Introduction to mathematical statistical physics
Minlos, R A
1999-01-01
This book presents a mathematically rigorous approach to the main ideas and phenomena of statistical physics. The introduction addresses the physical motivation, focussing on the basic concept of modern statistical physics, that is the notion of Gibbsian random fields. Properties of Gibbsian fields are analyzed in two ranges of physical parameters: "regular" (corresponding to high-temperature and low-density regimes) where no phase transition is exhibited, and "singular" (low temperature regimes) where such transitions occur. Next, a detailed approach to the analysis of the phenomena of phase transitions of the first kind, the Pirogov-Sinai theory, is presented. The author discusses this theory in a general way and illustrates it with the example of a lattice gas with three types of particles. The conclusion gives a brief review of recent developments arising from this theory. The volume is written for the beginner, yet advanced students will benefit from it as well. The book will serve nicely as a supplement...
Methods of contemporary mathematical statistical physics
2009-01-01
This volume presents a collection of courses introducing the reader to the recent progress with attention being paid to laying solid grounds and developing various basic tools. An introductory chapter on lattice spin models is useful as a background for other lectures of the collection. The topics include new results on phase transitions for gradient lattice models (with introduction to the techniques of the reflection positivity), stochastic geometry reformulation of classical and quantum Ising models, the localization/delocalization transition for directed polymers. A general rigorous framework for theory of metastability is presented and particular applications in the context of Glauber and Kawasaki dynamics of lattice models are discussed. A pedagogical account of several recently discussed topics in nonequilibrium statistical mechanics with an emphasis on general principles is followed by a discussion of kinetically constrained spin models that are reflecting important peculiar features of glassy dynamic...
Pestman, Wiebe R
2009-01-01
This textbook provides a broad and solid introduction to mathematical statistics, including the classical subjects hypothesis testing, normal regression analysis, and normal analysis of variance. In addition, non-parametric statistics and vectorial statistics are considered, as well as applications of stochastic analysis in modern statistics, e.g., Kolmogorov-Smirnov testing, smoothing techniques, robustness and density estimation. For students with some elementary mathematical background. With many exercises. Prerequisites from measure theory and linear algebra are presented.
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.
Guénault, Tony
2007-01-01
In this revised and enlarged second edition of an established text Tony Guénault provides a clear and refreshingly readable introduction to statistical physics, an essential component of any first degree in physics. The treatment itself is self-contained and concentrates on an understanding of the physical ideas, without requiring a high level of mathematical sophistication. A straightforward quantum approach to statistical averaging is adopted from the outset (easier, the author believes, than the classical approach). The initial part of the book is geared towards explaining the equilibrium properties of a simple isolated assembly of particles. Thus, several important topics, for example an ideal spin-½ solid, can be discussed at an early stage. The treatment of gases gives full coverage to Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein statistics. Towards the end of the book the student is introduced to a wider viewpoint and new chapters are included on chemical thermodynamics, interactions in, for exam...
Geroch, Robert
1985-01-01
Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the ""whys"" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle
Mandl, Franz
1988-01-01
The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition E. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A. C. Phillips Computing for Scient
Sadovskii, Michael V
2012-01-01
This volume provides a compact presentation of modern statistical physics at an advanced level. Beginning with questions on the foundations of statistical mechanics all important aspects of statistical physics are included, such as applications to ideal gases, the theory of quantum liquids and superconductivity and the modern theory of critical phenomena. Beyond that attention is given to new approaches, such as quantum field theory methods and non-equilibrium problems.
Tayurskii, Dmitrii; Abe, Sumiyoshi; Alexandre Wang, Q.
2012-11-01
The 3rd International Workshop on Statistical Physics and Mathematics for Complex Systems (SPMCS2012) was held between 25-30 August at Kazan (Volga Region) Federal University, Kazan, Russian Federation. This workshop was jointly organized by Kazan Federal University and Institut Supérieur des Matériaux et Mécaniques Avancées (ISMANS), France. The series of SPMCS workshops was created in 2008 with the aim to be an interdisciplinary incubator for the worldwide exchange of innovative ideas and information about the latest results. The first workshop was held at ISMANS, Le Mans (France) in 2008, and the third at Huazhong Normal University, Wuhan (China) in 2010. At SPMCS2012, we wished to bring together a broad community of researchers from the different branches of the rapidly developing complexity science to discuss the fundamental theoretical challenges (geometry/topology, number theory, statistical physics, dynamical systems, etc) as well as experimental and applied aspects of many practical problems (condensed matter, disordered systems, financial markets, chemistry, biology, geoscience, etc). The program of SPMCS2012 was prepared based on three categories: (i) physical and mathematical studies (quantum mechanics, generalized nonequilibrium thermodynamics, nonlinear dynamics, condensed matter physics, nanoscience); (ii) natural complex systems (physical, geophysical, chemical and biological); (iii) social, economical, political agent systems and man-made complex systems. The conference attracted 64 participants from 10 countries. There were 10 invited lectures, 12 invited talks and 28 regular oral talks in the morning and afternoon sessions. The book of Abstracts is available from the conference website (http://www.ksu.ru/conf/spmcs2012/?id=3). A round table was also held, the topic of which was 'Recent and Anticipated Future Progress in Science of Complexity', discussing a variety of questions and opinions important for the understanding of the concept of
Wannier, Gregory Hugh
1966-01-01
Until recently, the field of statistical physics was traditionally taught as three separate subjects: thermodynamics, statistical mechanics, and kinetic theory. This text, a forerunner in its field and now a classic, was the first to recognize the outdated reasons for their separation and to combine the essentials of the three subjects into one unified presentation of thermal physics. It has been widely adopted in graduate and advanced undergraduate courses, and is recommended throughout the field as an indispensable aid to the independent study and research of statistical physics.Designed for
Theoretical physics 8 statistical physics
Nolting, Wolfgang
2018-01-01
This textbook offers a clear and comprehensive introduction to statistical physics, one of the core components of advanced undergraduate physics courses. It follows on naturally from the previous volumes in this series, using methods of probability theory and statistics to solve physical problems. The first part of the book gives a detailed overview on classical statistical physics and introduces all mathematical tools needed. The second part of the book covers topics related to quantized states, gives a thorough introduction to quantum statistics, followed by a concise treatment of quantum gases. Ideally suited to undergraduate students with some grounding in quantum mechanics, the book is enhanced throughout with learning features such as boxed inserts and chapter summaries, with key mathematical derivations highlighted to aid understanding. The text is supported by numerous worked examples and end of chapter problem sets. About the Theoretical Physics series Translated from the renowned and highly successf...
Experimental Mathematics and Computational Statistics
Energy Technology Data Exchange (ETDEWEB)
Bailey, David H.; Borwein, Jonathan M.
2009-04-30
The field of statistics has long been noted for techniques to detect patterns and regularities in numerical data. In this article we explore connections between statistics and the emerging field of 'experimental mathematics'. These includes both applications of experimental mathematics in statistics, as well as statistical methods applied to computational mathematics.
Statistical Physics An Introduction
Yoshioka, Daijiro
2007-01-01
This book provides a comprehensive presentation of the basics of statistical physics. The first part explains the essence of statistical physics and how it provides a bridge between microscopic and macroscopic phenomena, allowing one to derive quantities such as entropy. Here the author avoids going into details such as Liouville’s theorem or the ergodic theorem, which are difficult for beginners and unnecessary for the actual application of the statistical mechanics. In the second part, statistical mechanics is applied to various systems which, although they look different, share the same mathematical structure. In this way readers can deepen their understanding of statistical physics. The book also features applications to quantum dynamics, thermodynamics, the Ising model and the statistical dynamics of free spins.
Blessing of dimensionality: mathematical foundations of the statistical physics of data.
Gorban, A N; Tyukin, I Y
2018-04-28
The concentrations of measure phenomena were discovered as the mathematical background to statistical mechanics at the end of the nineteenth/beginning of the twentieth century and have been explored in mathematics ever since. At the beginning of the twenty-first century, it became clear that the proper utilization of these phenomena in machine learning might transform the curse of dimensionality into the blessing of dimensionality This paper summarizes recently discovered phenomena of measure concentration which drastically simplify some machine learning problems in high dimension, and allow us to correct legacy artificial intelligence systems. The classical concentration of measure theorems state that i.i.d. random points are concentrated in a thin layer near a surface (a sphere or equators of a sphere, an average or median-level set of energy or another Lipschitz function, etc.). The new stochastic separation theorems describe the thin structure of these thin layers: the random points are not only concentrated in a thin layer but are all linearly separable from the rest of the set, even for exponentially large random sets. The linear functionals for separation of points can be selected in the form of the linear Fisher's discriminant. All artificial intelligence systems make errors. Non-destructive correction requires separation of the situations (samples) with errors from the samples corresponding to correct behaviour by a simple and robust classifier. The stochastic separation theorems provide us with such classifiers and determine a non-iterative (one-shot) procedure for their construction.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).
Blessing of dimensionality: mathematical foundations of the statistical physics of data
Gorban, A. N.; Tyukin, I. Y.
2018-04-01
The concentrations of measure phenomena were discovered as the mathematical background to statistical mechanics at the end of the nineteenth/beginning of the twentieth century and have been explored in mathematics ever since. At the beginning of the twenty-first century, it became clear that the proper utilization of these phenomena in machine learning might transform the curse of dimensionality into the blessing of dimensionality. This paper summarizes recently discovered phenomena of measure concentration which drastically simplify some machine learning problems in high dimension, and allow us to correct legacy artificial intelligence systems. The classical concentration of measure theorems state that i.i.d. random points are concentrated in a thin layer near a surface (a sphere or equators of a sphere, an average or median-level set of energy or another Lipschitz function, etc.). The new stochastic separation theorems describe the thin structure of these thin layers: the random points are not only concentrated in a thin layer but are all linearly separable from the rest of the set, even for exponentially large random sets. The linear functionals for separation of points can be selected in the form of the linear Fisher's discriminant. All artificial intelligence systems make errors. Non-destructive correction requires separation of the situations (samples) with errors from the samples corresponding to correct behaviour by a simple and robust classifier. The stochastic separation theorems provide us with such classifiers and determine a non-iterative (one-shot) procedure for their construction. This article is part of the theme issue `Hilbert's sixth problem'.
Riandry, M. A.; Ismet, I.; Akhsan, H.
2017-09-01
This study aims to produce a valid and practical statistical physics course handout on distribution function materials based on STEM. Rowntree development model is used to produce this handout. The model consists of three stages: planning, development and evaluation stages. In this study, the evaluation stage used Tessmer formative evaluation. It consists of 5 stages: self-evaluation, expert review, one-to-one evaluation, small group evaluation and field test stages. However, the handout is limited to be tested on validity and practicality aspects, so the field test stage is not implemented. The data collection technique used walkthroughs and questionnaires. Subjects of this study are students of 6th and 8th semester of academic year 2016/2017 Physics Education Study Program of Sriwijaya University. The average result of expert review is 87.31% (very valid category). One-to-one evaluation obtained the average result is 89.42%. The result of small group evaluation is 85.92%. From one-to-one and small group evaluation stages, averagestudent response to this handout is 87,67% (very practical category). Based on the results of the study, it can be concluded that the handout is valid and practical.
Basics of modern mathematical statistics
Spokoiny, Vladimir
2015-01-01
This textbook provides a unified and self-contained presentation of the main approaches to and ideas of mathematical statistics. It collects the basic mathematical ideas and tools needed as a basis for more serious studies or even independent research in statistics. The majority of existing textbooks in mathematical statistics follow the classical asymptotic framework. Yet, as modern statistics has changed rapidly in recent years, new methods and approaches have appeared. The emphasis is on finite sample behavior, large parameter dimensions, and model misspecifications. The present book provides a fully self-contained introduction to the world of modern mathematical statistics, collecting the basic knowledge, concepts and findings needed for doing further research in the modern theoretical and applied statistics. This textbook is primarily intended for graduate and postdoc students and young researchers who are interested in modern statistical methods.
Mathematics for physics with calculus
Das, Biman
2005-01-01
Designed for students who plan to take or who are presently taking calculus-based physics courses. This book will develop necessary mathematical skills and help students gain the competence to use precalculus, calculus, vector algebra, vector calculus, and the statistical analysis of experimental data. Students taking intermediate physics, engineering, and other science courses will also find the book useful-and will be able to use the book as a mathematical resource for these intermediate level courses. The book emphasizes primarily the use of mathematical techniques and mathematical concepts in Physics and does not go into their rigorous developments.
Mathematical statistics and stochastic processes
Bosq, Denis
2013-01-01
Generally, books on mathematical statistics are restricted to the case of independent identically distributed random variables. In this book however, both this case AND the case of dependent variables, i.e. statistics for discrete and continuous time processes, are studied. This second case is very important for today's practitioners.Mathematical Statistics and Stochastic Processes is based on decision theory and asymptotic statistics and contains up-to-date information on the relevant topics of theory of probability, estimation, confidence intervals, non-parametric statistics and rob
Nuclear physics mathematical methods
International Nuclear Information System (INIS)
Balian, R.; Gervois, A.; Giannoni, M.J.; Levesque, D.; Maille, M.
1984-01-01
The nuclear physics mathematical methods, applied to the collective motion theory, to the reduction of the degrees of freedom and to the order and disorder phenomena; are investigated. In the scope of the study, the following aspects are discussed: the entropy of an ensemble of collective variables; the interpretation of the dissipation, applying the information theory; the chaos and the universality; the Monte-Carlo method applied to the classical statistical mechanics and quantum mechanics; the finite elements method, and the classical ergodicity [fr
Manin, Yu I
1981-01-01
A bird's eye view of mathematics ; physical quantities, dimensions and constants : the source of numbers in physics ; a drop of milk : observer, observation, observable and unobservable ; space-time as a physical system ; action and symmetry.
Mathematics for physical chemistry
Mortimer, Robert G
2013-01-01
Mathematics for Physical Chemistry is the ideal supplementary text for practicing chemists and students who want to sharpen their mathematics skills while enrolled in general through physical chemistry courses. This book specifically emphasizes the use of mathematics in the context of physical chemistry, as opposed to being simply a mathematics text. This 4e includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The early chapters are constructed around a sequence of mathematical topics, wit
Statistical Content in Middle Grades Mathematics Textbooks
Pickle, Maria Consuelo Capiral
2012-01-01
This study analyzed the treatment and scope of statistical concepts in four, widely-used, contemporary, middle grades mathematics textbook series: "Glencoe Math Connects," "Prentice Hall Mathematics," "Connected Mathematics Project," and "University of Chicago School Mathematics Project." There were three…
Equations of mathematical physics
Tikhonov, A N
2011-01-01
Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri
Mathematization in introductory physics
Brahmia, Suzanne M.
Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in
Contemporary mathematical physics
Dobrushin, R L; Shubin, M A; Vershik, Anatoly M
1996-01-01
This first of a two-volume collection is a celebration of the scientific heritage of F. A. Berezin (1931-1980). Before his untimely death, Berezin had an important influence on physics and mathematics, discovering new ideas in mathematical physics, representation theory, analysis, geometry, and other areas of mathematics. His crowning achievements were the introduction of a new notion of deformation quantization, and Grassmannian analysis ("supermathematics"). Collected here are papers by his many of his colleagues and others who worked in related areas, representing a wide spectrum of topics
Quantum physics and statistical physics. 5. ed.
International Nuclear Information System (INIS)
Alonso, Marcelo; Finn, Edward J.
2012-01-01
By logical and uniform presentation this recognized introduction in modern physics treats both the experimental and theoretical aspects. The first part of the book deals with quantum mechanics and their application to atoms, molecules, nuclei, solids, and elementary particles. The statistical physics with classical statistics, thermodynamics, and quantum statistics is theme of the second part. Alsonso and Finn avoid complicated mathematical developments; by numerous sketches and diagrams as well as many problems and examples they make the reader early and above all easily understandably familiar with the formations of concepts of modern physics.
Mathematics for physical chemistry
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 ...
Statistical physics of vaccination
Wang, Zhen; Bauch, Chris T.; Bhattacharyya, Samit; d'Onofrio, Alberto; Manfredi, Piero; Perc, Matjaž; Perra, Nicola; Salathé, Marcel; Zhao, Dawei
2016-12-01
Historically, infectious diseases caused considerable damage to human societies, and they continue to do so today. To help reduce their impact, mathematical models of disease transmission have been studied to help understand disease dynamics and inform prevention strategies. Vaccination-one of the most important preventive measures of modern times-is of great interest both theoretically and empirically. And in contrast to traditional approaches, recent research increasingly explores the pivotal implications of individual behavior and heterogeneous contact patterns in populations. Our report reviews the developmental arc of theoretical epidemiology with emphasis on vaccination, as it led from classical models assuming homogeneously mixing (mean-field) populations and ignoring human behavior, to recent models that account for behavioral feedback and/or population spatial/social structure. Many of the methods used originated in statistical physics, such as lattice and network models, and their associated analytical frameworks. Similarly, the feedback loop between vaccinating behavior and disease propagation forms a coupled nonlinear system with analogs in physics. We also review the new paradigm of digital epidemiology, wherein sources of digital data such as online social media are mined for high-resolution information on epidemiologically relevant individual behavior. Armed with the tools and concepts of statistical physics, and further assisted by new sources of digital data, models that capture nonlinear interactions between behavior and disease dynamics offer a novel way of modeling real-world phenomena, and can help improve health outcomes. We conclude the review by discussing open problems in the field and promising directions for future research.
Rodríguez, Nancy
2015-03-01
The use of mathematical tools has long proved to be useful in gaining understanding of complex systems in physics [1]. Recently, many researchers have realized that there is an analogy between emerging phenomena in complex social systems and complex physical or biological systems [4,5,12]. This realization has particularly benefited the modeling and understanding of crime, a ubiquitous phenomena that is far from being understood. In fact, when one is interested in the bulk behavior of patterns that emerge from small and seemingly unrelated interactions as well as decisions that occur at the individual level, the mathematical tools that have been developed in statistical physics, game theory, network theory, dynamical systems, and partial differential equations can be useful in shedding light into the dynamics of these patterns [2-4,6,12].
Mathematical Rigor in Introductory Physics
Vandyke, Michael; Bassichis, William
2011-10-01
Calculus-based introductory physics courses intended for future engineers and physicists are often designed and taught in the same fashion as those intended for students of other disciplines. A more mathematically rigorous curriculum should be more appropriate and, ultimately, more beneficial for the student in his or her future coursework. This work investigates the effects of mathematical rigor on student understanding of introductory mechanics. Using a series of diagnostic tools in conjunction with individual student course performance, a statistical analysis will be performed to examine student learning of introductory mechanics and its relation to student understanding of the underlying calculus.
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
Mathematical methods for physical and analytical chemistry
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
Mathematical physics classical mechanics
Knauf, Andreas
2018-01-01
As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics. The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.
International Conference on Mathematical Sciences and Statistics 2013 : Selected Papers
Leong, Wah; Eshkuvatov, Zainidin
2014-01-01
This volume is devoted to the most recent discoveries in mathematics and statistics. It also serves as a platform for knowledge and information exchange between experts from industrial and academic sectors. The book covers a wide range of topics, including mathematical analyses, probability, statistics, algebra, geometry, mathematical physics, wave propagation, stochastic processes, ordinary and partial differential equations, boundary value problems, linear operators, cybernetics and number and functional theory. It is a valuable resource for pure and applied mathematicians, statisticians, engineers and scientists.
Statistical symmetries in physics
International Nuclear Information System (INIS)
Green, H.S.; Adelaide Univ., SA
1994-01-01
Every law of physics is invariant under some group of transformations and is therefore the expression of some type of symmetry. Symmetries are classified as geometrical, dynamical or statistical. At the most fundamental level, statistical symmetries are expressed in the field theories of the elementary particles. This paper traces some of the developments from the discovery of Bose statistics, one of the two fundamental symmetries of physics. A series of generalizations of Bose statistics is described. A supersymmetric generalization accommodates fermions as well as bosons, and further generalizations, including parastatistics, modular statistics and graded statistics, accommodate particles with properties such as 'colour'. A factorization of elements of ggl(n b ,n f ) can be used to define truncated boson operators. A general construction is given for q-deformed boson operators, and explicit constructions of the same type are given for various 'deformed' algebras. A summary is given of some of the applications and potential applications. 39 refs., 2 figs
Cluster algebras in mathematical physics
International Nuclear Information System (INIS)
Francesco, Philippe Di; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito
2014-01-01
This special issue of Journal of Physics A: Mathematical and Theoretical contains reviews and original research articles on cluster algebras and their applications to mathematical physics. Cluster algebras were introduced by S Fomin and A Zelevinsky around 2000 as a tool for studying total positivity and dual canonical bases in Lie theory. Since then the theory has found diverse applications in mathematics and mathematical physics. Cluster algebras are axiomatically defined commutative rings equipped with a distinguished set of generators (cluster variables) subdivided into overlapping subsets (clusters) of the same cardinality subject to certain polynomial relations. A cluster algebra of rank n can be viewed as a subring of the field of rational functions in n variables. Rather than being presented, at the outset, by a complete set of generators and relations, it is constructed from the initial seed via an iterative procedure called mutation producing new seeds successively to generate the whole algebra. A seed consists of an n-tuple of rational functions called cluster variables and an exchange matrix controlling the mutation. Relations of cluster algebra type can be observed in many areas of mathematics (Plücker and Ptolemy relations, Stokes curves and wall-crossing phenomena, Feynman integrals, Somos sequences and Hirota equations to name just a few examples). The cluster variables enjoy a remarkable combinatorial pattern; in particular, they exhibit the Laurent phenomenon: they are expressed as Laurent polynomials rather than more general rational functions in terms of the cluster variables in any seed. These characteristic features are often referred to as the cluster algebra structure. In the last decade, it became apparent that cluster structures are ubiquitous in mathematical physics. Examples include supersymmetric gauge theories, Poisson geometry, integrable systems, statistical mechanics, fusion products in infinite dimensional algebras, dilogarithm
Methods of statistical physics
Akhiezer, Aleksandr I
1981-01-01
Methods of Statistical Physics is an exposition of the tools of statistical mechanics, which evaluates the kinetic equations of classical and quantized systems. The book also analyzes the equations of macroscopic physics, such as the equations of hydrodynamics for normal and superfluid liquids and macroscopic electrodynamics. The text gives particular attention to the study of quantum systems. This study begins with a discussion of problems of quantum statistics with a detailed description of the basics of quantum mechanics along with the theory of measurement. An analysis of the asymptotic be
Mathematical Anxiety among Business Statistics Students.
High, Robert V.
A survey instrument was developed to identify sources of mathematics anxiety among undergraduate business students in a statistics class. A number of statistics classes were selected at two colleges in Long Island, New York. A final sample of n=102 respondents indicated that there was a relationship between the mathematics grade in prior…
15th International Congress on Mathematical Physics
New Trends in Mathematical Physics
2009-01-01
This book collects selected papers written by invited and plenary speakers of the 15th International Congress on Mathematical Physics (ICMP) in the aftermath of the conference. In extensive review articles and expository texts as well as advanced research articles the world leading experts present the state of the art in modern mathematical physics. New mathematical concepts and ideas are introduced by prominent mathematicalphysicists and mathematicians, covering among others the fields of Dynamical Systems, Operator Algebras, Partial Differential Equations, Probability Theory, Random Matrices, Condensed Matter Physics, Statistical Mechanics, General Relativity, Quantum Mechanics, Quantum Field Theory, Quantum Information and String Theory. All together the contributions in this book give a panoramic view of the latest developments in mathematical physics. They will help readers with a general interest in mathematical physics to get an update on the most recent developments in their field, and give a broad ov...
Müller-Kirsten, Harald J W
2013-01-01
Statistics links microscopic and macroscopic phenomena, and requires for this reason a large number of microscopic elements like atoms. The results are values of maximum probability or of averaging. This introduction to statistical physics concentrates on the basic principles, and attempts to explain these in simple terms supplemented by numerous examples. These basic principles include the difference between classical and quantum statistics, a priori probabilities as related to degeneracies, the vital aspect of indistinguishability as compared with distinguishability in classical physics, the differences between conserved and non-conserved elements, the different ways of counting arrangements in the three statistics (Maxwell-Boltzmann, Fermi-Dirac, Bose-Einstein), the difference between maximization of the number of arrangements of elements, and averaging in the Darwin-Fowler method. Significant applications to solids, radiation and electrons in metals are treated in separate chapters, as well as Bose-Eins...
Elementary statistical physics
Kittel, C
1965-01-01
This book is intended to help physics students attain a modest working knowledge of several areas of statistical mechanics, including stochastic processes and transport theory. The areas discussed are among those forming a useful part of the intellectual background of a physicist.
The logical structure of mathematical physics
Sneed, Joseph D
1971-01-01
This book is about scientific theories of a particular kind - theories of mathematical physics. Examples of such theories are classical and relativis tic particle mechanics, classical electrodynamics, classical thermodynamics, statistical mechanics, hydrodynamics, and quantum mechanics. Roughly, these are theories in which a certain mathematical structure is employed to make statements about some fragment of the world. Most of the book is simply an elaboration of this rough characterization of theories of mathematical physics. It is argued that each theory of mathematical physics has associated with it a certain characteristic mathematical struc ture. This structure may be used in a variety of ways to make empirical claims about putative applications of the theory. Typically - though not necessarily - the way this structure is used in making such claims requires that certain elements in the structure play essentially different roles. Some playa "theoretical" role; others playa "non-theoretical" role. For ...
Probability theory and mathematical statistics for engineers
Pugachev, V S
1984-01-01
Probability Theory and Mathematical Statistics for Engineers focuses on the concepts of probability theory and mathematical statistics for finite-dimensional random variables.The publication first underscores the probabilities of events, random variables, and numerical characteristics of random variables. Discussions focus on canonical expansions of random vectors, second-order moments of random vectors, generalization of the density concept, entropy of a distribution, direct evaluation of probabilities, and conditional probabilities. The text then examines projections of random vector
Statistics for Physical Sciences An Introduction
Martin, Brian
2012-01-01
Statistical Methods for the Physical Sciences is an informal, relatively short, but systematic, guide to the more commonly used ideas and techniques in statistical analysis, as used in physical sciences, together with explanations of their origins. It steers a path between the extremes of a recipe of methods with a collection of useful formulas, and a full mathematical account of statistics, while at the same time developing the subject in a logical way. The book can be read in its entirety by anyone with a basic exposure to mathematics at the level of a first-year undergraduate student
Science Academies' Refresher Course in Statistical Physics
Indian Academy of Sciences (India)
The Course is aimed at college teachers of statistical physics at BSc/MSc level. ... teachers, with at least a masters degree in Physics/Mathematics/Engineering are ... Topics: There will be six courses dealing with, Basic principles and general ...
When Mathematics and Statistics Collide in Assessment Tasks
Bargagliotti, Anna; Groth, Randall
2016-01-01
Because the disciplines of mathematics and statistics are naturally intertwined, designing assessment questions that disentangle mathematical and statistical reasoning can be challenging. We explore the writing statistics assessment tasks that take into consideration potential mathematical reasoning they may inadvertently activate.
Quantum mechanics as applied mathematical statistics
International Nuclear Information System (INIS)
Skala, L.; Cizek, J.; Kapsa, V.
2011-01-01
Basic mathematical apparatus of quantum mechanics like the wave function, probability density, probability density current, coordinate and momentum operators, corresponding commutation relation, Schroedinger equation, kinetic energy, uncertainty relations and continuity equation is discussed from the point of view of mathematical statistics. It is shown that the basic structure of quantum mechanics can be understood as generalization of classical mechanics in which the statistical character of results of measurement of the coordinate and momentum is taken into account and the most important general properties of statistical theories are correctly respected.
Topics in statistical and theoretical physics
Dobrushin, R L; Shubin, M A
1996-01-01
This is the second of two volumes dedicated to the scientific heritage of F. A. Berezin (1931-1980). Before his untimely death, Berezin had an important influence on physics and mathematics, discovering new ideas in mathematical physics, representation theory, analysis, geometry, and other areas of mathematics. His crowning achievements were the introduction of a new notion of deformation quantization and Grassmannian analysis ("supermathematics"). Collected here are papers by many of his colleagues and others who worked in related areas, representing a wide spectrum of topics in statistical a
Mathematical statistics essays on history and methodology
Pfanzagl, Johann
2017-01-01
This book presents a detailed description of the development of statistical theory. In the mid twentieth century, the development of mathematical statistics underwent an enduring change, due to the advent of more refined mathematical tools. New concepts like sufficiency, superefficiency, adaptivity etc. motivated scholars to reflect upon the interpretation of mathematical concepts in terms of their real-world relevance. Questions concerning the optimality of estimators, for instance, had remained unanswered for decades, because a meaningful concept of optimality (based on the regularity of the estimators, the representation of their limit distribution and assertions about their concentration by means of Anderson’s Theorem) was not yet available. The rapidly developing asymptotic theory provided approximate answers to questions for which non-asymptotic theory had found no satisfying solutions. In four engaging essays, this book presents a detailed description of how the use of mathematical methods stimulated...
Savard, Annie; Manuel, Dominic
2015-01-01
Statistics is a domain that is taught in Mathematics in all school levels. We suggest a potential in using an interdisciplinary approach with this concept. Thus the development of the understanding of a situation might mean to use both mathematical and statistical reasoning. In this paper, we present two case studies where two middle school…
The functions of mathematical physics
Hochstadt, Harry
2012-01-01
A modern classic, this clearly written, incisive textbook provides a comprehensive, detailed survey of the functions of mathematical physics, a field of study straddling the somewhat artificial boundary between pure and applied mathematics.In the 18th and 19th centuries, the theorists who devoted themselves to this field - pioneers such as Gauss, Euler, Fourier, Legendre, and Bessel - were searching for mathematical solutions to physical problems. Today, although most of the functions have practical applications, in areas ranging from the quantum-theoretical model of the atom to the vibrating
Open problems in mathematical physics
International Nuclear Information System (INIS)
Coley, Alan A
2017-01-01
We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of mathematical physics, particularly in the topical fields of classical general relativity, cosmology and the quantum realm. This list is motivated by the recent article proposing 42 fundamental questions (in physics) which must be answered on the road to full enlightenment (Allen and Lidstrom 2017 Phys. Scr . 92 012501). But paraphrasing a famous quote by the British football manager Bill Shankly, in response to the question of whether mathematics can answer the Ultimate Question of Life, the Universe, and Everything, mathematics is, of course, much more important than that. (invited comment)
Open problems in mathematical physics
Coley, Alan A.
2017-09-01
We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of mathematical physics, particularly in the topical fields of classical general relativity, cosmology and the quantum realm. This list is motivated by the recent article proposing 42 fundamental questions (in physics) which must be answered on the road to full enlightenment (Allen and Lidstrom 2017 Phys. Scr. 92 012501). But paraphrasing a famous quote by the British football manager Bill Shankly, in response to the question of whether mathematics can answer the Ultimate Question of Life, the Universe, and Everything, mathematics is, of course, much more important than that.
Mathematical and Statistical Opportunities in Cyber Security
Energy Technology Data Exchange (ETDEWEB)
Meza, Juan; Campbell, Scott; Bailey, David
2009-03-23
The role of mathematics in a complex system such as the Internet has yet to be deeply explored. In this paper, we summarize some of the important and pressing problems in cyber security from the viewpoint of open science environments. We start by posing the question 'What fundamental problems exist within cyber security research that can be helped by advanced mathematics and statistics'? Our first and most important assumption is that access to real-world data is necessary to understand large and complex systems like the Internet. Our second assumption is that many proposed cyber security solutions could critically damage both the openness and the productivity of scientific research. After examining a range of cyber security problems, we come to the conclusion that the field of cyber security poses a rich set of new and exciting research opportunities for the mathematical and statistical sciences.
GeoGebra for Mathematical Statistics
Hewson, Paul
2009-01-01
The GeoGebra software is attracting a lot of interest in the mathematical community, consequently there is a wide range of experience and resources to help use this application. This article briefly outlines how GeoGebra will be of great value in statistical education. The release of GeoGebra is an excellent example of the power of free software…
Mathematics of statistical mechanics and the chaos theory
International Nuclear Information System (INIS)
Llave, R. de la; Haro, A.
2000-01-01
Statistical mechanics requires a language that unifies probabilistic and deterministic description of physical systems. We describe briefly some of the mathematical ideas needed for this unification. These ideas have also proved important in the study of chaotic systems. (Author) 17 refs
Mathematical methods of classical physics
Cortés, Vicente
2017-01-01
This short primer, geared towards students with a strong interest in mathematically rigorous approaches, introduces the essentials of classical physics, briefly points out its place in the history of physics and its relation to modern physics, and explains what benefits can be gained from a mathematical perspective. As a starting point, Newtonian mechanics is introduced and its limitations are discussed. This leads to and motivates the study of different formulations of classical mechanics, such as Lagrangian and Hamiltonian mechanics, which are the subjects of later chapters. In the second part, a chapter on classical field theories introduces more advanced material. Numerous exercises are collected in the appendix.
Supersymmetry in mathematics and physics
Energy Technology Data Exchange (ETDEWEB)
Ferrara, Sergio [CERN, Geneve (Switzerland). Div. Theorie; Fioresi, Rita [Bologna Univ. (Italy). Dept. of Mathematics; Varadarajan, V.S. (eds.) [UCLA, Los Angeles, CA (United States). Dept. of Mathematics
2011-07-01
Supersymmetry was created by the physicists in the 1970's to give a unified treatment of fermions and bosons, the basic constituents of matter. Since then its mathematical structure has been recognized as that of a new development in geometry, and mathematicians have busied themselves with exploring this aspect. This volume collects recent advances in this field, both from a physical and a mathematical point of view, with an accent on a rigorous treatment of the various questions raised. (orig.)
Concept of probability in statistical physics
Guttmann, Y M
1999-01-01
Foundational issues in statistical mechanics and the more general question of how probability is to be understood in the context of physical theories are both areas that have been neglected by philosophers of physics. This book fills an important gap in the literature by providing a most systematic study of how to interpret probabilistic assertions in the context of statistical mechanics. The book explores both subjectivist and objectivist accounts of probability, and takes full measure of work in the foundations of probability theory, in statistical mechanics, and in mathematical theory. It will be of particular interest to philosophers of science, physicists and mathematicians interested in foundational issues, and also to historians of science.
Methods of modern mathematical physics
Reed, Michael
1980-01-01
This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations.
African Journals Online: Chemistry, Mathematics & Physics
African Journals Online (AJOL)
Items 1 - 36 of 36 ... African Journal of Educational Studies in Mathematics and Sciences ... statistics, operational research, financial mathematics and about the annexes ... research work in all areas of mathematical sciences and application at all ...
Mathematical and statistical approaches to AIDS epidemiology
1989-01-01
The 18 research articles of this volume discuss the major themes that have emerged from mathematical and statistical research in the epidemiology of HIV. The opening paper reviews important recent contributions. Five sections follow: Statistical Methodology and Forecasting, Infectivity and the HIV, Heterogeneity and HIV Transmission Dynamics, Social Dynamics and AIDS, and The Immune System and The HIV. In each, leading experts in AIDS epidemiology present the recent results. Some address the role of variable infectivity, heterogeneous mixing, and long periods of infectiousness in the dynamics of HIV; others concentrate on parameter estimation and short-term forecasting. The last section looks at the interaction between the HIV and the immune system.
Examples and problems in mathematical statistics
Zacks, Shelemyahu
2013-01-01
This book presents examples that illustrate the theory of mathematical statistics and details how to apply the methods for solving problems. While other books on the topic contain problems and exercises, they do not focus on problem solving. This book fills an important niche in the statistical theory literature by providing a theory/example/problem approach. Each chapter is divided into four parts: Part I provides the needed theory so readers can become familiar with the concepts, notations, and proven results; Part II presents examples from a variety of fields including engineering, mathem
Nonequilibrium statistical physics
Röpke, Gerd
2013-01-01
Authored by one of the top theoretical physicists in Germany, and a well-known authority in the field, this is the only coherent presentation of the subject suitable for masters and PhD students, as well as postdocs in physics and related disciplines.Starting from a general discussion of the nonequilibrium state, different standard approaches such as master equations, and kinetic and linear response theory, are derived after special assumptions. This allows for an insight into the problems of nonequilibrium physics, a discussion of the limits, and suggestions for improvements. Applications
Mathematical SETI Statistics, Signal Processing, Space Missions
Maccone, Claudio
2012-01-01
This book introduces the Statistical Drake Equation where, from a simple product of seven positive numbers, the Drake Equation is turned into the product of seven positive random variables. The mathematical consequences of this transformation are demonstrated and it is proven that the new random variable N for the number of communicating civilizations in the Galaxy must follow the lognormal probability distribution when the number of factors in the Drake equation is allowed to increase at will. Mathematical SETI also studies the proposed FOCAL (Fast Outgoing Cyclopean Astronomical Lens) space mission to the nearest Sun Focal Sphere at 550 AU and describes its consequences for future interstellar precursor missions and truly interstellar missions. In addition the author shows how SETI signal processing may be dramatically improved by use of the Karhunen-Loève Transform (KLT) rather than Fast Fourier Transform (FFT). Finally, he describes the efforts made to persuade the United Nations to make the central part...
Fluctuations of physical values in statistical mechanics
International Nuclear Information System (INIS)
Zaripov, R.G.
1999-01-01
The new matrix inequalities for the boundary of measurement accuracy of physical values in the ensemble of quantum systems were obtained. The multidimensional thermodynamical parameter measurement is estimated. The matrix inequalities obtained are quantum analogs of the Cramer-Rao information inequalities in mathematical statistics. The quantity of information in quantum mechanical measurement, connected with the boundaries of jointly measurable values in one macroscopic experiment was determined. The lower boundary of the variance of estimation of multidimensional quantum mechanical parameter was found. (author)
XVIIth Interntional Congress on Mathematical Physics
DEFF Research Database (Denmark)
This volume contains the proceedings of the XVIIth International Congress on Mathematical Physics. It is the main scientific event of the International Association of Mathematical Physics (IAMP). The Congress was held in Aalborg, Denmark, August 6-11, 2012.......This volume contains the proceedings of the XVIIth International Congress on Mathematical Physics. It is the main scientific event of the International Association of Mathematical Physics (IAMP). The Congress was held in Aalborg, Denmark, August 6-11, 2012....
Some mathematical methods of physics
Goertzel, Gerald
2014-01-01
This well-rounded, thorough treatment for advanced undergraduates and graduate students introduces basic concepts of mathematical physics involved in the study of linear systems. The text emphasizes eigenvalues, eigenfunctions, and Green's functions. Prerequisites include differential equations and a first course in theoretical physics.The three-part presentation begins with an exploration of systems with a finite number of degrees of freedom (described by matrices). In part two, the concepts developed for discrete systems in previous chapters are extended to continuous systems. New concepts u
Physical Consequences of Mathematical Principles
Directory of Open Access Journals (Sweden)
Comay E.
2009-10-01
Full Text Available Physical consequences are derived from the following mathematical structures: the variational principle, Wigner’s classifications of the irreducible representations of the Poincar ́ e group and the duality invariance of the homogeneous Maxwell equations. The analysis is carried out within the validity domain of special relativity. Hierarchical re- lations between physical theories are used. Some new results are pointed out together with their comparison with experimental data. It is also predicted that a genuine Higgs particle will not be detected.
Bovier, Anton
2006-06-01
Our mathematical understanding of the statistical mechanics of disordered systems is going through a period of stunning progress. This self-contained book is a graduate-level introduction for mathematicians and for physicists interested in the mathematical foundations of the field, and can be used as a textbook for a two-semester course on mathematical statistical mechanics. It assumes only basic knowledge of classical physics and, on the mathematics side, a good working knowledge of graduate-level probability theory. The book starts with a concise introduction to statistical mechanics, proceeds to disordered lattice spin systems, and concludes with a presentation of the latest developments in the mathematical understanding of mean-field spin glass models. In particular, recent progress towards a rigorous understanding of the replica symmetry-breaking solutions of the Sherrington-Kirkpatrick spin glass models, due to Guerra, Aizenman-Sims-Starr and Talagrand, is reviewed in some detail. Comprehensive introduction to an active and fascinating area of research Clear exposition that builds to the state of the art in the mathematics of spin glasses Written by a well-known and active researcher in the field
Interactions Between Mathematics and Physics
DEFF Research Database (Denmark)
Kjeldsen, Tinne Hoff; Lützen, Jesper
2015-01-01
In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a var......In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined...... it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction...... of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student...
