines, as well as applied models and algorithms for their application. The methodological aspects of the discipline "Informatics" study include the pedagogical feasibility of the forms, methods and means of training for students who are qualified as a teacher of mathematics and a physics teacher respectively. The discipline program includes issues on informatics theoretical foundations, applied software, and the basics of programming. Students are encouraged to consider the basics of programming in the C ++ environment. Basic C ++ language designs have a convenient, professional programming toolkit. Integrated C ++ environment is characterized by speed, convenience in debugging and compiling of the program. Therefore, the article focuses on the practical skills formation in the C ++ environment for the students of the physical and mathematical profile and highlights the methodological aspects of the C ++ programming language use in the course of the discipline "Informatics" teaching. The formation of practical skills takes place during the performance of laboratory works, namely: the original problem setting, the construction of an algorithm for its solution, analysis of the received results.

Mathematics for physical chemistry

CERN Document Server

Mortimer, Robert G

2005-01-01

Mathematics for Physical Chemistry, Third Edition, is the ideal text for students and physical chemists who want to sharpen their mathematics skills. It can help prepare the reader for an undergraduate course, serve as a supplementary text for use during a course, or serve as a reference for graduate students and practicing chemists. The text concentrates on applications instead of theory, and, although the emphasis is on physical chemistry, it can also be useful in general chemistry courses. The Third Edition includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The first ten chapters are constructed around a sequence of mathematical topics, with a gradual progression into more advanced material. The final chapter discusses mathematical topics needed in the analysis of experimental data.* Numerous examples and problems interspersed throughout the presentations * Each extensive chapter contains a preview, objectives, and ...

Gender Differences in Boys' and Girls' Perception of Teaching and Learning Mathematics

Science.gov (United States)

Samuelsson, Marcus; Samuelsson, Joakim

2016-01-01

Gender differences between boys and girls in the perception of the classroom setting, and their relationship to achievement in mathematics and aspects of self-regulated learning skills are the focus for this article. Throughout the component analysis of answers from 6758 Swedish students we found some differences in how boys and girls perceive…

Mathematics of large eddy simulation of turbulent flows

Energy Technology Data Exchange (ETDEWEB)

Berselli, L.C. [Pisa Univ. (Italy). Dept. of Applied Mathematics ' ' U. Dini' ' ; Iliescu, T. [Virginia Polytechnic Inst. and State Univ., Blacksburg, VA (United States). Dept. of Mathematics; Layton, W.J. [Pittsburgh Univ., PA (United States). Dept. of Mathematics

2006-07-01

Large eddy simulation (LES) is a method of scientific computation seeking to predict the dynamics of organized structures in turbulent flows by approximating local, spatial averages of the flow. Since its birth in 1970, LES has undergone an explosive development and has matured into a highly-developed computational technology. It uses the tools of turbulence theory and the experience gained from practical computation. This book focuses on the mathematical foundations of LES and its models and provides a connection between the powerful tools of applied mathematics, partial differential equations and LES. Thus, it is concerned with fundamental aspects not treated so deeply in the other books in the field, aspects such as well-posedness of the models, their energy balance and the connection to the Leray theory of weak solutions of the Navier-Stokes equations. The authors give a mathematically informed and detailed treatment of an interesting selection of models, focusing on issues connected with understanding and expanding the correctness and universality of LES. This volume offers a useful entry point into the field for PhD students in applied mathematics, computational mathematics and partial differential equations. Non-mathematicians will appreciate it as a reference that introduces them to current tools and advances in the mathematical theory of LES. (orig.)

Concept Map as an Assessment Tool in Secondary School Mathematics: An Analysis of Teachers' Perspectives

Science.gov (United States)

Mutodi, Paul; Chigonga, Benard

2016-01-01

This paper reports on teachers' views on concept mapping: its applicability; reliability; advantages and; difficulties. A close-ended questionnaire was administered to 50 purposefully selected secondary school mathematics teachers from Sekhukhune District, Limpopo, South Africa. The findings indicate that mathematics teachers generally perceive…

Tenth-Grade High School Students' Mathematical Self-Efficacy, Mathematics Anxiety, Attitudes toward Mathematics, and Performance on the New York State Integrated Algebra Regents Examination

Science.gov (United States)

Catapano, Michael

2013-01-01

Strong mathematical abilities are important for the continuation of a successful society. Mathematics is required and involved in all aspects of daily life: banking, communications, business, education, and travel are just a few examples. More specifically the areas of finance, engineering, architecture, and technology require individuals with…

Organisational aspects of dental practices: do dental students think like patients or like general dental practitioners?