Differential geometry and mathematical physics
Rudolph, Gerd
Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous d...
Statistical methods in radiation physics
Turner, James E; Bogard, James S
2012-01-01
This statistics textbook, with particular emphasis on radiation protection and dosimetry, deals with statistical solutions to problems inherent in health physics measurements and decision making. The authors begin with a description of our current understanding of the statistical nature of physical processes at the atomic level, including radioactive decay and interactions of radiation with matter. Examples are taken from problems encountered in health physics, and the material is presented such that health physicists and most other nuclear professionals will more readily understand the application of statistical principles in the familiar context of the examples. Problems are presented at the end of each chapter, with solutions to selected problems provided online. In addition, numerous worked examples are included throughout the text.
Yang, Kai-Lin
2014-01-01
This study used phenomenography, a qualitative method, to investigate Taiwanese mathematics teachers' conceptions of school mathematics, school statistics, and their differences. To collect data, we interviewed five mathematics teachers by open questions. They also responded to statements drawn on mathematical/statistical conceptions and…
Mathematics in physics and engineering
Irving, J; Massey, H S W; Brueckner, Keith A
1959-01-01
Mathematics in Physics and Engineering describes the analytical and numerical (desk-machine) methods that arise in pure and applied science, including wave equations, Bessel and Legendre functions, and matrices. The manuscript first discusses partial differential equations, as well as the method of separation of variables, three-dimensional wave equation, diffusion or heat flow equation, and wave equation in plane and cylindrical polar coordinates. The text also ponders on Frobenius' and other methods of solution. Discussions focus on hypergeometric equation, Bessel's equation, confluent hyper
Statistical Physics of Colloidal Dispersions.
Canessa, E.
Available from UMI in association with The British Library. Requires signed TDF. This thesis is concerned with the equilibrium statistical mechanics of colloidal dispersions which represent useful model systems for the study of condensed matter physics; namely, charge stabilized colloidal dispersions and polymer stabilized colloidal dispersions. A one-component macroparticle approach is adopted in order to treat the macroscopic and microscopic properties of these systems in a simple and comprehensive manner. The thesis opens with the description of the nature of the colloidal state before reviewing some basic definitions and theory in Chapter II. In Chapter III a variational theory of phase equilibria based on the Gibbs-Bogolyobov inequality is applied to sterically stabilized colloidal dispersions. Hard spheres are chosen as the reference system for the disordered phases while an Einstein model is used for the ordered phases. The new choice of pair potential, taken for mathematical convenience, is a superposition of two Yukawa functions. By matching a double Yukawa potential to the van der Waals attractive potential at different temperatures and introducing a purely temperature dependent coefficient to the repulsive part, a rich variety of observed phase separation phenomena is qualitatively described. The behaviour of the potential is found to be consistent with a small decrease of the polymer layer thickness with increasing temperature. Using the same concept of a collapse transition the non-monotonic second virial coefficient is also explained and quantified. It is shown that a reduction of the effective macroparticle diameter with increasing temperature can only be partially examined from the point of view of a (binary-) polymer solution theory. This chapter concludes with the description of the observed, reversible, depletion flocculation behaviour. This is accomplished by using the variational formalism and by invoking the double Yukawa potential to allow
Statistical methods for physical science
Stanford, John L
1994-01-01
This volume of Methods of Experimental Physics provides an extensive introduction to probability and statistics in many areas of the physical sciences, with an emphasis on the emerging area of spatial statistics. The scope of topics covered is wide-ranging-the text discusses a variety of the most commonly used classical methods and addresses newer methods that are applicable or potentially important. The chapter authors motivate readers with their insightful discussions, augmenting their material withKey Features* Examines basic probability, including coverage of standard distributions, time s
Introduction to mathematical physics methods and concepts
Wong, Chun Wa
2013-01-01
Mathematical physics provides physical theories with their logical basis and the tools for drawing conclusions from hypotheses. Introduction to Mathematical Physics explains to the reader why and how mathematics is needed in the description of physical events in space. For undergraduates in physics, it is a classroom-tested textbook on vector analysis, linear operators, Fourier series and integrals, differential equations, special functions and functions of a complex variable. Strongly correlated with core undergraduate courses on classical and quantum mechanics and electromagnetism, it helps the student master these necessary mathematical skills. It contains advanced topics of interest to graduate students on relativistic square-root spaces and nonlinear systems. It contains many tables of mathematical formulas and references to useful materials on the Internet. It includes short tutorials on basic mathematical topics to help readers refresh their mathematical knowledge. An appendix on Mathematica encourages...
Teachers and Textbooks: On Statistical Definitions in Senior Secondary Mathematics
Dunn, Peter K.; Marshman, Margaret; McDougall, Robert; Wiegand, Aaron
2015-01-01
The new "Australian Senior Secondary Curriculum: Mathematics" contains more statistics than the existing Australian Curricula. This case study examines how a group of Queensland mathematics teachers define the word "statistics" and five statistical terms from the new curricula. These definitions are compared to those used in…
Interaction between Mathematics and Physics
Directory of Open Access Journals (Sweden)
Hitchin, Nigel
2007-06-01
Full Text Available There is at the moment a highly active interface between mathematics and theoretical physics, which extends into completely new areas of both disciplines. This article, based on a round table discussion which took place as part of the activities around the 2006 International Congress of Mathematicians in Madrid, explores some of the issues involved: the differing goals and backgrounds of the two communities, today’s interactions and their precedents, the possibilities for the future and the role of mathematics itself in understanding the world in which we live.Actualmente existe una importante interfaz entre matemáticas y física teórica, que ha producido áreas completamente nuevas. Este artículo está basado en un debate en una mesa redonda organizada en el entorno del International Congress of Mathematicians en 2006 de Madrid, explora algunos de estos temas: los diferentes objetivos y pasado de ambas disciplinas, las interacciones actuales y sus precedentes, las posibilidades para el futuro y el papel de las matemáticas para entender el mundo en que vivimos.
Obstacle problems in mathematical physics
Rodrigues, J-F
1987-01-01
The aim of this research monograph is to present a general account of the applicability of elliptic variational inequalities to the important class of free boundary problems of obstacle type from a unifying point of view of classical Mathematical Physics.The first part of the volume introduces some obstacle type problems which can be reduced to variational inequalities. Part II presents some of the main aspects of the theory of elliptic variational inequalities, from the abstract hilbertian framework to the smoothness of the variational solution, discussing in general the properties of the free boundary and including some results on the obstacle Plateau problem. The last part examines the application to free boundary problems, namely the lubrication-cavitation problem, the elastoplastic problem, the Signorini (or the boundary obstacle) problem, the dam problem, the continuous casting problem, the electrochemical machining problem and the problem of the flow with wake in a channel past a profile.
Mathematics and Statistics Research Department progress report for period ending June 30, 1976
International Nuclear Information System (INIS)
Gosslee, D.G.; Shelton, B.K.; Ward, R.C.; Wilson, D.G.
1976-10-01
Brief summaries of work done in mathematics and related fields are presented. Research in mathematics and statistics concerned statistical estimation, statistical testing, experiment design, probability, continuum mechanics, functional integration, matrices and other operators, and mathematical software. More applied studies were conducted in the areas of analytical chemistry, biological research, chemistry and physics research, energy research, environmental research, health physics research, materials research, reactor and thermonuclear research, sampling inspection, quality control, and life testing, and uranium resource evaluation research. Additional sections deal with educational activities, presentation of research results, and professional activities. 7 figures, 9 tables
Mathematical and conceptual foundations of 20th-century physics
International Nuclear Information System (INIS)
Emch, G.G.
1984-01-01
This volume presents a unified mathematical account of the conceptual foundations of 20th-century Physics. Part 1 provides a survey of classical physics divided in separate chapters on mechanics, thermodynamics and statistical mechanics, and electromagnetism. This study provides opportunities to place in perspective the successive advents of calculus, of probability and statistics, of differential and sympletic geometry, and of classical functional analysis. Relativity is presented in part 2 of this book and quantum theory in part 3. The motivation provided by physical problems in the development of mathematical disciplines such as, for instance, pseudo-Riemannian geometries, Hilbert spaces and operator algebras, are emphasized. (H.W.). refs.; figs.; schemes
Non-equilibrium statistical physics with application to disordered systems
Cáceres, Manuel Osvaldo
2017-01-01
This textbook is the result of the enhancement of several courses on non-equilibrium statistics, stochastic processes, stochastic differential equations, anomalous diffusion and disorder. The target audience includes students of physics, mathematics, biology, chemistry, and engineering at undergraduate and graduate level with a grasp of the basic elements of mathematics and physics of the fourth year of a typical undergraduate course. The little-known physical and mathematical concepts are described in sections and specific exercises throughout the text, as well as in appendices. Physical-mathematical motivation is the main driving force for the development of this text. It presents the academic topics of probability theory and stochastic processes as well as new educational aspects in the presentation of non-equilibrium statistical theory and stochastic differential equations.. In particular it discusses the problem of irreversibility in that context and the dynamics of Fokker-Planck. An introduction on fluc...
Modelling Mathematical Reasoning in Physics Education
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 physics applied mathematics for scientists and engineers
Kusse, Bruce R
2006-01-01
What sets this volume apart from other mathematics texts is its emphasis on mathematical tools commonly used by scientists and engineers to solve real-world problems. Using a unique approach, it covers intermediate and advanced material in a manner appropriate for undergraduate students. Based on author Bruce Kusse's course at the Department of Applied and Engineering Physics at Cornell University, Mathematical Physics begins with essentials such as vector and tensor algebra, curvilinear coordinate systems, complex variables, Fourier series, Fourier and Laplace transforms, differential and integral equations, and solutions to Laplace's equations
Statistical methods in physical mapping
International Nuclear Information System (INIS)
Nelson, D.O.
1995-05-01
One of the great success stories of modern molecular genetics has been the ability of biologists to isolate and characterize the genes responsible for serious inherited diseases like fragile X syndrome, cystic fibrosis and myotonic muscular dystrophy. This dissertation concentrates on constructing high-resolution physical maps. It demonstrates how probabilistic modeling and statistical analysis can aid molecular geneticists in the tasks of planning, execution, and evaluation of physical maps of chromosomes and large chromosomal regions. The dissertation is divided into six chapters. Chapter 1 provides an introduction to the field of physical mapping, describing the role of physical mapping in gene isolation and ill past efforts at mapping chromosomal regions. The next two chapters review and extend known results on predicting progress in large mapping projects. Such predictions help project planners decide between various approaches and tactics for mapping large regions of the human genome. Chapter 2 shows how probability models have been used in the past to predict progress in mapping projects. Chapter 3 presents new results, based on stationary point process theory, for progress measures for mapping projects based on directed mapping strategies. Chapter 4 describes in detail the construction of all initial high-resolution physical map for human chromosome 19. This chapter introduces the probability and statistical models involved in map construction in the context of a large, ongoing physical mapping project. Chapter 5 concentrates on one such model, the trinomial model. This chapter contains new results on the large-sample behavior of this model, including distributional results, asymptotic moments, and detection error rates. In addition, it contains an optimality result concerning experimental procedures based on the trinomial model. The last chapter explores unsolved problems and describes future work
Statistical methods in physical mapping
Energy Technology Data Exchange (ETDEWEB)
Nelson, David O. [Univ. of California, Berkeley, CA (United States)
1995-05-01
One of the great success stories of modern molecular genetics has been the ability of biologists to isolate and characterize the genes responsible for serious inherited diseases like fragile X syndrome, cystic fibrosis and myotonic muscular dystrophy. This dissertation concentrates on constructing high-resolution physical maps. It demonstrates how probabilistic modeling and statistical analysis can aid molecular geneticists in the tasks of planning, execution, and evaluation of physical maps of chromosomes and large chromosomal regions. The dissertation is divided into six chapters. Chapter 1 provides an introduction to the field of physical mapping, describing the role of physical mapping in gene isolation and ill past efforts at mapping chromosomal regions. The next two chapters review and extend known results on predicting progress in large mapping projects. Such predictions help project planners decide between various approaches and tactics for mapping large regions of the human genome. Chapter 2 shows how probability models have been used in the past to predict progress in mapping projects. Chapter 3 presents new results, based on stationary point process theory, for progress measures for mapping projects based on directed mapping strategies. Chapter 4 describes in detail the construction of all initial high-resolution physical map for human chromosome 19. This chapter introduces the probability and statistical models involved in map construction in the context of a large, ongoing physical mapping project. Chapter 5 concentrates on one such model, the trinomial model. This chapter contains new results on the large-sample behavior of this model, including distributional results, asymptotic moments, and detection error rates. In addition, it contains an optimality result concerning experimental procedures based on the trinomial model. The last chapter explores unsolved problems and describes future work.
Models and structures: mathematical physics
International Nuclear Information System (INIS)
2003-01-01
This document gathers research activities along 5 main directions. 1) Quantum chaos and dynamical systems. Recent results concern the extension of the exact WKB method that has led to a host of new results on the spectrum and wave functions. Progress have also been made in the description of the wave functions of chaotic quantum systems. Renormalization has been applied to the analysis of dynamical systems. 2) Combinatorial statistical physics. We see the emergence of new techniques applied to various such combinatorial problems, from random walks to random lattices. 3) Integrability: from structures to applications. Techniques of conformal field theory and integrable model systems have been developed. Progress is still made in particular for open systems with boundary conditions, in connection to strings and branes physics. Noticeable links between integrability and exact WKB quantization to 2-dimensional disordered systems have been highlighted. New correlations of eigenvalues and better connections to integrability have been formulated for random matrices. 4) Gravities and string theories. We have developed aspects of 2-dimensional string theory with a particular emphasis on its connection to matrix models as well as non-perturbative properties of M-theory. We have also followed an alternative path known as loop quantum gravity. 5) Quantum field theory. The results obtained lately concern its foundations, in flat or curved spaces, but also applications to second-order phase transitions in statistical systems
Mathematics and Statistics Research Department progress report for period ending June 30, 1977
International Nuclear Information System (INIS)
Lever, W.E.; Shepherd, D.E.; Ward, R.C.; Wilson, D.G.
1977-09-01
Brief descriptions are given of work done in mathematical and statistical research (moving-boundary problems; numerical analysis; continuum mechanics; matrices and other operators; experiment design; statistical testing; multivariate, multipopulation classification; statistical estimation) and statistical and mathematical collaboration (analytical chemistry, biological research, chemistry and physics research, energy research, engineering technology research, environmental sciences research, health physics research, meterials research, sampling inspection and quality control, uranium resource evaluation research). Most of the descriptions are a page or less in length. Educational activities, publications, seminar titles, etc., are also included
Attitude Towards Physics and Additional Mathematics Achievement Towards Physics Achievement
Veloo, Arsaythamby; Nor, Rahimah; Khalid, Rozalina
2015-01-01
The purpose of this research is to identify the difference in students' attitude towards Physics and Additional Mathematics achievement based on gender and relationship between attitudinal variables towards Physics and Additional Mathematics achievement with achievement in Physics. This research focused on six variables, which is attitude towards…
Statistics for High Energy Physics
CERN. Geneva
2018-01-01
The lectures emphasize the frequentist approach used for Dark Matter search and the Higgs search, discovery and measurements of its properties. An emphasis is put on hypothesis test using the asymptotic formulae formalism and its derivation, and on the derivation of the trial factor formulae in one and two dimensions. Various test statistics and their applications are discussed. Some keywords: Profile Likelihood, Neyman Pearson, Feldman Cousins, Coverage, CLs. Nuisance Parameters Impact, Look Elsewhere Effect... Selected Bibliography: G. J. Feldman and R. D. Cousins, A Unified approach to the classical statistical analysis of small signals, Phys.\\ Rev.\\ D {\\bf 57}, 3873 (1998). A. L. Read, Presentation of search results: The CL(s) technique,'' J.\\ Phys.\\ G {\\bf 28}, 2693 (2002). G. Cowan, K. Cranmer, E. Gross and O. Vitells, Asymptotic formulae for likelihood-based tests of new physics,' Eur.\\ Phys.\\ J.\\ C {\\bf 71}, 1554 (2011) Erratum: [Eur.\\ Phys.\\ J.\\ C {\\bf 73}...
Partial differential equations of mathematical physics
Sobolev, S L
1964-01-01
Partial Differential Equations of Mathematical Physics emphasizes the study of second-order partial differential equations of mathematical physics, which is deemed as the foundation of investigations into waves, heat conduction, hydrodynamics, and other physical problems. The book discusses in detail a wide spectrum of topics related to partial differential equations, such as the theories of sets and of Lebesgue integration, integral equations, Green's function, and the proof of the Fourier method. Theoretical physicists, experimental physicists, mathematicians engaged in pure and applied math
Mathematics and the physical world
Kline, Morris
1981-01-01
Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.
Computer Algebra Recipes for Mathematical Physics
Enns, Richard H
2005-01-01
Over two hundred novel and innovative computer algebra worksheets or "recipes" will enable readers in engineering, physics, and mathematics to easily and rapidly solve and explore most problems they encounter in their mathematical physics studies. While the aim of this text is to illustrate applications, a brief synopsis of the fundamentals for each topic is presented, the topics being organized to correlate with those found in traditional mathematical physics texts. The recipes are presented in the form of stories and anecdotes, a pedagogical approach that makes a mathematically challenging subject easier and more fun to learn. Key features: * Uses the MAPLE computer algebra system to allow the reader to easily and quickly change the mathematical models and the parameters and then generate new answers * No prior knowledge of MAPLE is assumed; the relevant MAPLE commands are introduced on a need-to-know basis * All MAPLE commands are indexed for easy reference * A classroom-tested story/anecdote format is use...
Mathematics and Statistics Research Department progress report for period ending June 30, 1975
International Nuclear Information System (INIS)
Coveyou, R.R.; Gosslee, D.G.; Wilson, D.G.
1975-10-01
Brief reports on mathematical and statistical research and consulting and collaboration are given for the following areas: statistical estimation, statistical testing, experimental design, probability, energy systems modeling, continuum mechanics, matrices and other operators, numerical analysis, biomathematics and biostatistics, analytical chemistry, biology and medicine, health physics research, management, materials research, physics research, and programming. Information on seminars, publications, etc., is also included. (10 figures, 4 tables)
Focus in High School Mathematics: Statistics and Probability
National Council of Teachers of Mathematics, 2009
2009-01-01
Reasoning about and making sense of statistics and probability are essential to students' future success. This volume belongs to a series that supports National Council of Teachers of Mathematics' (NCTM's) "Focus in High School Mathematics: Reasoning and Sense Making" by providing additional guidance for making reasoning and sense making part of…
Teaching Primary School Mathematics and Statistics: Evidence-Based Practice
Averill, Robin; Harvey, Roger
2010-01-01
Here is the only reference book you will ever need for teaching primary school mathematics and statistics. It is full of exciting and engaging snapshots of excellent classroom practice relevant to "The New Zealand Curriculum" and national mathematics standards. There are many fascinating examples of investigative learning experiences,…
A course in mathematical statistics and large sample theory
Bhattacharya, Rabi; Patrangenaru, Victor
2016-01-01
This graduate-level textbook is primarily aimed at graduate students of statistics, mathematics, science, and engineering who have had an undergraduate course in statistics, an upper division course in analysis, and some acquaintance with measure theoretic probability. It provides a rigorous presentation of the core of mathematical statistics. Part I of this book constitutes a one-semester course on basic parametric mathematical statistics. Part II deals with the large sample theory of statistics — parametric and nonparametric, and its contents may be covered in one semester as well. Part III provides brief accounts of a number of topics of current interest for practitioners and other disciplines whose work involves statistical methods. Large Sample theory with many worked examples, numerical calculations, and simulations to illustrate theory Appendices provide ready access to a number of standard results, with many proofs Solutions given to a number of selected exercises from Part I Part II exercises with ...
9th Annual UNCG Regional Mathematics and Statistics Conference
Chhetri, Maya; Gupta, Sat; Shivaji, Ratnasingham
2015-01-01
This volume contains rigorously reviewed papers on the topics presented by students at The 9th Annual University of North Carolina at Greensboro Regional Mathematics and Statistics Conference (UNCG RMSC) that took place on November 2, 2013. All papers are coauthored by student researchers and their faculty mentors. This conference series was inaugurated in 2005, and it now attracts over 150 participants from over 30 universities from North Carolina and surrounding states. The conference is specifically tailored for students to present their research projects that encompass a broad spectrum of topics in mathematics, mathematical biology, statistics, and computer science.
The Physical Origin of Physically Useful Mathematics
DEFF Research Database (Denmark)
Lützen, Jesper
2011-01-01
Der argumenteres for at anvendelser i fysik er afgørende i udviklingen af de dele af matematikken, som har været nyttig for beskrivelsen af den fysiske verden. Dermed kastes et nyt lys på Eugine Wigner's 50 år gamle artikel om The unreasonable effectiveness of mathematics. Der gives en række hist...
Statistical physics of crime: a review.
D'Orsogna, Maria R; Perc, Matjaž
2015-03-01
Containing the spread of crime in urban societies remains a major challenge. Empirical evidence suggests that, if left unchecked, crimes may be recurrent and proliferate. On the other hand, eradicating a culture of crime may be difficult, especially under extreme social circumstances that impair the creation of a shared sense of social responsibility. Although our understanding of the mechanisms that drive the emergence and diffusion of crime is still incomplete, recent research highlights applied mathematics and methods of statistical physics as valuable theoretical resources that may help us better understand criminal activity. We review different approaches aimed at modeling and improving our understanding of crime, focusing on the nucleation of crime hotspots using partial differential equations, self-exciting point process and agent-based modeling, adversarial evolutionary games, and the network science behind the formation of gangs and large-scale organized crime. We emphasize that statistical physics of crime can relevantly inform the design of successful crime prevention strategies, as well as improve the accuracy of expectations about how different policing interventions should impact malicious human activity that deviates from social norms. We also outline possible directions for future research, related to the effects of social and coevolving networks and to the hierarchical growth of criminal structures due to self-organization. Copyright © 2014 Elsevier B.V. All rights reserved.
Mathematical and physical theory of turbulence
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...
Contributions in mathematical physics a tribute to Gerard G. Emch
Sinha, Kalyan
2007-01-01
Professor Gerard G. Emch has been one of the pioneers of the C-algebraic approach to quantum and classical statistical mechanics. In a prolific scientific career, spanning nearly five decades, Professor Emch has been one of the creative influences in the general area of mathematical physics. The present volume is a collection of tributes, from former students, colleagues and friends of Professor Emch, on the occasion of his 70th birthday. The articles featured here are a small yet representative sample of the breadth and reach of some of the ideas from mathematical physics.It is also a testimony to the impact that Professor Emch's work has had on several generations of mathematical physicists as well as to the diversity of mathematical methods used to understand them.
Algebra, Geometry and Mathematical Physics Conference
Paal, Eugen; Silvestrov, Sergei; Stolin, Alexander
2014-01-01
This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book benefits a broad audience of researchers a...
The mysterious connection between mathematics and physics.
Kauffman, Louis H; Ul-Haq, Rukhsan
2015-12-01
The essay is in the form of a dialogue between the two authors. We take John Wheeler's idea of "It from Bit" as an essential clue and we rework the structure of the bit not to the qubit, but to a logical particle that is its own anti-particle, a logical Marjorana particle. This is our key example of the amphibian nature of mathematics and the external world. We emphasize that mathematics is a combination of calculation and concept. At the conceptual level, mathematics is structured to be independent of time and multiplicity. Mathematics in this way occurs before number and counting. From this timeless domain, mathematics and mathematicians can explore worlds of multiplicity and infinity beyond the apparent limitations of the physical world and see that among these possible worlds there are coincidences with what is observed. Copyright © 2015. Published by Elsevier Ltd.
International Conference on Quantum Mathematical Physics : a Bridge between Mathematics and Physics
Kleiner, Johannes; Röken, Christian; Tolksdorf, Jürgen
2016-01-01
Quantum physics has been highly successful for more than 90 years. Nevertheless, a rigorous construction of interacting quantum field theory is still missing. Moreover, it is still unclear how to combine quantum physics and general relativity in a unified physical theory. Attacking these challenging problems of contemporary physics requires highly advanced mathematical methods as well as radically new physical concepts. This book presents different physical ideas and mathematical approaches in this direction. It contains a carefully selected cross-section of lectures which took place in autumn 2014 at the sixth conference ``Quantum Mathematical Physics - A Bridge between Mathematics and Physics'' in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fu...
Statistical physics and condensed matter
Energy Technology Data Exchange (ETDEWEB)
NONE
2003-07-01
This document is divided into 4 sections: 1) General aspects of statistical physics. The themes include: possible geometrical structures of thermodynamics, the thermodynamical foundation of quantum measurement, transport phenomena (kinetic theory, hydrodynamics and turbulence) and out of equilibrium systems (stochastic dynamics and turbulence). The techniques involved here are typical of applied analysis: stability criteria, mode decomposition, shocks and stochastic equations. 2) Disordered, glassy and granular systems: statics and dynamics. The complexity of the systems can be studied through the structure of their phase space. The geometry of this phase space is studied in several works: the overlap distribution can now be computed with a very high precision; the boundary energy between low lying states does not behave like in ordinary systems; and the Edward's hypothesis of equi-probability of low lying metastable states is invalidated. The phenomenon of aging, characteristic of glassy dynamics, is studied in several models. Dynamics of biological systems or of fracture is shown to bear some resemblance with that of disordered systems. 3) Quantum systems. The themes include: mesoscopic superconductors, supersymmetric approach to strongly correlated electrons, quantum criticality and heavy fermion compounds, optical sum rule violation in the cuprates, heat capacity of lattice spin models from high-temperature series expansion, Lieb-Schultz-Mattis theorem in dimension larger than one, quantum Hall effect, Bose-Einstein condensation and multiple-spin exchange model on the triangular lattice. 4) Soft condensed matter and biological systems. Path integral representations are invaluable to describe polymers, proteins and self-avoiding membranes. Using these methods, problems as diverse as the titration of a weak poly-acid by a strong base, the denaturation transition of DNA or bridge-hopping in conducting polymers have been addressed. The problems of RNA folding
Statistical physics and condensed matter
International Nuclear Information System (INIS)
2003-01-01
This document is divided into 4 sections: 1) General aspects of statistical physics. The themes include: possible geometrical structures of thermodynamics, the thermodynamical foundation of quantum measurement, transport phenomena (kinetic theory, hydrodynamics and turbulence) and out of equilibrium systems (stochastic dynamics and turbulence). The techniques involved here are typical of applied analysis: stability criteria, mode decomposition, shocks and stochastic equations. 2) Disordered, glassy and granular systems: statics and dynamics. The complexity of the systems can be studied through the structure of their phase space. The geometry of this phase space is studied in several works: the overlap distribution can now be computed with a very high precision; the boundary energy between low lying states does not behave like in ordinary systems; and the Edward's hypothesis of equi-probability of low lying metastable states is invalidated. The phenomenon of aging, characteristic of glassy dynamics, is studied in several models. Dynamics of biological systems or of fracture is shown to bear some resemblance with that of disordered systems. 3) Quantum systems. The themes include: mesoscopic superconductors, supersymmetric approach to strongly correlated electrons, quantum criticality and heavy fermion compounds, optical sum rule violation in the cuprates, heat capacity of lattice spin models from high-temperature series expansion, Lieb-Schultz-Mattis theorem in dimension larger than one, quantum Hall effect, Bose-Einstein condensation and multiple-spin exchange model on the triangular lattice. 4) Soft condensed matter and biological systems. Path integral representations are invaluable to describe polymers, proteins and self-avoiding membranes. Using these methods, problems as diverse as the titration of a weak poly-acid by a strong base, the denaturation transition of DNA or bridge-hopping in conducting polymers have been addressed. The problems of RNA folding has
Workshop on Supersymmetry in Mathematics and Physics
Fioresi, Rita; Varadarajan, VS
2011-01-01
Supersymmetry was created by the physicists in the 1970's to give a unified treatment of fermions and bosons, the basic constituents of matter. Since then its mathematical structure has been recognized as that of a new development in geometry, and mathematicians have busied themselves with exploring this aspect. This volume collects recent advances in this field, both from a physical and a mathematical point of view, with an accent on a rigorous treatment of the various questions raised.
PREFACE: Statistical Physics of Complex Fluids
Golestanian, R.; Khajehpour, M. R. H.; Kolahchi, M. R.; Rouhani, S.
2005-04-01
The field of complex fluids is a rapidly developing, highly interdisciplinary field that brings together people from a plethora of backgrounds such as mechanical engineering, chemical engineering, materials science, applied mathematics, physics, chemistry and biology. In this melting pot of science, the traditional boundaries of various scientific disciplines have been set aside. It is this very property of the field that has guaranteed its richness and prosperity since the final decade of the 20th century and into the 21st. The C3 Commission of the International Union of Pure and Applied Physics (IUPAP), which is the commission for statistical physics that organizes the international STATPHYS conferences, encourages various, more focused, satellite meetings to complement the main event. For the STATPHYS22 conference in Bangalore (July 2004), Iran was recognized by the STATPHYS22 organizers as suitable to host such a satellite meeting and the Institute for Advanced Studies in Basic Sciences (IASBS) was chosen to be the site of this meeting. It was decided to organize a meeting in the field of complex fluids, which is a fairly developed field in Iran. This international meeting, and an accompanying summer school, were intended to boost international connections for both the research groups working in Iran, and several other groups working in the Middle East, South Asia and North Africa. The meeting, entitled `Statistical Physics of Complex Fluids' was held at the Institute for Advanced Studies in Basic Sciences (IASBS) in Zanjan, Iran, from 27 June to 1 July 2004. The main topics discussed at the meeting included: biological statistical physics, wetting and microfluidics, transport in complex media, soft and granular matter, and rheology of complex fluids. At this meeting, 22 invited lectures by eminent scientists were attended by 107 participants from different countries. The poster session consisted of 45 presentations which, in addition to the main topics of the
2nd International Conference on Mathematics and Statistics
Jarrah, Abdul; Kallel, Sadok; Sulieman, Hana
2017-01-01
This work presents invited contributions from the second "International Conference on Mathematics and Statistics" jointly organized by the AUS (American University of Sharjah) and the AMS (American Mathematical Society). Addressing several research fields across the mathematical sciences, all of the papers were prepared by faculty members at universities in the Gulf region or prominent international researchers. The current volume is the first of its kind in the UAE and is intended to set new standards of excellence for collaboration and scholarship in the region.
On Dobrushin's way from probability theory to statistical physics
Minlos, R A; Suhov, Yu M; Suhov, Yu
2000-01-01
R. Dobrushin worked in several branches of mathematics (probability theory, information theory), but his deepest influence was on mathematical physics. He was one of the founders of the rigorous study of statistical physics. When Dobrushin began working in that direction in the early sixties, only a few people worldwide were thinking along the same lines. Now there is an army of researchers in the field. This collection is devoted to the memory of R. L. Dobrushin. The authors who contributed to this collection knew him quite well and were his colleagues. The title, "On Dobrushin's Way", is mea
Negotiating the Boundaries Between Mathematics and Physics
Radtka, Catherine
2015-07-01
This paper examines physics and mathematics textbooks published in France at the end of the 1950s and at the beginning of the 1960s for children aged 11-15 years old. It argues that at this "middle school" level, textbooks contributed to shape cultural representations of both disciplines and their mutual boundaries through their contents and their material aspect. Further, this paper argues that far from presenting clearly delimited subjects, late 1950s textbooks offered possible connections between mathematics and physics. It highlights that such connections depended upon the type of schools the textbooks aimed at, at a time when educational organization still differentiated pupils of this age. It thus stresses how the audience and its projected aptitudes and needs, as well as the cultural teaching traditions of the teachers in charge, were inseparable from the diverse conceptions of mathematics and physics and their relationships promoted through textbooks of the time.
Mathematical and statistical applications in life sciences and engineering
Adhikari, Mahima; Chaubey, Yogendra
2017-01-01
The book includes articles from eminent international scientists discussing a wide spectrum of topics of current importance in mathematics and statistics and their applications. It presents state-of-the-art material along with a clear and detailed review of the relevant topics and issues concerned. The topics discussed include message transmission, colouring problem, control of stochastic structures and information dynamics, image denoising, life testing and reliability, survival and frailty models, analysis of drought periods, prediction of genomic profiles, competing risks, environmental applications and chronic disease control. It is a valuable resource for researchers and practitioners in the relevant areas of mathematics and statistics.
The interface of mathematics and particle physics
Energy Technology Data Exchange (ETDEWEB)
Quillen, D.G.; Segal, G.B.; Tsousheung Tsun (Oxford Univ. (UK). Mathematical Inst.) (eds.)
1990-01-01
This collection of papers is based on the proceedings of a conference organized by the Institute of Mathematics and its Applications on the Interface of Mathematics and Particle Physics held at Oxford University in September 1988. There are twenty-five papers, all of which are indexed separately. Many contribute to the search for an understanding of how gravity can be unified with other interactions in one field theory. String and twistor theories are important in this search and many of the papers refer to strings, superstrings or twistor. All the papers seek a physical interpretation of theories and elementary particles. (author).
Birds and frogs in mathematics and physics
Energy Technology Data Exchange (ETDEWEB)
Dyson, Freeman J [Institute for Advanced Study, Princeton, NJ (United States)
2010-11-15
Some scientists are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time. A brief history of mathematics and its applications in physics is presented in this article. (from the history of physics)
Attractors for equations of mathematical physics
Chepyzhov, Vladimir V
2001-01-01
One of the major problems in the study of evolution equations of mathematical physics is the investigation of the behavior of the solutions to these equations when time is large or tends to infinity. The related important questions concern the stability of solutions or the character of the instability if a solution is unstable. In the last few decades, considerable progress in this area has been achieved in the study of autonomous evolution partial differential equations. For a number of basic evolution equations of mathematical physics, it was shown that the long time behavior of their soluti
Birds and frogs in mathematics and physics
International Nuclear Information System (INIS)
Dyson, Freeman J
2010-01-01
Some scientists are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time. A brief history of mathematics and its applications in physics is presented in this article. (from the history of physics)
A first course in mathematical physics
Whelan, Colm T
2016-01-01
The book assumes next to no prior knowledge of the topic. The first part introduces the core mathematics, always in conjunction with the physical context. In the second part of the book, a series of examples showcases some of the more conceptually advanced areas of physics, the presentation of which draws on the developments in the first part. A large number of problems helps students to hone their skills in using the presented mathematical methods. Solutions to the problems are available to instructors on an associated password-protected website for lecturers.
Curvature in mathematics and physics
Sternberg, Shlomo
2012-01-01
This original Dover textbook is based on an advanced undergraduate course taught by the author for more than 50 years. It introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.
Statistical and thermal physics with computer applications
Gould, Harvey
2010-01-01
This textbook carefully develops the main ideas and techniques of statistical and thermal physics and is intended for upper-level undergraduate courses. The authors each have more than thirty years' experience in teaching, curriculum development, and research in statistical and computational physics. Statistical and Thermal Physics begins with a qualitative discussion of the relation between the macroscopic and microscopic worlds and incorporates computer simulations throughout the book to provide concrete examples of important conceptual ideas. Unlike many contemporary texts on the
Applied Mathematical Methods in Theoretical Physics
Masujima, Michio
2005-04-01
All there is to know about functional analysis, integral equations and calculus of variations in a single volume. This advanced textbook is divided into two parts: The first on integral equations and the second on the calculus of variations. It begins with a short introduction to functional analysis, including a short review of complex analysis, before continuing a systematic discussion of different types of equations, such as Volterra integral equations, singular integral equations of Cauchy type, integral equations of the Fredholm type, with a special emphasis on Wiener-Hopf integral equations and Wiener-Hopf sum equations. After a few remarks on the historical development, the second part starts with an introduction to the calculus of variations and the relationship between integral equations and applications of the calculus of variations. It further covers applications of the calculus of variations developed in the second half of the 20th century in the fields of quantum mechanics, quantum statistical mechanics and quantum field theory. Throughout the book, the author presents over 150 problems and exercises -- many from such branches of physics as quantum mechanics, quantum statistical mechanics, and quantum field theory -- together with outlines of the solutions in each case. Detailed solutions are given, supplementing the materials discussed in the main text, allowing problems to be solved making direct use of the method illustrated. The original references are given for difficult problems. The result is complete coverage of the mathematical tools and techniques used by physicists and applied mathematicians Intended for senior undergraduates and first-year graduates in science and engineering, this is equally useful as a reference and self-study guide.
Mathematical and physical models and radiobiology
International Nuclear Information System (INIS)
Lokajicek, M.
1980-01-01
The hit theory of the mechanism of biological radiation effects in the cell is discussed with respect to radiotherapy. The mechanisms of biological effects and of intracellular recovery, the cumulative radiation effect and the cumulative biological effect in fractionated irradiation are described. The benefit is shown of consistent application of mathematical and physical models in radiobiology and radiotherapy. (J.P.)
Exploring teachers' practices in teaching Mathematics and Statistics ...
African Journals Online (AJOL)
Teaching approaches and assessment practices are key factors that contribute to the improvement of learner outcomes. The study on which this article is based, explored the methods used by KwaZulu-Natal (KZN) teachers in teaching and assessing mathematics and statistics. An instrument containing closed and ...
Research, statistics and mathematics educators in Nigeria: effect ...
African Journals Online (AJOL)
Over reliance on the perspective of a dichotomous reject or fail-to-reject outcome from a null hypothesis testing framework to answer research questions has become a worrisome issue to research methodologists and statistics experts. Thus, the Journals of Mathematical Association of Nigeria, Abacus (2013 & 2014) were ...
Cook, Samuel A.; Fukawa-Connelly, Timothy
2016-01-01
Studies have shown that at the end of an introductory statistics course, students struggle with building block concepts, such as mean and standard deviation, and rely on procedural understandings of the concepts. This study aims to investigate the understandings entering freshman of a department of mathematics and statistics (including mathematics…
Statistical Physics of Complex Substitutive Systems
Jin, Qing
Diffusion processes are central to human interactions. Despite extensive studies that span multiple disciplines, our knowledge is limited to spreading processes in non-substitutive systems. Yet, a considerable number of ideas, products, and behaviors spread by substitution; to adopt a new one, agents must give up an existing one. This captures the spread of scientific constructs--forcing scientists to choose, for example, a deterministic or probabilistic worldview, as well as the adoption of durable items, such as mobile phones, cars, or homes. In this dissertation, I develop a statistical physics framework to describe, quantify, and understand substitutive systems. By empirically exploring three collected high-resolution datasets pertaining to such systems, I build a mechanistic model describing substitutions, which not only analytically predicts the universal macroscopic phenomenon discovered in the collected datasets, but also accurately captures the trajectories of individual items in a complex substitutive system, demonstrating a high degree of regularity and universality in substitutive systems. I also discuss the origins and insights of the parameters in the substitution model and possible generalization form of the mathematical framework. The systematical study of substitutive systems presented in this dissertation could potentially guide the understanding and prediction of all spreading phenomena driven by substitutions, from electric cars to scientific paradigms, and from renewable energy to new healthy habits.
Equations in mathematical physics a practical course
Pikulin, Victor P
2001-01-01
Many physical processes in fields such as mechanics, thermodynamics, electricity, magnetism or optics are described by means of partial differential equations. The aim of the present book is to demonstrate the basic methods for solving the classical linear problems in mathematical physics of elliptic, parabolic and hyperbolic type. In particular, the methods of conformal mappings, Fourier analysis and Green`s functions are considered, as well as the perturbation method and integral transformation method, among others. Every chapter contains concrete examples with a detailed analysis of their solution. The book is intended as a textbook for students in mathematical physics, but will also serve as a handbook for scientists and engineers. ------------ [A] manual for future engineers must strongly differ from the textbook for pure mathematicians, and the book by Pikulin and Pohozaev is the good example. (…) The purpose (…) is to offer quick access to the principal facts (…) This well written book is a...
McLoughlin, M. Padraig M. M.
2008-01-01
The author of this paper submits the thesis that learning requires doing; only through inquiry is learning achieved, and hence this paper proposes a programme of use of a modified Moore method in a Probability and Mathematical Statistics (PAMS) course sequence to teach students PAMS. Furthermore, the author of this paper opines that set theory…
Thermodynamic formalism the mathematical structures of equilibrium statistical mechanics
Ruelle, David
2004-01-01
Reissued in the Cambridge Mathematical Library, this classic book outlines the theory of thermodynamic formalism which was developed to describe the properties of certain physical systems consisting of a large number of subunits. Background material on physics has been collected in appendices to help the reader. Supplementary work is provided in the form of exercises and problems that were "open" at the original time of writing.
Mathematical and conceptual foundations of 20th-century physics
International Nuclear Information System (INIS)
Emch, G.G.
1984-01-01
This book is primarily intended for Mathematicians, but it is also hoped that students in the physical sciences, will find here information not usually available in physics texts. The main aim of the book is to provide a unified mathematical account of the conceptual foundations of 20th-century Physics, in a form suitable for a one-year survey course in Mathematics or Mathematical Physics. Emphasis is laid on the interlocked historical development of mathematical and physical ideas. (Auth.)
Mathematics and Statistics Research Department progress report for period ending June 30, 1978
International Nuclear Information System (INIS)
Gardiner, D.A.; Lever, W.E.; Shepherd, D.E.; Ward, R.C.; Wilson, D.G.
1978-09-01
This report is the twenty-first of a series of annual reports dating back to the February 28, 1957, report of the ORNL Mathematics Panel. The current report is divided into five parts: Mathematical and Statistical Research, Statistical and Mathematical Collaboration, Educational Activities, Presentations of Research Results, and Professional Activities. The section entitled Mathematical and Statistical Research contains summaries of the research conducted on Moving Boundary Problems, Multivariate Multipopulation Classification, Numerical Linear Algebra, Statistical Model Development and Evaluation, Materials Science Applications, Biomedical and Environmental Applications, and Complementary Areas. Recorded under Statistical and Mathematical Collaboration are brief accounts of consulting and collaboration with other scientists and engineers in the Nuclear Division of Union Carbide Corporation. These are in the areas of Analytical Chemistry, Biology, Chemistry and Physics, Engineering, Environmental Sciences, Materials Sciences, Security and Communication, and Uranium Resource Evaluation. The Educational Activities section contains descriptions of symposia, workshops, seminar series, short courses, lectures, and student and faculty participation in which the staff was engaged during the report period. The last two parts of the report list the staff's publications and oral presentations as well as its participation in the activities of professional societies and academic institutions. The summaries given here are quite brief; completed work is published in journals or reports as appropriate. 7 figures, 8 tables
Energy Technology Data Exchange (ETDEWEB)
Gardiner, D.A.; Lever, W.E.; Shepherd, D.E.; Ward, R.C.; Wilson, D.G. (comps.)
1978-09-01
This report is the twenty-first of a series of annual reports dating back to the February 28, 1957, report of the ORNL Mathematics Panel. The current report is divided into five parts: Mathematical and Statistical Research, Statistical and Mathematical Collaboration, Educational Activities, Presentations of Research Results, and Professional Activities. The section entitled Mathematical and Statistical Research contains summaries of the research conducted on Moving Boundary Problems, Multivariate Multipopulation Classification, Numerical Linear Algebra, Statistical Model Development and Evaluation, Materials Science Applications, Biomedical and Environmental Applications, and Complementary Areas. Recorded under Statistical and Mathematical Collaboration are brief accounts of consulting and collaboration with other scientists and engineers in the Nuclear Division of Union Carbide Corporation. These are in the areas of Analytical Chemistry, Biology, Chemistry and Physics, Engineering, Environmental Sciences, Materials Sciences, Security and Communication, and Uranium Resource Evaluation. The Educational Activities section contains descriptions of symposia, workshops, seminar series, short courses, lectures, and student and faculty participation in which the staff was engaged during the report period. The last two parts of the report list the staff's publications and oral presentations as well as its participation in the activities of professional societies and academic institutions. The summaries given here are quite brief; completed work is published in journals or reports as appropriate. 7 figures, 8 tables.
Vol. 3: Statistical Physics and Phase Transitions
International Nuclear Information System (INIS)
Sitenko, A.
1993-01-01
Problems of modern physics and the situation with physical research in Ukraine are considered. Programme of the conference includes scientific and general problems. Its proceedings are published in 6 volumes. The papers presented in this volume refer to statistical physics and phase transition theory
A modern course in statistical physics
Reichl, Linda E
2016-01-01
"A Modern Course in Statistical Physics" is a textbook that illustrates the foundations of equilibrium and non-equilibrium statistical physics, and the universal nature of thermodynamic processes, from the point of view of contemporary research problems. The book treats such diverse topics as the microscopic theory of critical phenomena, superfluid dynamics, quantum conductance, light scattering, transport processes, and dissipative structures, all in the framework of the foundations of statistical physics and thermodynamics. It shows the quantum origins of problems in classical statistical physics. One focus of the book is fluctuations that occur due to the discrete nature of matter, a topic of growing importance for nanometer scale physics and biophysics. Another focus concerns classical and quantum phase transitions, in both monatomic and mixed particle systems. This fourth edition extends the range of topics considered to include, for example, entropic forces, electrochemical processes in biological syste...
Physics and Mathematics as Interwoven Disciplines in Science Education
Galili, Igal
2018-03-01
The relationship between physics and mathematics is reviewed upgrading the common in physics classes' perspective of mathematics as a toolkit for physics. The nature of the physics-mathematics relationship is considered along a certain historical path. The triadic hierarchical structure of discipline-culture helps to identify different ways in which mathematics is used in physics and to appreciate its contribution, to recognize the difference between mathematics and physics as disciplines in approaches, values, methods, and forms. We mentioned certain forms of mathematical knowledge important for physics but often missing in school curricula. The geometrical mode of codification of mathematical knowledge is compared with the analytical one in context of teaching school physics and mathematics; their complementarity is exemplified. Teaching may adopt the examples facilitating the claims of the study to reach science literacy and meaningful learning.
Archives: Journal of the Nigerian Association of Mathematical Physics
African Journals Online (AJOL)
Items 1 - 14 of 14 ... Archives: Journal of the Nigerian Association of Mathematical Physics. Journal Home > Archives: Journal of the Nigerian Association of Mathematical Physics. Log in or Register to get access to full text downloads.
Journal of the Nigerian Association of Mathematical Physics: Journal ...
African Journals Online (AJOL)
Journal of the Nigerian Association of Mathematical Physics: Journal Sponsorship. Journal Home > About the Journal > Journal of the Nigerian Association of Mathematical Physics: Journal Sponsorship. Log in or Register to get access to full text downloads.
Global Conference on Applied Physics and Mathematics
2016-01-01
The Global Conference on Applied Physics and Mathematics is organized by academics and researchers belonging to different scientific areas of the C3i/Polytechnic Institute of Portalegre (Portugal) and the University of Extremadura (Spain) with the technical support of ScienceKnow Conferences. The event has the objective of creating an international forum for academics, researchers and scientists from worldwide to discuss worldwide results and proposals regarding to the soundest issues related to Applied Physics and Mathematics. This event will include the participation of renowned keynote speakers, oral presentations, posters sessions and technical conferences related to the topics dealt with in the Scientific Program as well as an attractive social and cultural program. The papers will be published in the Proceedings e-books. The proceedings of the conference will be sent to possible indexing on Thomson Reuters (selective by Thomson Reuters, not all-inclusive) and Google Scholar. Those communications con...
Equations in mathematical physics a practical course
Pikulin, Victor P
2001-01-01
This handbook is addressed to students of technology institutf's where a course on mathematical physics of relatively reduced volume is offered, as well as to engineers and scientists. The aim of the handbook is to treat (demonstrate) the basic methods for solving the simplest problems of classical mathematical physics. The most basic among the methods considered hrre i8 the superposition method. It allows one, based on particular linearly indepmdent HolutionH (solution "atoms"), to obtain the solution of a given problem. To that end the "Hupply" of solution atoms must be complete. This method is a development of the well-known method of particular solutions from the theory of ordinar~' differelltial equations. In contrast to the case of ordinary differential equations, where the number of linearly independent 80lutions is always finite, for a linear partial differrntial equation a complete "supply" of solution atoms is always infinite. This infinite set of Holutions may be discrete (for example, for regular ...
The Computer Student Worksheet Based Mathematical Literacy for Statistics
Manoy, J. T.; Indarasati, N. A.
2018-01-01
The student worksheet is one of media teaching which is able to improve teaching an activity in the classroom. Indicators in mathematical literacy were included in a student worksheet is able to help the students for applying the concept in daily life. Then, the use of computers in learning can create learning with environment-friendly. This research used developmental research which was Thiagarajan (Four-D) development design. There are 4 stages in the Four-D, define, design, develop, and disseminate. However, this research was finish until the third stage, develop stage. The computer student worksheet based mathematical literacy for statistics executed good quality. This student worksheet is achieving the criteria if able to achieve three aspects, validity, practicality, and effectiveness. The subject in this research was the students at The 1st State Senior High School of Driyorejo, Gresik, grade eleven of The 5th Mathematics and Natural Sciences. The computer student worksheet products based mathematical literacy for statistics executed good quality, while it achieved the aspects for validity, practical, and effectiveness. This student worksheet achieved the validity aspects with an average of 3.79 (94.72%), and practical aspects with an average of 2.85 (71.43%). Besides, it achieved the effectiveness aspects with a percentage of the classical complete students of 94.74% and a percentage of the student positive response of 75%.
Reconstructing Macroeconomics Based on Statistical Physics
Aoki, Masanao; Yoshikawa, Hiroshi
We believe that time has come to integrate the new approach based on statistical physics or econophysics into macroeconomics. Toward this goal, there must be more dialogues between physicists and economists. In this paper, we argue that there is no reason why the methods of statistical physics so successful in many fields of natural sciences cannot be usefully applied to macroeconomics that is meant to analyze the macroeconomy comprising a large number of economic agents. It is, in fact, weird to regard the macroeconomy as a homothetic enlargement of the representative micro agent. We trust the bright future of the new approach to macroeconomies based on statistical physics.
Recent developments of the ROOT mathematical and statistical software
International Nuclear Information System (INIS)
Moneta, L; Antcheva, I; Brun, R
2008-01-01
Advanced mathematical and statistical computational methods are required by the LHC experiments to analyzed their data. These methods are provided by the Math work package of the ROOT project. An overview of the recent developments of this work package is presented by describing the restructuring of the core mathematical library in a coherent set of C++ classes and interfaces. The achieved improvements, in terms of performances and quality, of numerical methods present in ROOT are shown as well. New developments in the fitting and minimization packages are reviewed. A new graphics interface has been developed to drive the fitting process and new classes are being introduced to extend the fitting functionality. Furthermore, recent and planned developments of integrating in the ROOT environment new advanced statistical tools required for the analysis of the LHC data are presented
Mathematical and Statistical Methods for Actuarial Sciences and Finance
Legros, Florence; Perna, Cira; Sibillo, Marilena
2017-01-01
This volume gathers selected peer-reviewed papers presented at the international conference "MAF 2016 – Mathematical and Statistical Methods for Actuarial Sciences and Finance”, held in Paris (France) at the Université Paris-Dauphine from March 30 to April 1, 2016. The contributions highlight new ideas on mathematical and statistical methods in actuarial sciences and finance. The cooperation between mathematicians and statisticians working in insurance and finance is a very fruitful field, one that yields unique theoretical models and practical applications, as well as new insights in the discussion of problems of national and international interest. This volume is addressed to academicians, researchers, Ph.D. students and professionals.
PREFACE: Algebra, Geometry, and Mathematical Physics 2010
Stolin, A.; Abramov, V.; Fuchs, J.; Paal, E.; Shestopalov, Y.; Silvestrov, S.
2012-02-01
This proceedings volume presents results obtained by the participants of the 6th Baltic-Nordic workshop 'Algebra, Geometry, and Mathematical Physics (AGMP-6)' held at the Sven Lovén Centre for Marine Sciences in Tjärnö, Sweden on October 25-30, 2010. The Baltic-Nordic Network AGMP 'Algebra, Geometry, and Mathematical Physics' http://www.agmp.eu was created in 2005 on the initiative of two Estonian universities and two Swedish universities: Tallinn University of Technology represented by Eugen Paal (coordinator of the network), Tartu University represented by Viktor Abramov, Lund University represented by Sergei Silvestrov, and Chalmers University of Technology and the University of Gothenburg represented by Alexander Stolin. The goal was to promote international and interdisciplinary cooperation between scientists and research groups in the countries of the Baltic-Nordic region in mathematics and mathematical physics, with special emphasis on the important role played by algebra and geometry in modern physics, engineering and technologies. The main activities of the AGMP network consist of a series of regular annual international workshops, conferences and research schools. The AGMP network also constitutes an important educational forum for scientific exchange and dissimilation of research results for PhD students and Postdocs. The network has expanded since its creation, and nowadays its activities extend beyond countries in the Baltic-Nordic region to universities in other European countries and participants from elsewhere in the world. As one of the important research-dissimilation outcomes of its activities, the network has a tradition of producing high-quality research proceedings volumes after network events, publishing them with various international publishers. The PDF also contains the following: List of AGMP workshops and other AGMP activities Main topics discussed at AGMP-6 Review of AGMP-6 proceedings Acknowledgments List of Conference Participants
Statistical physics of complex systems a concise introduction
Bertin, Eric
2016-01-01
This course-tested primer provides graduate students and non-specialists with a basic understanding of the concepts and methods of statistical physics and demonstrates their wide range of applications to interdisciplinary topics in the field of complex system sciences, including selected aspects of theoretical modeling in biology and the social sciences. Generally speaking, the goals of statistical physics may be summarized as follows: on the one hand to study systems composed of a large number of interacting units, and on the other to predict the macroscopic, collective behavior of the system considered from the perspective of the microscopic laws governing the dynamics of the individual entities. These two goals are essentially also shared by what is now called 'complex systems science', and as such, systems studied in the framework of statistical physics may be considered to be among the simplest examples of complex systems – while also offering a rather well developed mathematical treatment. The second ...
Trajectory attractors of equations of mathematical physics
International Nuclear Information System (INIS)
Vishik, Marko I; Chepyzhov, Vladimir V
2011-01-01
In this survey the method of trajectory dynamical systems and trajectory attractors is described, and is applied in the study of the limiting asymptotic behaviour of solutions of non-linear evolution equations. This method is especially useful in the study of dissipative equations of mathematical physics for which the corresponding Cauchy initial-value problem has a global (weak) solution with respect to the time but the uniqueness of this solution either has not been established or does not hold. An important example of such an equation is the 3D Navier-Stokes system in a bounded domain. In such a situation one cannot use directly the classical scheme of construction of a dynamical system in the phase space of initial conditions of the Cauchy problem of a given equation and find a global attractor of this dynamical system. Nevertheless, for such equations it is possible to construct a trajectory dynamical system and investigate a trajectory attractor of the corresponding translation semigroup. This universal method is applied for various types of equations arising in mathematical physics: for general dissipative reaction-diffusion systems, for the 3D Navier-Stokes system, for dissipative wave equations, for non-linear elliptic equations in cylindrical domains, and for other equations and systems. Special attention is given to using the method of trajectory attractors in approximation and perturbation problems arising in complicated models of mathematical physics. Bibliography: 96 titles.
Mathematical models of physics problems (physics research and technology)
Anchordoqui, Luis Alfredo
2013-01-01
This textbook is intended to provide a foundation for a one-semester introductory course on the advanced mathematical methods that form the cornerstones of the hard sciences and engineering. The work is suitable for first year graduate or advanced undergraduate students in the fields of Physics, Astronomy and Engineering. This text therefore employs a condensed narrative sufficient to prepare graduate and advanced undergraduate students for the level of mathematics expected in more advanced graduate physics courses, without too much exposition on related but non-essential material. In contrast to the two semesters traditionally devoted to mathematical methods for physicists, the material in this book has been quite distilled, making it a suitable guide for a one-semester course. The assumption is that the student, once versed in the fundamentals, can master more esoteric aspects of these topics on his or her own if and when the need arises during the course of conducting research. The book focuses on two cor...
The mathematics and physics of knots
Energy Technology Data Exchange (ETDEWEB)
Kauffman, Louis H [Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607-7045 (United States)
2005-12-01
This paper is an introduction to relationships between knot theory and theoretical physics. We give an exposition of the theory of polynomial invariants of knots and links, the Witten functional integral formulation of knot and link invariants, and the beginnings of topological quantum field theory, and show how the theory of knots is related to a number of key issues in mathematical physics, including loop quantum gravity and quantum information theory. Along with the references cited in the text below, we also recommend the following as sources of background information.
Prospective elementary and secondary school mathematics teachers’ statistical reasoning
Directory of Open Access Journals (Sweden)
Rabia KARATOPRAK
2015-04-01
Full Text Available This study investigated prospective elementary (PEMTs and secondary (PSMTs school mathematics teachers’ statistical reasoning. The study began with the adaptation of the Statistical Reasoning Assessment (Garfield, 2003 test. Then, the test was administered to 82 PEMTs and 91 PSMTs in a metropolitan city of Turkey. Results showed that both groups were equally successful in understanding independence, and understanding importance of large samples. However, results from selecting appropriate measures of center together with the misconceptions assessing the same subscales showed that both groups selected mode rather than mean as an appropriate average. This suggested their lack of attention to the categorical and interval/ratio variables while examining data. Similarly, both groups were successful in interpreting and computing probability; however, they had equiprobability bias, law of small numbers and representativeness misconceptions. The results imply a change in some questions in the Statistical Reasoning Assessment test and that teacher training programs should include statistics courses focusing on studying characteristics of samples.
Focus group discussion in mathematical physics learning
Ellianawati; Rudiana, D.; Sabandar, J.; Subali, B.
2018-03-01
The Focus Group Discussion (FGD) activity in Mathematical Physics learning has helped students perform the stages of problem solving reflectively. The FGD implementation was conducted to explore the problems and find the right strategy to improve the students' ability to solve the problem accurately which is one of reflective thinking component that has been difficult to improve. The research method used is descriptive qualitative by using single subject response in Physics student. During the FGD process, one student was observed of her reflective thinking development in solving the physics problem. The strategy chosen in the discussion activity was the Cognitive Apprenticeship-Instruction (CA-I) syntax. Based on the results of this study, it is obtained the information that after going through a series of stages of discussion, the students' reflective thinking skills is increased significantly. The scaffolding stage in the CA-I model plays an important role in the process of solving physics problems accurately. Students are able to recognize and formulate problems by describing problem sketches, identifying the variables involved, applying mathematical equations that accord to physics concepts, executing accurately, and applying evaluation by explaining the solution to various contexts.
Understanding search trees via statistical physics
Indian Academy of Sciences (India)
ary search tree model (where stands for the number of branches of the search tree), an important problem for data storage in computer science, using a variety of statistical physics techniques that allow us to obtain exact asymptotic results.
Statistical physics including applications to condensed matter
Hermann, Claudine
2005-01-01
Statistical Physics bridges the properties of a macroscopic system and the microscopic behavior of its constituting particles, otherwise impossible due to the giant magnitude of Avogadro's number. Numerous systems of today's key technologies -- as e.g. semiconductors or lasers -- are macroscopic quantum objects; only statistical physics allows for understanding their fundamentals. Therefore, this graduate text also focuses on particular applications such as the properties of electrons in solids with applications, and radiation thermodynamics and the greenhouse effect.
Statistical physics of hard combinatorial optimization: Vertex cover problem
Zhao, Jin-Hua; Zhou, Hai-Jun
2014-07-01
Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years, the replica-symmetry-breaking mean field theory of spin glasses and the associated message-passing algorithms have greatly deepened our understanding of typical-case computation complexity. In this paper, we use the vertex cover problem, a basic nondeterministic-polynomial (NP)-complete combinatorial optimization problem of wide application, as an example to introduce the statistical physical methods and algorithms. We do not go into the technical details but emphasize mainly the intuitive physical meanings of the message-passing equations. A nonfamiliar reader shall be able to understand to a large extent the physics behind the mean field approaches and to adjust the mean field methods in solving other optimization problems.
Bowyer, Jessica; Darlington, Ellie
2017-01-01
It is essential that physics undergraduates are appropriately prepared for the mathematical demands of their course. This study investigated physics students’ perceptions of post-compulsory mathematics as preparation for their degree course. 494 physics undergraduates responded to an online questionnaire about their experiences of A-level Mathematics and Further Mathematics. The findings suggest that physics undergraduates would benefit from studying Further Mathematics and specialising in mechanics during their A-level studies. As both A-level Mathematics and Further Mathematics are being reformed, universities should look closely at the benefits of Further Mathematics as preparation for their physics courses and either increase their admissions requirements, or recommend that students take Further Mathematics.
Proceedings of the 6th Pannonian Symposium on Mathematical Statistics
Révész, P; Wertz, W; Bauer, P; Konecny, F; Mathematical Statistics and Probability Theory, Volume A : Theoretical Aspects; Mathematical Statistics and Probability Theory, Volume B : Statistical Inference and Methods
1987-01-01
The past several years have seen the creation and extension of a very conclusive theory of statistics and probability. Many of the research workers who have been concerned with both probability and statistics felt the need for meetings that provide an opportunity for personal con tacts among scholars whose fields of specialization cover broad spectra in bothstatistics and probability: to discuss major open problems and new solutions, and to provide encouragement for further research through the lectures of carefully selected scholars, moreover to introduce to younger colleagues the latest research techniques and thus to stimulate their interest in research. To meet these goals, the series of Pannonian Symposia on Mathematical Statistics was organized, beginning in the year 1979: the first, second and fourth one in Bad Tatzmannsdorf, Burgenland, Austria, the third and fifth in Visegrad, Hungary. The Sixth Pannonian Symposium was held in Bad Tatzmannsdorf again, in the time between 14 and 20 September...
Mathematics and physics of emerging biomedical imaging
International Nuclear Information System (INIS)
1996-01-01
Although the mathematical sciences were used in a general way for image processing, they were of little importance in biomedical work until the development in the 1970s of computed tomography (CT) for the imaging of x-rays and isotope emission tomography. In the 1980s, MRI eclipsed the other modalities in many ways as the most informative medical imaging methodology. Besides these well-established techniques, computer-based mathematical methods are being explored in applications to other well-known methods, such as ultrasound and electroencephalography, as well as new techniques of optical imaging, impedance tomography, and magnetic source imaging. It is worth pointing out that, while the final images of many of these techniques bear many similarities to each other, the technologies involved in each are completely different and the parameters represented in the images are very different in character as well as in medical usefulness. In each case, rather different mathematical or statistical models are used, with different equations. One common thread is the paradigm of reconstruction from indirect measurements--this is the unifying theme of this report. The imaging methods used in biomedical applications that this report discusses include: (1) x-ray projection imaging; (2) x-ray computed tomography (CT); (3) magnetic resonance imaging (MRI) and magnetic resonance spectroscopy; (4) single photon emission computed tomography (SPECT); (5) positron emission tomography (PET); (6) ultrasonics; (7) electrical source imaging (ESI); (8) electrical impedance tomography (EIT); (9) magnetic source imaging (MSI); and (10) medical optical imaging
Mathematical methods in physics and engineering
Dettman, John W
2011-01-01
Intended for college-level physics, engineering, or mathematics students, this volume offers an algebraically based approach to various topics in applied math. It is accessible to undergraduates with a good course in calculus which includes infinite series and uniform convergence. Exercises follow each chapter to test the student's grasp of the material; however, the author has also included exercises that extend the results to new situations and lay the groundwork for new concepts to be introduced later. A list of references for further reading will be found at the end of each chapter. For t
Mathematical Reasoning Requirements in Swedish National Physics Tests
Johansson, Helena
2016-01-01
This paper focuses on one aspect of mathematical competence, namely mathematical reasoning, and how this competency influences students' knowing of physics. This influence was studied by analysing the mathematical reasoning requirements upper secondary students meet when solving tasks in national physics tests. National tests are constructed to…
Application of mathematical statistics methods to study fluorite deposits
International Nuclear Information System (INIS)
Chermeninov, V.B.
1980-01-01
Considered are the applicability of mathematical-statistical methods for the increase of reliability of sampling and geological tasks (study of regularities of ore formation). Compared is the reliability of core sampling (regarding the selective abrasion of fluorite) and neutron activation logging for fluorine. The core sampling data are characterized by higher dispersion than neutron activation logging results (mean value of variation coefficients are 75% and 56% respectively). However the hypothesis of the equality of average two sampling is confirmed; this fact testifies to the absence of considerable variability of ore bodies
Modellus: Learning Physics with Mathematical Modelling
Teodoro, Vitor
Computers are now a major tool in research and development in almost all scientific and technological fields. Despite recent developments, this is far from true for learning environments in schools and most undergraduate studies. This thesis proposes a framework for designing curricula where computers, and computer modelling in particular, are a major tool for learning. The framework, based on research on learning science and mathematics and on computer user interface, assumes that: 1) learning is an active process of creating meaning from representations; 2) learning takes place in a community of practice where students learn both from their own effort and from external guidance; 3) learning is a process of becoming familiar with concepts, with links between concepts, and with representations; 4) direct manipulation user interfaces allow students to explore concrete-abstract objects such as those of physics and can be used by students with minimal computer knowledge. Physics is the science of constructing models and explanations about the physical world. And mathematical models are an important type of models that are difficult for many students. These difficulties can be rooted in the fact that most students do not have an environment where they can explore functions, differential equations and iterations as primary objects that model physical phenomena--as objects-to-think-with, reifying the formal objects of physics. The framework proposes that students should be introduced to modelling in a very early stage of learning physics and mathematics, two scientific areas that must be taught in very closely related way, as they were developed since Galileo and Newton until the beginning of our century, before the rise of overspecialisation in science. At an early stage, functions are the main type of objects used to model real phenomena, such as motions. At a later stage, rates of change and equations with rates of change play an important role. This type of equations
Statistical and physical evolution of QSO's
International Nuclear Information System (INIS)
Caditz, D.; Petrosian, V.
1989-09-01
The relationship between the physical evolution of discrete extragalactic sources, the statistical evolution of the observed population of sources, and the cosmological model is discussed. Three simple forms of statistical evolution: pure luminosity evolution (PLE), pure density evolution (PDE), and generalized luminosity evolution (GLE), are considered in detail together with what these forms imply about the physical evolution of individual sources. Two methods are used to analyze the statistical evolution of the observed distribution of QSO's (quasars) from combined flux limited samples. It is shown that both PLE and PDE are inconsistent with the data over the redshift range 0 less than z less than 2.2, and that a more complicated form of evolution such as GLE is required, independent of the cosmological model. This result is important for physical models of AGN, and in particular, for the accretion disk model which recent results show may be inconsistent with PLE
A Moonshine Dialogue in Mathematical Physics
Directory of Open Access Journals (Sweden)
Michel Planat
2015-08-01
Full Text Available Phys and Math are two colleagues at the University of Saçenbon (Crefan Kingdom, dialoguing about the remarkable efficiency of mathematics for physics. They talk about the notches on the Ishango bone and the various uses of psi in maths and physics; they arrive at dessins d’enfants, moonshine concepts, Rademacher sums and their significance in the quantum world. You should not miss their eccentric proposal of relating Bell’s theorem to the Baby Monster group. Their hyperbolic polygons show a considerable singularity/cusp structure that our modern age of computers is able to capture. Henri Poincaré would have been happy to see it.
Probability and statistics in particle physics
International Nuclear Information System (INIS)
Frodesen, A.G.; Skjeggestad, O.
1979-01-01
Probability theory is entered into at an elementary level and given a simple and detailed exposition. The material on statistics has been organised with an eye to the experimental physicist's practical need, which is likely to be statistical methods for estimation or decision-making. The book is intended for graduate students and research workers in experimental high energy and elementary particle physics, and numerous examples from these fields are presented. (JIW)
My view of mathematics and physics (integration of mathematics into physics
Directory of Open Access Journals (Sweden)
Safronov S.V.
2017-09-01
Full Text Available this paper explores a new view of modern physics. New material is added to the modern mathematical physics. Filling a gap in physics theory and physical laws already in existence is the purpose of the article. The paper is devoted to contemporary issues. The work contains first development of formulas: gravitational pulse formula, vibration in pendulum formula, photon formula, three field energy density in atom formula, neutrino energy formula, equal energy of two kinds conversion formula and ray of light energy formula. The author introduces the conversion sign for scientific use in this article. The practical importance of the work involves innovative technology development.
Problem solving in the borderland between mathematics and physics
DEFF Research Database (Denmark)
Jensen, Jens Højgaard; Niss, Martin; Jankvist, Uffe Thomas
2017-01-01
The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it fo......The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect...
Partial differential equations of mathematical physics and integral equations
Guenther, Ronald B
1996-01-01
This book was written to help mathematics students and those in the physical sciences learn modern mathematical techniques for setting up and analyzing problems. The mathematics used is rigorous, but not overwhelming, while the authors carefully model physical situations, emphasizing feedback among a beginning model, physical experiments, mathematical predictions, and the subsequent refinement and reevaluation of the physical model itself. Chapter 1 begins with a discussion of various physical problems and equations that play a central role in applications. The following chapters take up the t
XIII Modave Summer School in Mathematical Physics
2017-09-01
The Modave Summer School on Mathematical Physics is a yearly summer school in topics of theoretical physics. Various topics ranging from quantum gravity and cosmology to theoretical particle physics and string theory. The school takes place in Modave, a charming village in the Belgian Ardennes close to Huy. Modave School is organised by PhD students for PhD students, and this makes it rather unique. The courses are taught by Post-Docs or late PhD students, and they are all made of pedagogical, basic blackboard lectures about recent topics in theoretical physics. Participants and lecturers eat and sleep in the same place where the lectures are given. The absence of senior members, and the fact of spending day and night together in an isolated, peaceful place contribute to creating an informal atmosphere and facilitating interactions. Lectures of the thirteenth edition are centered around the following subjects: bulk reconstruction in AdS/CFT, twistor theory, AdS_2/CFT_1 and SYK, geometry and topology, and asymptotic charges.
Science Academies' Refresher Course in Statistical Physics
Indian Academy of Sciences (India)
The Course is aimed at college teachers of statistical physics at BSc/MSc level. It will cover basic principles and techniques, in a pedagogical manner, through lectures and tutorials, with illustrative problems. Some advanced topics, and common difficulties faced by students will also be discussed. College/University ...
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.
Bowyer, Jessica; Darlington, Ellie
2017-01-01
It is essential that physics undergraduates are appropriately prepared for the mathematical demands of their course. This study investigated physics students' perceptions of post-compulsory mathematics as preparation for their degree course. 494 physics undergraduates responded to an online questionnaire about their experiences of A-level…
Theoretical mechanics an introduction to mathematical physics
Sweetman Ames, Joseph
1958-01-01
In this book Professors Ames and Murnaghan undertake a mathematically rigorous development of theoretical mechanics from the point of view of modern physics. It gives an intensive survey of this basis field with extensive and extremely thorough discussions of vector and tensor methods, the displacement and motion of a rigid body, dynamics of inertial and non-inertial reference frames, dynamics of a particle, harmonic vibrations, nonrectilinear motion of a particle, central forces and universal gravitation, dynamics of a systems of material particle,impulsive forces, motion of a rigid body about a fixed point, gyroscopic and barygyroscopic theory, general dynamical theorems, vibrations about a point of equilibrium, the principle of least action, holonomic and nonholonomic systems, the principle of least constraint, general methods of integration and the three body problem, the potential function (including simple-layer and double-layer potentials), wave motion, the Lorentz-Einstein transformation and an illumi...
Current problems in applied mathematics and mathematical physics
Samarskii, A. A.
Papers are presented on such topics as mathematical models in immunology, mathematical problems of medical computer tomography, classical orthogonal polynomials depending on a discrete variable, and boundary layer methods for singular perturbation problems in partial derivatives. Consideration is also given to the computer simulation of supernova explosion, nonstationary internal waves in a stratified fluid, the description of turbulent flows by unsteady solutions of the Navier-Stokes equations, and the reduced Galerkin method for external diffraction problems using the spline approximation of fields.
Use of Mathematical Methods of Statistics for Analyzing Engine Characteristics
Directory of Open Access Journals (Sweden)
Aivaras Jasilionis
2012-11-01
Full Text Available For the development of new models, automobile manufacturers are trying to come up with optimal software for engine control in all movement modes. However, in this case, a vehicle cannot reach outstanding characteristics in none of them. This is the main reason why modifications in engine control software used for adapting the vehicle for driver’s needs are becoming more and more popular. The article presents a short analysis of development trends towards engine control software. Also, models of mathematical statistics for engine power and torque growth are created. The introduced models give an opportunity to predict the probabilities of engine power or torque growth after individual reprogramming of engine control software.
Statistical mechanics of lattice systems a concrete mathematical introduction
Friedli, Sacha
2017-01-01
This motivating textbook gives a friendly, rigorous introduction to fundamental concepts in equilibrium statistical mechanics, covering a selection of specific models, including the Curie–Weiss and Ising models, the Gaussian free field, O(n) models, and models with Kać interactions. Using classical concepts such as Gibbs measures, pressure, free energy, and entropy, the book exposes the main features of the classical description of large systems in equilibrium, in particular the central problem of phase transitions. It treats such important topics as the Peierls argument, the Dobrushin uniqueness, Mermin–Wagner and Lee–Yang theorems, and develops from scratch such workhorses as correlation inequalities, the cluster expansion, Pirogov–Sinai Theory, and reflection positivity. Written as a self-contained course for advanced undergraduate or beginning graduate students, the detailed explanations, large collection of exercises (with solutions), and appendix of mathematical results and concepts also make i...
Mathematical and statistical methods for actuarial sciences and finance
Sibillo, Marilena
2014-01-01
The interaction between mathematicians and statisticians working in the actuarial and financial fields is producing numerous meaningful scientific results. This volume, comprising a series of four-page papers, gathers new ideas relating to mathematical and statistical methods in the actuarial sciences and finance. The book covers a variety of topics of interest from both theoretical and applied perspectives, including: actuarial models; alternative testing approaches; behavioral finance; clustering techniques; coherent and non-coherent risk measures; credit-scoring approaches; data envelopment analysis; dynamic stochastic programming; financial contagion models; financial ratios; intelligent financial trading systems; mixture normality approaches; Monte Carlo-based methodologies; multicriteria methods; nonlinear parameter estimation techniques; nonlinear threshold models; particle swarm optimization; performance measures; portfolio optimization; pricing methods for structured and non-structured derivatives; r...
Simple mathematical models of symmetry breaking. Application to particle physics
International Nuclear Information System (INIS)
Michel, L.
1976-01-01
Some mathematical facts relevant to symmetry breaking are presented. A first mathematical model deals with the smooth action of compact Lie groups on real manifolds, a second model considers linear action of any group on real or complex finite dimensional vector spaces. Application of the mathematical models to particle physics is considered. (B.R.H.)
Statistical physics of pairwise probability models
DEFF Research Database (Denmark)
Roudi, Yasser; Aurell, Erik; Hertz, John
2009-01-01
(dansk abstrakt findes ikke) Statistical models for describing the probability distribution over the states of biological systems are commonly used for dimensional reduction. Among these models, pairwise models are very attractive in part because they can be fit using a reasonable amount of data......: knowledge of the means and correlations between pairs of elements in the system is sufficient. Not surprisingly, then, using pairwise models for studying neural data has been the focus of many studies in recent years. In this paper, we describe how tools from statistical physics can be employed for studying...
Hannigan, Ailish; Gill, Olivia; Leavy, Aisling M.
2013-01-01
The development of statistical literacy is fast becoming the focus of a large part of mathematics instruction at primary, secondary and tertiary levels. This broadening of the mathematics curriculum to encompass a focus on statistics makes considerable demands on teachers. Most mathematics teachers acknowledge the practical importance of…
Conference: Statistical Physics and Biological Information
International Nuclear Information System (INIS)
Gross, David J.; Hwa, Terence
2001-01-01
In the spring of 2001, the Institute for Theoretical Physics ran a 6 month scientific program on Statistical Physics and Biological Information. This program was organized by Walter Fitch (UC Irvine), Terence Hwa (UC San Diego), Luca Peliti (University Federico II), Naples Gary Stormo (Washington University School of Medicine) and Chao Tang (NEC). Overall scientific supervision was provided by David Gross, Director, ITP. The ITP has an online conference/program proceeding which consists of audio and transparencies of almost all of the talks held during this program. Over 100 talks are available on the site at http://online.kitp.ucsb.edu/online/infobio01/
Conference: Statistical Physics and Biological Information; F
International Nuclear Information System (INIS)
Gross, David J.; Hwa, Terence
2001-01-01
In the spring of 2001, the Institute for Theoretical Physics ran a 6 month scientific program on Statistical Physics and Biological Information. This program was organized by Walter Fitch (UC Irvine), Terence Hwa (UC San Diego), Luca Peliti (University Federico II), Naples Gary Stormo (Washington University School of Medicine) and Chao Tang (NEC). Overall scientific supervision was provided by David Gross, Director, ITP. The ITP has an online conference/program proceeding which consists of audio and transparencies of almost all of the talks held during this program. Over 100 talks are available on the site at http://online.kitp.ucsb.edu/online/infobio01/
Statistical and thermal physics an introduction
Hoch, Michael JR
2011-01-01
""When I started reading Michael J.R. Hoch's book Statistical and Thermal Physics: An Introduction I thought to myself that this is another book the same as a large group of others with similar content. … But during my reading this unjustified belief changed. … The main reason for this change was the way of information presentation: … the way of presentation is designed so that the reader receives only the information that is necessary to give the essence of the problem. … this book will provide an introduction to the subject especially for those who are interested in basic or applied physics.
Index Theory with Applications to Mathematics and Physics
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm; Bleecker, David
Index Theory with Applications to Mathematics and Physics describes, explains, and explores the Index Theorem of Atiyah and Singer, one of the truly great accomplishments of twentieth-century mathematics whose influence continues to grow, fifty years after its discovery. The Index Theorem has giv...... birth to many mathematical research areas and exposed profound connections between analysis, geometry, topology, algebra, and mathematical physics. Hardly any topic of modern mathematics stands independent of its influence.......Index Theory with Applications to Mathematics and Physics describes, explains, and explores the Index Theorem of Atiyah and Singer, one of the truly great accomplishments of twentieth-century mathematics whose influence continues to grow, fifty years after its discovery. The Index Theorem has given...
Statistical Issues in Searches for New Physics
CERN. Geneva
2015-01-01
Given the cost, both financial and even more importantly in terms of human effort, in building High Energy Physics accelerators and detectors and running them, it is important to use good statistical techniques in analysing data. This talk covers some of the statistical issues that arise in searches for New Physics. They include topics such as: Should we insist on the 5 sigma criterion for discovery claims? What are the relative merits of a Raster Scan or a "2-D" approach? P(A|B) is not the same as P(B|A) The meaning of p-values Example of a problematic likelihood What is Wilks Theorem and when does it not apply? How should we deal with the "Look Elsewhere Effect"? Dealing with systematics such as background parametrisation Coverage: What is it and does my method have the correct coverage? The use of p0 vs. p1 plots
Statistical physics of medical ultrasonic images
International Nuclear Information System (INIS)
Wagner, R.F.; Insana, M.F.; Brown, D.G.; Smith, S.W.