Science.gov (United States)

Sonneveld, R E; Brands, W G; Bronkhorst, E M; Welie, J V M; Truin, G J

2013-02-01

In view of transparency in health care, the widespread desire for more patient-centred care, and in an attempt to facilitate educational programmes that effectively respond to these changes, two research questions are formulated: (i) How do dental students rate the importance of various organisational aspects of dental practices compared with dental patients and general dental practitioners (GDPs), and what prescripts, defined as specific operational responsibilities of GDPs in these matters, do dental students propose? and (ii) In doing so, do students resemble patients or GDPs? In two survey studies, dental students (n = 198), patients (n = 3127) and GDPs (n = 303) were asked to rate by questionnaire the importance of 41 organisational aspects of a general dental practice and proposed specific operational responsibilities ('prescripts'). Seven of 41 aspects were rated as important by the majority of the students. Although in a different rank order, three aspects were predominantly selected by all three groups: continuing education, accessibility by telephone and Dutch-speaking GDP. For most aspects, significant differences were found between the prescripts proposed by students and those proposed by patients, and few differences were found between students and GDPs. The findings do not permit the general conclusion that the views of dental students resemble those of patients or GPDs. Looking at the overall rank order, the three respondent groups showed a great resemblance although significant differences were found for specific aspects. With regard to the proposed prescripts, students showed realistic views and the majority wants to participate in continuing education and work with protocols and guidelines. In this, they tend to resemble GDPs more than they resemble patients. © 2012 John Wiley & Sons A/S.

APPLYING PROFESSIONALLY ORIENTED PROBLEMS OF MATHEMATICAL MODELING IN TEACHING STUDENTS OF ENGINEERING DEPARTMENTS

Directory of Open Access Journals (Sweden)

Natal’ya Yur’evna Gorbunova

2017-06-01

Full Text Available We described several aspects of organizing student research work, as well as solving a number of mathematical modeling problems: professionally-oriented, multi-stage, etc. We underlined the importance of their economic content. Samples of using such problems in teaching Mathematics at agricultural university were given. Several questions connected with information material selection and peculiarities of research problems application were described. Purpose. The author aims to show the possibility and necessity of using professionally-oriented problems of mathematical modeling in teaching Mathematics at agricultural university. The subject of analysis is including such problems into educational process. Methodology. The main research method is dialectical method of obtaining knowledge of finding approaches to selection, writing and using mathematical modeling and professionally-oriented problems in educational process; the methodology is study of these methods of obtaining knowledge. Results. As a result of analysis of literature, students opinions, observation of students work, and taking into account personal teaching experience, it is possible to make conclusion about importance of using mathematical modeling problems, as it helps to systemize theoretical knowledge, apply it to practice, raise students study motivation in engineering sphere. Practical implications. Results of the research can be of interest for teachers of Mathematics in preparing Bachelor and Master students of engineering departments of agricultural university both for theoretical research and for modernization of study courses.

Mathematical aspects of ground state tunneling models in luminescence materials

International Nuclear Information System (INIS)

Pagonis, Vasilis; Kitis, George

2015-01-01

Luminescence signals from a variety of natural materials have been known to decrease with storage time at room temperature due to quantum tunneling, a phenomenon known as anomalous fading. This paper is a study of several mathematical aspects of two previously published luminescence models which describe tunneling phenomena from the ground state of a donor–acceptor system. It is shown that both models are described by the same type of integral equation, and two new analytical equations are presented. The first new analytical equation describes the effect of anomalous fading on the dose response curves (DRCs) of naturally irradiated samples. The DRCs in the model were previously expressed in the form of integral equations requiring numerical integration, while the new analytical equation can be used immediately as a tool for analyzing experimental data. The second analytical equation presented in this paper describes the anomalous fading rate (g-Value per decade) as a function of the charge density in the model. This new analytical expression for the g-Value is tested using experimental anomalous fading data for several apatite crystals which exhibit high rate of anomalous fading. The two new analytical results can be useful tools for analyzing anomalous fading data from luminescence materials. In addition to the two new analytical equations, an explanation is provided for the numerical value of a constant previously introduced in the models. - Highlights: • Comparative study of two luminescence models for feldspars. • Two new analytical equations for dose response curves and anomalous fading rate. • The numerical value z=1.8 of previously introduced constant in models explained.