1987-01-01
The physical and statistical properties of backscattered signals in medical ultrasonic imaging are reviewed in terms of: 1) the radiofrequency signal; 2) the envelope (video or magnitude) signal; and 3) the density of samples in simple and in compounded images. There is a wealth of physical information in backscattered signals in medical ultrasound. This information is contained in the radiofrequency spectrum - which is not typically displayed to the viewer - as well as in the higher statistical moments of the envelope or video signal - which are not readily accessed by the human viewer of typical B-scans. This information may be extracted from the detected backscattered signals by straightforward signal processing techniques at low resolution
Schindler, Maike; Mackrell, Kate; Pratt, Dave; Bakker, A.
2017-01-01
Schindler, M., Mackrell, K., Pratt, D., & Bakker, A. (2017). Applying contemporary philosophy in mathematics and statistics education: The perspective of inferentialism. In G. Kaiser (Ed.). Proceedings of the 13th International Congress on Mathematical Education, ICME-13
Mathematical background and attitudes toward statistics in a sample of Spanish college students.
Carmona, José; Martínez, Rafael J; Sánchez, Manuel
2005-08-01
To examine the relation of mathematical background and initial attitudes toward statistics of Spanish college students in social sciences the Survey of Attitudes Toward Statistics was given to 827 students. Multivariate analyses tested the effects of two indicators of mathematical background (amount of exposure and achievement in previous courses) on the four subscales. Analysis suggested grades in previous courses are more related to initial attitudes toward statistics than the number of mathematics courses taken. Mathematical background was related with students' affective responses to statistics but not with their valuing of statistics. Implications of possible research are discussed.
Nonequilibrium statistical physics a modern perspective
Livi, Roberto
2017-01-01
Statistical mechanics has been proven to be successful at describing physical systems at thermodynamic equilibrium. Since most natural phenomena occur in nonequilibrium conditions, the present challenge is to find suitable physical approaches for such conditions: this book provides a pedagogical pathway that explores various perspectives. The use of clear language, and explanatory figures and diagrams to describe models, simulations and experimental findings makes the book a valuable resource for undergraduate and graduate students, and also for lecturers organizing teaching at varying levels of experience in the field. Written in three parts, it covers basic and traditional concepts of nonequilibrium physics, modern aspects concerning nonequilibrium phase transitions, and application-orientated topics from a modern perspective. A broad range of topics is covered, including Langevin equations, Levy processes, directed percolation, kinetic roughening and pattern formation.
Statistical physics of an anyon gas
International Nuclear Information System (INIS)
Dasnieres de Veigy, A.
1994-01-01
In quantum two-dimensional physics, anyons are particles which have an intermediate statistics between Bose-Einstein and Fermi-Dirac statistics. The wave amplitude can change by an arbitrary phase under particle exchanges. Contrary to bosons or fermions, the permutation group cannot uniquely characterize this phase and one must introduce the braid group. One shows that the statistical ''interaction'' is equivalent to an Aharonov-Bohm interaction which derives from a Chern-Simons lagrangian. The main subject of this thesis is the thermodynamics of an anyon gas. Since the complete spectrum of N anyons seems out of reach, we have done a perturbative computation of the equation of state at second order near Bose or Fermi statistics. One avoids ultraviolet divergences by noticing that the short-range singularities of the statistical interaction enforce the wave functions to vanish when two particles approach each other (statistical exclusion). The gas is confined in a harmonic well in order to obtain the thermodynamics limit when the harmonic attraction goes to zero. Infrared divergences thus cancel in this limit and a finite virial expansion is obtained. The complexity of the anyon model appears in this result. We have also computed the equation of state of an anyon gas in a magnetic field strong enough to project the system in its degenerate groundstate. This result concerns anyons with any statistics. One then finds an exclusion principle generalizing the Pauli principle to anyons. On the other hand, we have defined a model of two-dimensional particles topologically interacting at a distance. The anyon model is recovered as a particular case where all particles are identical. (orig.)
Promoting the Understanding of Mathematics in Physics at Secondary Level
Thompson, Alaric
2016-01-01
This article explores some of the common mathematical difficulties that 11- to 16-year-old students experience with respect to their learning of physics. The definition of "understanding" expressed in the article is in the sense of transferability of mathematical skills from topic to topic within physics as well as between the separate…
Kapucu, Serkan
2017-01-01
This study aims to explore the relationships among Turkish high school students' attitude towards physics, self-efficacy of learning physics, mathematics achievement, and physics achievement. To investigate the relationships, a unique questionnaire that identifies the attitude, self-efficacy and achievements were delivered to a total of 301 high…
Statistical physics of hard optimization problems
International Nuclear Information System (INIS)
Zdeborova, L.
2009-01-01
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the non-deterministic polynomial (NP)-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system size. However, even in an NP-complete problem the practically arising instances might, in fact, be easy to solve. The principal question we address in this article is: How to recognize if an NP-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisfy ability and random graph coloring. We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem. Based on these insights, we introduce a new class of problems which we named ”locked” constraint satisfaction, where the statistical description is easily solvable, but from the algorithmic point of view they are even more challenging than the canonical satisfy ability.
Statistical physics of hard optimization problems
International Nuclear Information System (INIS)
Zdeborova, L.
2009-01-01
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the non-deterministic polynomial-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system size. However, even in an non-deterministic polynomial-complete problem the practically arising instances might, in fact, be easy to solve. The principal the question we address in the article is: How to recognize if an non-deterministic polynomial-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisfiability and random graph coloring. We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem. Based on these insights, we introduce a new class of problems which we named 'locked' constraint satisfaction, where the statistical description is easily solvable, but from the algorithmic point of view they are even more challenging than the canonical satisfiability (Authors)
Statistical physics of hard optimization problems
Zdeborová, Lenka
2009-06-01
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the non-deterministic polynomial (NP)-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system size. However, even in an NP-complete problem the practically arising instances might, in fact, be easy to solve. The principal question we address in this article is: How to recognize if an NP-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisfiability and random graph coloring. We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem. Based on these insights, we introduce a new class of problems which we named "locked" constraint satisfaction, where the statistical description is easily solvable, but from the algorithmic point of view they are even more challenging than the canonical satisfiability.
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.)
Networking—a statistical physics perspective
International Nuclear Information System (INIS)
Yeung, Chi Ho; Saad, David
2013-01-01
Networking encompasses a variety of tasks related to the communication of information on networks; it has a substantial economic and societal impact on a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption requires new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with nonlinear large-scale systems. This review aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications. (topical review)
Networking—a statistical physics perspective
Yeung, Chi Ho; Saad, David
2013-03-01
Networking encompasses a variety of tasks related to the communication of information on networks; it has a substantial economic and societal impact on a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption requires new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with nonlinear large-scale systems. This review aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications.
Mathematics and physics of emerging biomedical imaging
National Research Council Canada - National Science Library
Committee on the Mathematics and Physics of Emerging Dynamic Biomedical Imaging, National Research Council
.... Incorporating input from dozens of biomedical researchers who described what they perceived as key open problems of imaging that are amenable to attack by mathematical scientists and physicists...
Statistical mechanics and the physics of fluids
Tosi, Mario
This volume collects the lecture notes of a course on statistical mechanics, held at Scuola Normale Superiore di Pisa for third-to-fifth year students in physics and chemistry. Three main themes are covered in the book. The first part gives a compact presentation of the foundations of statistical mechanics and their connections with thermodynamics. Applications to ideal gases of material particles and of excitation quanta are followed by a brief introduction to a real classical gas and to a weakly coupled classical plasma, and by a broad overview on the three states of matter.The second part is devoted to fluctuations around equilibrium and their correlations. Coverage of liquid structure and critical phenomena is followed by a discussion of irreversible processes as exemplified by diffusive motions and by the dynamics of density and heat fluctuations. Finally, the third part is an introduction to some advanced themes: supercooling and the glassy state, non-Newtonian fluids including polymers and liquid cryst...
Quantum theoretical physics is statistical and relativistic
International Nuclear Information System (INIS)
Harding, C.
1980-01-01
A new theoretical framework for the quantum mechanism is presented. It is based on a strict deterministic behavior of single systems. The conventional QM equation, however, is found to describe statistical results of many classical systems. It will be seen, moreover, that a rigorous synthesis of our theory requires relativistic kinematics. So, QM is not only a classical statistical theory, it is, of necessity, a relativistic theory. The equation of the theory does not just duplicate QM, it indicates an inherent nonlinearity in QM which is subject to experimental verification. It is shown, therefore, that conventional QM is a corollary of classical deterministic principles. It is suggested that this concept of nature conflicts with that prevalent in modern physics. (author)
Simple and Intuitive Mathematics for Learning Elementary Physics
Kobayashi, Yukio
Mathematics is the language of physics and simple and intuitive mathematics is effective for imaging physical pictures of phenomena. This is important because geometrical viewpoints inspire ideas in physics. For example, some problems on the motion of a particle in a uniform gravitational field can be well illustrated by simple diagrams. Calculus is not only a way of calculating but is also closely related to the law of inertia through slope on a position-time graph. As such, cross-curricular study between mathematics and physics is effective for broadly developing thinking power at the high school and college levels.
Addressing Mathematization Obstacles with Unformalized Problems in Physics Education
DEFF Research Database (Denmark)
Niss, Martin
2018-01-01
Abstract: Solving a physics problem requires that the problem solver either implicitly or explicitly structure the problem situation in such a way that she can set up the mathematical equations based on the relevant physics. This part of the mathematization process has been shown to cause obstacles...... for students (Niss, 2016). In the paper, we show how the students’ ability to perform this mathematization process can be trained by using so-called unformalized physics problems. Some examples of how this training can be done are provided from a course on problem solving in physics taught at Roskilde...
Statistical physics of interacting neural networks
Kinzel, Wolfgang; Metzler, Richard; Kanter, Ido
2001-12-01
Recent results on the statistical physics of time series generation and prediction are presented. A neural network is trained on quasi-periodic and chaotic sequences and overlaps to the sequence generator as well as the prediction errors are calculated numerically. For each network there exists a sequence for which it completely fails to make predictions. Two interacting networks show a transition to perfect synchronization. A pool of interacting networks shows good coordination in the minority game-a model of competition in a closed market. Finally, as a demonstration, a perceptron predicts bit sequences produced by human beings.
Paechter, Manuela; Macher, Daniel; Martskvishvili, Khatuna; Wimmer, Sigrid; Papousek, Ilona
2017-01-01
In many social science majors, e.g., psychology, students report high levels of statistics anxiety. However, these majors are often chosen by students who are less prone to mathematics and who might have experienced difficulties and unpleasant feelings in their mathematics courses at school. The present study investigates whether statistics anxiety is a genuine form of anxiety that impairs students' achievements or whether learners mainly transfer previous experiences in mathematics and their anxiety in mathematics to statistics. The relationship between mathematics anxiety and statistics anxiety, their relationship to learning behaviors and to performance in a statistics examination were investigated in a sample of 225 undergraduate psychology students (164 women, 61 men). Data were recorded at three points in time: At the beginning of term students' mathematics anxiety, general proneness to anxiety, school grades, and demographic data were assessed; 2 weeks before the end of term, they completed questionnaires on statistics anxiety and their learning behaviors. At the end of term, examination scores were recorded. Mathematics anxiety and statistics anxiety correlated highly but the comparison of different structural equation models showed that they had genuine and even antagonistic contributions to learning behaviors and performance in the examination. Surprisingly, mathematics anxiety was positively related to performance. It might be that students realized over the course of their first term that knowledge and skills in higher secondary education mathematics are not sufficient to be successful in statistics. Part of mathematics anxiety may then have strengthened positive extrinsic effort motivation by the intention to avoid failure and may have led to higher effort for the exam preparation. However, via statistics anxiety mathematics anxiety also had a negative contribution to performance. Statistics anxiety led to higher procrastination in the structural
Paechter, Manuela; Macher, Daniel; Martskvishvili, Khatuna; Wimmer, Sigrid; Papousek, Ilona
2017-01-01
In many social science majors, e.g., psychology, students report high levels of statistics anxiety. However, these majors are often chosen by students who are less prone to mathematics and who might have experienced difficulties and unpleasant feelings in their mathematics courses at school. The present study investigates whether statistics anxiety is a genuine form of anxiety that impairs students' achievements or whether learners mainly transfer previous experiences in mathematics and their anxiety in mathematics to statistics. The relationship between mathematics anxiety and statistics anxiety, their relationship to learning behaviors and to performance in a statistics examination were investigated in a sample of 225 undergraduate psychology students (164 women, 61 men). Data were recorded at three points in time: At the beginning of term students' mathematics anxiety, general proneness to anxiety, school grades, and demographic data were assessed; 2 weeks before the end of term, they completed questionnaires on statistics anxiety and their learning behaviors. At the end of term, examination scores were recorded. Mathematics anxiety and statistics anxiety correlated highly but the comparison of different structural equation models showed that they had genuine and even antagonistic contributions to learning behaviors and performance in the examination. Surprisingly, mathematics anxiety was positively related to performance. It might be that students realized over the course of their first term that knowledge and skills in higher secondary education mathematics are not sufficient to be successful in statistics. Part of mathematics anxiety may then have strengthened positive extrinsic effort motivation by the intention to avoid failure and may have led to higher effort for the exam preparation. However, via statistics anxiety mathematics anxiety also had a negative contribution to performance. Statistics anxiety led to higher procrastination in the structural
Directory of Open Access Journals (Sweden)
Manuela Paechter
2017-07-01
Full Text Available In many social science majors, e.g., psychology, students report high levels of statistics anxiety. However, these majors are often chosen by students who are less prone to mathematics and who might have experienced difficulties and unpleasant feelings in their mathematics courses at school. The present study investigates whether statistics anxiety is a genuine form of anxiety that impairs students' achievements or whether learners mainly transfer previous experiences in mathematics and their anxiety in mathematics to statistics. The relationship between mathematics anxiety and statistics anxiety, their relationship to learning behaviors and to performance in a statistics examination were investigated in a sample of 225 undergraduate psychology students (164 women, 61 men. Data were recorded at three points in time: At the beginning of term students' mathematics anxiety, general proneness to anxiety, school grades, and demographic data were assessed; 2 weeks before the end of term, they completed questionnaires on statistics anxiety and their learning behaviors. At the end of term, examination scores were recorded. Mathematics anxiety and statistics anxiety correlated highly but the comparison of different structural equation models showed that they had genuine and even antagonistic contributions to learning behaviors and performance in the examination. Surprisingly, mathematics anxiety was positively related to performance. It might be that students realized over the course of their first term that knowledge and skills in higher secondary education mathematics are not sufficient to be successful in statistics. Part of mathematics anxiety may then have strengthened positive extrinsic effort motivation by the intention to avoid failure and may have led to higher effort for the exam preparation. However, via statistics anxiety mathematics anxiety also had a negative contribution to performance. Statistics anxiety led to higher procrastination in
XI. The Relation between Mathematics and Physic
Indian Academy of Sciences (India)
of mathematics in this scheme is to represent the laws of motion by equations, and to obtain solutions ... What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical peauty. This is a quality ... The difference may be expressed concisely, but in·a ...
Energy Technology Data Exchange (ETDEWEB)
Llave, R. de la; Haro, A.
2000-07-01
Statistical mechanics requires a language that unifies probabilistic and deterministic description of physical systems. We describe briefly some of the mathematical ideas needed for this unification. These ideas have also proved important in the study of chaotic systems. (Author) 17 refs.
Some applications of mathematics in theoretical physics - A review
Energy Technology Data Exchange (ETDEWEB)
Bora, Kalpana [Physics Department, Gauhati University, Guwahati-781014, Assam (India)
2016-06-21
Mathematics is a very beautiful subject−very much an indispensible tool for Physics, more so for Theoretical Physics (by which we mean here mainly Field Theory and High Energy Physics). These branches of Physics are based on Quantum Mechanics and Special Theory of Relativity, and many mathematical concepts are used in them. In this work, we shall elucidate upon only some of them, like−differential geometry, infinite series, Mellin transforms, Fourier and integral transforms, special functions, calculus, complex algebra, topology, group theory, Riemannian geometry, functional analysis, linear algebra, operator algebra, etc. We shall also present, some physics issues, where these mathematical tools are used. It is not wrong to say that Mathematics is such a powerful tool, without which, there can not be any Physics theory!! A brief review on our research work is also presented.
Some applications of mathematics in theoretical physics - A review
Bora, Kalpana
2016-06-01
Mathematics is a very beautiful subject-very much an indispensible tool for Physics, more so for Theoretical Physics (by which we mean here mainly Field Theory and High Energy Physics). These branches of Physics are based on Quantum Mechanics and Special Theory of Relativity, and many mathematical concepts are used in them. In this work, we shall elucidate upon only some of them, like-differential geometry, infinite series, Mellin transforms, Fourier and integral transforms, special functions, calculus, complex algebra, topology, group theory, Riemannian geometry, functional analysis, linear algebra, operator algebra, etc. We shall also present, some physics issues, where these mathematical tools are used. It is not wrong to say that Mathematics is such a powerful tool, without which, there can not be any Physics theory!! A brief review on our research work is also presented.
Some applications of mathematics in theoretical physics - A review
International Nuclear Information System (INIS)
Bora, Kalpana
2016-01-01
Mathematics is a very beautiful subject−very much an indispensible tool for Physics, more so for Theoretical Physics (by which we mean here mainly Field Theory and High Energy Physics). These branches of Physics are based on Quantum Mechanics and Special Theory of Relativity, and many mathematical concepts are used in them. In this work, we shall elucidate upon only some of them, like−differential geometry, infinite series, Mellin transforms, Fourier and integral transforms, special functions, calculus, complex algebra, topology, group theory, Riemannian geometry, functional analysis, linear algebra, operator algebra, etc. We shall also present, some physics issues, where these mathematical tools are used. It is not wrong to say that Mathematics is such a powerful tool, without which, there can not be any Physics theory!! A brief review on our research work is also presented.
Scattering theory in quantum mechanics. Physical principles and mathematical methods
International Nuclear Information System (INIS)
Amrein, W.O.; Jauch, J.M.; Sinha, K.B.
1977-01-01
A contemporary approach is given to the classical topics of physics. The purpose is to explain the basic physical concepts of quantum scattering theory, to develop the necessary mathematical tools for their description, to display the interrelation between the three methods (the Schroedinger equation solutions, stationary scattering theory, and time dependence) to derive the properties of various quantities of physical interest with mathematically rigorous methods
International Nuclear Information System (INIS)
Tadaki, Kohtaro
2010-01-01
The statistical mechanical interpretation of algorithmic information theory (AIT, for short) was introduced and developed by our former works [K. Tadaki, Local Proceedings of CiE 2008, pp. 425-434, 2008] and [K. Tadaki, Proceedings of LFCS'09, Springer's LNCS, vol. 5407, pp. 422-440, 2009], where we introduced the notion of thermodynamic quantities, such as partition function Z(T), free energy F(T), energy E(T), statistical mechanical entropy S(T), and specific heat C(T), into AIT. We then discovered that, in the interpretation, the temperature T equals to the partial randomness of the values of all these thermodynamic quantities, where the notion of partial randomness is a stronger representation of the compression rate by means of program-size complexity. Furthermore, we showed that this situation holds for the temperature T itself, which is one of the most typical thermodynamic quantities. Namely, we showed that, for each of the thermodynamic quantities Z(T), F(T), E(T), and S(T) above, the computability of its value at temperature T gives a sufficient condition for T is an element of (0,1) to satisfy the condition that the partial randomness of T equals to T. In this paper, based on a physical argument on the same level of mathematical strictness as normal statistical mechanics in physics, we develop a total statistical mechanical interpretation of AIT which actualizes a perfect correspondence to normal statistical mechanics. We do this by identifying a microcanonical ensemble in the framework of AIT. As a result, we clarify the statistical mechanical meaning of the thermodynamic quantities of AIT.
A Framework for Authenticity in the Mathematics and Statistics Classroom
Garrett, Lauretta; Huang, Li; Charleton, Maria Calhoun
2016-01-01
Authenticity is a term commonly used in reference to pedagogical and curricular qualities of mathematics teaching and learning, but its use lacks a coherent framework. The work of researchers in engineering education provides such a framework. Authentic qualities of mathematics teaching and learning are fit within a model described by Strobel,…
Statistical physics of networks, information and complex systems
Energy Technology Data Exchange (ETDEWEB)
Ecke, Robert E [Los Alamos National Laboratory
2009-01-01
In this project we explore the mathematical methods and concepts of statistical physics that are fmding abundant applications across the scientific and technological spectrum from soft condensed matter systems and bio-infonnatics to economic and social systems. Our approach exploits the considerable similarity of concepts between statistical physics and computer science, allowing for a powerful multi-disciplinary approach that draws its strength from cross-fertilization and mUltiple interactions of researchers with different backgrounds. The work on this project takes advantage of the newly appreciated connection between computer science and statistics and addresses important problems in data storage, decoding, optimization, the infonnation processing properties of the brain, the interface between quantum and classical infonnation science, the verification of large software programs, modeling of complex systems including disease epidemiology, resource distribution issues, and the nature of highly fluctuating complex systems. Common themes that the project has been emphasizing are (i) neural computation, (ii) network theory and its applications, and (iii) a statistical physics approach to infonnation theory. The project's efforts focus on the general problem of optimization and variational techniques, algorithm development and infonnation theoretic approaches to quantum systems. These efforts are responsible for fruitful collaborations and the nucleation of science efforts that span multiple divisions such as EES, CCS, 0 , T, ISR and P. This project supports the DOE mission in Energy Security and Nuclear Non-Proliferation by developing novel infonnation science tools for communication, sensing, and interacting complex networks such as the internet or energy distribution system. The work also supports programs in Threat Reduction and Homeland Security.
Primi, Caterina; Donati, Maria Anna; Chiesi, Francesca
2016-01-01
Among the wide range of factors related to the acquisition of statistical knowledge, competence in basic mathematics, including basic probability, has received much attention. In this study, a mediation model was estimated to derive the total, direct, and indirect effects of mathematical competence on statistics achievement taking into account…
Statistical Physics Approaches to RNA Editing
Bundschuh, Ralf
2012-02-01
The central dogma of molecular Biology states that DNA is transcribed base by base into RNA which is in turn translated into proteins. However, some organisms edit their RNA before translation by inserting, deleting, or substituting individual or short stretches of bases. In many instances the mechanisms by which an organism recognizes the positions at which to edit or by which it performs the actual editing are unknown. One model system that stands out by its very high rate of on average one out of 25 bases being edited are the Myxomycetes, a class of slime molds. In this talk we will show how the computational methods and concepts from statistical Physics can be used to analyze DNA and protein sequence data to predict editing sites in these slime molds and to guide experiments that identified previously unknown types of editing as well as the complete set of editing events in the slime mold Physarum polycephalum.
Statistical Physics Approaches to Microbial Ecology
Mehta, Pankaj
The unprecedented ability to quantitatively measure and probe complex microbial communities has renewed interest in identifying the fundamental ecological principles governing community ecology in microbial ecosystems. Here, we present work from our group and others showing how ideas from statistical physics can help us uncover these ecological principles. Two major lessons emerge from this work. First, large, ecosystems with many species often display new, emergent ecological behaviors that are absent in small ecosystems with just a few species. To paraphrase Nobel laureate Phil Anderson, ''More is Different'', especially in community ecology. Second, the lack of trophic layer separation in microbial ecology fundamentally distinguishes microbial ecology from classical paradigms of community ecology and leads to qualitative different rules for community assembly in microbes. I illustrate these ideas using both theoretical modeling and novel new experiments on large microbial ecosystems performed by our collaborators (Joshua Goldford and Alvaro Sanchez). Work supported by Simons Investigator in MMLS and NIH R35 R35 GM119461.
Statistical physics of pairwise probability models
Directory of Open Access Journals (Sweden)
Yasser Roudi
2009-11-01
Full Text Available Statistical models for describing the probability distribution over the states of biological systems are commonly used for dimensional reduction. Among these models, pairwise models are very attractive in part because they can be fit using a reasonable amount of data: knowledge of the means and correlations between pairs of elements in the system is sufficient. Not surprisingly, then, using pairwise models for studying neural data has been the focus of many studies in recent years. In this paper, we describe how tools from statistical physics can be employed for studying and using pairwise models. We build on our previous work on the subject and study the relation between different methods for fitting these models and evaluating their quality. In particular, using data from simulated cortical networks we study how the quality of various approximate methods for inferring the parameters in a pairwise model depends on the time bin chosen for binning the data. We also study the effect of the size of the time bin on the model quality itself, again using simulated data. We show that using finer time bins increases the quality of the pairwise model. We offer new ways of deriving the expressions reported in our previous work for assessing the quality of pairwise models.
The philosophical aspect of learning inverse problems of mathematical physics
Directory of Open Access Journals (Sweden)
Виктор Семенович Корнилов
2018-12-01
Full Text Available The article describes specific questions student learning inverse problems of mathematical physics. When teaching inverse problems of mathematical physics to the understanding of the students brought the information that the inverse problems of mathematical physics with a philosophical point of view are the problems of determining the unknown causes of known consequences, and the search for their solutions have great scientific and educational potential. The reasons are specified in the form of unknown coefficients, right side, initial conditions of the mathematical model of inverse problems, and as a consequence are functionals of the solution of this mathematical model. In the process of learning the inverse problems of mathematical physics focuses on the philosophical aspects of the phenomenon of information and identify cause-effect relations. It is emphasized that in the process of logical analysis applied and humanitarian character, students realize that information is always related to the fundamental philosophical questions that the analysis applied and the humanitarian aspects of the obtained results the inverse problem of mathematical physics allows students to make appropriate inferences about the studied process and to, ultimately, new information, to study its properties and understand its value. Philosophical understanding of the notion of information opens up to students a new methodological opportunities to comprehend the world and helps us to reinterpret existing science and philosophy of the theory related to the disclosure of the interrelationship of all phenomena of reality.
Mathematics, Physics and Computer Sciences The computation of ...
African Journals Online (AJOL)
Mathematics, Physics and Computer Sciences The computation of system matrices for biquadraticsquare finite ... Global Journal of Pure and Applied Sciences ... The computation of system matrices for biquadraticsquare finite elements.
Fractional derivative and its application in mathematics and physics
International Nuclear Information System (INIS)
Namsrai, K.
2004-12-01
We propose fractional derivatives and to study those mathematical and physical consequences. It is shown that fractional derivatives possess noncommutative and nonassociative properties and within which motion of a particle, differential and integral calculuses are investigated. (author)
Effects of Vigorous Intensity Physical Activity on Mathematics Test Performance
Phillips, David S.; Hannon, James C.; Castelli, Darla M.
2015-01-01
The effect of an acute bout of physical activity on academic performance in school-based settings is under researched. The purpose of this study was to examine associations between a single, vigorous (70-85%) bout of physical activity completed during physical education on standardized mathematics test performance among 72, eighth grade students…
Support of Study on Engineering Technology from Physics and Mathematics
Mynbaev, Djafar K.; Cabo, Candido; Kezerashvili, Roman Ya.; Liou-Mark, Janet
2008-01-01
An approach that provides students with an ability to transfer learning in physics and mathematics to the engineering-technology courses through e-teaching and e-learning process is proposed. E-modules of courses in mathematics, physics, computer systems technology, and electrical and telecommunications engineering technology have been developed. These modules being used in the Blackboard and Web-based communications systems create a virtual interdisciplinary learning community, which helps t...
Ganikhodjaev, Nasir; Mukhamedov, Farrukh; Hee, Pah Chin
2013-04-01
The 4th International Conference on the Advancement of Science and Technology 2012 (iCAST 2012), with theme 'Contemporary Mathematics, Mathematical Physics and their Applications', took place in Kuantan, Malaysia, from Wednesday 7 to Friday 9 November 2012. The conference was attended by more than 100 participants, and hosted about 160 oral and poster papers by more than 140 pre-registered authors. The key topics of the 4th iCAST 2012 include Pure Mathematics, Applied Mathematics, Theoretical/Mathematical Physics, Dynamical Systems, Statistics and Financial Mathematics. The scientific program was rather full since after the Keynote and Invited Talks in the morning, four parallel sessions ran every day. However, according to all attendees, the program was excellent with a high level of talks and the scientific environment was fruitful; thus all attendees had a creative time. The conference aimed to promote the knowledge and development of high-quality research in mathematical fields concerned with the application of other scientific fields as well as modern technological trends in physics, chemistry, biology, medicine, economics, sociology and environmental sciences. We would like to thank the Keynote and the Invited Speakers for their significant contributions to 4th iCAST 2012. We would also like to thank the members of the International Scientific Committee and the members of the Organizing Committee. We cannot end without expressing our many thanks to International Islamic University Malaysia and our sponsors for their financial support . This volume presents selected papers which have been peer-reviewed. The editors hope that it may be useful and fruitful for scholars, researchers, and advanced technical members of the industrial laboratory facilities for developing new tools and products. Guest Editors Nasir Ganikhodjaev, Farrukh Mukhamedov and Pah Chin Hee The PDF contains the committee lists, board list and biographies of the plenary speakers.
The role of a posteriori mathematics in physics
MacKinnon, Edward
2018-05-01
The calculus that co-evolved with classical mechanics relied on definitions of functions and differentials that accommodated physical intuitions. In the early nineteenth century mathematicians began the rigorous reformulation of calculus and eventually succeeded in putting almost all of mathematics on a set-theoretic foundation. Physicists traditionally ignore this rigorous mathematics. Physicists often rely on a posteriori math, a practice of using physical considerations to determine mathematical formulations. This is illustrated by examples from classical and quantum physics. A justification of such practice stems from a consideration of the role of phenomenological theories in classical physics and effective theories in contemporary physics. This relates to the larger question of how physical theories should be interpreted.
Directory of Open Access Journals (Sweden)
Syarifah Fadillah
2017-03-01
Full Text Available The problem in this research is to know how the process of developing mathematics physics instructional book based on inquiry approach and its supporting documents to improve students' mathematical problem-solving ability. The purpose of this research is to provide mathematical physics instruction based on inquiry approach and its supporting documents (semester learning activity plan, lesson plan and mathematical problem-solving test to improve students' mathematical problem-solving ability. The development of textbook refers to the ADDIE model, including analysis, design, development, implementation, and evaluation. The validation result from the expert team shows that the textbook and its supporting documents are valid. The test results of the mathematical problem-solving skills show that all test questions are valid and reliable. The result of the incorporation of the textbook in teaching and learning process revealed that students' mathematical problem-solving ability using mathematical physics instruction based on inquiry approach book was better than the students who use the regular book.
Statistical physics, seismogenesis, and seismic hazard
Main, Ian
1996-11-01
The scaling properties of earthquake populations show remarkable similarities to those observed at or near the critical point of other composite systems in statistical physics. This has led to the development of a variety of different physical models of seismogenesis as a critical phenomenon, involving locally nonlinear dynamics, with simplified rheologies exhibiting instability or avalanche-type behavior, in a material composed of a large number of discrete elements. In particular, it has been suggested that earthquakes are an example of a "self-organized critical phenomenon" analogous to a sandpile that spontaneously evolves to a critical angle of repose in response to the steady supply of new grains at the summit. In this stationary state of marginal stability the distribution of avalanche energies is a power law, equivalent to the Gutenberg-Richter frequency-magnitude law, and the behavior is relatively insensitive to the details of the dynamics. Here we review the results of some of the composite physical models that have been developed to simulate seismogenesis on different scales during (1) dynamic slip on a preexisting fault, (2) fault growth, and (3) fault nucleation. The individual physical models share some generic features, such as a dynamic energy flux applied by tectonic loading at a constant strain rate, strong local interactions, and fluctuations generated either dynamically or by fixed material heterogeneity, but they differ significantly in the details of the assumed dynamics and in the methods of numerical solution. However, all exhibit critical or near-critical behavior, with behavior quantitatively consistent with many of the observed fractal or multifractal scaling laws of brittle faulting and earthquakes, including the Gutenberg-Richter law. Some of the results are sensitive to the details of the dynamics and hence are not strict examples of self-organized criticality. Nevertheless, the results of these different physical models share some
A mathematical look at a physical power prediction model
DEFF Research Database (Denmark)
Landberg, L.
1998-01-01
This article takes a mathematical look at a physical model used to predict the power produced from wind farms. The reason is to see whether simple mathematical expressions can replace the original equations and to give guidelines as to where simplifications can be made and where they cannot....... The article shows that there is a linear dependence between the geostrophic wind and the local wind at the surface, but also that great care must be taken in the selection of the simple mathematical models, since physical dependences play a very important role, e.g. through the dependence of the turning...
A few recent examples of mathematics at work in physics
International Nuclear Information System (INIS)
Zee, A.
1984-01-01
In this paper, the authors discuss some recent applications of mathematics to physics, in the hope that the mathematical sophisticates among you may be able to see ways of carrying the discussion further. The authors believe that mathematics is sometimes a necessary fact of life but in general to be avoided if possible. The absence of significant experimental result can do strange things to a field of physics. They highlight some recent developments and they focus exclusively on papers to which the reader is referred for further details
The scientifiv way of thinking in statistics, statistical physics and quantum mechanics
Săvoiu, Gheorghe
2008-01-01
This paper focuses on the way of thinking in both classical and modern Physics and Statistics, Statistical Mechanics or Statistical Physics and Quantum Mechanics. These different statistical ways of thinking and their specific methods have generated new fields for new activities and new scientific disciplines, like Econophysics (between Economics and Physics), Sociophysics (between Sociology and Physics), Mediaphysics (between all media and comunication sciences), etc. After describing some r...
The scientific way of thinking in statistics, statistical physics and quantum mechanics
Săvoiu, Gheorghe
2008-01-01
This paper focuses on the way of thinking in both classical and modern Physics and Statistics, Statistical Mechanics or Statistical Physics and Quantum Mechanics. These different statistical ways of thinking and their specific methods have generated new fields for new activities and new scientific disciplines, like Econophysics (between Economics and Physics), Sociophysics (between Sociology and Physics), Mediaphysics (between all media and comunication sciences), etc. After describing some r...
Mathematical Representation Ability by Using Project Based Learning on the Topic of Statistics
Widakdo, W. A.
2017-09-01
Seeing the importance of the role of mathematics in everyday life, mastery of the subject areas of mathematics is a must. Representation ability is one of the fundamental ability that used in mathematics to make connection between abstract idea with logical thinking to understanding mathematics. Researcher see the lack of mathematical representation and try to find alternative solution to dolve it by using project based learning. This research use literature study from some books and articles in journals to see the importance of mathematical representation abiliy in mathemtics learning and how project based learning able to increase this mathematical representation ability on the topic of Statistics. The indicators for mathematical representation ability in this research classifies namely visual representation (picture, diagram, graph, or table); symbolize representation (mathematical statement. Mathematical notation, numerical/algebra symbol) and verbal representation (written text). This article explain about why project based learning able to influence student’s mathematical representation by using some theories in cognitive psychology, also showing the example of project based learning that able to use in teaching statistics, one of mathematics topic that very useful to analyze data.
Assessment of climate change using methods of mathematic statistics and theory of probability
International Nuclear Information System (INIS)
Trajanoska, Lidija; Kaevski, Ivancho
2004-01-01
In simple terms: 'Climate' is the average of 'weather'. The Earth's weather system is a complex machine composed of coupled sub-systems (ocean, air, land, ice and the biosphere) between which energy are exchanged. The understanding and study of climate change does not only rely on the understanding of the physics of climate change but is linked to the following question: 'How we can detect change in a system that is changing all the time under its own volition'? What is even the meaning of 'change' in such a situation? The concept of 'change' we should transform into the concept of 'significant and long-term' then this re-phrasing allows for a definition in mathematical terms. Significant change in a system becomes a measure of how large an observed change is in terms of the variability one would see under 'normal' conditions. Example could be the analyses of the yearly temperature of the air and precipitations, like in this paper. A large amount of data are selected as representing the 'before' case (change) and another set of data are selected as being the 'after' case and then the average in these two cases are compared. These comparisons are in the form of 'hypothesis tests' in which one tests whether the hypothesis that there has Open no change can be rejected. Both parameter and nonparametric statistic methods are used in the theory of mathematic statistic. The most indicative changeable which show global change is an average, standard deviation and probability function distribution on examined time series. Examined meteorological series are taken like haphazard process so we can mathematic statistic applied.(Author)
Mathematical mechanic using physical reasoning to solve problems
Levi, Mark
2009-01-01
Everybody knows that mathematics is indispensable to physics--imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of entertaining problems and mind-bending puzzlers that will amuse and inspire their inner physicist. Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can
Statistical physics of media processes: Mediaphysics
Kuznetsov, Dmitri V.; Mandel, Igor
2007-04-01
The processes of mass communications in complicated social or sociobiological systems such as marketing, economics, politics, animal populations, etc. as a subject for the special scientific subbranch-“mediaphysics”-are considered in its relation with sociophysics. A new statistical physics approach to analyze these phenomena is proposed. A keystone of the approach is an analysis of population distribution between two or many alternatives: brands, political affiliations, or opinions. Relative distances between a state of a “person's mind” and the alternatives are measures of propensity to buy (to affiliate, or to have a certain opinion). The distribution of population by those relative distances is time dependent and affected by external (economic, social, marketing, natural) and internal (influential propagation of opinions, “word of mouth”, etc.) factors, considered as fields. Specifically, the interaction and opinion-influence field can be generalized to incorporate important elements of Ising-spin-based sociophysical models and kinetic-equation ones. The distributions were described by a Schrödinger-type equation in terms of Green's functions. The developed approach has been applied to a real mass-media efficiency problem for a large company and generally demonstrated very good results despite low initial correlations of factors and the target variable.
Mathematics and physics of neutron radiography
International Nuclear Information System (INIS)
Harms, A.A.; Wyman, D.R.
1985-01-01
This book provides detailed descriptions and analyses of selected experiments and their mathematical characterization. Also included are illustrative and quantitative procedures for applications. This book also discusses the radiography, nondestructive testing and nuclear reactor utilization. The contents discussed are: I: Introduction. II: Component Characterization. III: Object-Image Relations. IV: Rectangular Geometry. V: Cylindrical Geometry. VI: Two-Dimensional Analysis. VII: Object Scattering. VIII: Linear Systems Formulation. IX: Selected Topics. X: Neutron Radiographs. XI: Bibliography and References. Subject Index
Marriages of mathematics and physics: A challenge for biology.
Islami, Arezoo; Longo, Giuseppe
2017-12-01
The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of "geometric judgments" from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) "space" should be revisited for the purposes of life sciences. Copyright © 2017. Published by Elsevier Ltd.
Mathematics and social science : a statistical mechanics approach to immigration
Contucci, P.; Giardinà, C.
2008-01-01
Is modern science able to study social matters like those related to immigration phenomena on solid mathematical grounds? Can we for instance determine cultural robustness and the causes behind abrupt changes from cultural legacies? Can we predict, cause or avoid swings? A novel approach is under
Explorations in Mathematical Physics The Concepts Behind an Elegant Language
Koks, Don
2006-01-01
Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You'll see how the accelerated frames of special relativity tell us about gravity. On the journey, you'll discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis buil...
Excel 2013 for physical sciences statistics a guide to solving practical problems
Quirk, Thomas J; Horton, Howard F
2016-01-01
This book shows the capabilities of Microsoft Excel in teaching physical sciences statistics effectively. Similar to the previously published Excel 2010 for Physical Sciences Statistics, this book is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical science problems. If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in science courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. However, Excel 2013 for Physical Sciences Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how to apply Excel to statistical techniques necessary in their ...
Quaternions and the heuristic role of mathematical structures in physics
International Nuclear Information System (INIS)
Anderson, R.S.J.; Joshi, G.C.
1992-07-01
One of the important ways development takes place in mathematics is via a process of generalization. On the basis of a recent characterization of the process the authors propose that generalizations of mathematical structures that are already part of successful physical theories serve as good guides for the development of new physical theories. The principle is a more formal presentation and extension of a position stated earlier this century by Dirac. Quaternions form an excellent example of such a generalization, and a number of the ways in which their use in physical theories illustrates this principle, are discussed. 114 refs
Summer Workshop on Physics, Mathematics, and All That Quantum Jazz
Bando, Masamitsu; Güngördü, Utkan; Physics, Mathematics, and All That Quantum Jazz
2014-01-01
This book is a collection of contributions from a Summer Workshop on Physics, Mathematics, and All That Quantum Jazz . Subjects of the symposium include quantum information theory, quantum annealing, Bose gases, and thermodynamics from a viewpoint of quantum physics. Contributions to this book are prepared in a self-contained manner so that readers with a modest background may understand the subjects.
Exercises and problems in mathematical methods of physics
Cicogna, Giampaolo
2018-01-01
This book presents exercises and problems in the mathematical methods of physics with the aim of offering undergraduate students an alternative way to explore and fully understand the mathematical notions on which modern physics is based. The exercises and problems are proposed not in a random order but rather in a sequence that maximizes their educational value. Each section and subsection starts with exercises based on first definitions, followed by groups of problems devoted to intermediate and, subsequently, more elaborate situations. Some of the problems are unavoidably "routine", but others bring to the forenontrivial properties that are often omitted or barely mentioned in textbooks. There are also problems where the reader is guided to obtain important results that are usually stated in textbooks without complete proofs. In all, some 350 solved problems covering all mathematical notions useful to physics are included. While the book is intended primarily for undergraduate students of physics, students...
Statistical physics approach to earthquake occurrence and forecasting
Energy Technology Data Exchange (ETDEWEB)
Arcangelis, Lucilla de [Department of Industrial and Information Engineering, Second University of Naples, Aversa (CE) (Italy); Godano, Cataldo [Department of Mathematics and Physics, Second University of Naples, Caserta (Italy); Grasso, Jean Robert [ISTerre, IRD-CNRS-OSUG, University of Grenoble, Saint Martin d’Héres (France); Lippiello, Eugenio, E-mail: eugenio.lippiello@unina2.it [Department of Mathematics and Physics, Second University of Naples, Caserta (Italy)
2016-04-25
There is striking evidence that the dynamics of the Earth crust is controlled by a wide variety of mutually dependent mechanisms acting at different spatial and temporal scales. The interplay of these mechanisms produces instabilities in the stress field, leading to abrupt energy releases, i.e., earthquakes. As a consequence, the evolution towards instability before a single event is very difficult to monitor. On the other hand, collective behavior in stress transfer and relaxation within the Earth crust leads to emergent properties described by stable phenomenological laws for a population of many earthquakes in size, time and space domains. This observation has stimulated a statistical mechanics approach to earthquake occurrence, applying ideas and methods as scaling laws, universality, fractal dimension, renormalization group, to characterize the physics of earthquakes. In this review we first present a description of the phenomenological laws of earthquake occurrence which represent the frame of reference for a variety of statistical mechanical models, ranging from the spring-block to more complex fault models. Next, we discuss the problem of seismic forecasting in the general framework of stochastic processes, where seismic occurrence can be described as a branching process implementing space–time-energy correlations between earthquakes. In this context we show how correlations originate from dynamical scaling relations between time and energy, able to account for universality and provide a unifying description for the phenomenological power laws. Then we discuss how branching models can be implemented to forecast the temporal evolution of the earthquake occurrence probability and allow to discriminate among different physical mechanisms responsible for earthquake triggering. In particular, the forecasting problem will be presented in a rigorous mathematical framework, discussing the relevance of the processes acting at different temporal scales for
Statistical spectroscopic studies in nuclear structure physics
International Nuclear Information System (INIS)
Halemane, T.R.
1979-01-01
The spectral distribution theory establishes the centroid and width of the energy spectrum as quantities of fundamental importance and gives credence to a geometry associated with averages of the product of pairs of operators acting within a model space. Utilizing this fact and partitioning the model space according to different group symmetries, simple and physically meaningful expansions are obtained for the model interactions. In the process, a global measure for the goodness of group symmetries is also developed. This procedure could eventually lead to a new way of constructing model interactions for nuclear structure studies. Numerical results for six (ds)-shell interactions and for scalar-isospin, configuration-isospin, space symmetry, supermultiplet and SU(e) x SU(4) group structures are presented. The notion of simultaneous propagation of operator averages in the irreps of two or more groups (not necessarily commuting) is also introduced. The non-energy-weighted sum rule (NEWSR) for electric and magnetic multipole excitations in the (ds)-shell nuclei 20 Ne, 24 Mg, 28 Si, 32 S, and 36 Ar are evaluated. A generally applicable procedure for evaluating the eigenvalue bound to the NEWSR is presented and numerical results obtained for the said excitations and nuclei. Comparisons are made with experimental data and shell-model results. Further, a general theory is given for the linear-energy-weighted sum rule (LEWSR). When the Hamiltonian is one-body, this has a very simple form (expressible in terms of occupancies) and amounts to an extension of the Kurath sum rule to other types of excitations and to arbitrary one-body Hamiltonians. Finally, we develop a statistical approach to perturbation theory and inverse-energy-weighted sum rules, and indicate some applications
Eringen, A Cemal
2013-01-01
Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th
Topics in the mathematical physics of E-infinity theory
International Nuclear Information System (INIS)
El Naschie, M.S.
2006-01-01
This is the fourth contribution in a series of papers aimed at directing the attention of the prospective E-infinity researcher to the most important mathematical background and sources needed for an easy understanding and successful application of this theory. The present paper is mainly concerned with the mathematical physics relevant to E-infinity theory with emphasis on super Yang-Mills theory and superstrings
The Pythagorean world why mathematics is unreasonably effective in physics
McDonnell, Jane
2017-01-01
This book explores precisely how mathematics allows us to model and predict the behaviour of physical systems, to an amazing degree of accuracy. One of the oldest explanations for this is that, in some profound way, the structure of the world is mathematical. The ancient Pythagoreans stated that “everything is number”. However, while exploring the Pythagorean method, this book chooses to add a second principle of the universe: the mind. This work defends the proposition that mind and mathematical structure are the grounds of reality.
The role of mathematics for physics teaching and understanding
Pospiech, Gesche; Eylon, BatSheva; Bagno, Esther; Lehavi, Yaron; Geyer, Marie-Annette
2016-05-01
-1That mathematics is the "language of physics" implies that both areas are deeply interconnected, such that often no separation between "pure" mathematics and "pure" physics is possible. To clarify their interplay a technical and a structural role of mathematics can be distinguished. A thorough understanding of this twofold role in physics is also important for shaping physics education especially with respect to teaching the nature of physics. Herewith the teachers and their pedagogical content knowledge play an important role. Therefore we develop a model of PCK concerning the interplay of mathematics and physics in order to provide a theoretical framework for the views and teaching strategies of teachers. In an exploratory study four teachers from Germany and four teachers from Israel have been interviewed concerning their views and its transfer to teaching physics. Here we describe the results from Germany. Besides general views and knowledge held by all or nearly all teachers we also observe specific individual focus depending on the teachers' background and experiences. The results fit well into the derived model of PCK.
New Standards Require Teaching More Statistics: Are Preservice Secondary Mathematics Teachers Ready?
Lovett, Jennifer N.; Lee, Hollylynne S.
2017-01-01
Mathematics teacher education programs often need to respond to changing expectations and standards for K-12 curriculum and accreditation. New standards for high school mathematics in the United States include a strong emphasis in statistics. This article reports results from a mixed methods cross-institutional study examining the preparedness of…
MacLean, Adam L.; Harrington, Heather A.; Stumpf, Michael P. H.; Byrne, Helen M.
2015-01-01
mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since
Stochastic Spatial Models in Ecology: A Statistical Physics Approach
Pigolotti, Simone; Cencini, Massimo; Molina, Daniel; Muñoz, Miguel A.
2017-11-01
Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions accounting for general empirical patterns in communities of competing species. However, while neutral theory in well-mixed ecosystems is mathematically well understood, spatial models still present several open problems, limiting the quantitative understanding of spatial biodiversity. In this review, we discuss the state of the art in spatial neutral theory. We emphasize the connection between spatial ecological models and the physics of non-equilibrium phase transitions and how concepts developed in statistical physics translate in population dynamics, and vice versa. We focus on non-trivial scaling laws arising at the critical dimension D = 2 of spatial neutral models, and their relevance for biological populations inhabiting two-dimensional environments. We conclude by discussing models incorporating non-neutral effects in the form of spatial and temporal disorder, and analyze how their predictions deviate from those of purely neutral theories.
High-Precision Computation and Mathematical Physics
International Nuclear Information System (INIS)
Bailey, David H.; Borwein, Jonathan M.
2008-01-01
At the present time, IEEE 64-bit floating-point arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications, a higher level of numeric precision is required. Such calculations are facilitated by high-precision software packages that include high-level language translation modules to minimize the conversion effort. This paper presents a survey of recent applications of these techniques and provides some analysis of their numerical requirements. These applications include supernova simulations, climate modeling, planetary orbit calculations, Coulomb n-body atomic systems, scattering amplitudes of quarks, gluons and bosons, nonlinear oscillator theory, Ising theory, quantum field theory and experimental mathematics. We conclude that high-precision arithmetic facilities are now an indispensable component of a modern large-scale scientific computing environment.
Medical Statistics – Mathematics or Oracle? Farewell Lecture
Directory of Open Access Journals (Sweden)
Gaus, Wilhelm
2005-06-01
Full Text Available Certainty is rare in medicine. This is a direct consequence of the individuality of each and every human being and the reason why we need medical statistics. However, statistics have their pitfalls, too. Fig. 1 shows that the suicide rate peaks in youth, while in Fig. 2 the rate is highest in midlife and Fig. 3 in old age. Which of these contradictory messages is right? After an introduction to the principles of statistical testing, this lecture examines the probability with which statistical test results are correct. For this purpose the level of significance and the power of the test are compared with the sensitivity and specificity of a diagnostic procedure. The probability of obtaining correct statistical test results is the same as that for the positive and negative correctness of a diagnostic procedure and therefore depends on prevalence. The focus then shifts to the problem of multiple statistical testing. The lecture demonstrates that for each data set of reasonable size at least one test result proves to be significant - even if the data set is produced by a random number generator. It is extremely important that a hypothesis is generated independently from the data used for its testing. These considerations enable us to understand the gradation of "lame excuses, lies and statistics" and the difference between pure truth and the full truth. Finally, two historical oracles are cited.
Thermodynamics and statistical physics. 2. rev. ed.
International Nuclear Information System (INIS)
Schnakenberg, J.
2002-01-01
This textbook covers tthe following topics: Thermodynamic systems and equilibrium, irreversible thermodynamics, thermodynamic potentials, stability, thermodynamic processes, ideal systems, real gases and phase transformations, magnetic systems and Landau model, low temperature thermodynamics, canonical ensembles, statistical theory, quantum statistics, fermions and bosons, kinetic theory, Bose-Einstein condensation, photon gas
Statistical physics approaches to Alzheimer's disease
Peng, Shouyong
Alzheimer's disease (AD) is the most common cause of late life dementia. In the brain of an AD patient, neurons are lost and spatial neuronal organizations (microcolumns) are disrupted. An adequate quantitative analysis of microcolumns requires that we automate the neuron recognition stage in the analysis of microscopic images of human brain tissue. We propose a recognition method based on statistical physics. Specifically, Monte Carlo simulations of an inhomogeneous Potts model are applied for image segmentation. Unlike most traditional methods, this method improves the recognition of overlapped neurons, and thus improves the overall recognition percentage. Although the exact causes of AD are unknown, as experimental advances have revealed the molecular origin of AD, they have continued to support the amyloid cascade hypothesis, which states that early stages of aggregation of amyloid beta (Abeta) peptides lead to neurodegeneration and death. X-ray diffraction studies reveal the common cross-beta structural features of the final stable aggregates-amyloid fibrils. Solid-state NMR studies also reveal structural features for some well-ordered fibrils. But currently there is no feasible experimental technique that can reveal the exact structure or the precise dynamics of assembly and thus help us understand the aggregation mechanism. Computer simulation offers a way to understand the aggregation mechanism on the molecular level. Because traditional all-atom continuous molecular dynamics simulations are not fast enough to investigate the whole aggregation process, we apply coarse-grained models and discrete molecular dynamics methods to increase the simulation speed. First we use a coarse-grained two-bead (two beads per amino acid) model. Simulations show that peptides can aggregate into multilayer beta-sheet structures, which agree with X-ray diffraction experiments. To better represent the secondary structure transition happening during aggregation, we refine the
Mathematical statistics and limit theorems Festschrift in honour of Paul Deheuvels
Mason, David; Pfeifer, Dietmar; Steinebach, Josef
2015-01-01
This Festschrift in honour of Paul Deheuvels’ 65th birthday compiles recent research results in the area between mathematical statistics and probability theory with a special emphasis on limit theorems. The book brings together contributions from invited international experts to provide an up-to-date survey of the field. Written in textbook style, this collection of original material addresses researchers, PhD and advanced Master students with a solid grasp of mathematical statistics and probability theory.
Essentials of Mathematica With Applications to Mathematics and Physics
Boccara, Nino
2007-01-01
Essentials of Mathematica: With Applications to Mathematics and Physics, based on the lecture notes of a course taught at the University of Illinois at Chicago to advanced undergraduate and graduate students, teaches how to use Mathematica to solve a wide variety problems in mathematics and physics. The text assumes no previous exposure to Mathematica. It is illustrated with many detailed examples that require the student to construct meticulous, step-by-step, easy-to-read Mathematica programs. It includes many detailed graphics, with instructions to students on how to achieve similar results. The aim of Essentials of Mathematica is to provide the reader with Mathematica proficiency quickly and efficiently. The first part, in which the reader learns how to use a variety of Mathematica commands, avoids long discussions and overly sophisticated techniques. The second part covers a broad range of applications in physics and applied mathematics, including negative and complex bases, the double pendulum, fractals,...
6th International School of Mathematical Physics "Ettore Majorana"
Wightman, Arthur Strong
1986-01-01
The sixth Ettore Majorana International School of Mathematical Physics was held at the Centro della Cultura Scientifica Erice, Sicily, 1-14 July 1985. The present volume collects lecture notes on the ses sion which was devoted to Fundamental Problems of Gauge Field Theory. The School was a NATO Advanced Study Institute sponsored by the Italian Ministry of Public Education, the Italian Ministry of Scientific and Technological Research and the Regional Sicilian Government. As a result of the experimental and theoretical developments of the last two decades, gauge field theory, in one form or another, now pro vides the standard language for the description of Nature; QCD and the standard model of the electroweak interactions illustrate this point. It is a basic task of mathematical physics to provide a solid foundation for these developments by putting the theory in a physically transparent and mathematically rigorous form. The lectures and seminars of the school concentrated on the many unsolved pro...
The role of mathematics for physics teaching and understanding
International Nuclear Information System (INIS)
Pospiech, G; Geyer, M.A.; Eylon, B.; Bagno, E.; Lehavi, Y.
2015-01-01
That mathematics is the “language of physics” implies that both areas are deeply interconnected, such that often no separation between “pure” mathematics and “pure” physics is possible. To clarify their interplay a technical and a structural role of mathematics can be distinguished. A thorough understanding of this twofold role in physics is also important for shaping physics education especially with respect to teaching the nature of physics. Herewith the teachers and their pedagogical content knowledge play an important role. Therefore we develop a model of PCK concerning the interplay of mathematics and physics in order to provide a theoretical framework for the views and teaching strategies of teachers. In an exploratory study four teachers from Germany and four teachers from Israel have been interviewed concerning their views and its transfer to teaching physics. Here we describe the results from Germany. Besides general views and knowledge held by all or nearly all teachers we also observe specific individual focus depending on the teachers’ background and experiences. The results fit well into the derived model of PCK.
D. D. Kosambi selected works in mathematics and statistics
2016-01-01
This book fills an important gap in studies on D. D. Kosambi. For the first time, the mathematical work of Kosambi is described, collected and presented in a manner that is accessible to non-mathematicians as well. A number of his papers that are difficult to obtain in these areas are made available here. In addition, there are essays by Kosambi that have not been published earlier as well as some of his lesser known works. Each of the twenty four papers is prefaced by a commentary on the significance of the work, and where possible, extracts from technical reviews by other mathematicians.
The Study of Second Higher Education through Mathematical Statistics
Directory of Open Access Journals (Sweden)
Olga V. Kremer
2014-05-01
Full Text Available The article deals with the statistic reasons, age and wages of people who get the second higher education. People opt for the second higher education mostly due to many economical and physiological factors. According to our research, the age is a key motivator for the second higher education. Based on statistical data the portrait of a second higher education student was drawn.
Mathematical methods in engineering and physics
Felder, Gary N
2016-01-01
This text is intended for the undergraduate course in math methods, with an audience of physics and engineering majors. As a required course in most departments, the text relies heavily on explained examples, real-world applications and student engagement. Supporting the use of active learning, a strong focus is placed upon physical motivation combined with a versatile coverage of topics that can be used as a reference after students complete the course. Each chapter begins with an overview that includes a list of prerequisite knowledge, a list of skills that will be covered in the chapter, and an outline of the sections. Next comes the motivating exercise, which steps the students through a real-world physical problem that requires the techniques taught in each chapter.
Excel 2016 for physical sciences statistics a guide to solving practical problems
Quirk, Thomas J; Horton, Howard F
2016-01-01
This book is a step-by-step exercise-driven guide for students and practitioners who need to master Excel to solve practical physical science problems. If understanding statistics isn’t your strongest suit, you are not especially mathematically-inclined, or if you are wary of computers, this is the right book for you. Excel is an effective learning tool for quantitative analyses in environmental science courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. However, Excel 2016 for Physical Sciences Statistics: A Guide to Solving Practical Problems is the first book to capitalize on these improvements by teaching students and managers how to apply Excel 2016 to statistical techniques necessary in their courses and work. Each chapter explains statistical formulas and directs the reader to use Excel commands to solve specific, easy-to-understand physical science problems. Practice problems are provided at the end of each chapter with their s...
STATISTICAL EVALUATION OF EXAMINATION TESTS IN MATHEMATICS FOR ECONOMISTS
Directory of Open Access Journals (Sweden)
KASPŘÍKOVÁ, Nikola
2012-12-01
Full Text Available Examination results are rather important for many students with regard to their future profession development. Results of exams should be carefully inspected by the teachers to help improve design and evaluation of tests and education process in general. Analysis of examination papers in mathematics taken by students of basic mathematics course at University of Economics in Prague is reported. The first issue addressed is identification of significant dependencies between performance in particular problem areas covered in the test and also between particular items and total score in test or ability level as a latent trait. The assessment is first performed with Spearman correlation coefficient, items in the test are then evaluated within Item Response Theory framework. The second analytical task addressed is a search for groups of students who are similar with respect to performance in test. Cluster analysis is performed using partitioning around medoids method and final model selection is made according to average silhouette width. Results of clustering, which may be also considered in connection with setting of the minimum score for passing the exam, show that two groups of students can be identified. The group which may be called "well-performers" is the more clearly defined one.
A mathematical look at a physical power prediction model
Energy Technology Data Exchange (ETDEWEB)
Landberg, L. [Riso National Lab., Roskilde (Denmark)
1997-12-31
This paper takes a mathematical look at a physical model used to predict the power produced from wind farms. The reason is to see whether simple mathematical expressions can replace the original equations, and to give guidelines as to where the simplifications can be made and where they can not. This paper shows that there is a linear dependence between the geostrophic wind and the wind at the surface, but also that great care must be taken in the selection of the models since physical dependencies play a very important role, e.g. through the dependence of the turning of the wind on the wind speed.
Some beautiful equations of mathematical physics
International Nuclear Information System (INIS)
Freedman, D.Z.
1995-01-01
The basic ideas and the important role of gauge principles in modern elementary particle physics are outlined. There are three theoretically consistent gauge principles in quantum field theory: the spin-1 gauge principle of electromagnetism and the standard model, the spin-2 gauge principle of general relativity, and the spin-3/2 gauge principle of supergravity. (author)
Mathematics of classical and quantum physics
Byron, Frederick W
Well-organized text designed to complement graduate-level physics texts in classical mechanics, electricity, magnetism, and quantum mechanics. Topics include theory of vector spaces, analytic function theory, Green's function method of solving differential and partial differential equations, theory of groups, more. Many problems, suggestions for further reading.
Some beautiful equations of mathematical physics
Energy Technology Data Exchange (ETDEWEB)
Freedman, D Z [Theoretical Physics Division, CERN, Geneva (Switzerland); [Department of Mathematics and Center for Theoretical Physics, M.I.T., Cambridge, MA (United States)
1996-12-31
The basic ideas and the important role of gauge principles in modern elementary particle physics are outlined. There are three theoretically consistent gauge principles in quantum field theory: the spin-1 gauge principle of electromagnetism and the standard model, the spin-2 gauge principle of general relativity, and the spin-3/2 gauge principle of supergravity. (author)
Physical and mathematical modelling of extrusion processes
DEFF Research Database (Denmark)
Arentoft, Mogens; Gronostajski, Z.; Niechajowics, A.
2000-01-01
The main objective of the work is to study the extrusion process using physical modelling and to compare the findings of the study with finite element predictions. The possibilities and advantages of the simultaneous application of both of these methods for the analysis of metal forming processes...
Brownian quasi-particles in statistical physics
International Nuclear Information System (INIS)
Tellez-Arenas, A.; Fronteau, J.; Combis, P.
1979-01-01
The idea of a Brownian quasi-particle and the associated differentiable flow (with nonselfadjoint forces) are used here in the context of a stochastic description of the approach towards statistical equilibrium. We show that this quasi-particle flow acquires, at equilibrium, the principal properties of a conservative Hamiltonian flow. Thus the model of Brownian quasi-particles permits us to establish a link between the stochastic description and the Gibbs description of statistical equilibrium
Rays, waves, and scattering topics in classical mathematical physics
Adam, John A
2017-01-01
This one-of-a-kind book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. Panoramic in scope, it includes discussions of how ocean waves are refracted around islands and underwater ridges, how seismic waves are refracted in the earth's interior, how atmospheric waves are scattered by mountains and ridges, how the scattering of light waves produces the blue sky, and meteorological phenomena such as rainbows and coronas. Rays, Waves, and Scattering is a valuable resource for practitioners, graduate students, and advanced undergraduates in applied mathematics, theoretical physics, and engineering. Bridging the gap between advanced treatments of the subject written for specialists and less mathematical books aimed at beginners, this unique mathematical compendium features problems and exercises throughout that are geared to various levels of sophistication, covering everything from Ptolemy's theorem to Airy integrals (as well as more technica...
Analytical calculations by computer in physics and mathematics
International Nuclear Information System (INIS)
Gerdt, V.P.; Tarasov, O.V.; Shirokov, D.V.
1978-01-01
The review of present status of analytical calculations by computer is given. Some programming systems for analytical computations are considered. Such systems as SCHOONSCHIP, CLAM, REDUCE-2, SYMBAL, CAMAL, AVTO-ANALITIK which are implemented or will be implemented in JINR, and MACSYMA - one of the most developed systems - are discussed. It is shown on the basis of mathematical operations, realized in these systems, that they are appropriated for different problems of theoretical physics and mathematics, for example, for problems of quantum field theory, celestial mechanics, general relativity and so on. Some problems solved in JINR by programming systems for analytical computations are described. The review is intended for specialists in different fields of theoretical physics and mathematics
Engineering Physics and Mathematics Division progress report for period ending September 30, 1987
Energy Technology Data Exchange (ETDEWEB)
1987-12-01
This report provides an archival record of the activities of the Engineering Physics and Mathematics Division during the period June 30, 1985 through September 30, 1987. Work in Mathematical Sciences continues to include applied mathematics research, statistics research, and computer science. Nuclear-data measurements and evaluations continue for fusion reactors, fission reactors, and other nuclear systems. Also discussed are long-standing studies of fission-reactor shields through experiments and related analysis, of accelerator shielding, and of fusion-reactor neutronics. Work in Machine Intelligence continues to feature the development of an autonomous robot. The last descriptive part of this report reflects the work in our Engineering Physics Information Center, which again concentrates primarily upon radiation-shielding methods and related data.
Engineering Physics and Mathematics Division progress report for period ending September 30, 1987
International Nuclear Information System (INIS)
1987-12-01
This report provides an archival record of the activities of the Engineering Physics and Mathematics Division during the period June 30, 1985 through September 30, 1987. Work in Mathematical Sciences continues to include applied mathematics research, statistics research, and computer science. Nuclear-data measurements and evaluations continue for fusion reactors, fission reactors, and other nuclear systems. Also discussed are long-standing studies of fission-reactor shields through experiments and related analysis, of accelerator shielding, and of fusion-reactor neutronics. Work in Machine Intelligence continues to feature the development of an autonomous robot. The last descriptive part of this report reflects the work in our Engineering Physics Information Center, which again concentrates primarily upon radiation-shielding methods and related data
Symmetry and the Standard Model mathematics and particle physics
Robinson, Matthew
2011-01-01
While elementary particle physics is an extraordinarily fascinating field, the huge amount of knowledge necessary to perform cutting-edge research poses a formidable challenge for students. The leap from the material contained in the standard graduate course sequence to the frontiers of M-theory, for example, is tremendous. To make substantial contributions to the field, students must first confront a long reading list of texts on quantum field theory, general relativity, gauge theory, particle interactions, conformal field theory, and string theory. Moreover, waves of new mathematics are required at each stage, spanning a broad set of topics including algebra, geometry, topology, and analysis. Symmetry and the Standard Model: Mathematics and Particle Physics, by Matthew Robinson, is the first volume of a series intended to teach math in a way that is catered to physicists. Following a brief review of classical physics at the undergraduate level and a preview of particle physics from an experimentalist's per...
Mathematical methods for students of physics and related fields
Hassani, Sadri
2000-01-01
Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics This new edition has been made more user-friendly through organization into convenient, shorter chapters Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms Some praise for the previous edi...
Mathematical Methods For Students of Physics and Related Fields
Hassani, Sadri
2009-01-01
Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material. Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics. This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms. Some praise for the previo...
Interpreting mathematics in physics: Charting the applications of SU(2) in 20th century physics
International Nuclear Information System (INIS)
Anderson, Ronald; Joshi, G.C.
2008-01-01
The role mathematics plays within physics has been of sustained interest for physicists as well as for philosophers and historians of science. We explore this topic by tracing the role the mathematical structure associated with SU(2) has played in three key episodes in 20th century physics - intrinsic spin, isospin, and gauge theory and electroweak unification. We also briefly consider its role in loop quantum gravity. Each episode has led to profound and new physical notions of a space other than the traditional ones of space and spacetime, and each has had associated with it a complex and in places, contested history. The episodes also reveal ways mathematical structures provide resources for new physical theorizing and we propose our study as a contribution to a need Roger Penrose has identified to develop a 'profoundly sensitive aesthetic' sense for locating physically relevant mathematics
Interpreting mathematics in physics: Charting the applications of SU(2) in 20th century physics
Energy Technology Data Exchange (ETDEWEB)
Anderson, Ronald [Department of Philosophy, Boston College, Chestnut Hill, MA 02467 (United States)], E-mail: ronald.anderson@bc.edu; Joshi, G.C. [School of Physics, University of Melbourne, Victoria 3010 (Australia)], E-mail: joshi@physics.unimelb.edu.au
2008-04-15
The role mathematics plays within physics has been of sustained interest for physicists as well as for philosophers and historians of science. We explore this topic by tracing the role the mathematical structure associated with SU(2) has played in three key episodes in 20th century physics - intrinsic spin, isospin, and gauge theory and electroweak unification. We also briefly consider its role in loop quantum gravity. Each episode has led to profound and new physical notions of a space other than the traditional ones of space and spacetime, and each has had associated with it a complex and in places, contested history. The episodes also reveal ways mathematical structures provide resources for new physical theorizing and we propose our study as a contribution to a need Roger Penrose has identified to develop a 'profoundly sensitive aesthetic' sense for locating physically relevant mathematics.
Advances in Reactor physics, mathematics and computation. Volume 3
Energy Technology Data Exchange (ETDEWEB)
1987-01-01
These proceedings of the international topical meeting on advances in reactor physics, mathematics and computation, volume 3, are divided into sessions bearing on: - poster sessions on benchmark and codes: 35 conferences - review of status of assembly spectrum codes: 9 conferences - Numerical methods in fluid mechanics and thermal hydraulics: 16 conferences - stochastic transport and methods: 7 conferences.
The essential harmony in the classical equations of mathematical physics
Nucci, M C
2001-01-01
The possibility to transform any system of linear ordinary differential equations into a system of constant coefficient equations is demonstrated using Lie theory. Some examples relate the classical equations of mathematical physics to the simple harmonic oscillator. The roles of the third order form of the Ermakov-Pinney equation and of Fleischen-von Weltunter systems are explained.
Quantum algebras and Poisson geometry in mathematical physics
Karasev, M V
2005-01-01
This collection presents new and interesting applications of Poisson geometry to some fundamental well-known problems in mathematical physics. The methods used by the authors include, in addition to advanced Poisson geometry, unexpected algebras with non-Lie commutation relations, nontrivial (quantum) Kählerian structures of hypergeometric type, dynamical systems theory, semiclassical asymptotics, etc.
Physics to Mathematics: from Lintearia to Lemniscate - I
Indian Academy of Sciences (India)
Physics to Mathematics: from Lintearia to Lemniscate - I. R Sridharan. The elastic curve, also called elastica, is the name given to the shape assumed by a uniform elastic rod when bent into a plane curve under a stress of a certain kind. This curve, defined by James Bernoulli in the lSth century has been an interesting object ...
Journal of the Nigerian Association of Mathematical Physics ...
African Journals Online (AJOL)
This journal is aimed at any scientist who applies fairly rigorous mathematics to physics, chemistry, engineering or other sciences and also any mathematician ... Section Policies. Articles ... Browse By Category · Browse Alphabetically · Browse By Country · List All Titles · Free To Read Titles This Journal is Open Access.
Journal of the Nigerian Association of Mathematical Physics
African Journals Online (AJOL)
Bibliometric techniques were used to study the authorship characteristics of the Journal of the Nigerian Association of Mathematical Physics (JNAMP). Relevant data was obtained through an examination of volume 10 of the Journal. Author productivity, average productivity per author, authorship collaboration, most ...
Nonextensive statistical mechanics and high energy physics
Directory of Open Access Journals (Sweden)
Tsallis Constantino
2014-04-01
Full Text Available The use of the celebrated Boltzmann-Gibbs entropy and statistical mechanics is justified for ergodic-like systems. In contrast, complex systems typically require more powerful theories. We will provide a brief introduction to nonadditive entropies (characterized by indices like q, which, in the q → 1 limit, recovers the standard Boltzmann-Gibbs entropy and associated nonextensive statistical mechanics. We then present somerecent applications to systems such as high-energy collisions, black holes and others. In addition to that, we clarify and illustrate the neat distinction that exists between Lévy distributions and q-exponential ones, a point which occasionally causes some confusion in the literature, very particularly in the LHC literature
On fractional spin symmetries and statistical physics
International Nuclear Information System (INIS)
Saidi, E.H.
1995-09-01
The partition function Z and the quantum distribution of systems Σ of identical particles of fractional spin s = 1/k mod 1, k ≥ 2, generalizing the well-known Bose and Fermi ones, are derived. The generalized Sommerfeld development of the distribution around T = O deg. K is given. The low temperature analysis of statistical systems Σ is made. Known results are recovered. (author). 26 refs, 6 figs
Ramler, Ivan P.; Chapman, Jessica L.
2011-01-01
In this article we describe a semester-long project, based on the popular video game series Guitar Hero, designed to introduce upper-level undergraduate statistics students to statistical research. Some of the goals of this project are to help students develop statistical thinking that allows them to approach and answer open-ended research…
Information Theory - The Bridge Connecting Bounded Rational Game Theory and Statistical Physics
Wolpert, David H.
2005-01-01
A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all red-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. This paper shows that the same information theoretic mathematical structure, known as Product Distribution (PD) theory, addresses both issues. In this, PD theory not only provides a principle formulation of bounded rationality and a set of new types of mean field theory in statistical physics; it also shows that those topics are fundamentally one and the same.
Quantum Gravity (Cambridge Monographs on Mathematical Physics)
International Nuclear Information System (INIS)
Kiefer, C
2005-01-01
The most difficult unsolved problem in fundamental theoretical physics is the consistent implementation of the gravitational interaction into a quantum framework, which would lead to a theory of quantum gravity. Although a final answer is still pending, several promising attempts do exist. Despite the general title, this book is about one of them - loop quantum gravity. This approach proceeds from the idea that a direct quantization of Einstein's theory of general relativity is possible. In contrast to string theory, it presupposes that the unification of all interactions is not needed as a prerequisite for quantum gravity. Usually one divides theories of quantum general relativity into covariant and canonical approaches. Covariant theories employ four-dimensional concepts in its formulation, one example being the path integral approach. Canonical theories start from a classical Hamiltonian version of the theory in which spacetime is foliated into spacelike hypersurfaces. Loop quantum gravity is a variant of the canonical approach, the oldest being quantum geometrodynamics where the fundamental configuration variable is the three-metric. Loop quantum gravity has developed from a new choice of canonical variables introduced by Abhay Ashtekar in 1986, the new configuration variable being a connection defined on a three-manifold. Instead of the connection itself, the loop approach employs a non-local version in which the connection is integrated over closed loops. This is similar to the Wilson loops used in gauge theories. Carlo Rovelli is one of the pioneers of loop quantum gravity which he started to develop with Lee Smolin in two papers written in 1988 and 1990. In his book, he presents a comprehensive and competent overview of this approach and provides at the same time the necessary technical background in order to make the treatment self-contained. In fact, half of the book is devoted to 'preparations' giving a detailed account of Hamiltonian mechanics, quantum
Statistical and particle physics: Common problems and techniques
International Nuclear Information System (INIS)
Bowler, K.C.; Mc Kane, A.J.
1984-01-01
These proceedings contain statistical mechanical studies in condensed matter physics; interfacial problems in statistical physics; string theory; general monte carlo methods and their application to Lattice gauge theories; topological excitations in field theory; phase transformation kinetics; and studies of chaotic systems
78 FR 37590 - Advisory Committee for Mathematical and Physical Sciences #66; Notice of Meeting
2013-06-21
... Science Foundation and to provide advice and recommendations concerning research in mathematics and... NATIONAL SCIENCE FOUNDATION Advisory Committee for Mathematical and Physical Sciences 66; Notice... National Science Foundation announces the following meeting. Name: Advisory Committee for Mathematical and...
Statistics a guide to the use of statistical methods in the physical sciences
Barlow, Roger J
1989-01-01
The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A.C. Phillips Computing for Scienti
Marshman, Margaret; Dunn, Peter K.; McDougall, Robert; Wiegand, Aaron
2015-01-01
The new secondary Australian mathematics curricula have more statistics than the existing Queensland senior mathematics curricula. This paper discusses the attitudes to, and preparedness for, aspects of the implementation of the Australian Senior Mathematics Curricula within a group of Sunshine Coast (Queensland) mathematics educators. We found on…
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.
Becchi, Carlo Maria
2007-01-01
These notes are designed as a text book for a course on the Modern Physics Theory for undergraduate students. The purpose is providing a rigorous and self-contained presentation of the simplest theoretical framework using elementary mathematical tools. A number of examples of relevant applications and an appropriate list of exercises and answered questions are also given. The first part is devoted to Special Relativity concerning in particular space-time relativity and relativistic kinematics. The second part deals with Schroedinger's formulation of quantum mechanics. The presentation concerns mainly one dimensional problems, in particular tunnel effect, discrete energy levels and band spectra. The third part concerns the application of Gibbs statistical methods to quantum systems and in particular to Bose and Fermi gasses.
The role of mathematics in physical sciences interdisciplinary and philosophical aspects
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.
Chern-Simons terms and cocycles in physics and mathematics
Energy Technology Data Exchange (ETDEWEB)
Jackiw, R.
1984-12-01
Contemporary topological research in Yang-Mills theory is reviewed, emphasizing the Chern-Simons terms and their relatives. Three applications of the Chern-Simons terms in physical theory are described: to help understanding gauge theories in even dimensional space-time; gauge field dynamics in odd dimensional space-time; and mathematically coherent description of even-dimensional gauge theories with chiral fermions that are apparently inconsistent due to chiral anomalies. Discussion of these applications is preceded by explanation of the mathematical preliminaries and examples in simple quantum mechanical settings. 24 refs. (LEW)
Mathematical methods for mathematicians, physical scientists and engineers
Dunning-Davies, J
2003-01-01
This practical introduction encapsulates the entire content of teaching material for UK honours degree courses in mathematics, physics, chemistry and engineering, and is also appropriate for post-graduate study. It imparts the necessary mathematics for use of the techniques, with subject-related worked examples throughout. The text is supported by challenging problem exercises (and answers) to test student comprehension. Index notation used in the text simplifies manipulations in the sections on vectors and tensors. Partial differential equations are discussed, and special functions introduced
The mathematical knowledge of physics graduates: Primary data and conclusions
Breitenberger, Ernst
1992-04-01
Systematic observations were made of the mathematical knowledge of physics students from the U.S. and other countries during their first years of graduate study at Ohio University. It was found that all were deficient in general and in ``modern'' mathematical concepts, and in problem-solving skills. Sizable fractions of them did not even possess adequate concepts of ``derivative,'' ``integration,'' and ``truth.'' Nearly all were limited to some familiarity with rather elementary calculus, and with equally elementary differential and linear equations, but they showed some ability and a pronounced willingness to perform manipulations. Roughly, they regarded mathematics as mechanical method, not as constructive thinking. In view of the significantly higher levels of mathematical fluency demanded by contemporary advances in physics and in computer usage, none of these students was adequately prepared for future-oriented study, or for research and employment in physics and related areas at the close of the 20th century. It is intended to discuss the likely causes of this state of affairs elsewhere with a view toward remedial actions.
Safety bey statistics? A critical view on statistical methods applied in health physics
International Nuclear Information System (INIS)
Kraut, W.
2016-01-01
The only proper way to describe uncertainties in health physics is by statistical means. But statistics never can replace Your personal evaluation of effect, nor can statistics transmute randomness into certainty like an ''uncertainty laundry''. The paper discusses these problems in routine practical work.
Statistical Physics and Light-Front Quantization
Energy Technology Data Exchange (ETDEWEB)
Raufeisen, J
2004-08-12
Light-front quantization has important advantages for describing relativistic statistical systems, particularly systems for which boost invariance is essential, such as the fireball created in a heavy ion collisions. In this paper the authors develop light-front field theory at finite temperature and density with special attention to quantum chromodynamics. They construct the most general form of the statistical operator allowed by the Poincare algebra and show that there are no zero-mode related problems when describing phase transitions. They then demonstrate a direct connection between densities in light-front thermal field theory and the parton distributions measured in hard scattering experiments. The approach thus generalizes the concept of a parton distribution to finite temperature. In light-front quantization, the gauge-invariant Green's functions of a quark in a medium can be defined in terms of just 2-component spinors and have a much simpler spinor structure than the equal-time fermion propagator. From the Green's function, the authors introduce the new concept of a light-front density matrix, whose matrix elements are related to forward and to off-diagonal parton distributions. Furthermore, they explain how thermodynamic quantities can be calculated in discretized light-cone quantization, which is applicable at high chemical potential and is not plagued by the fermion-doubling problems.