Mathematical methods in the theory of queuing

CERN Document Server

Khinchin, A Y; Quenouille, M H

2013-01-01

Written by a prominent Russian mathematician, this concise monograph examines aspects of queuing theory as an application of probability. The three-part treatment begins with a study of the stream of incoming demands (or ""calls,"" in the author's terminology). Subsequent sections explore systems with losses and systems allowing delay. Prerequisites include a familiarity with the theory of probability and mathematical analysis. A. Y. Khinchin made significant contributions to probability theory, statistical physics, and several other fields. His elegant, groundbreaking work will prove of subs

Mathematics and communication skills using educational software in math classes

Directory of Open Access Journals (Sweden)

Marjolis Laffita-Cuza

2017-04-01

Full Text Available The current transformations conceive among others, to form in the race of Mathematics-Physics a professor who imparts indistinctly the subjects of Mathematics and Physics in the upper secondary education from the third year of this race which requires putting more emphasis in the orientation of those Subjects to achieve greater professionalism. The present paper approaches from the theoretical aspects the essential aspects in the educational process of the learning of mathematics for the Mathematics-Physics career of the university of pedagogical sciences such as mathematical communicative competences and the use of educational software, all in function of achieving A greater development of student's mathematical logical thinking.

The Object Metaphor and Synecdoche in Mathematics Classroom Discourse

Science.gov (United States)

Font, Vicenc; Godino, Juan D.; Planas, Nuria; Acevedo, Jorge I.

2010-01-01

This article describes aspects of classroom discourse, illustrated through vignettes, that reveal the complex relationship between the forms in which mathematical objects exist and their ostensive representations. We illustrate various aspects of the process through which students come to consider the reality of mathematical objects that are…

Aspect of the conformal invariance

International Nuclear Information System (INIS)

Bauer, M.

1990-11-01

This thesis is about the study of several physical and mathematical aspects of critical phenomena at two dimensions. These phenomena have remarkable symmetry properties in the coordonnates changes keeping the angles. They are named conformal theories

Numerical capacities as domain-specific predictors beyond early mathematics learning: a longitudinal study.

Science.gov (United States)

Reigosa-Crespo, Vivian; González-Alemañy, Eduardo; León, Teresa; Torres, Rosario; Mosquera, Raysil; Valdés-Sosa, Mitchell

2013-01-01

The first aim of the present study was to investigate whether numerical effects (Numerical Distance Effect, Counting Effect and Subitizing Effect) are domain-specific predictors of mathematics development at the end of elementary school by exploring whether they explain additional variance of later mathematics fluency after controlling for the effects of general cognitive skills, focused on nonnumerical aspects. The second aim was to address the same issues but applied to achievement in mathematics curriculum that requires solutions to fluency in calculation. These analyses assess whether the relationship found for fluency are generalized to mathematics content beyond fluency in calculation. As a third aim, the domain specificity of the numerical effects was examined by analyzing whether they contribute to the development of reading skills, such as decoding fluency and reading comprehension, after controlling for general cognitive skills and phonological processing. Basic numerical capacities were evaluated in children of 3(rd) and 4(th) grades (n=49). Mathematics and reading achievements were assessed in these children one year later. Results showed that the size of the Subitizing Effect was a significant domain-specific predictor of fluency in calculation and also in curricular mathematics achievement, but not in reading skills, assessed at the end of elementary school. Furthermore, the size of the Counting Effect also predicted fluency in calculation, although this association only approached significance. These findings contrast with proposals that the core numerical competencies measured by enumeration will bear little relationship to mathematics achievement. We conclude that basic numerical capacities constitute domain-specific predictors and that they are not exclusively "start-up" tools for the acquisition of Mathematics; but they continue modulating this learning at the end of elementary school.

Introduction to Generalized Functions with Applications in Aerodynamics and Aeroacoustics

Science.gov (United States)

Farassat, F.

1994-01-01

Generalized functions have many applications in science and engineering. One useful aspect is that discontinuous functions can be handled as easily as continuous or differentiable functions and provide a powerful tool in formulating and solving many problems of aerodynamics and acoustics. Furthermore, generalized function theory elucidates and unifies many ad hoc mathematical approaches used by engineers and scientists. We define generalized functions as continuous linear functionals on the space of infinitely differentiable functions with compact support, then introduce the concept of generalized differentiation. Generalized differentiation is the most important concept in generalized function theory and the applications we present utilize mainly this concept. First, some results of classical analysis, are derived with the generalized function theory. Other applications of the generalized function theory in aerodynamics discussed here are the derivations of general transport theorems for deriving governing equations of fluid mechanics, the interpretation of the finite part of divergent integrals, the derivation of the Oswatitsch integral equation of transonic flow, and the analysis of velocity field discontinuities as sources of vorticity. Applications in aeroacoustics include the derivation of the Kirchhoff formula for moving surfaces, the noise from moving surfaces, and shock noise source strength based on the Ffowcs Williams-Hawkings equation.