Is poker a skill game? New insights from statistical physics
Javarone, Marco Alberto
2015-06-01
During last years poker has gained a lot of prestige in several countries and, besides being one of the most famous card games, it represents a modern challenge for scientists belonging to different communities, spanning from artificial intelligence to physics and from psychology to mathematics. Unlike games like chess, the task of classifying the nature of poker (i.e., as “skill game” or gambling) seems really hard and it also constitutes a current problem, whose solution has several implications. In general, gambling offers equal winning probabilities both to rational players (i.e., those that use a strategy) and to irrational ones (i.e., those without a strategy). Therefore, in order to uncover the nature of poker, a viable way is comparing performances of rational vs. irrational players during a series of challenges. Recently, a work on this topic revealed that rationality is a fundamental ingredient to succeed in poker tournaments. In this study we analyze a simple model of poker challenges by a statistical physics approach, with the aim to uncover the nature of this game. As main result we found that, under particular conditions, few irrational players can turn poker into gambling. Therefore, although rationality is a key ingredient to succeed in poker, also the format of challenges has an important role in these dynamics, as it can strongly influence the underlying nature of the game. The importance of our results lies on the related implications, as for instance in identifying the limits within which poker can be considered as a “skill game” and, as a consequence, which kind of format must be chosen to devise algorithms able to face humans.
Framing the Structural Role of Mathematics in Physics Lectures: A Case Study on Electromagnetism
Karam, Ricardo
2014-01-01
Physics education research has shown that students tend to struggle when trying to use mathematics in a meaningful way in physics (e.g., mathematizing a physical situation or making sense of equations). Concerning the possible reasons for these difficulties, little attention has been paid to the way mathematics is treated in physics instruction.…
Mathematics for plasma physics; Mathematiques pour la physique des plasmas
Energy Technology Data Exchange (ETDEWEB)
Sentis, R. [CEA Bruyeres-le-Chatel, 91 (France)
2011-01-15
The plasma physics is in the heart of the research of the CEA-DAM. Using mathematics in this domain is necessary, particularly for a precise statement of the partial differential equations systems which are on the basis of the numerical simulations. Examples are given concerning hydrodynamics, models for the thermal conduction and laser-plasma interaction. For the bi-temperature compressible Euler model, the mathematical study of the problem has allowed us to understand why the role of the energy equations dealing with ions on one hand and electrons on the other hand are not identical despite the symmetrical appearance of the system. The mathematical study is also necessary to be sure of the existence and uniqueness of the solution
Mai, Lan-Yin; Li, Yi-Xuan; Chen, Yong; Xie, Zhen; Li, Jie; Zhong, Ming-Yu
2014-05-01
The compatibility of traditional Chinese medicines (TCMs) formulae containing enormous information, is a complex component system. Applications of mathematical statistics methods on the compatibility researches of traditional Chinese medicines formulae have great significance for promoting the modernization of traditional Chinese medicines and improving clinical efficacies and optimizations of formulae. As a tool for quantitative analysis, data inference and exploring inherent rules of substances, the mathematical statistics method can be used to reveal the working mechanisms of the compatibility of traditional Chinese medicines formulae in qualitatively and quantitatively. By reviewing studies based on the applications of mathematical statistics methods, this paper were summarized from perspective of dosages optimization, efficacies and changes of chemical components as well as the rules of incompatibility and contraindication of formulae, will provide the references for further studying and revealing the working mechanisms and the connotations of traditional Chinese medicines.
Mathematical-statistical models and qualitative theories for economic and social sciences
Maturo, Fabrizio; Kacprzyk, Janusz
2017-01-01
This book presents a broad spectrum of problems related to statistics, mathematics, teaching, social science, and economics as well as a range of tools and techniques that can be used to solve these problems. It is the result of a scientific collaboration between experts in the field of economic and social systems from the University of Defence in Brno (Czech Republic), G. d’Annunzio University of Chieti-Pescara (Italy), Pablo de Olavid eUniversity of Sevilla (Spain), and Ovidius University in Constanţa, (Romania). The studies included were selected using a peer-review process and reflect heterogeneity and complexity of economic and social phenomena. They and present interesting empirical research from around the globe and from several research fields, such as statistics, decision making, mathematics, complexity, psychology, sociology and economics. The volume is divided into two parts. The first part, “Recent trends in mathematical and statistical models for economic and social sciences”, collects pap...
Statistical physics, neural networks, brain studies
International Nuclear Information System (INIS)
Toulouse, G.
1999-01-01
An overview of some aspects of a vast domain, located at the crossroads of physics, biology and computer science is presented: (1) During the last fifteen years, physicists advancing along various pathways have come into contact with biology (computational neurosciences) and engineering (formal neural nets). (2) This move may actually be viewed as one component in a larger picture. A prominent trend of recent years, observable over many countries, has been the establishment of interdisciplinary centers devoted to the study of: cognitive sciences; natural and artificial intelligence; brain, mind and behaviour; perception and action; learning and memory; robotics; man-machine communication, etc. What are the promising lines of development? What opportunities for physicists? An attempt will be made to address such questions and related issues
Probability and statistics for particle physics
Mana, Carlos
2017-01-01
This book comprehensively presents the basic concepts of probability and Bayesian inference with sufficient generality to make them applicable to current problems in scientific research. The first chapter provides the fundamentals of probability theory that are essential for the analysis of random phenomena. The second chapter includes a full and pragmatic review of the Bayesian methods that constitute a natural and coherent framework with enough freedom to analyze all the information available from experimental data in a conceptually simple manner. The third chapter presents the basic Monte Carlo techniques used in scientific research, allowing a large variety of problems to be handled difficult to tackle by other procedures. The author also introduces a basic algorithm, which enables readers to simulate samples from simple distribution, and describes useful cases for researchers in particle physics.The final chapter is devoted to the basic ideas of Information Theory, which are important in the Bayesian me...
What can we learn from noise? - Mesoscopic nonequilibrium statistical physics.
Kobayashi, Kensuke
2016-01-01
Mesoscopic systems - small electric circuits working in quantum regime - offer us a unique experimental stage to explorer quantum transport in a tunable and precise way. The purpose of this Review is to show how they can contribute to statistical physics. We introduce the significance of fluctuation, or equivalently noise, as noise measurement enables us to address the fundamental aspects of a physical system. The significance of the fluctuation theorem (FT) in statistical physics is noted. We explain what information can be deduced from the current noise measurement in mesoscopic systems. As an important application of the noise measurement to statistical physics, we describe our experimental work on the current and current noise in an electron interferometer, which is the first experimental test of FT in quantum regime. Our attempt will shed new light in the research field of mesoscopic quantum statistical physics.
Mathematical analogies in physics. Thin-layer wave theory
Directory of Open Access Journals (Sweden)
José M. Carcione
2014-03-01
Full Text Available Field theory applies to elastodynamics, electromagnetism, quantum mechanics, gravitation and other similar fields of physics, where the basic equations describing the phenomenon are based on constitutive relations and balance equations. For instance, in elastodynamics, these are the stress-strain relations and the equations of momentum conservation (Euler-Newton law. In these cases, the same mathematical theory can be used, by establishing appropriate mathematical equivalences (or analogies between material properties and field variables. For instance, the wave equation and the related mathematical developments can be used to describe anelastic and electromagnetic wave propagation, and are extensively used in quantum mechanics. In this work, we obtain the mathematical analogy for the reflection/refraction (transmission problem of a thin layer embedded between dissimilar media, considering the presence of anisotropy and attenuation/viscosity in the viscoelastic case, conductivity in the electromagnetic case and a potential barrier in quantum physics (the tunnel effect. The analogy is mainly illustrated with geophysical examples of propagation of S (shear, P (compressional, TM (transverse-magnetic and TE (transverse-electric waves. The tunnel effect is obtained as a special case of viscoelastic waves at normal incidence.
Quantum Entropy and Its Applications to Quantum Communication and Statistical Physics
Directory of Open Access Journals (Sweden)
Masanori Ohya
2010-05-01
Full Text Available Quantum entropy is a fundamental concept for quantum information recently developed in various directions. We will review the mathematical aspects of quantum entropy (entropies and discuss some applications to quantum communication, statistical physics. All topics taken here are somehow related to the quantum entropy that the present authors have been studied. Many other fields recently developed in quantum information theory, such as quantum algorithm, quantum teleportation, quantum cryptography, etc., are totally discussed in the book (reference number 60.
Intuitive physics knowledge, physics problem solving and the role of mathematical equations
Directory of Open Access Journals (Sweden)
Laura Buteler
2012-09-01
Full Text Available The present work explores the role that mathematical equations play in modifying students’ physical intuition (diSessa, 1993. The work is carried out assuming that students achieve a great deal of the refinement in their physical intuitions during problem solving (Sherin, 2006. The study is guided by the question of how the use of mathematical equations contributes to this refinement. The authors aim at expanding on Sherin´s (2006 hypothesis, suggesting a more bounding relation between physical intuitions and mathematics. In this scenario, intuitions play a more compelling role in “deciding” which equations are acceptable and which are not. Our hypothesis is constructed on the basis of three cases: the first published by Sherin (2006 and two more from registries of our own. The three cases are compared and analyzed in relation to the role of mathematical equations in refining – or not – the intuitive knowledge students bring to play during problem solving.
Special issue on cluster algebras in mathematical physics
Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito
2014-02-01
This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March
The limitations of mathematical modeling in high school physics education
Forjan, Matej
The theme of the doctoral dissertation falls within the scope of didactics of physics. Theoretical analysis of the key constraints that occur in the transmission of mathematical modeling of dynamical systems into field of physics education in secondary schools is presented. In an effort to explore the extent to which current physics education promotes understanding of models and modeling, we analyze the curriculum and the three most commonly used textbooks for high school physics. We focus primarily on the representation of the various stages of modeling in the solved tasks in textbooks and on the presentation of certain simplifications and idealizations, which are in high school physics frequently used. We show that one of the textbooks in most cases fairly and reasonably presents the simplifications, while the other two half of the analyzed simplifications do not explain. It also turns out that the vast majority of solved tasks in all the textbooks do not explicitly represent model assumptions based on what we can conclude that in high school physics the students do not develop sufficiently a sense of simplification and idealizations, which is a key part of the conceptual phase of modeling. For the introduction of modeling of dynamical systems the knowledge of students is also important, therefore we performed an empirical study on the extent to which high school students are able to understand the time evolution of some dynamical systems in the field of physics. The research results show the students have a very weak understanding of the dynamics of systems in which the feedbacks are present. This is independent of the year or final grade in physics and mathematics. When modeling dynamical systems in high school physics we also encounter the limitations which result from the lack of mathematical knowledge of students, because they don't know how analytically solve the differential equations. We show that when dealing with one-dimensional dynamical systems
Classical Methods of Statistics With Applications in Fusion-Oriented Plasma Physics
Kardaun, Otto J W F
2005-01-01
Classical Methods of Statistics is a blend of theory and practical statistical methods written for graduate students and researchers interested in applications to plasma physics and its experimental aspects. It can also fruitfully be used by students majoring in probability theory and statistics. In the first part, the mathematical framework and some of the history of the subject are described. Many exercises help readers to understand the underlying concepts. In the second part, two case studies are presented exemplifying discriminant analysis and multivariate profile analysis. The introductions of these case studies outline contextual magnetic plasma fusion research. In the third part, an overview of statistical software is given and, in particular, SAS and S-PLUS are discussed. In the last chapter, several datasets with guided exercises, predominantly from the ASDEX Upgrade tokamak, are included and their physical background is concisely described. The book concludes with a list of essential keyword transl...
The Bogolyubov renormalization group in theoretical and mathematical physics
International Nuclear Information System (INIS)
Shirkov, D.V.
1999-01-01
This text follows the line of a talk on Ringberg symposium dedicated to Wolfhart Zimmermann 70th birthday. The historical overview (Part I) partially overlaps with corresponding text of my previous commemorative paper - see Ref. [6] in the list. At the same time the second part includes some fresh results in QFT (Sect. 2.1.) and summarizes (Sect. 2.4) an impressive recent progress of the 'QFT renormalization group' application in mathematical physics
Symmetry, Invariance and Ontology in Physics and Statistics
Directory of Open Access Journals (Sweden)
Julio Michael Stern
2011-09-01
Full Text Available This paper has three main objectives: (a Discuss the formal analogy between some important symmetry-invariance arguments used in physics, probability and statistics. Specifically, we will focus on Noether’s theorem in physics, the maximum entropy principle in probability theory, and de Finetti-type theorems in Bayesian statistics; (b Discuss the epistemological and ontological implications of these theorems, as they are interpreted in physics and statistics. Specifically, we will focus on the positivist (in physics or subjective (in statistics interpretations vs. objective interpretations that are suggested by symmetry and invariance arguments; (c Introduce the cognitive constructivism epistemological framework as a solution that overcomes the realism-subjectivism dilemma and its pitfalls. The work of the physicist and philosopher Max Born will be particularly important in our discussion.
Statistical physics and thermodynamics an introduction to key concepts
Rau, Jochen
2017-01-01
Statistical physics and thermodynamics describe the behaviour of systems on the macroscopic scale. Their methods are applicable to a wide range of phenomena: from refrigerators to the interior of stars, from chemical reactions to magnetism. Indeed, of all physical laws, the laws of thermodynamics are perhaps the most universal. This text provides a concise yet thorough introduction to the key concepts which underlie statistical physics and thermodynamics. It begins with a review of classical probability theory and quantum theory, as well as a careful discussion of the notions of information and entropy, prior to embarking on the development of statistical physics proper. The crucial steps leading from the microscopic to the macroscopic domain are rendered transparent. In particular, the laws of thermodynamics are shown to emerge as natural consequences of the statistical framework. While the emphasis is on clarifying the basic concepts, the text also contains many applications and classroom-tested exercises,...
Advances in Reactor Physics, Mathematics and Computation. Volume 2
Energy Technology Data Exchange (ETDEWEB)
1987-01-01
These proceedings of the international topical meeting on advances in reactor physics, mathematics and computation, Volume 2, are divided into 7 sessions bearing on: - session 7: Deterministic transport methods 1 (7 conferences), - session 8: Interpretation and analysis of reactor instrumentation (6 conferences), - session 9: High speed computing applied to reactor operations (5 conferences), - session 10: Diffusion theory and kinetics (7 conferences), - session 11: Fast reactor design, validation and operating experience (8 conferences), - session 12: Deterministic transport methods 2 (7 conferences), - session 13: Application of expert systems to physical aspects of reactor design and operation.
Advances in Reactor Physics, Mathematics and Computation. Volume 1
Energy Technology Data Exchange (ETDEWEB)
1987-01-01
These proceedings of the international topical meeting on advances in reactor physics, mathematics and computation, volume one, are divided into 6 sessions bearing on: - session 1: Advances in computational methods including utilization of parallel processing and vectorization (7 conferences) - session 2: Fast, epithermal, reactor physics, calculation, versus measurements (9 conferences) - session 3: New fast and thermal reactor designs (9 conferences) - session 4: Thermal radiation and charged particles transport (7 conferences) - session 5: Super computers (7 conferences) - session 6: Thermal reactor design, validation and operating experience (8 conferences).
d=4 N=2 Field Theory And Physical Mathematics
CERN. Geneva
2017-01-01
I will explain the meaning of the two phrases in the title. Much of the talk will be a review of the renowned Seiberg-Witten formulation of the low-energy physics of certain four dimensional supersymmetric interacting quantum field theories. In the latter part of the talk I will briefly describe some of the significant progress that has been made in solving for the so-called BPS sector of the Hilbert space of these theories. Investigations into these physical questions have had a nontrivial impact on mathematics.
1. Warsaw School of Statistical Physics - Poster Abstracts
International Nuclear Information System (INIS)
2005-01-01
The abstracts of information presented in posters during '1st Warsaw School of Statistical Physics' which held in Kazimierz Dolny - Poland are presented. They cover different aspects of statistical processes like diffusion, fluid hydrodynamics as well as modern quantum mechanical methods of their solutions
Gill, R.D.
1997-01-01
The speaker wants to make clear from the start that he is a mathematical statistician---i.e., a mathematician who studies and developes statistical theory---with certainly a great (layman's) interest in environmental matters, but with very little actual professional practical experience in this big
From Research to Practice: Basic Mathematics Skills and Success in Introductory Statistics
Lunsford, M. Leigh; Poplin, Phillip
2011-01-01
Based on previous research of Johnson and Kuennen (2006), we conducted a study to determine factors that would possibly predict student success in an introductory statistics course. Our results were similar to Johnson and Kuennen in that we found students' basic mathematical skills, as measured on a test created by Johnson and Kuennen, were a…
Logue, Alexandra W.; Watanabe-Rose, Mari
2014-01-01
This study used a randomized controlled trial to determine whether students, assessed by their community colleges as needing an elementary algebra (remedial) mathematics course, could instead succeed at least as well in a college-level, credit-bearing introductory statistics course with extra support (a weekly workshop). Researchers randomly…
Mathematical-statistical model for analysis of Ulva algal net photosynthesis in Venice lagoon
International Nuclear Information System (INIS)
Izzo, G.; Rizzo, V.; Bella, A.; Picci, M.; Giordano, P.
1996-08-01
The algal net photosynthesis, an important factor for the characterization of water quality in Venice lagoon, has been studied experimentally providing a mathematical model, validated by using statistical methods. This model relates oxygen production with irradiance, according to a well known law in biological literature. Its observed an inverted proportion between algal oxygen production and temperature, thus seasonality
Bourne, Victoria J.
2018-01-01
Statistics anxiety is experienced by a large number of psychology students, and previous research has examined a range of potential correlates, including academic performance, mathematical ability and psychological predictors. These varying predictors are often considered separately, although there may be shared variance between them. In the…
Exploring Teachers' Practices in Teaching Mathematics and Statistics in Kwazulu-Natal Schools
Umugiraneza, Odette; Bansilal, Sarah; North, Delia
2017-01-01
Teaching approaches and assessment practices are key factors that contribute to the improvement of learner outcomes. The study on which this article is based, explored the methods used by KwaZulu-Natal (KZN) teachers in teaching and assessing mathematics and statistics. An instrument containing closed and open-ended questions was distributed to…
Correlated randomness: Some examples of exotic statistical physics
Indian Academy of Sciences (India)
journal of. May 2005 physics pp. 645–660. Correlated randomness: Some examples of exotic statistical physics .... The key idea is that scale invariance is a statement not about algebraic .... Very recently an article appeared in Phys. Rev. ... One quarter of any newspaper with a financial section is filled with economic fluc-.
Rock Burst Mechanics: Insight from Physical and Mathematical Modelling
Directory of Open Access Journals (Sweden)
J. Vacek
2008-01-01
Full Text Available Rock burst processes in mines are studied by many groups active in the field of geomechanics. Physical and mathematical modelling can be used to better understand the phenomena and mechanisms involved in the bursts. In the present paper we describe both physical and mathematical models of a rock burst occurring in a gallery of a coal mine.For rock bursts (also called bumps to occur, the rock has to possess certain particular rock burst properties leading to accumulation of energy and the potential to release this energy. Such materials may be brittle, or the rock burst may arise at the interfacial zones of two parts of the rock, which have principally different material properties (e.g. in the Poíbram uranium mines.The solution is based on experimental and mathematical modelling. These two methods have to allow the problem to be studied on the basis of three presumptions:· the solution must be time dependent,· the solution must allow the creation of cracks in the rock mass,· the solution must allow an extrusion of rock into an open space (bump effect.
Physical and mathematical modeling of antimicrobial photodynamic therapy
Bürgermeister, Lisa; López, Fernando Romero; Schulz, Wolfgang
2014-07-01
Antimicrobial photodynamic therapy (aPDT) is a promising method to treat local bacterial infections. The therapy is painless and does not cause bacterial resistances. However, there are gaps in understanding the dynamics of the processes, especially in periodontal treatment. This work describes the advances in fundamental physical and mathematical modeling of aPDT used for interpretation of experimental evidence. The result is a two-dimensional model of aPDT in a dental pocket phantom model. In this model, the propagation of laser light and the kinetics of the chemical reactions are described as coupled processes. The laser light induces the chemical processes depending on its intensity. As a consequence of the chemical processes, the local optical properties and distribution of laser light change as well as the reaction rates. The mathematical description of these coupled processes will help to develop treatment protocols and is the first step toward an inline feedback system for aPDT users.
Statistical physics of human beings in games: Controlled experiments
International Nuclear Information System (INIS)
Liang Yuan; Huang Ji-Ping
2014-01-01
It is important to know whether the laws or phenomena in statistical physics for natural systems with non-adaptive agents still hold for social human systems with adaptive agents, because this implies whether it is possible to study or understand social human systems by using statistical physics originating from natural systems. For this purpose, we review the role of human adaptability in four kinds of specific human behaviors, namely, normal behavior, herd behavior, contrarian behavior, and hedge behavior. The approach is based on controlled experiments in the framework of market-directed resource-allocation games. The role of the controlled experiments could be at least two-fold: adopting the real human decision-making process so that the system under consideration could reflect the performance of genuine human beings; making it possible to obtain macroscopic physical properties of a human system by tuning a particular factor of the system, thus directly revealing cause and effect. As a result, both computer simulations and theoretical analyses help to show a few counterparts of some laws or phenomena in statistical physics for social human systems: two-phase phenomena or phase transitions, entropy-related phenomena, and a non-equilibrium steady state. This review highlights the role of human adaptability in these counterparts, and makes it possible to study or understand some particular social human systems by means of statistical physics coming from natural systems. (topical review - statistical physics and complex systems)
Schaid, Daniel J
2010-01-01
Measures of genomic similarity are the basis of many statistical analytic methods. We review the mathematical and statistical basis of similarity methods, particularly based on kernel methods. A kernel function converts information for a pair of subjects to a quantitative value representing either similarity (larger values meaning more similar) or distance (smaller values meaning more similar), with the requirement that it must create a positive semidefinite matrix when applied to all pairs of subjects. This review emphasizes the wide range of statistical methods and software that can be used when similarity is based on kernel methods, such as nonparametric regression, linear mixed models and generalized linear mixed models, hierarchical models, score statistics, and support vector machines. The mathematical rigor for these methods is summarized, as is the mathematical framework for making kernels. This review provides a framework to move from intuitive and heuristic approaches to define genomic similarities to more rigorous methods that can take advantage of powerful statistical modeling and existing software. A companion paper reviews novel approaches to creating kernels that might be useful for genomic analyses, providing insights with examples [1]. Copyright © 2010 S. Karger AG, Basel.
Mathematical problem solving ability of sport students in the statistical study
Sari, E. F. P.; Zulkardi; Putri, R. I. I.
2017-12-01
This study aims to determine the problem-solving ability of sport students of PGRI Palembang semester V in the statistics course. Subjects in this study were sport students of PGRI Palembang semester V which amounted to 31 people. The research method used is quasi experiment type one case shoot study. Data collection techniques in this study use the test and data analysis used is quantitative descriptive statistics. The conclusion of this study shown that the mathematical problem solving ability of PGRI Palembang sport students of V semester in the statistical course is categorized well with the average of the final test score of 80.3.
Blanchard, Philippe
2015-01-01
The second edition of this textbook presents the basic mathematical knowledge and skills that are needed for courses on modern theoretical physics, such as those on quantum mechanics, classical and quantum field theory, and related areas. The authors stress that learning mathematical physics is not a passive process and include numerous detailed proofs, examples, and over 200 exercises, as well as hints linking mathematical concepts and results to the relevant physical concepts and theories. All of the material from the first edition has been updated, and five new chapters have been added on such topics as distributions, Hilbert space operators, and variational methods. The text is divided into three main parts. Part I is a brief introduction to distribution theory, in which elements from the theories of ultradistributions and hyperfunctions are considered in addition to some deeper results for Schwartz distributions, thus providing a comprehensive introduction to the theory of generalized functions. P...
2014-03-01
The second International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place at Prague, Czech Republic, from Sunday 1 September to Thursday 5 September 2013. The Conference was attended by more than 280 participants and hosted about 400 oral, poster, and virtual presentations while counted more than 600 pre-registered authors. The second IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics. The scientific program was rather heavy since after the Keynote and Invited Talks in the morning, three parallel sessions were running every day. However, according to all attendees, the program was excellent with high level of talks and the scientific environment was fruitful, thus all attendees had a creative time. We would like to thank the Keynote Speaker and the Invited Speakers for their significant contribution to IC-MSQUARE. We also would like to thank the Members of the International Advisory and Scientific Committees as well as the Members of the Organizing Committee. Further information on the editors, speakers and committees is available in the attached pdf.
PREFACE: 4th International Conference on Mathematical Modeling in Physical Sciences (IC-MSquare2015)
Vlachos, Dimitrios; Vagenas, Elias C.
2015-09-01
The 4th International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place in Mykonos, Greece, from Friday 5th June to Monday 8th June 2015. The Conference was attended by more than 150 participants and hosted about 200 oral, poster, and virtual presentations. There were more than 600 pre-registered authors. The 4th IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics etc. The scientific program was rather intense as after the Keynote and Invited Talks in the morning, three parallel oral and one poster session were running every day. However, according to all attendees, the program was excellent with a high quality of talks creating an innovative and productive scientific environment for all attendees. We would like to thank the Keynote Speaker and the Invited Speakers for their significant contribution to IC-MSQUARE. We also would like to thank the Members of the International Advisory and Scientific Committees as well as the Members of the Organizing Committee.
2015-01-01
The third International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place at Madrid, Spain, from Thursday 28 to Sunday 31 August 2014. The Conference was attended by more than 200 participants and hosted about 350 oral, poster, and virtual presentations. More than 600 pre-registered authors were also counted. The third IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics etc. The scientific program was rather heavy since after the Keynote and Invited Talks in the morning, three parallel oral sessions and one poster session were running every day. However, according to all attendees, the program was excellent with high level of talks and the scientific environment was fruitful, thus all attendees had a creative time. We would like to thank the Keynote Speaker and the Invited Speakers for their significant contribution to IC-MSQUARE. We also would like to thank the Members of the International Advisory and Scientific Committees as well as the Members of the Organizing Committee.
5th International Conference on Mathematical Modeling in Physical Sciences (IC-MSquare 2016)
International Nuclear Information System (INIS)
Vagenas, Elias C.; Vlachos, Dimitrios S.
2016-01-01
The 5th International Conference on Mathematical Modeling in Physical Sciences (IC- MSQUARE) took place at Athens, Greece, from Monday, 23"t"h of May, to Thursday, 26"t"h of May 2016. The Conference was attended by more than 130 participants and hosted about 170 oral, poster, and virtual presentations while counted more than 500 pre-registered authors. The 5"t"h IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics etc. The scientific program was rather heavy since after the Keynote and Invited Talks in the morning, three parallel oral and one poster session were running every day. However, according to all attendees, the program was excellent with high level talks and the scientific environment was fruitful, thus all attendees had a creative time. We would like to thank the Keynote Speaker and the Invited Speakers for their significant contribution to IC-MSQUARE. We also would like to thank the Members of the International Advisory and Scientific Committees as well as the Members of the Organizing Committee. (paper)
Twareque Ali, Syed; Antoine, Jean-Pierre; Bagarello, Fabio; Gazeau, Jean-Pierre
2011-07-01
This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to coherent states. The motivation behind this special issue is to gather in a single comprehensive volume the main aspects (past and present), latest developments, different viewpoints and directions being followed in this multidisciplinary field. Given the impressive development of the field in the past two decades, the topicality of such a volume can hardly be overemphasized. We strongly believe that such a special issue could become a particularly valuable reference for the broad scientific community working in mathematical and theoretical physics, as well as in signal processing and mathematics. Editorial policy The Guest Editors for this issue will be Syed Twareque Ali, Jean-Pierre Antoine, Fabio Bagarello and Jean-Pierre Gazeau. Potential topics include, but are not limited to, developments in the theory and applications of coherent states in: quantum optics, optomechanics, Bose-Einstein condensates quantum information, quantum measurement signal processing quantum gravity pseudo-Hermitian quantum mechanics supersymmetric quantum mechanics non-commutative quantum mechanics quantization theory harmonic and functional analysis operator theory Berezin-Toeplitz operators, PT-symmetric operators holomorphic representation theory, reproducing kernel spaces generalization of coherent states All contributions will be refereed and processed according to the usual procedure of the journal. Papers should report original and significant research that has not already been published. Guidelines for preparation of contributions The deadline for contributed papers will be 31 October 2011. This deadline will allow the special issue to appear before the end of May 2012 There is a nominal page limit of 15 printed pages per contribution (invited review papers can be longer). For papers exceeding this limit, the Guest Editors reserve the right to request a
Wegner, Franz
2016-01-01
This text presents the mathematical concepts of Grassmann variables and the method of supersymmetry to a broad audience of physicists interested in applying these tools to disordered and critical systems, as well as related topics in statistical physics. Based on many courses and seminars held by the author, one of the pioneers in this field, the reader is given a systematic and tutorial introduction to the subject matter. The algebra and analysis of Grassmann variables is presented in part I. The mathematics of these variables is applied to a random matrix model, path integrals for fermions, dimer models and the Ising model in two dimensions. Supermathematics - the use of commuting and anticommuting variables on an equal footing - is the subject of part II. The properties of supervectors and supermatrices, which contain both commuting and Grassmann components, are treated in great detail, including the derivation of integral theorems. In part III, supersymmetric physical models are considered. While supersym...
Special functions of mathematical physics a unified introduction with applications
Nikiforov, Arnold F
1988-01-01
With students of Physics chiefly in mind, we have collected the material on special functions that is most important in mathematical physics and quan tum mechanics. We have not attempted to provide the most extensive collec tion possible of information about special functions, but have set ourselves the task of finding an exposition which, based on a unified approach, ensures the possibility of applying the theory in other natural sciences, since it pro vides a simple and effective method for the independent solution of problems that arise in practice in physics, engineering and mathematics. For the American edition we have been able to improve a number of proofs; in particular, we have given a new proof of the basic theorem (§3). This is the fundamental theorem of the book; it has now been extended to cover difference equations of hypergeometric type (§§12, 13). Several sections have been simplified and contain new material. We believe that this is the first time that the theory of classical or th...
Non-Commutative Mechanics in Mathematical & in Condensed Matter Physics
Directory of Open Access Journals (Sweden)
Peter A. Horváthy
2006-12-01
Full Text Available Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table 1. Souriau's construction applied to the two-parameter central extension of the planar Galilei group leads to the ''exotic'' particle, which has non-commuting position coordinates. A Berry-phase argument applied to the Bloch electron yields in turn a semiclassical model that has been used to explain the anomalous/spin/optical Hall effects. The non-commutative parameter is momentum-dependent in this case, and can take the form of a monopole in momentum space.
Fundamentals of Cryobiology Physical Phenomena and Mathematical Models
Zhmakin, Alexander I
2009-01-01
The book gives a summary of the state-of-the-art of cryobiology and its applications. The accent is on the underlying physical phenomena, which are common in such opposite applications as cryosurgery and cryoconservation, and the corresponding mathematical models, including numerical ones. The treatment of some more special issues is moved to the appendices. The glossary contains definitions and explanations of the major entities. All the topics considered are well referenced. The book is useful to both biologists and physicits of different level including practioners and graduate students.
Weyl's search for a difference between 'physical' and 'mathematical' automorphisms
Scholz, Erhard
2018-02-01
During his whole scientific life Hermann Weyl was fascinated by the interrelation of physical and mathematical theories. From the mid 1920s onward he reflected also on the typical difference between the two epistemic fields and tried to identify it by comparing their respective automorphism structures. In a talk given at the end of the 1940s (ETH, Hs 91a:31) he gave the most detailed and coherent discussion of his thoughts on this topic. This paper presents his arguments in the talk and puts it in the context of the later development of gauge theories.
Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics
Directory of Open Access Journals (Sweden)
Khaled A. Gepreel
2013-01-01
Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.
International Conference on Differential Equations and Mathematical Physics
Saitō, Yoshimi
1987-01-01
The meeting in Birmingham, Alabama, provided a forum for the discussion of recent developments in the theory of ordinary and partial differential equations, both linear and non-linear, with particular reference to work relating to the equations of mathematical physics. The meeting was attended by about 250 mathematicians from 22 countries. The papers in this volume all involve new research material, with at least outline proofs; some papers also contain survey material. Topics covered include: Schrödinger theory, scattering and inverse scattering, fluid mechanics (including conservative systems and inertial manifold theory attractors), elasticity, non-linear waves, and feedback control theory.
Proceedings, 3rd International Satellite Conference on Mathematical Methods in Physics (ICMP13)
2013-01-01
The aim of the Conference is to present the latest advances in Mathematical Methods to researchers, post-docs and graduated students acting in the areas of Physics of Particles and Fields, Mathematical Physics and Applied Mathematics. Topics: Methods of Spectral and Group Theory, Differential and Algebraic Geometry and Topology in Field Theory, Quantum Gravity, String Theory and Cosmology.
Kjeldsen, Tinne Hoff; Lützen, Jesper
2015-07-01
In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit-reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.
A Concise Introduction to the Statistical Physics of Complex Systems
Bertin, Eric
2012-01-01
This concise primer (based on lectures given at summer schools on complex systems and on a masters degree course in complex systems modeling) will provide graduate students and newcomers to the field with the basic knowledge of the concepts and methods of statistical physics and its potential for application to interdisciplinary topics. Indeed, in recent years, statistical physics has begun to attract the interest of a broad community of researchers in the field of complex system sciences, ranging from biology to the social sciences, economics and computer science. More generally, a growing number of graduate students and researchers feel the need to learn some basic concepts and questions originating in other disciplines without necessarily having to master all of the corresponding technicalities and jargon. Generally speaking, the goals of statistical physics may be summarized as follows: on the one hand to study systems composed of a large number of interacting ‘entities’, and on the other to predict...
Heuristic versus statistical physics approach to optimization problems
International Nuclear Information System (INIS)
Jedrzejek, C.; Cieplinski, L.
1995-01-01
Optimization is a crucial ingredient of many calculation schemes in science and engineering. In this paper we assess several classes of methods: heuristic algorithms, methods directly relying on statistical physics such as the mean-field method and simulated annealing; and Hopfield-type neural networks and genetic algorithms partly related to statistical physics. We perform the analysis for three types of problems: (1) the Travelling Salesman Problem, (2) vector quantization, and (3) traffic control problem in multistage interconnection network. In general, heuristic algorithms perform better (except for genetic algorithms) and much faster but have to be specific for every problem. The key to improving the performance could be to include heuristic features into general purpose statistical physics methods. (author)
A statistical physics perspective on criticality in financial markets
International Nuclear Information System (INIS)
Bury, Thomas
2013-01-01
Stock markets are complex systems exhibiting collective phenomena and particular features such as synchronization, fluctuations distributed as power-laws, non-random structures and similarity to neural networks. Such specific properties suggest that markets operate at a very special point. Financial markets are believed to be critical by analogy to physical systems, but little statistically founded evidence has been given. Through a data-based methodology and comparison to simulations inspired by the statistical physics of complex systems, we show that the Dow Jones and index sets are not rigorously critical. However, financial systems are closer to criticality in the crash neighborhood. (paper)
The complex road to mathematization in physics instruction
DEFF Research Database (Denmark)
Avelar Sotomaior Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche
2012-01-01
to the research in this field, we have analysed a set of lectures given by a distinguished physics professor. In this proposal we present the analysis of two lectures where the abstract concepts of charge density and electric flux are taught. The complexity of the mathematization of these concepts is evident both...... explicitly and made punctual metacognitive remarks. Taking into account the future perspectives of our research, the categorization of the didactical strategies used by this professor shall allows us to develop comparative studies with other lectures on the same topic. Moreover, the derivation promising......How to facilitate students’ understanding of science’s abstract concepts is definitely a major concern of every dedicated physics teacher. However, discussions about promising ways to be successful at this task are not always part of teacher training curricula. With the goal of contributing...
Mathematical physics a modern introduction to its foundations
Hassani, Sadri
2013-01-01
The goal of this book is to expose the reader to the indispensable role that mathematics---often very abstract---plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics as diverse as algebras, classical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups, manifolds, Lie groups and their representations, Clifford algebras and their representations, and fiber bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision of the first one with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras and spinors, fiber bundles, and gauge theories. The spirit of the first edition, namely the balance between rigor and physical application, has been maintained, as is the abundance...
Statistical physics of human beings in games: Controlled experiments
Liang, Yuan; Huang, Ji-Ping
2014-07-01
It is important to know whether the laws or phenomena in statistical physics for natural systems with non-adaptive agents still hold for social human systems with adaptive agents, because this implies whether it is possible to study or understand social human systems by using statistical physics originating from natural systems. For this purpose, we review the role of human adaptability in four kinds of specific human behaviors, namely, normal behavior, herd behavior, contrarian behavior, and hedge behavior. The approach is based on controlled experiments in the framework of market-directed resource-allocation games. The role of the controlled experiments could be at least two-fold: adopting the real human decision-making process so that the system under consideration could reflect the performance of genuine human beings; making it possible to obtain macroscopic physical properties of a human system by tuning a particular factor of the system, thus directly revealing cause and effect. As a result, both computer simulations and theoretical analyses help to show a few counterparts of some laws or phenomena in statistical physics for social human systems: two-phase phenomena or phase transitions, entropy-related phenomena, and a non-equilibrium steady state. This review highlights the role of human adaptability in these counterparts, and makes it possible to study or understand some particular social human systems by means of statistical physics coming from natural systems.
A course in mathematical physics 2 classical field theory
Thirring, Walter
1978-01-01
In the past decade the language and methods ofmodern differential geometry have been increasingly used in theoretical physics. What seemed extravagant when this book first appeared 12 years ago, as lecture notes, is now a commonplace. This fact has strengthened my belief that today students of theoretical physics have to learn that language-and the sooner the better. Afterall, they willbe the professors ofthe twenty-first century and it would be absurd if they were to teach then the mathematics of the nineteenth century. Thus for this new edition I did not change the mathematical language. Apart from correcting some mistakes I have only added a section on gauge theories. In the last decade it has become evident that these theories describe fundamental interactions, and on the classical level their structure is suffi cientlyclear to qualify them for the minimum amount ofknowledge required by a theoretician. It is with much regret that I had to refrain from in corporating the interesting developments in Kal...
Fitzmaurice, Olivia; Leavy, Aisling; Hannigan, Ailish
2014-01-01
An investigation into prospective mathematics/statistics teachers' (n = 134) conceptual understanding of statistics and attitudes to statistics carried out at the University of Limerick revealed an overall positive attitude to statistics but a perception that it can be a difficult subject, in particular that it requires a great deal of discipline…
"Statistical Techniques for Particle Physics" (2/4)
CERN. Geneva
2009-01-01
This series will consist of four 1-hour lectures on statistics for particle physics. The goal will be to build up to techniques meant for dealing with problems of realistic complexity while maintaining a formal approach. I will also try to incorporate usage of common tools like ROOT, RooFit, and the newly developed RooStats framework into the lectures. The first lecture will begin with a review the basic principles of probability, some terminology, and the three main approaches towards statistical inference (Frequentist, Bayesian, and Likelihood-based). I will then outline the statistical basis for multivariate analysis techniques (the Neyman-Pearson lemma) and the motivation for machine learning algorithms. Later, I will extend simple hypothesis testing to the case in which the statistical model has one or many parameters (the Neyman Construction and the Feldman-Cousins technique). From there I will outline techniques to incorporate background uncertainties. If time allows, I will touch on the statist...
"Statistical Techniques for Particle Physics" (1/4)
CERN. Geneva
2009-01-01
This series will consist of four 1-hour lectures on statistics for particle physics. The goal will be to build up to techniques meant for dealing with problems of realistic complexity while maintaining a formal approach. I will also try to incorporate usage of common tools like ROOT, RooFit, and the newly developed RooStats framework into the lectures. The first lecture will begin with a review the basic principles of probability, some terminology, and the three main approaches towards statistical inference (Frequentist, Bayesian, and Likelihood-based). I will then outline the statistical basis for multivariate analysis techniques (the Neyman-Pearson lemma) and the motivation for machine learning algorithms. Later, I will extend simple hypothesis testing to the case in which the statistical model has one or many parameters (the Neyman Construction and the Feldman-Cousins technique). From there I will outline techniques to incorporate background uncertainties. If time allows, I will touch on the statist...
"Statistical Techniques for Particle Physics" (4/4)
CERN. Geneva
2009-01-01
This series will consist of four 1-hour lectures on statistics for particle physics. The goal will be to build up to techniques meant for dealing with problems of realistic complexity while maintaining a formal approach. I will also try to incorporate usage of common tools like ROOT, RooFit, and the newly developed RooStats framework into the lectures. The first lecture will begin with a review the basic principles of probability, some terminology, and the three main approaches towards statistical inference (Frequentist, Bayesian, and Likelihood-based). I will then outline the statistical basis for multivariate analysis techniques (the Neyman-Pearson lemma) and the motivation for machine learning algorithms. Later, I will extend simple hypothesis testing to the case in which the statistical model has one or many parameters (the Neyman Construction and the Feldman-Cousins technique). From there I will outline techniques to incorporate background uncertainties. If time allows, I will touch on the statist...
"Statistical Techniques for Particle Physics" (3/4)
CERN. Geneva
2009-01-01
This series will consist of four 1-hour lectures on statistics for particle physics. The goal will be to build up to techniques meant for dealing with problems of realistic complexity while maintaining a formal approach. I will also try to incorporate usage of common tools like ROOT, RooFit, and the newly developed RooStats framework into the lectures. The first lecture will begin with a review the basic principles of probability, some terminology, and the three main approaches towards statistical inference (Frequentist, Bayesian, and Likelihood-based). I will then outline the statistical basis for multivariate analysis techniques (the Neyman-Pearson lemma) and the motivation for machine learning algorithms. Later, I will extend simple hypothesis testing to the case in which the statistical model has one or many parameters (the Neyman Construction and the Feldman-Cousins technique). From there I will outline techniques to incorporate background uncertainties. If time allows, I will touch on the statist...
From statistics to mathematical finance festschrift in honour of Winfried Stute
Manteiga, Wenceslao; Schmidt, Thorsten; Wang, Jane-Ling
2017-01-01
This book, dedicated to Winfried Stute on the occasion of his 70th birthday, presents a unique collection of contributions by leading experts in statistics, stochastic processes, mathematical finance and insurance. The individual chapters cover a wide variety of topics ranging from nonparametric estimation, regression modelling and asymptotic bounds for estimators, to shot-noise processes in finance, option pricing and volatility modelling. The book also features review articles, e.g. on survival analysis.
Stochastic modeling and mathematical statistics a text for statisticians and quantitative scientists
Samaniego, Francisco J
2014-01-01
""Stochastic Modeling and Mathematical Statistics is a new and welcome addition to the corpus of undergraduate statistical textbooks in the market. The singular thing that struck me when I initially perused the book was its lucid and endearing conversational tone, which pervades the entire text. It radiated warmth. … In my course at the University of Michigan, I rely primarily on my own lecture notes and have used Rice as supplementary material. Having gone through this text, I am strongly inclined to add this to the supplementary list as well. I have little doubt that this book will be very s
Statistical Physics in the Era of Big Data
Wang, Dashun
2013-01-01
With the wealth of data provided by a wide range of high-throughout measurement tools and technologies, statistical physics of complex systems is entering a new phase, impacting in a meaningful fashion a wide range of fields, from cell biology to computer science to economics. In this dissertation, by applying tools and techniques developed in…
Renormalization group in statistical physics - momentum and real spaces
International Nuclear Information System (INIS)
Yukalov, V.I.
1988-01-01
Two variants of the renormalization group approach in statistical physics are considered, the renormalization group in the momentum and the renormalization group in the real spaces. Common properties of these methods and their differences are cleared up. A simple model for investigating the crossover between different universality classes is suggested. 27 refs
The conceptual basis of mathematics in cardiology IV: statistics and model fitting.
Bates, Jason H T; Sobel, Burton E
2003-06-01
This is the fourth in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to
Academic Training Lecture: Statistical Methods for Particle Physics
PH Department
2012-01-01
2, 3, 4 and 5 April 2012 Academic Training Lecture Regular Programme from 11:00 to 12:00 - Bldg. 222-R-001 - Filtration Plant Statistical Methods for Particle Physics by Glen Cowan (Royal Holloway) The series of four lectures will introduce some of the important statistical methods used in Particle Physics, and should be particularly relevant to those involved in the analysis of LHC data. The lectures will include an introduction to statistical tests, parameter estimation, and the application of these tools to searches for new phenomena. Both frequentist and Bayesian methods will be described, with particular emphasis on treatment of systematic uncertainties. The lectures will also cover unfolding, that is, estimation of a distribution in binned form where the variable in question is subject to measurement errors.
Bohmian mechanics. The physics and mathematics of quantum theory
International Nuclear Information System (INIS)
Duerr, Detlef; Teufel, Stefan
2009-01-01
Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. This book provides a systematic introduction to Bohmian mechanics and to the mathematical abstractions of quantum mechanics, which range from the self-adjointness of the Schroedinger operator to scattering theory. It explains how the quantum formalism emerges when Boltzmann's ideas about statistical mechanics are applied to Bohmian mechanics. The book is self-contained, mathematically rigorous and an ideal starting point for a fundamental approach to quantum mechanics. It will appeal to students and newcomers to the field, as well as to established scientists seeking a clear exposition of the theory. (orig.)
Bohmian mechanics. The physics and mathematics of quantum theory
Energy Technology Data Exchange (ETDEWEB)
Duerr, Detlef [Muenchen Univ. (Germany). Fakultaet Mathematik; Teufel, Stefan [Tuebingen Univ. (Germany). Mathematisches Inst.
2009-07-01
Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. This book provides a systematic introduction to Bohmian mechanics and to the mathematical abstractions of quantum mechanics, which range from the self-adjointness of the Schroedinger operator to scattering theory. It explains how the quantum formalism emerges when Boltzmann's ideas about statistical mechanics are applied to Bohmian mechanics. The book is self-contained, mathematically rigorous and an ideal starting point for a fundamental approach to quantum mechanics. It will appeal to students and newcomers to the field, as well as to established scientists seeking a clear exposition of the theory. (orig.)
PREFACE: Physics-Based Mathematical Models for Nanotechnology
Voon, Lok C. Lew Yan; Melnik, Roderick; Willatzen, Morten
2008-03-01
In November 2007, some of the world's best nanoscientists and nanoengineers met at the Banff Centre, where the Banff International Research Station hosted a workshop on recent developments in the mathematical study of the physics of nanomaterials and nanostructures. The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located in a scenic part of Alberta, Canada and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). We would like to thank the BIRS and its sponsors for the given opportunity and the BIRS staff for their excellent support during the workshop. Nanotechnology is the study and application of phenomena at or below the dimensions of 100 nm and has received a lot of public attention following popular accounts such as in the bestselling book by Michael Crichton, Prey. It is an area where fundamental questions of applied mathematics and mathematical physics, design of computational methodologies, physical insight, engineering and experimental techniques are meeting together in a quest for an adequate description of nanomaterials and nanostructures for applications in optoelectronics, medicine, energy-saving, bio- and other key technologies which will profoundly influence our life in the 21st century and beyond. There are already hundreds of applications in daily life such as in cosmetics and the hard drives in MP3 players (the 2007 Nobel prize in physics was recently awarded for the science that allowed the miniaturization of the drives), delivering drugs, high-definition DVD players and
Statistical physics a prelude and fugue for engineers
Piazza, Roberto
2017-01-01
This book, provides a general introduction to the ideas and methods of statistical mechanics with the principal aim of meeting the needs of Master’s students in chemical, mechanical, and materials science engineering. Extensive introductory information is presented on many general physics topics in which students in engineering are inadequately trained, ranging from the Hamiltonian formulation of classical mechanics to basic quantum mechanics, electromagnetic fields in matter, intermolecular forces, and transport phenomena. Since engineers should be able to apply physical concepts, the book also focuses on the practical applications of statistical physics to material science and to cutting-edge technologies, with brief but informative sections on, for example, interfacial properties, disperse systems, nucleation, magnetic materials, superfluidity, and ultralow temperature technologies. The book adopts a graded approach to learning, the opening four basic-level chapters being followed by advanced “starred�...
Statistical Physics of Nanoparticles in the Gas Phase
Hansen, Klavs
2013-01-01
Thermal processes are ubiquitous and an understanding of thermal phenomena is essential for a complete description of the physics of nanoparticles, both for the purpose of modeling the dynamics of the particles and for the correct interpretation of experimental data. This book has the twofold aim to present coherently the relevant results coming from the recent scientific literature and to guide the readers through the process of deriving results, enabling them to explore the limits of the mathematical approximations and test the power of the method. The book is focused on the fundamental properties of nanosystems in the gas phase. For this reason there is a strong emphasis on microcanonical physics. Each chapter is enriched with exercises and 3 Appendices provide additional useful materials.
The epistemology of mathematical and statistical modeling: a quiet methodological revolution.
Rodgers, Joseph Lee
2010-01-01
A quiet methodological revolution, a modeling revolution, has occurred over the past several decades, almost without discussion. In contrast, the 20th century ended with contentious argument over the utility of null hypothesis significance testing (NHST). The NHST controversy may have been at least partially irrelevant, because in certain ways the modeling revolution obviated the NHST argument. I begin with a history of NHST and modeling and their relation to one another. Next, I define and illustrate principles involved in developing and evaluating mathematical models. Following, I discuss the difference between using statistical procedures within a rule-based framework and building mathematical models from a scientific epistemology. Only the former is treated carefully in most psychology graduate training. The pedagogical implications of this imbalance and the revised pedagogy required to account for the modeling revolution are described. To conclude, I discuss how attention to modeling implies shifting statistical practice in certain progressive ways. The epistemological basis of statistics has moved away from being a set of procedures, applied mechanistically, and moved toward building and evaluating statistical and scientific models. Copyrigiht 2009 APA, all rights reserved.
The Challenge of Learning Physics before Mathematics: A Case Study of Curriculum Change in Taiwan
Chiu, Mei-Shiu
2016-01-01
The aim of this study was to identify challenges in implementing a physics-before- 10 mathematics curriculum. Obviously, students need to learn necessary mathematics skills in order to develop advanced physics knowledge. In the 2010 high school curriculum in Taiwan, however, grade 11 science students study two-dimensional motion in physics without…
Understanding space weather with new physical, mathematical and philosophical approaches
Mateev, Lachezar; Velinov, Peter; Tassev, Yordan
2016-07-01
The actual problems of solar-terrestrial physics, in particular of space weather are related to the prediction of the space environment state and are solved by means of different analyses and models. The development of these investigations can be considered also from another side. This is the philosophical and mathematical approach towards this physical reality. What does it constitute? We have a set of physical processes which occur in the Sun and interplanetary space. All these processes interact with each other and simultaneously participate in the general process which forms the space weather. Let us now consider the Leibniz's monads (G.W. von Leibniz, 1714, Monadologie, Wien; Id., 1710, Théodicée, Amsterdam) and use some of their properties. There are total 90 theses for monads in the Leibniz's work (1714), f.e. "(1) The Monad, of which we shall here speak, is nothing but a simple substance, which enters into compounds. By 'simple' is meant 'without parts'. (Theod. 10.); … (56) Now this connexion or adaptation of all created things to each and of each to all, means that each simple substance has relations which express all the others, and, consequently, that it is a perpetual living mirror of the universe. (Theod. 130, 360.); (59) … this universal harmony, according to which every substance exactly expresses all others through the relations it has with them. (63) … every Monad is, in its own way, a mirror of the universe, and the universe is ruled according to a perfect order. (Theod. 403.)", etc. Let us introduce in the properties of monads instead of the word "monad" the word "process". We obtain the following statement: Each process reflects all other processes and all other processes reflect this process. This analogy is not formal at all, it reflects accurately the relation between the physical processes and their unity. The category monad which in the Leibniz's Monadology reflects generally the philosophical sense is fully identical with the
Mathematics authentic assessment on statistics learning: the case for student mini projects
Fauziah, D.; Mardiyana; Saputro, D. R. S.
2018-03-01
Mathematics authentic assessment is a form of meaningful measurement of student learning outcomes for the sphere of attitude, skill and knowledge in mathematics. The construction of attitude, skill and knowledge achieved through the fulfilment of tasks which involve active and creative role of the students. One type of authentic assessment is student mini projects, started from planning, data collecting, organizing, processing, analysing and presenting the data. The purpose of this research is to learn the process of using authentic assessments on statistics learning which is conducted by teachers and to discuss specifically the use of mini projects to improving students’ learning in the school of Surakarta. This research is an action research, where the data collected through the results of the assessments rubric of student mini projects. The result of data analysis shows that the average score of rubric of student mini projects result is 82 with 96% classical completeness. This study shows that the application of authentic assessment can improve students’ mathematics learning outcomes. Findings showed that teachers and students participate actively during teaching and learning process, both inside and outside of the school. Student mini projects also provide opportunities to interact with other people in the real context while collecting information and giving presentation to the community. Additionally, students are able to exceed more on the process of statistics learning using authentic assessment.
Fifty years of mathematical physics selected works of Ludwig Faddeev
Faddeev, Ludwig; Niemi, Antti J
2016-01-01
This unique volume summarizes with a historical perspective several of the major scientific achievements of Ludwig Faddeev, with a foreword by Nobel Laureate C N Yang. The volume that spans over fifty years of Faddeev's career begins where he started his own scientific research, in the subject of scattering theory and the three-body problem. It then continues to describe Faddeev's contributions to automorphic functions, followed by an extensive account of his many fundamental contributions to quantum field theory including his original article on ghosts with Popov. Faddeev's contributions to soliton theory and integrable models are then described, followed by a survey of his work on quantum groups. The final scientific section is devoted to Faddeev's contemporary research including articles on his long-term interest in constructing knotted solitons and understanding confinement. The volume concludes with his personal view on science and mathematical physics in particular.
Dynamical chaos and uniformly hyperbolic attractors: from mathematics to physics
Energy Technology Data Exchange (ETDEWEB)
Kuznetsov, Sergei P [Saratov Branch, Kotel' nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Saratov (Russian Federation)
2011-02-28
Research is reviewed on the identification and construction of physical systems with chaotic dynamics due to uniformly hyperbolic attractors (such as the Plykin attraction or the Smale-Williams solenoid). Basic concepts of the mathematics involved and approaches proposed in the literature for constructing systems with hyperbolic attractors are discussed. Topics covered include periodic pulse-driven models; dynamics models consisting of periodically repeated stages, each described by its own differential equations; the construction of systems of alternately excited coupled oscillators; the use of parametrically excited oscillations; and the introduction of delayed feedback. Some maps, differential equations, and simple mechanical and electronic systems exhibiting chaotic dynamics due to the presence of uniformly hyperbolic attractors are presented as examples. (reviews of topical problems)
Operator Semigroups meet Complex Analysis, Harmonic Analysis and Mathematical Physics
Chill, Ralph; Tomilov, Yuri
2015-01-01
This proceedings volume originates from a conference held in Herrnhut in June 2013. It provides unique insights into the power of abstract methods and techniques in dealing successfully with numerous applications stemming from classical analysis and mathematical physics. The book features diverse topics in the area of operator semigroups, including partial differential equations, martingale and Hilbert transforms, Banach and von Neumann algebras, Schrödinger operators, maximal regularity and Fourier multipliers, interpolation, operator-theoretical problems (concerning generation, perturbation and dilation, for example), and various qualitative and quantitative Tauberian theorems with a focus on transfinite induction and magics of Cantor. The last fifteen years have seen the dawn of a new era for semigroup theory with the emphasis on applications of abstract results, often unexpected and far removed from traditional ones. The aim of the conference was to bring together prominent experts in the field of modern...
New Editor-in-Chief for Journal of Physics A: Mathematical and Theoretical
Gillan, Rebecca
2014-04-01
We are delighted to announce that Professor Martin Evans of University of Edinburgh has been appointed as the new Editor-in-Chief of Journal of Physics A: Mathematical and Theoretical. Martin Evans has been Editor of the Statistical Physics section of the journal since 2009. Prior to this, he served as a Board Member for the journal. His areas of research include statistical mechanics of nonequilibrium systems, phase transitions and scaling regimes in nonequilibrium statistical physics, glassy dynamics, phase transitions and ordering in driven diffusive systems, mass transport models, condensation models, zero range processes and exclusion processes. We very much look forward to working with Martin to continue to improve the journal's quality and interest to the readership. We would like to thank our outgoing Editor-in-Chief, Professor Murray Batchelor. Murray has worked hard and provided excellent guidance in improving the quality of the journal and the service that the journal provides to authors, referees and readers. During the last five years, we have raised the quality threshold for acceptance in the journal and currently reject over 70% of submissions. As a result, papers published in Journal of Physics A: Mathematical and Theoretical are amongst the best in the field. We have also maintained and improved on our excellent receipt-to-first-decision times, which now average under 40 days for papers. With the help of Martin Evans and our distinguished Editorial Board, we will be working to further improve the quality of the journal whilst continuing to offer excellent services to our readers, authors and referees. We hope that you benefit from reading the journal. If you have any comments or questions, please do not hesitate to contact us at jphysa@iop.org. Rebecca Gillan Publisher
Behaviour of mathematics and physics students in solving problem of Vector-Physics context
Sardi; Rizal, M.; Mansyur, J.
2018-04-01
This research aimed to describe behaviors of mathematics and physics students in solving problem of the vector concept in physics context. The subjects of the research were students who enrolled in Mathematics Education Study Program and Physics Education Study Program of FKIP Universitas Tadulako. The selected participants were students who received the highest score in vector fundamental concept test in each study program. The data were collected through thinking-aloud activity followed by an interview. The steps of data analysis included data reduction, display, and conclusion drawing. The credibility of the data was tested using a triangulation method. Based on the data analysis, it can be concluded that the two groups of students did not show fundamental differences in problem-solving behavior, especially in the steps of understanding the problem (identifying, collecting and analyzing facts and information), planning (looking for alternative strategies) and conducting the alternative strategy. The two groups were differ only in the evaluation aspect. In contrast to Physics students who evaluated their answer, mathematics students did not conducted an evaluation activity on their work. However, the difference was not caused by the differences in background knowledge.
Statistical Methods for Particle Physics (4/4)
CERN. Geneva
2012-01-01
The series of four lectures will introduce some of the important statistical methods used in Particle Physics, and should be particularly relevant to those involved in the analysis of LHC data. The lectures will include an introduction to statistical tests, parameter estimation, and the application of these tools to searches for new phenomena. Both frequentist and Bayesian methods will be described, with particular emphasis on treatment of systematic uncertainties. The lectures will also cover unfolding, that is, estimation of a distribution in binned form where the variable in question is subject to measurement errors.
Statistical Methods for Particle Physics (1/4)
CERN. Geneva
2012-01-01
The series of four lectures will introduce some of the important statistical methods used in Particle Physics, and should be particularly relevant to those involved in the analysis of LHC data. The lectures will include an introduction to statistical tests, parameter estimation, and the application of these tools to searches for new phenomena. Both frequentist and Bayesian methods will be described, with particular emphasis on treatment of systematic uncertainties. The lectures will also cover unfolding, that is, estimation of a distribution in binned form where the variable in question is subject to measurement errors.
Statistical Methods for Particle Physics (2/4)
CERN. Geneva
2012-01-01
The series of four lectures will introduce some of the important statistical methods used in Particle Physics, and should be particularly relevant to those involved in the analysis of LHC data. The lectures will include an introduction to statistical tests, parameter estimation, and the application of these tools to searches for new phenomena. Both frequentist and Bayesian methods will be described, with particular emphasis on treatment of systematic uncertainties. The lectures will also cover unfolding, that is, estimation of a distribution in binned form where the variable in question is subject to measurement errors.
Statistical Methods for Particle Physics (3/4)
CERN. Geneva
2012-01-01
The series of four lectures will introduce some of the important statistical methods used in Particle Physics, and should be particularly relevant to those involved in the analysis of LHC data. The lectures will include an introduction to statistical tests, parameter estimation, and the application of these tools to searches for new phenomena. Both frequentist and Bayesian methods will be described, with particular emphasis on treatment of systematic uncertainties. The lectures will also cover unfolding, that is, estimation of a distribution in binned form where the variable in question is subject to measurement errors.
Tuminaro, Jonathan
Many introductory, algebra-based physics students perform poorly on mathematical problem solving tasks in physics. There are at least two possible, distinct reasons for this poor performance: (1) students simply lack the mathematical skills needed to solve problems in physics, or (2) students do not know how to apply the mathematical skills they have to particular problem situations in physics. While many students do lack the requisite mathematical skills, a major finding from this work is that the majority of students possess the requisite mathematical skills, yet fail to use or interpret them in the context of physics. In this thesis I propose a theoretical framework to analyze and describe students' mathematical thinking in physics. In particular, I attempt to answer two questions. What are the cognitive tools involved in formal mathematical thinking in physics? And, why do students make the kinds of mistakes they do when using mathematics in physics? According to the proposed theoretical framework there are three major theoretical constructs: mathematical resources, which are the knowledge elements that are activated in mathematical thinking and problem solving; epistemic games, which are patterns of activities that use particular kinds of knowledge to create new knowledge or solve a problem; and frames, which are structures of expectations that determine how individuals interpret situations or events. The empirical basis for this study comes from videotaped sessions of college students solving homework problems. The students are enrolled in an algebra-based introductory physics course. The videotapes were transcribed and analyzed using the aforementioned theoretical framework. Two important results from this work are: (1) the construction of a theoretical framework that offers researchers a vocabulary (ontological classification of cognitive structures) and grammar (relationship between the cognitive structures) for understanding the nature and origin of
Monte Carlo Simulation in Statistical Physics An Introduction
Binder, Kurt
2010-01-01
Monte Carlo Simulation in Statistical Physics deals with the computer simulation of many-body systems in condensed-matter physics and related fields of physics, chemistry and beyond, to traffic flows, stock market fluctuations, etc.). Using random numbers generated by a computer, probability distributions are calculated, allowing the estimation of the thermodynamic properties of various systems. This book describes the theoretical background to several variants of these Monte Carlo methods and gives a systematic presentation from which newcomers can learn to perform such simulations and to analyze their results. The fifth edition covers Classical as well as Quantum Monte Carlo methods. Furthermore a new chapter on the sampling of free-energy landscapes has been added. To help students in their work a special web server has been installed to host programs and discussion groups (http://wwwcp.tphys.uni-heidelberg.de). Prof. Binder was awarded the Berni J. Alder CECAM Award for Computational Physics 2001 as well ...
Noser, Thomas C.; Tanner, John R.; Shah, Situl
2008-01-01
The purpose of this study was to measure the comprehension of basic mathematical skills of students enrolled in statistics classes at a large regional university, and to determine if the scores earned on a basic math skills test are useful in forecasting student performance in these statistics classes, and to determine if students' basic math…
Askerov, Bahram M
2010-01-01
This book deals with theoretical thermodynamics and the statistical physics of electron and particle gases. While treating the laws of thermodynamics from both classical and quantum theoretical viewpoints, it posits that the basis of the statistical theory of macroscopic properties of a system is the microcanonical distribution of isolated systems, from which all canonical distributions stem. To calculate the free energy, the Gibbs method is applied to ideal and non-ideal gases, and also to a crystalline solid. Considerable attention is paid to the Fermi-Dirac and Bose-Einstein quantum statistics and its application to different quantum gases, and electron gas in both metals and semiconductors is considered in a nonequilibrium state. A separate chapter treats the statistical theory of thermodynamic properties of an electron gas in a quantizing magnetic field.
DEFF Research Database (Denmark)
Niss, Martin
2017-01-01
This paper studies the cognitive obstacles related to one aspect of mathematization in physics problem-solving, namely, what might be called structuring for mathematization, where the problem situation is structured in such a way that a translation to a mathematical universe can be done. We report...
Foundations of Complex Systems Nonlinear Dynamics, Statistical Physics, and Prediction
Nicolis, Gregoire
2007-01-01
Complexity is emerging as a post-Newtonian paradigm for approaching a large body of phenomena of concern at the crossroads of physical, engineering, environmental, life and human sciences from a unifying point of view. This book outlines the foundations of modern complexity research as it arose from the cross-fertilization of ideas and tools from nonlinear science, statistical physics and numerical simulation. It is shown how these developments lead to an understanding, both qualitative and quantitative, of the complex systems encountered in nature and in everyday experience and, conversely, h
Statistical physics and computational methods for evolutionary game theory
Javarone, Marco Alberto
2018-01-01
This book presents an introduction to Evolutionary Game Theory (EGT) which is an emerging field in the area of complex systems attracting the attention of researchers from disparate scientific communities. EGT allows one to represent and study several complex phenomena, such as the emergence of cooperation in social systems, the role of conformity in shaping the equilibrium of a population, and the dynamics in biological and ecological systems. Since EGT models belong to the area of complex systems, statistical physics constitutes a fundamental ingredient for investigating their behavior. At the same time, the complexity of some EGT models, such as those realized by means of agent-based methods, often require the implementation of numerical simulations. Therefore, beyond providing an introduction to EGT, this book gives a brief overview of the main statistical physics tools (such as phase transitions and the Ising model) and computational strategies for simulating evolutionary games (such as Monte Carlo algor...
Dierdorp, Adri; Bakker, Arthur; van Maanen, Jan A.; Eijkelhof, Harrie M. C.
2014-01-01
Background: Creating coherence between school subjects mathematics and science and making these school subjects meaningful are still topical challenges. This study investigates how students make meaningful connections between mathematics, statistics, science and applications when they engage in a specially developed unit that is based on…
STATISTICAL CHALLENGES FOR SEARCHES FOR NEW PHYSICS AT THE LHC.
Energy Technology Data Exchange (ETDEWEB)
CRANMER, K.
2005-09-12
Because the emphasis of the LHC is on 5{sigma} discoveries and the LHC environment induces high systematic errors, many of the common statistical procedures used in High Energy Physics are not adequate. I review the basic ingredients of LHC searches, the sources of systematics, and the performance of several methods. Finally, I indicate the methods that seem most promising for the LHC and areas that are in need of further study.
Representative volume size: A comparison of statistical continuum mechanics and statistical physics
Energy Technology Data Exchange (ETDEWEB)
AIDUN,JOHN B.; TRUCANO,TIMOTHY G.; LO,CHI S.; FYE,RICHARD M.
1999-05-01
In this combination background and position paper, the authors argue that careful work is needed to develop accurate methods for relating the results of fine-scale numerical simulations of material processes to meaningful values of macroscopic properties for use in constitutive models suitable for finite element solid mechanics simulations. To provide a definite context for this discussion, the problem is couched in terms of the lack of general objective criteria for identifying the size of the representative volume (RV) of a material. The objective of this report is to lay out at least the beginnings of an approach for applying results and methods from statistical physics to develop concepts and tools necessary for determining the RV size, as well as alternatives to RV volume-averaging for situations in which the RV is unmanageably large. The background necessary to understand the pertinent issues and statistical physics concepts is presented.
Bruijn, de N.G.
1972-01-01
Recently A. W. Joseph described an algorithm providing combinatorial insight into E. Sparre Andersen's so-called Principle of Equivalence in mathematical statistics. In the present paper such algorithms are discussed systematically.
High-dimensional data: p >> n in mathematical statistics and bio-medical applications
Van De Geer, Sara A.; Van Houwelingen, Hans C.
2004-01-01
The workshop 'High-dimensional data: p >> n in mathematical statistics and bio-medical applications' was held at the Lorentz Center in Leiden from 9 to 20 September 2002. This special issue of Bernoulli contains a selection of papers presented at that workshop. ¶ The introduction of high-throughput micro-array technology to measure gene-expression levels and the publication of the pioneering paper by Golub et al. (1999) has brought to life a whole new branch of data analysis under the name of...
Advanced statistics to improve the physical interpretation of atomization processes
International Nuclear Information System (INIS)
Panão, Miguel R.O.; Radu, Lucian
2013-01-01
Highlights: ► Finite pdf mixtures improves physical interpretation of sprays. ► Bayesian approach using MCMC algorithm is used to find the best finite mixture. ► Statistical method identifies multiple droplet clusters in a spray. ► Multiple drop clusters eventually associated with multiple atomization mechanisms. ► Spray described by drop size distribution and not only its moments. -- Abstract: This paper reports an analysis of the physics of atomization processes using advanced statistical tools. Namely, finite mixtures of probability density functions, which best fitting is found using a Bayesian approach based on a Markov chain Monte Carlo (MCMC) algorithm. This approach takes into account eventual multimodality and heterogeneities in drop size distributions. Therefore, it provides information about the complete probability density function of multimodal drop size distributions and allows the identification of subgroups in the heterogeneous data. This allows improving the physical interpretation of atomization processes. Moreover, it also overcomes the limitations induced by analyzing the spray droplets characteristics through moments alone, particularly, the hindering of different natures of droplet formation. Finally, the method is applied to physically interpret a case-study based on multijet atomization processes
International Nuclear Information System (INIS)
Zeidler, Eberhard
2009-01-01
This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Zeidler, Eberhard [Max-Planck-Institut fuer Mathematik in den Naturwissenschaften, Leipzig (Germany)
2009-07-01
This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics. (orig.)
Pursell, David P
2009-01-01
BIO2010 advocates enhancing the interdisciplinary, mathematics, and physical science components of the undergraduate biology curriculum. The Department of Chemistry and Life Science at West Point responded by developing a required physical chemistry course tailored to the interests of life science majors. To overcome student resistance to physical chemistry, students were enabled as long-term stakeholders who would shape the syllabus by selecting life science topics of interest to them. The initial 2 yr of assessment indicates that students have a positive view of the course, feel they have succeeded in achieving course outcome goals, and that the course is relevant to their professional future. Instructor assessment of student outcome goal achievement via performance on exams and labs is comparable to that of students in traditional physical chemistry courses. Perhaps more noteworthy, both student and instructor assessment indicate positive trends from year 1 to year 2, presumably due to the student stakeholder effect.
Engineering Physics and Mathematics Division progress report for period ending August 31, 1989
International Nuclear Information System (INIS)
1989-12-01
This paper contains abstracts on research performed at the Engineering Physics and Mathematics Division of Oak Ridge National Laboratory. The areas covered are: mathematical science; nuclear-data measurement and evaluation; intelligent systems; nuclear analysis and shielding; and Engineering Physics Information Center
Engineering Physics and Mathematics Division progress report for period ending August 31, 1989
Energy Technology Data Exchange (ETDEWEB)
1989-12-01
This paper contains abstracts on research performed at the Engineering Physics and Mathematics Division of Oak Ridge National Laboratory. The areas covered are: mathematical science; nuclear-data measurement and evaluation; intelligent systems; nuclear analysis and shielding; and Engineering Physics Information Center. (LSP)
Noted astrophysicist Michael S. Turner to Head NSF'S mathematical and physical sciences directorate
2003-01-01
"The National Science Foundation has named celebrated astrophysicist Michael S. Turner of the University of Chicago as Assistant Director for Mathematical and Physical Sciences. He will head a $1 billion directorate that supports research in mathematics, physics, chemistry, materials and astronomy, as well as multidisciplinary programs and education" (1/2 page).
Energy Technology Data Exchange (ETDEWEB)
Lepore, J.V. (ed.)
1977-01-01
This annual report of the Physics, Computer Science and Mathematics Division describes the scientific research and other work carried out within the Division during 1977. The Division is concerned with work in experimental and theoretical physics, with computer science and applied mathematics, and with the operation of a computer center. The major physics research activity is in high-energy physics, although there is a relatively small program of medium-energy research. The High Energy Physics research program in the Physics Division is concerned with fundamental research which will enable man to comprehend the nature of the physical world. The major effort is now directed toward experiments with positron-electron colliding beam at PEP. The Medium Energy Physics program is concerned with research using mesons and nucleons to probe the properties of matter. This research is concerned with the study of nuclear structure, nuclear reactions, and the interactions between nuclei and electromagnetic radiation and mesons. The Computer Science and Applied Mathematics Department engages in research in a variety of computer science and mathematics disciplines. Work in computer science and applied mathematics includes construction of data bases, computer graphics, computational physics and data analysis, mathematical modeling, and mathematical analysis of differential and integral equations resulting from physical problems. The Computer Center provides large-scale computational support to LBL's scientific programs. Descriptions of the various activities are quite short; references to published results are given. 24 figures. (RWR)
Physics, Computer Science and Mathematics Division. Annual report, 1 January--31 December 1977
International Nuclear Information System (INIS)
Lepore, J.V.
1977-01-01
This annual report of the Physics, Computer Science and Mathematics Division describes the scientific research and other work carried out within the Division during 1977. The Division is concerned with work in experimental and theoretical physics, with computer science and applied mathematics, and with the operation of a computer center. The major physics research activity is in high-energy physics, although there is a relatively small program of medium-energy research. The High Energy Physics research program in the Physics Division is concerned with fundamental research which will enable man to comprehend the nature of the physical world. The major effort is now directed toward experiments with positron-electron colliding beam at PEP. The Medium Energy Physics program is concerned with research using mesons and nucleons to probe the properties of matter. This research is concerned with the study of nuclear structure, nuclear reactions, and the interactions between nuclei and electromagnetic radiation and mesons. The Computer Science and Applied Mathematics Department engages in research in a variety of computer science and mathematics disciplines. Work in computer science and applied mathematics includes construction of data bases, computer graphics, computational physics and data analysis, mathematical modeling, and mathematical analysis of differential and integral equations resulting from physical problems. The Computer Center provides large-scale computational support to LBL's scientific programs. Descriptions of the various activities are quite short; references to published results are given. 24 figures
Literature in Focus: Statistical Methods in Experimental Physics
2007-01-01
Frederick James was a high-energy physicist who became the CERN "expert" on statistics and is now well-known around the world, in part for this famous text. The first edition of Statistical Methods in Experimental Physics was originally co-written with four other authors and was published in 1971 by North Holland (now an imprint of Elsevier). It became such an important text that demand for it has continued for more than 30 years. Fred has updated it and it was released in a second edition by World Scientific in 2006. It is still a top seller and there is no exaggeration in calling it «the» reference on the subject. A full review of the title appeared in the October CERN Courier.Come and meet the author to hear more about how this book has flourished during its 35-year lifetime. Frederick James Statistical Methods in Experimental Physics Monday, 26th of November, 4 p.m. Council Chamber (Bldg. 503-1-001) The author will be introduced...
Engineering Physics and Mathematics Division progress report for period ending December 31, 1994
International Nuclear Information System (INIS)
Sincovec, R.F.
1995-07-01
This report provides a record of the research activities of the Engineering Physics and Mathematics Division for the period January 1, 1993, through December 31, 1994. This report is the final archival record of the EPM Division. On October 1, 1994, ORELA was transferred to Physics Division and on January 1, 1995, the Engineering Physics and Mathematics Division and the Computer Applications Division reorganized to form the Computer Science and Mathematics Division and the Computational Physics and Engineering Division. Earlier reports in this series are identified on the previous pages, along with the progress reports describing ORNL's research in the mathematical sciences prior to 1984 when those activities moved into the Engineering Physics and Mathematics Division
Engineering Physics and Mathematics Division progress report for period ending December 31, 1994
Energy Technology Data Exchange (ETDEWEB)
Sincovec, R.F.
1995-07-01
This report provides a record of the research activities of the Engineering Physics and Mathematics Division for the period January 1, 1993, through December 31, 1994. This report is the final archival record of the EPM Division. On October 1, 1994, ORELA was transferred to Physics Division and on January 1, 1995, the Engineering Physics and Mathematics Division and the Computer Applications Division reorganized to form the Computer Science and Mathematics Division and the Computational Physics and Engineering Division. Earlier reports in this series are identified on the previous pages, along with the progress reports describing ORNL`s research in the mathematical sciences prior to 1984 when those activities moved into the Engineering Physics and Mathematics Division.
Tropical limit and a micro-macro correspondence in statistical physics
Angelelli, Mario
2017-10-01
Tropical mathematics is used to establish a correspondence between certain microscopic and macroscopic objects in statistical models. Tropical algebra gives a common framework for macrosystems (subsets) and their elementary constituents (elements) that is well-behaved with respect to composition. This kind of connection is studied with maps that preserve a monoid structure. The approach highlights an underlying order relation that is explored through the concepts of filter and ideal. Particular attention is paid to asymmetry and duality between max- and min-criteria. Physical implementations are presented through simple examples in thermodynamics and non-equilibrium physics. The phenomenon of ultrametricity, the notion of tropical equilibrium and the role of ground energy in non-equilibrium models are discussed. Tropical symmetry, i.e. idempotence, is investigated.
Are there common mathematical structures in economics and physics?
Mimkes, Jürgen
2016-12-01
Economics is a field that looks into the future. We may know a few things ahead (ex ante), but most things we only know, afterwards (ex post). How can we work in a field, where much of the important information is missing? Mathematics gives two answers: 1. Probability theory leads to microeconomics: the Lagrange function optimizes utility under constraints of economic terms (like costs). The utility function is the entropy, the logarithm of probability. The optimal result is given by a probability distribution and an integrating factor. 2. Calculus leads to macroeconomics: In economics we have two production factors, capital and labour. This requires two dimensional calculus with exact and not-exact differentials, which represent the "ex ante" and "ex post" terms of economics. An integrating factor turns a not-exact term (like income) into an exact term (entropy, the natural production function). The integrating factor is the same as in microeconomics and turns the not-exact field of economics into an exact physical science.
Fourier series, Fourier transform and their applications to mathematical physics
Serov, Valery
2017-01-01
This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences. Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts. The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing. The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations. The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory o...
Statistical methods for data analysis in particle physics
Lista, Luca
2017-01-01
This concise set of course-based notes provides the reader with the main concepts and tools needed to perform statistical analyses of experimental data, in particular in the field of high-energy physics (HEP). First, the book provides an introduction to probability theory and basic statistics, mainly intended as a refresher from readers’ advanced undergraduate studies, but also to help them clearly distinguish between the Frequentist and Bayesian approaches and interpretations in subsequent applications. More advanced concepts and applications are gradually introduced, culminating in the chapter on both discoveries and upper limits, as many applications in HEP concern hypothesis testing, where the main goal is often to provide better and better limits so as to eventually be able to distinguish between competing hypotheses, or to rule out some of them altogether. Many worked-out examples will help newcomers to the field and graduate students alike understand the pitfalls involved in applying theoretical co...
Inverse statistical physics of protein sequences: a key issues review.
Cocco, Simona; Feinauer, Christoph; Figliuzzi, Matteo; Monasson, Rémi; Weigt, Martin
2018-03-01
In the course of evolution, proteins undergo important changes in their amino acid sequences, while their three-dimensional folded structure and their biological function remain remarkably conserved. Thanks to modern sequencing techniques, sequence data accumulate at unprecedented pace. This provides large sets of so-called homologous, i.e. evolutionarily related protein sequences, to which methods of inverse statistical physics can be applied. Using sequence data as the basis for the inference of Boltzmann distributions from samples of microscopic configurations or observables, it is possible to extract information about evolutionary constraints and thus protein function and structure. Here we give an overview over some biologically important questions, and how statistical-mechanics inspired modeling approaches can help to answer them. Finally, we discuss some open questions, which we expect to be addressed over the next years.
Statistical methods for data analysis in particle physics
AUTHOR|(CDS)2070643
2015-01-01
This concise set of course-based notes provides the reader with the main concepts and tools to perform statistical analysis of experimental data, in particular in the field of high-energy physics (HEP). First, an introduction to probability theory and basic statistics is given, mainly as reminder from advanced undergraduate studies, yet also in view to clearly distinguish the Frequentist versus Bayesian approaches and interpretations in subsequent applications. More advanced concepts and applications are gradually introduced, culminating in the chapter on upper limits as many applications in HEP concern hypothesis testing, where often the main goal is to provide better and better limits so as to be able to distinguish eventually between competing hypotheses or to rule out some of them altogether. Many worked examples will help newcomers to the field and graduate students to understand the pitfalls in applying theoretical concepts to actual data
Topics in statistical data analysis for high-energy physics
International Nuclear Information System (INIS)
Cowan, G.