Methods of applied mathematics with a software overview

CERN Document Server

Davis, Jon H

2016-01-01

This textbook, now in its second edition, provides students with a firm grasp of the fundamental notions and techniques of applied mathematics as well as the software skills to implement them. The text emphasizes the computational aspects of problem solving as well as the limitations and implicit assumptions inherent in the formal methods. Readers are also given a sense of the wide variety of problems in which the presented techniques are useful. Broadly organized around the theme of applied Fourier analysis, the treatment covers classical applications in partial differential equations and boundary value problems, and a substantial number of topics associated with Laplace, Fourier, and discrete transform theories. Some advanced topics are explored in the final chapters such as short-time Fourier analysis and geometrically based transforms applicable to boundary value problems. The topics covered are useful in a variety of applied fields such as continuum mechanics, mathematical physics, control theory, and si...

The quantitation of buffering action II. Applications of the formal & general approach

Science.gov (United States)

Schmitt, Bernhard M

2005-01-01

Background The paradigm of "buffering" originated in acid-base physiology, but was subsequently extended to other fields and is now used for a wide and diverse set of phenomena. In the preceding article, we have presented a formal and general approach to the quantitation of buffering action. Here, we use that buffering concept for a systematic treatment of selected classical and other buffering phenomena. Results H+ buffering by weak acids and "self-buffering" in pure water represent "conservative buffered systems" whose analysis reveals buffering properties that contrast in important aspects from classical textbook descriptions. The buffering of organ perfusion in the face of variable perfusion pressure (also termed "autoregulation") can be treated in terms of "non-conservative buffered systems", the general form of the concept. For the analysis of cytoplasmic Ca++ concentration transients (also termed "muffling"), we develop a related unit that is able to faithfully reflect the time-dependent quantitative aspect of buffering during the pre-steady state period. Steady-state buffering is shown to represent the limiting case of time-dependent muffling, namely for infinitely long time intervals and infinitely small perturbations. Finally, our buffering concept provides a stringent definition of "buffering" on the level of systems and control theory, resulting in four absolute ratio scales for control performance that are suited to measure disturbance rejection and setpoint tracking, and both their static and dynamic aspects. Conclusion Our concept of buffering provides a powerful mathematical tool for the quantitation of buffering action in all its appearances. PMID:15771784

Mathematical methods in time series analysis and digital image processing

CERN Document Server

Kurths, J; Maass, P; Timmer, J

2008-01-01

The aim of this volume is to bring together research directions in theoretical signal and imaging processing developed rather independently in electrical engineering, theoretical physics, mathematics and the computer sciences. In particular, mathematically justified algorithms and methods, the mathematical analysis of these algorithms, and methods as well as the investigation of connections between methods from time series analysis and image processing are reviewed. An interdisciplinary comparison of these methods, drawing upon common sets of test problems from medicine and geophysical/enviromental sciences, is also addressed. This volume coherently summarizes work carried out in the field of theoretical signal and image processing. It focuses on non-linear and non-parametric models for time series as well as on adaptive methods in image processing.

Effective Mathematics Teaching in Finnish and Swedish Teacher Education Discourses

Science.gov (United States)

Hemmi, Kirsti; Ryve, Andreas

2015-01-01

This article explores effective mathematics teaching as constructed in Finnish and Swedish teacher educators' discourses. Based on interview data from teacher educators as well as data from feedback discussions between teacher educators and prospective teachers in Sweden and Finland, the analysis shows that several aspects of the recent…

Protocol Analysis of Group Problem Solving in Mathematics: A Cognitive-Metacognitive Framework for Assessment.

Science.gov (United States)

Artzt, Alice F.; Armour-Thomas, Eleanor

The roles of cognition and metacognition were examined in the mathematical problem-solving behaviors of students as they worked in small groups. As an outcome, a framework that links the literature of cognitive science and mathematical problem solving was developed for protocol analysis of mathematical problem solving. Within this framework, each…

Analysis mathematical literacy skills in terms of the students’ metacognition on PISA-CPS model

Science.gov (United States)

Ovan; Waluya, S. B.; Nugroho, S. E.

2018-03-01

This research was aimed to know the effectiveness of PISA-CPS model and desceibe the mathematical literacy skills (KLM) in terms of the students’ metacognition. This study used Mixed Methods approaches with the concurrent embedded desaign. The technique of data analysis on quantitative research done analysis of lesson plan, prerequisite test, test hypotesis 1 and hypotesis test. While qualitative research done data reduction, data presentation, and drawing conclution and data verification. The subject of this study was the students of Grade Eight (VIII) of SMP Islam Sultan Agung 4 Semarang, Central Java. The writer analyzed the data with quantitative and qualitative approaches based on the metacognition of the students in low, medium and high groups. Subsequently, taken the mathematical literacy skills (KLM) from students’ metacognition in low, medium, and high . The results of the study showed that the PISA-CPS model was complete and the students’ mathematical literacy skills in terms of the students’ metacognition taught by the PISA-CPS model was higher than the expository learning. metacognitions’ students classified low hadmathematical literacy skills (KLM) less good, metacognitions’ students classified medium had mathematical literacy skills (KLM) good enough, metacognitions’ students classified high had mathematical literacy skills (KLM) very good. Based onresult analysis got conclusion that the PISA-CPS model was effective toward the students’ mathematical literacy skills (KLM). To increase the students’ mathematical literacy skills (KLM), the teachers need to provide reinforcements in the form of the exercises so that the student’s mathematical literacy was achieved at level 5 and level 6.

Formal aspects of resilience

Directory of Open Access Journals (Sweden)

Diana-Maria Drigă

2015-12-01

Full Text Available The concept of resilience has represented during the recent years a leading concern both in Romania, within the European Union and worldwide. Specialists in economics, management, finance, legal sciences, political sciences, sociology, psychology, grant a particular interest to this concept. Multidisciplinary research of resilience has materialized throughout the time in multiple conceptualizations and theorizing, but without being a consensus between specialists in terms of content, specificity and scope. Through this paper it is intended to clarify the concept of resilience, achieving an exploration of the evolution of this concept in ecological, social and economic environment. At the same time, the paper presents aspects of feedback mechanisms and proposes a formalization of resilience using the logic and mathematical analysis.

Some medical aspects of radionuclide intakes

International Nuclear Information System (INIS)

Poda, G.A.

1983-01-01

In the field of medicine, particularly industrial medicine, the radiation aspect of the practice probably takes about 1/10 of 1% of our time. All the health physicist's tools of principles of internal dosimetry, lung models, mathematics, chemistry, etc. have little meaning until applied to an individual who has had an intake. This article discusses some of the medical aspects of internal dosimetry

The contribution of several Nobel Laureates in the development of the Theory of general economic equilibrium

Directory of Open Access Journals (Sweden)

Florentina Xhelili Krasniqi

2016-12-01

Full Text Available Nobel Laureates with their contributions to the development of the theory of general equilibrium have enabled this theory to be one of the most important for theoretical and practical analysis of the overall economy and the efficient use of economic resources. Results of the research showing that contributions of Nobel Laureates in the economy belong to two main frameworks of development of the general equilibrium theory: one was the mathematical model of general equilibrium developed by John R. Hicks (1939, Kenneth J.Arrow (1951 and Gerard Debreu (1954 and second frames of general equilibrium belongs to Paul A. Samuelson (1958. To highlight the contributions of these Nobel laureates in the development of the theory of general equilibrium have been selected and are presented in the paper some views, estimates and assumptions that have contributed not only in solving concrete problems, but also to the development of economic science in general. Their works represent a synthesis of theoretical and practical aspects of treatment of general equilibrium which are the starting point for further research in this field.

On the Formal-Logical Analysis of the Foundations of Mathematics Applied to Problems in Physics

Science.gov (United States)

Kalanov, Temur Z.

2016-03-01

Analysis of the foundations of mathematics applied to problems in physics was proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that critical analysis of the concept of mathematical quantity - central concept of mathematics - leads to the following conclusion: (1) The concept of ``mathematical quantity'' is the result of the following mental operations: (a) abstraction of the ``quantitative determinacy of physical quantity'' from the ``physical quantity'' at that the ``quantitative determinacy of physical quantity'' is an independent object of thought; (b) abstraction of the ``amount (i.e., abstract number)'' from the ``quantitative determinacy of physical quantity'' at that the ``amount (i.e., abstract number)'' is an independent object of thought. In this case, unnamed, abstract numbers are the only sign of the ``mathematical quantity''. This sign is not an essential sign of the material objects. (2) The concept of mathematical quantity is meaningless, erroneous, and inadmissible concept in science because it represents the following formal-logical and dialectical-materialistic error: negation of the existence of the essential sign of the concept (i.e., negation of the existence of the essence of the concept) and negation of the existence of measure of material object.