2011-01-01
These lectures concert two topics that are becoming increasingly important in the analysis of high-energy physics data: Bayesian statistics and multivariate methods. In the Bayesian approach, we extend the interpretation of probability not only to cover the frequency of repeatable outcomes but also to include a degree of belief. In this way we are able to associate probability with a hypothesis and thus to answer directly questions that cannot be addressed easily with traditional frequentist methods. In multivariate analysis, we try to exploit as much information as possible from the characteristics that we measure for each event to distinguish between event types. In particular we will look at a method that has gained popularity in high-energy physics in recent years: the boosted decision tree. Finally, we give a brief sketch of how multivariate methods may be applied in a search for a new signal process. (author)
Introduction to statistical physics and to computer simulations
Casquilho, João Paulo
2015-01-01
Rigorous and comprehensive, this textbook introduces undergraduate students to simulation methods in statistical physics. The book covers a number of topics, including the thermodynamics of magnetic and electric systems; the quantum-mechanical basis of magnetism; ferrimagnetism, antiferromagnetism, spin waves and magnons; liquid crystals as a non-ideal system of technological relevance; and diffusion in an external potential. It also covers hot topics such as cosmic microwave background, magnetic cooling and Bose-Einstein condensation. The book provides an elementary introduction to simulation methods through algorithms in pseudocode for random walks, the 2D Ising model, and a model liquid crystal. Any formalism is kept simple and derivations are worked out in detail to ensure the material is accessible to students from subjects other than physics.
Implementation of statistical analysis methods for medical physics data
International Nuclear Information System (INIS)
Teixeira, Marilia S.; Pinto, Nivia G.P.; Barroso, Regina C.; Oliveira, Luis F.
2009-01-01
The objective of biomedical research with different radiation natures is to contribute for the understanding of the basic physics and biochemistry of the biological systems, the disease diagnostic and the development of the therapeutic techniques. The main benefits are: the cure of tumors through the therapy, the anticipated detection of diseases through the diagnostic, the using as prophylactic mean for blood transfusion, etc. Therefore, for the better understanding of the biological interactions occurring after exposure to radiation, it is necessary for the optimization of therapeutic procedures and strategies for reduction of radioinduced effects. The group pf applied physics of the Physics Institute of UERJ have been working in the characterization of biological samples (human tissues, teeth, saliva, soil, plants, sediments, air, water, organic matrixes, ceramics, fossil material, among others) using X-rays diffraction and X-ray fluorescence. The application of these techniques for measurement, analysis and interpretation of the biological tissues characteristics are experimenting considerable interest in the Medical and Environmental Physics. All quantitative data analysis must be initiated with descriptive statistic calculation (means and standard deviations) in order to obtain a previous notion on what the analysis will reveal. It is well known que o high values of standard deviation found in experimental measurements of biologicals samples can be attributed to biological factors, due to the specific characteristics of each individual (age, gender, environment, alimentary habits, etc). This work has the main objective the development of a program for the use of specific statistic methods for the optimization of experimental data an analysis. The specialized programs for this analysis are proprietary, another objective of this work is the implementation of a code which is free and can be shared by the other research groups. As the program developed since the
Schmind, Kendra K.; Blankenship, Erin E.; Kerby. April T.; Green, Jennifer L.; Smith, Wendy M.
2014-01-01
The statistical preparation of in-service teachers, particularly middle school teachers, has been an area of concern for several years. This paper discusses the creation and delivery of an introductory statistics course as part of a master's degree program for in-service mathematics teachers. The initial course development took place before the…
Introduction of the Thematic Issue on the Interplay of Physics and Mathematics
DEFF Research Database (Denmark)
Avelar Sotomaior Karam, Ricardo
2015-01-01
for the students. They have a hard time understanding where mathematical concepts come from and why physics has little to do with their experiential world. This problem demands a systematic research effort from experts in different fields, especially the ones who aim at informing educational practices......Since their beginnings Physics (natural philosophy) and mathematics have been deeply interrelated, and this mutual influence has played an essential role in both their developments. However, the image typically found in educational contexts is often quite different. In physics education......, it is usual to find mathematics being seen as a mere tool to describe and calculate, whereas in mathematics education, physics is commonly viewed as a possible context for the application of mathematical concepts that were previously defined abstractly. This dichotomy creates significant learning problems...
Analytical derivation: An epistemic game for solving mathematically based physics problems
Bajracharya, Rabindra R.; Thompson, John R.
2016-06-01
Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the analytical derivation game. This game involves deriving an equation through symbolic manipulations and routine mathematical operations, usually without any physical interpretation of the processes. This game often creates cognitive obstacles in students, preventing them from using alternative resources or better approaches during problem solving. We conducted hour-long, semi-structured, individual interviews with fourteen introductory physics students. Students were asked to solve four "pseudophysics" problems containing algebraic and graphical representations. The problems required the application of the fundamental theorem of calculus (FTC), which is one of the most frequently used mathematical concepts in physics problem solving. We show that the analytical derivation game is necessary, but not sufficient, to solve mathematically based physics problems, specifically those involving graphical representations.
A New Approach to Monte Carlo Simulations in Statistical Physics
Landau, David P.
2002-08-01
Monte Carlo simulations [1] have become a powerful tool for the study of diverse problems in statistical/condensed matter physics. Standard methods sample the probability distribution for the states of the system, most often in the canonical ensemble, and over the past several decades enormous improvements have been made in performance. Nonetheless, difficulties arise near phase transitions-due to critical slowing down near 2nd order transitions and to metastability near 1st order transitions, and these complications limit the applicability of the method. We shall describe a new Monte Carlo approach [2] that uses a random walk in energy space to determine the density of states directly. Once the density of states is known, all thermodynamic properties can be calculated. This approach can be extended to multi-dimensional parameter spaces and should be effective for systems with complex energy landscapes, e.g., spin glasses, protein folding models, etc. Generalizations should produce a broadly applicable optimization tool. 1. A Guide to Monte Carlo Simulations in Statistical Physics, D. P. Landau and K. Binder (Cambridge U. Press, Cambridge, 2000). 2. Fugao Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001); Phys. Rev. E64, 056101-1 (2001).
Designing Tasks to Examine Mathematical Knowledge for Teaching Statistics for Primary Teachers
Siswono, T. Y. E.; Kohar, A. W.; Hartono, S.
2018-01-01
Mathematical knowledge for teaching (MKT) is viewed as fuel resources for conducting an orchestra in a teaching and learning process. By understanding MKT, especially for primary teachers, it can predict the success of a goal of an instruction and analyze the weaknesses and improvements of it. To explore what teachers think about subject matters, pedagogical terms, and appropriate curriculum, it needs a task which can be identified the teachers’ MKT including the subject matter knowledge (SMK) and pedagogical content knowledge (PCK). This study aims to design an appropriate task for exploring primary teachers’ MKT for statistics in primary school. We designed six tasks to examine 40 primary teachers’ MKT, of which each respectively represents the categories of SMK (common content knowledge (CCK) and specialised content knowledge (SCK)) and PCK (knowledge of content and students (KCS), knowledge of content and teaching (KCT), and knowledge of content and curriculum (KCC)). While MKT has much attention of numbers of scholars, we consider knowledge of content and culture (KCCl) to be hypothesized in the domains of MKT. Thus, we added one more task examining how the primary teachers used their knowledge of content (KC) regarding to MKT in statistics. Some examples of the teachers’ responses on the tasks are discussed and some refinements of MKT task in statistics for primary teachers are suggested.
Kjeldsen, Tinne Hoff; Lützen, Jesper
2015-01-01
In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another…
Mathematical model of statistical identification of information support of road transport
Directory of Open Access Journals (Sweden)
V. G. Kozlov
2016-01-01
Full Text Available In this paper based on the statistical identification method using the theory of self-organizing systems, built multifactor model the relationship of road transport and training system. Background information for the model represented by a number of parameters of average annual road transport operations and information provision, including training complex system parameters (inputs, road management and output parameters. Ask two criteria: stability criterion model and test correlation. The program determines their minimum, and is the only model of optimal complexity. The predetermined number of parameters established mathematical relationship of each output parameter with the others. To improve the accuracy and regularity of the forecast of the interpolation nodes allocated in the test data sequence. Other data form the training sequence. Decision model based on the principle of selection. Running it with the gradual complication of the mathematical description and exhaustive search of all possible variants of the models on the specified criteria. Advantages of the proposed model: adequately reflects the actual process, allows you to enter any additional input parameters and determine their impact on the individual output parameters of the road transport, allows in turn change the values of key parameters in a certain ratio and to determine the appropriate changes the output parameters of the road transport, allows to predict the output parameters road transport operations.
Framing the structural role of mathematics in physics lectures: A case study on electromagnetism
Directory of Open Access Journals (Sweden)
Ricardo Karam
2014-05-01
Full Text Available Physics education research has shown that students tend to struggle when trying to use mathematics in a meaningful way in physics (e.g., mathematizing a physical situation or making sense of equations. Concerning the possible reasons for these difficulties, little attention has been paid to the way mathematics is treated in physics instruction. Starting from an overall distinction between a technical approach, which involves an instrumental (tool-like use of mathematics, and a structural one, focused on reasoning about the physical world mathematically, the goal of this study is to characterize the development of the latter in didactic contexts. For this purpose, a case study was conducted on the electromagnetism course given by a distinguished physics professor. The analysis of selected teaching episodes with the software Videograph led to the identification of a set of categories that describe different strategies used by the professor to emphasize the structural role of mathematics in his lectures. As a consequence of this research, an analytic tool to enable future comparative studies between didactic approaches regarding the way mathematics is treated in physics teaching is provided.
Mathematics and statistics research department. Progress report, period ending June 30, 1981
Energy Technology Data Exchange (ETDEWEB)
Lever, W.E.; Kane, V.E.; Scott, D.S.; Shepherd, D.E.
1981-09-01
This report is the twenty-fourth in the series of progress reports of the Mathematics and Statistics Research Department of the Computer Sciences Division, Union Carbide Corporation - Nuclear Division (UCC-ND). Part A records research progress in biometrics research, materials science applications, model evaluation, moving boundary problems, multivariate analysis, numerical linear algebra, risk analysis, and complementary areas. Collaboration and consulting with others throughout the UCC-ND complex are recorded in Part B. Included are sections on biology and health sciences, chemistry, energy, engineering, environmental sciences, health and safety research, materials sciences, safeguards, surveys, and uranium resource evaluation. Part C summarizes the various educational activities in which the staff was engaged. Part D lists the presentations of research results, and Part E records the staff's other professional activities during the report period.
Vitanov, Nikolay K
2016-01-01
This book deals with methods to evaluate scientific productivity. In the book statistical methods, deterministic and stochastic models and numerous indexes are discussed that will help the reader to understand the nonlinear science dynamics and to be able to develop or construct systems for appropriate evaluation of research productivity and management of research groups and organizations. The dynamics of science structures and systems is complex, and the evaluation of research productivity requires a combination of qualitative and quantitative methods and measures. The book has three parts. The first part is devoted to mathematical models describing the importance of science for economic growth and systems for the evaluation of research organizations of different size. The second part contains descriptions and discussions of numerous indexes for the evaluation of the productivity of researchers and groups of researchers of different size (up to the comparison of research productivities of research communiti...
Mathematics and statistics research department. Progress report, period ending June 30, 1981
International Nuclear Information System (INIS)
Lever, W.E.; Kane, V.E.; Scott, D.S.; Shepherd, D.E.
1981-09-01
This report is the twenty-fourth in the series of progress reports of the Mathematics and Statistics Research Department of the Computer Sciences Division, Union Carbide Corporation - Nuclear Division (UCC-ND). Part A records research progress in biometrics research, materials science applications, model evaluation, moving boundary problems, multivariate analysis, numerical linear algebra, risk analysis, and complementary areas. Collaboration and consulting with others throughout the UCC-ND complex are recorded in Part B. Included are sections on biology and health sciences, chemistry, energy, engineering, environmental sciences, health and safety research, materials sciences, safeguards, surveys, and uranium resource evaluation. Part C summarizes the various educational activities in which the staff was engaged. Part D lists the presentations of research results, and Part E records the staff's other professional activities during the report period
Mathematics and Statistics Research Department progress report for period ending June 30, 1979
International Nuclear Information System (INIS)
Gardiner, D.A.; Beauchamp, J.J.; Gray, L.J.; Lever, W.E.; Shepherd, D.E.
1979-09-01
This is the twenty-second in the series of progress reports of the Mathematics and Statistics Research Department and its predecessor organizations. Part A reports research progress in biomedical and environmental applications, materials science applications, model development and evaluation, moving-boundary problems, multivariate multipopulation classification, numerical linear algebra, risk analysis, and complementary areas. The results of collaboration with other researchers on problems in biology, chemistry, energy, engineering, environmental sciences, geology, health and safety research, information sciences, and material sciences are recorded in Part B. Parts C, D, and E contain short accounts of educational activities, lists of written and oral presentations of research results, and a list of other professional activities in which the staff was engaged. Although a few results are shown, the reports in this volume are only of extended abstract length. One may expect completed research to be reported in the usual channels. 6 figures, 2 tables
Institutional supporting research highlights in physics and mathematics, fiscal year 1983
International Nuclear Information System (INIS)
Vigil, J.C.
1984-03-01
Highlights of FY 1983 Institutional Supporting Research and Development activities within the six Physics and Mathematics divisions and the Center for Nonlinear Studies are presented. The highlights are but a fraction of the ISRD activities in the Directorate and are intended to be a representative sample of progress in the various research areas. FY 1983 ISRD activities within the Physics and Mathematics divisions included both basic and applied research and were divided into 11 research areas: mathematics and numerical methods, low-energy nuclear physics, medium- and high-energy nuclear physics, atomic and molecular physics, solid-state physics and materials science, fluid dynamics, plasma physics and intense particle beam theory, astrophysics and space physics, particle transport methods, accelerator and fusion technology, and biophysics. Highlights from each of these areas are presented
New Directions in Statistical Physics: Econophysics, Bioinformatics, and Pattern Recognition
International Nuclear Information System (INIS)
Grassberger, P
2004-01-01
This book contains 18 contributions from different authors. Its subtitle 'Econophysics, Bioinformatics, and Pattern Recognition' says more precisely what it is about: not so much about central problems of conventional statistical physics like equilibrium phase transitions and critical phenomena, but about its interdisciplinary applications. After a long period of specialization, physicists have, over the last few decades, found more and more satisfaction in breaking out of the limitations set by the traditional classification of sciences. Indeed, this classification had never been strict, and physicists in particular had always ventured into other fields. Helmholtz, in the middle of the 19th century, had considered himself a physicist when working on physiology, stressing that the physics of animate nature is as much a legitimate field of activity as the physics of inanimate nature. Later, Max Delbrueck and Francis Crick did for experimental biology what Schroedinger did for its theoretical foundation. And many of the experimental techniques used in chemistry, biology, and medicine were developed by a steady stream of talented physicists who left their proper discipline to venture out into the wider world of science. The development we have witnessed over the last thirty years or so is different. It started with neural networks where methods could be applied which had been developed for spin glasses, but todays list includes vehicular traffic (driven lattice gases), geology (self-organized criticality), economy (fractal stochastic processes and large scale simulations), engineering (dynamical chaos), and many others. By staying in the physics departments, these activities have transformed the physics curriculum and the view physicists have of themselves. In many departments there are now courses on econophysics or on biological physics, and some universities offer degrees in the physics of traffic or in econophysics. In order to document this change of attitude
Thompson, John
2015-04-01
As the Physical Review Focused Collection demonstrates, recent frontiers in physics education research include systematic investigations at the upper division. As part of a collaborative project, we have examined student understanding of several topics in upper-division thermal and statistical physics. A fruitful context for research is the Boltzmann factor in statistical mechanics: the standard derivation involves several physically justified mathematical steps as well as the invocation of a Taylor series expansion. We have investigated student understanding of the physical significance of the Boltzmann factor as well as its utility in various circumstances, and identified various lines of student reasoning related to the use of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students do not use the Boltzmann factor when answering questions related to probability in applicable physical situations, even after lecture instruction. We designed an inquiry-based tutorial activity to guide students through a derivation of the Boltzmann factor and to encourage deep connections between the physical quantities involved and the mathematics. Observations of students working through the tutorial suggest that many students at this level can recognize and interpret Taylor series expansions, but they often lack fluency in creating and using Taylor series appropriately, despite previous exposure in both calculus and physics courses. Our findings also suggest that tutorial participation not only increases the prevalence of relevant invocation of the Boltzmann factor, but also helps students gain an appreciation of the physical implications and meaning of the mathematical formalism behind the formula. Supported in part by NSF Grants DUE-0817282, DUE-0837214, and DUE-1323426.
Physics, Computer Science and Mathematics Division annual report, 1 January--31 December 1975
International Nuclear Information System (INIS)
Lepore, J.L.
1975-01-01
This annual report describes the scientific research and other work carried out during the calendar year 1975. The report is nontechnical in nature, with almost no data. A 17-page bibliography lists the technical papers which detail the work. The contents of the report include the following: experimental physics (high-energy physics--SPEAR, PEP, SLAC, FNAL, BNL, Bevatron; particle data group; medium-energy physics; astrophysics, astronomy, and cosmic rays; instrumentation development), theoretical physics (particle theory and accelerator theory and design), computer science and applied mathematics (data management systems, socio-economic environment demographic information system, computer graphics, computer networks, management information systems, computational physics and data analysis, mathematical modeling, programing languages, applied mathematics research), real-time systems (ModComp and PDP networks), and computer center activities (systems programing, user services, hardware development, computer operations). A glossary of computer science and mathematics terms is also included. 32 figures
Mathematical gauge theory with applications to the standard model of particle physics
Hamilton, Mark J D
2017-01-01
The Standard Model is the foundation of modern particle and high energy physics. This book explains the mathematical background behind the Standard Model, translating ideas from physics into a mathematical language and vice versa. The first part of the book covers the mathematical theory of Lie groups and Lie algebras, fibre bundles, connections, curvature and spinors. The second part then gives a detailed exposition of how these concepts are applied in physics, concerning topics such as the Lagrangians of gauge and matter fields, spontaneous symmetry breaking, the Higgs boson and mass generation of gauge bosons and fermions. The book also contains a chapter on advanced and modern topics in particle physics, such as neutrino masses, CP violation and Grand Unification. This carefully written textbook is aimed at graduate students of mathematics and physics. It contains numerous examples and more than 150 exercises, making it suitable for self-study and use alongside lecture courses. Only a basic knowledge of d...
Physics, Computer Science and Mathematics Division annual report, 1 January--31 December 1975. [LBL
Energy Technology Data Exchange (ETDEWEB)
Lepore, J.L. (ed.)
1975-01-01
This annual report describes the scientific research and other work carried out during the calendar year 1975. The report is nontechnical in nature, with almost no data. A 17-page bibliography lists the technical papers which detail the work. The contents of the report include the following: experimental physics (high-energy physics--SPEAR, PEP, SLAC, FNAL, BNL, Bevatron; particle data group; medium-energy physics; astrophysics, astronomy, and cosmic rays; instrumentation development), theoretical physics (particle theory and accelerator theory and design), computer science and applied mathematics (data management systems, socio-economic environment demographic information system, computer graphics, computer networks, management information systems, computational physics and data analysis, mathematical modeling, programing languages, applied mathematics research), real-time systems (ModComp and PDP networks), and computer center activities (systems programing, user services, hardware development, computer operations). A glossary of computer science and mathematics terms is also included. 32 figures. (RWR)
[Flavouring estimation of quality of grape wines with use of methods of mathematical statistics].
Yakuba, Yu F; Khalaphyan, A A; Temerdashev, Z A; Bessonov, V V; Malinkin, A D
2016-01-01
The questions of forming of wine's flavour integral estimation during the tasting are discussed, the advantages and disadvantages of the procedures are declared. As investigating materials we used the natural white and red wines of Russian manufactures, which were made with the traditional technologies from Vitis Vinifera, straight hybrids, blending and experimental wines (more than 300 different samples). The aim of the research was to set the correlation between the content of wine's nonvolatile matter and wine's tasting quality rating by mathematical statistics methods. The content of organic acids, amino acids and cations in wines were considered as the main factors influencing on the flavor. Basically, they define the beverage's quality. The determination of those components in wine's samples was done by the electrophoretic method «CAPEL». Together with the analytical checking of wine's samples quality the representative group of specialists simultaneously carried out wine's tasting estimation using 100 scores system. The possibility of statistical modelling of correlation of wine's tasting estimation based on analytical data of amino acids and cations determination reasonably describing the wine's flavour was examined. The statistical modelling of correlation between the wine's tasting estimation and the content of major cations (ammonium, potassium, sodium, magnesium, calcium), free amino acids (proline, threonine, arginine) and the taking into account the level of influence on flavour and analytical valuation within fixed limits of quality accordance were done with Statistica. Adequate statistical models which are able to predict tasting estimation that is to determine the wine's quality using the content of components forming the flavour properties have been constructed. It is emphasized that along with aromatic (volatile) substances the nonvolatile matter - mineral substances and organic substances - amino acids such as proline, threonine, arginine
Tursucu, Süleyman; Spandaw, Jeroen; Flipse, Steven; de Vries, Marc J.
2017-01-01
Students in senior pre-university education encounter difficulties in the application of mathematics into physics. This paper presents the outcome of an explorative qualitative study of teachers' beliefs about improving the transfer of algebraic skills from mathematics into physics. We interviewed 10 mathematics and 10 physics teachers using a…
The dialectic relation between physics and mathematics in the XIXth century
Pisano, Raffaele
2013-01-01
The aim of this book is to analyse historical problems related to the use of mathematics in physics as well as to the use of physics in mathematics and to investigate Mathematical Physics as precisely the new discipline which is concerned with this dialectical link itself. So the main question is: When and why did the tension between mathematics and physics, explicitly practised at least since Galileo, evolve into such a new scientific theory? The authors explain the various ways in which this science allowed an advanced mathematical modelling in physics on the one hand, and the invention of new mathematical ideas on the other hand. Of course this problem is related to the links between institutions, universities, schools for engineers, and industries, and so it has social implications as well. The link by which physical ideas had influenced the world of mathematics was not new in the 19th century, but it came to a kind of maturity at that time. Recently, much historical research has been done into math...
Hobbes on natural philosophy as "True Physics" and mixed mathematics.
Adams, Marcus P
2016-04-01
In this paper, I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the 'that') with causal principles from geometry (the 'why'). My argument shows that Hobbesian natural philosophy relies upon suppositions that bodies plausibly behave according to these borrowed causal principles from geometry, acknowledging that bodies in the world may not actually behave this way. First, I consider Hobbes's relation to Aristotelian mixed mathematics and to Isaac Barrow's broadening of mixed mathematics in Mathematical Lectures (1683). I show that for Hobbes maker's knowledge from geometry provides the 'why' in mixed-mathematical explanations. Next, I examine two explanations from De corpore Part IV: (1) the explanation of sense in De corpore 25.1-2; and (2) the explanation of the swelling of parts of the body when they become warm in De corpore 27.3. In both explanations, I show Hobbes borrowing and citing geometrical principles and mixing these principles with appeals to experience. Copyright © 2015 Elsevier Ltd. All rights reserved.
GPU-computing in econophysics and statistical physics
Preis, T.
2011-03-01
A recent trend in computer science and related fields is general purpose computing on graphics processing units (GPUs), which can yield impressive performance. With multiple cores connected by high memory bandwidth, today's GPUs offer resources for non-graphics parallel processing. This article provides a brief introduction into the field of GPU computing and includes examples. In particular computationally expensive analyses employed in financial market context are coded on a graphics card architecture which leads to a significant reduction of computing time. In order to demonstrate the wide range of possible applications, a standard model in statistical physics - the Ising model - is ported to a graphics card architecture as well, resulting in large speedup values.
Engineering Physics and Mathematics Division progress report for period ending June 30, 1985
International Nuclear Information System (INIS)
1986-02-01
The report is divided into eight sections: (1) nuclear data measurements and evaluation; (2) systems analysis and shielding; (3) applied physics and fusion reactor analysis; (4) mathematical modeling and intelligent control; (5) reliability and human factors research; (6) applied risk and decision analysis; (7) information analysis and data management; and (8) mathematical sciences. Each section then consists of abstracts of presented or published papers
Increasing Mathematical Computation Skills for Students with Physical and Health Disabilities
Webb, Paula
2017-01-01
Students with physical and health disabilities struggle with basic mathematical concepts. The purpose of this research study was to increase the students' mathematical computation skills through implementing new strategies and/or methods. The strategies implemented with the students was utilizing the ten-frame tiles and technology with the purpose…
Chang, Jen-Mei; Kwon, Chuhee; Stevens, Lora; Buonora, Paul
2016-01-01
This article presents implementation details and findings of a National Science Foundation Scholarship in Science, Technology, Engineering, and Mathematics Program (S-STEM) consisting of many high-impact practices to recruit and retain students in the physical sciences and mathematics programs, particularly first-generation and underrepresented…
Stealing from Physics: Modeling with Mathematical Functions in Data-Rich Contexts
Erickson, Tim
2006-01-01
In the course of a project to create physics education materials for secondary schools in the USA we have, not surprisingly, had insights into how students develop certain mathematical understandings. Some of these translate directly into the mathematics classroom. With our materials, students get data from a variety of sources, data that arise in…
MacLean, Adam L.
2015-12-16
The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non-exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.
Directory of Open Access Journals (Sweden)
A. E. Pismak
2016-03-01
Full Text Available Subject of Research. The paper is focused on Wiktionary articles structural organization in the aspect of its usage as the base for semantic network. Wiktionary community references, article templates and articles markup features are analyzed. The problem of numerical estimation for semantic similarity of structural elements in Wiktionary articles is considered. Analysis of existing software for semantic similarity estimation of such elements is carried out; algorithms of their functioning are studied; their advantages and disadvantages are shown. Methods. Mathematical statistics methods were used to analyze Wiktionary articles markup features. The method of semantic similarity computing based on statistics data for compared structural elements was proposed.Main Results. We have concluded that there is no possibility for direct use of Wiktionary articles as the source for semantic network. We have proposed to find hidden similarity between article elements, and for that purpose we have developed the algorithm for calculation of confidence coefficients proving that each pair of sentences is semantically near. The research of quantitative and qualitative characteristics for the developed algorithm has shown its major performance advantage over the other existing solutions in the presence of insignificantly higher error rate. Practical Relevance. The resulting algorithm may be useful in developing tools for automatic Wiktionary articles parsing. The developed method could be used in computing of semantic similarity for short text fragments in natural language in case of algorithm performance requirements are higher than its accuracy specifications.
Graphene growth process modeling: a physical-statistical approach
Wu, Jian; Huang, Qiang
2014-09-01
As a zero-band semiconductor, graphene is an attractive material for a wide variety of applications such as optoelectronics. Among various techniques developed for graphene synthesis, chemical vapor deposition on copper foils shows high potential for producing few-layer and large-area graphene. Since fabrication of high-quality graphene sheets requires the understanding of growth mechanisms, and methods of characterization and control of grain size of graphene flakes, analytical modeling of graphene growth process is therefore essential for controlled fabrication. The graphene growth process starts with randomly nucleated islands that gradually develop into complex shapes, grow in size, and eventually connect together to cover the copper foil. To model this complex process, we develop a physical-statistical approach under the assumption of self-similarity during graphene growth. The growth kinetics is uncovered by separating island shapes from area growth rate. We propose to characterize the area growth velocity using a confined exponential model, which not only has clear physical explanation, but also fits the real data well. For the shape modeling, we develop a parametric shape model which can be well explained by the angular-dependent growth rate. This work can provide useful information for the control and optimization of graphene growth process on Cu foil.
Statistical classification techniques in high energy physics (SDDT algorithm)
International Nuclear Information System (INIS)
Bouř, Petr; Kůs, Václav; Franc, Jiří
2016-01-01
We present our proposal of the supervised binary divergence decision tree with nested separation method based on the generalized linear models. A key insight we provide is the clustering driven only by a few selected physical variables. The proper selection consists of the variables achieving the maximal divergence measure between two different classes. Further, we apply our method to Monte Carlo simulations of physics processes corresponding to a data sample of top quark-antiquark pair candidate events in the lepton+jets decay channel. The data sample is produced in pp̅ collisions at √S = 1.96 TeV. It corresponds to an integrated luminosity of 9.7 fb"-"1 recorded with the D0 detector during Run II of the Fermilab Tevatron Collider. The efficiency of our algorithm achieves 90% AUC in separating signal from background. We also briefly deal with the modification of statistical tests applicable to weighted data sets in order to test homogeneity of the Monte Carlo simulations and measured data. The justification of these modified tests is proposed through the divergence tests. (paper)
The interaction of physical properties of seawater via statistical approach
Hamzah, Firdaus Mohamad; Jaafar, Othman; Sabri, Samsul Rijal Mohd; Ismail, Mohd Tahir; Jaafar, Khamisah; Arbin, Norazman
2015-09-01
It is of importance to determine the relationships between physical parameters in marine ecology. Model and expert opinion are needed for exploration of the form of relationship between two parameters due to the complexity of the ecosystems. These need justification with observed data over a particular periods. Novel statistical techniques such as nonparametric regression is presented to investigate the ecological relationships. These are achieved by demonstrating the features of pH, salinity and conductivity at in Straits of Johor. The monthly data measurements from 2004 until 2013 at a chosen sampling location are examined. Testing for no-effect followed by linearity testing for the relationships between salinity and pH; conductivity and pH, and conductivity and salinity are carried out, with the ecological objectives of investigating the evidence of changes in each of the above physical parameters. The findings reveal the appropriateness of smooth function to explain the variation of pH in response to the changes in salinity whilst the changes in conductivity with regards to different concentrations of salinity could be modelled parametrically. The analysis highlights the importance of both parametric and nonparametric models for assessing ecological response to environmental change in seawater.
Holcman, David
2018-01-01
This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences. In more detail, the book presents the analytic methods and tools for approximating solutions of mixed boundary value problems, with particular emphasis on the narrow escape problem. Informed throughout by real-world applications, the book includes topics such as the Fokker-Planck equation, boundary layer analysis, WKB approximation, applications of spectral theory, as well as recent results in narrow escape theory. Numerical and stochastic aspects, including mean first passage time and extreme statistics, are discussed in detail and relevant applications are presented in parallel with the theory. Including background on the classical asymptotic theory of differential equations, this book is written for scientists of various backgrounds interested in deriving solutions to real-world proble...
Application of statistical physics approaches to complex organizations
Matia, Kaushik
The first part of this thesis studies two different kinds of financial markets, namely, the stock market and the commodity market. Stock price fluctuations display certain scale-free statistical features that are not unlike those found in strongly-interacting physical systems. The possibility that new insights can be gained using concepts and methods developed to understand scale-free physical phenomena has stimulated considerable research activity in the physics community. In the first part of this thesis a comparative study of stocks and commodities is performed in terms of probability density function and correlations of stock price fluctuations. It is found that the probability density of the stock price fluctuation has a power law functional form with an exponent 3, which is similar across different markets around the world. We present an autoregressive model to explain the origin of the power law functional form of the probability density function of the price fluctuation. The first part also presents the discovery of unique features of the Indian economy, which we find displays a scale-dependent probability density function. In the second part of this thesis we quantify the statistical properties of fluctuations of complex systems like business firms and world scientific publications. We analyze class size of these systems mentioned above where units agglomerate to form classes. We find that the width of the probability density function of growth rate decays with the class size as a power law with an exponent beta which is universal in the sense that beta is independent of the system studied. We also identify two other scaling exponents, gamma connecting the unit size to the class size and gamma connecting the number of units to the class size, where products are units and firms are classes. Finally we propose a generalized preferential attachment model to describe the class size distribution. This model is successful in explaining the growth rate and class
Applications of statistical physics to the social and economic sciences
Petersen, Alexander M.
2011-12-01
This thesis applies statistical physics concepts and methods to quantitatively analyze socioeconomic systems. For each system we combine theoretical models and empirical data analysis in order to better understand the real-world system in relation to the complex interactions between the underlying human agents. This thesis is separated into three parts: (i) response dynamics in financial markets, (ii) dynamics of career trajectories, and (iii) a stochastic opinion model with quenched disorder. In Part I we quantify the response of U.S. markets to financial shocks, which perturb markets and trigger "herding behavior" among traders. We use concepts from earthquake physics to quantify the decay of volatility shocks after the "main shock." We also find, surprisingly, that we can make quantitative statements even before the main shock. In order to analyze market behavior before as well as after "anticipated news" we use Federal Reserve interest-rate announcements, which are regular events that are also scheduled in advance. In Part II we analyze the statistical physics of career longevity. We construct a stochastic model for career progress which has two main ingredients: (a) random forward progress in the career and (b) random termination of the career. We incorporate the rich-get-richer (Matthew) effect into ingredient (a), meaning that it is easier to move forward in the career the farther along one is in the career. We verify the model predictions analyzing data on 400,000 scientific careers and 20,000 professional sports careers. Our model highlights the importance of early career development, showing that many careers are stunted by the relative disadvantage associated with inexperience. In Part III we analyze a stochastic two-state spin model which represents a system of voters embedded on a network. We investigate the role in consensus formation of "zealots", which are agents with time-independent opinion. Our main result is the unexpected finding that it is the
Younger Dryas Boundary (YDB) impact : physical and statistical impossibility.
Energy Technology Data Exchange (ETDEWEB)
Boslough, Mark Bruce Elrick
2010-08-01
The YDB impact hypothesis of Firestone et al. (2007) is so extremely improbable it can be considered statistically impossible in addition to being physically impossible. Comets make up only about 1% of the population of Earth-crossing objects. Broken comets are a vanishingly small fraction, and only exist as Earth-sized clusters for a very short period of time. Only a small fraction of impacts occur at angles as shallow as proposed by the YDB impact authors. Events that are exceptionally unlikely to take place in the age of the Universe are 'statistically impossible'. The size distribution of Earth-crossing asteroids is well-constrained by astronomical observations, DoD satellite bolide frequencies, and the cratering record. This distribution can be transformed to a probability density function (PDF) for the largest expected impact of the past 20,000 years. The largest impact of any kind expected over the period of interest is 250 m. Anything larger than 2 km is exceptionally unlikely (probability less than 1%). The impact hypothesis does not rely on any sound physical model. A 4-km diameter comet, even if it fragmented upon entry, would not disperse or explode in the atmosphere. It would generate a crater about 50 km in diameter with a transient cavity as deep as 10 km. There is no evidence for such a large, young crater associated with the YDB. There is no model to suggest that a comet impact of this size is capable of generating continental-wide fires or blast damage, and there is no physical mechanism that could cause a 4-km comet to explode at the optimum height of 500 km. The highest possible altitude for a cometary optimum height is about 15 km, for a 120-m diameter comet. To maximize blast and thermal damage, a 4-km comet would have to break into tens of thousands fragments of this size and spread out over the entire continent, but that would require lateral forces that greatly exceed the drag force, and would not conserve energy. Airbursts are
Foundations of mathematics and physics one century after Hilbert new perspectives
2018-01-01
This book explores the rich and deep interplay between mathematics and physics one century after David Hilbert’s works from 1891 to 1933, published by Springer in six volumes. The most prominent scientists in various domains of these disciplines contribute to this volume providing insight to their works, and analyzing the impact of the breakthrough and the perspectives of their own contributions. The result is a broad journey through the most recent developments in mathematical physics, such as string theory, quantum gravity, noncommutative geometry, twistor theory, Gauge and Quantum fields theories, just to mention a few. The reader, accompanied on this journey by some of the fathers of these theories, explores some far reaching interfaces where mathematics and theoretical physics interact profoundly and gets a broad and deep understanding of subjects which are at the core of recent developments in mathematical physics. The journey is not confined to the present state of the art, but sheds light on future ...
International Nuclear Information System (INIS)
Kotel'nikov, G.A.
1994-01-01
An algorithm id proposed for research the symmetries of mathematical physics equation. The application of this algorithm to the Schroedinger equation permitted to establish, that in addition to the known symmetry the Schroedinger equation possesses also the relativistic symmetry
National Research Council Canada - National Science Library
Stuhmiller, James H; Bykanova, Lucy; Chan, Philemon; Dang, Xinglai; Fournier, Adam; Long, Diane W; Lu, Zi; Masiello, Paul; Ng, Laurel; Niu, Eugene
2006-01-01
This report summarizes the first year of a 5-year program to develop physiologically and biomechanically based mathematical models that will allow the estimation of physical and cognitive performance...
The importante of physical and mathematical models for nuclear power plants site selection
International Nuclear Information System (INIS)
Rios, J.L.P.
1989-01-01
The importance of the release of effluents from nuclear installations for the site selection of nuclear power plants is discussed. The main available analysis methods, physical and mathematical, is presented [pt
Physics, Computer Science and Mathematics Division. Annual report, 1 January-31 December 1979
International Nuclear Information System (INIS)
Lepore, J.V.
1980-09-01
This annual report describes the research work carried out by the Physics, Computer Science and Mathematics Division during 1979. The major research effort of the Division remained High Energy Particle Physics with emphasis on preparing for experiments to be carried out at PEP. The largest effort in this field was for development and construction of the Time Projection Chamber, a powerful new particle detector. This work took a large fraction of the effort of the physics staff of the Division together with the equivalent of more than a hundred staff members in the Engineering Departments and shops. Research in the Computer Science and Mathematics Department of the Division (CSAM) has been rapidly expanding during the last few years. Cross fertilization of ideas and talents resulting from the diversity of effort in the Physics, Computer Science and Mathematics Division contributed to the software design for the Time Projection Chamber, made by the Computer Science and Applied Mathematics Department
Statistical Uncertainty Quantification of Physical Models during Reflood of LBLOCA
Energy Technology Data Exchange (ETDEWEB)
Oh, Deog Yeon; Seul, Kwang Won; Woo, Sweng Woong [Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of)
2015-05-15
The use of the best-estimate (BE) computer codes in safety analysis for loss-of-coolant accident (LOCA) is the major trend in many countries to reduce the significant conservatism. A key feature of this BE evaluation requires the licensee to quantify the uncertainty of the calculations. So, it is very important how to determine the uncertainty distribution before conducting the uncertainty evaluation. Uncertainty includes those of physical model and correlation, plant operational parameters, and so forth. The quantification process is often performed mainly by subjective expert judgment or obtained from reference documents of computer code. In this respect, more mathematical methods are needed to reasonably determine the uncertainty ranges. The first uncertainty quantification are performed with the various increments for two influential uncertainty parameters to get the calculated responses and their derivatives. The different data set with two influential uncertainty parameters for FEBA tests, are chosen applying more strict criteria for selecting responses and their derivatives, which may be considered as the user’s effect in the CIRCÉ applications. Finally, three influential uncertainty parameters are considered to study the effect on the number of uncertainty parameters due to the limitation of CIRCÉ method. With the determined uncertainty ranges, uncertainty evaluations for FEBA tests are performed to check whether the experimental responses such as the cladding temperature or pressure drop are inside the limits of calculated uncertainty bounds. A confirmation step will be performed to evaluate the quality of the information in the case of the different reflooding PERICLES experiments. The uncertainty ranges of physical model in MARS-KS thermal-hydraulic code during the reflooding were quantified by CIRCÉ method using FEBA experiment tests, instead of expert judgment. Also, through the uncertainty evaluation for FEBA and PERICLES tests, it was confirmed
THE EFFECTS OF ACUTE PHYSICAL EXERCISE TRAINING ON MATHEMATICAL COMPUTATION IN CHILDREN
Directory of Open Access Journals (Sweden)
Gustav Bala
2014-12-01
The results showed that the children’s computation performance was enhanced significantly in the groups with 30, or 45, or 60 min of physical exercise, but not in the groups without physical exercise. This means that even acute intensive physical training can yield positive effects on children's mathematical abilities.
Physics, Computer Science and Mathematics Division. Annual report, January 1-December 31, 1980
International Nuclear Information System (INIS)
Birge, R.W.
1981-12-01
Research in the physics, computer science, and mathematics division is described for the year 1980. While the division's major effort remains in high energy particle physics, there is a continually growing program in computer science and applied mathematics. Experimental programs are reported in e + e - annihilation, muon and neutrino reactions at FNAL, search for effects of a right-handed gauge boson, limits on neutrino oscillations from muon-decay neutrinos, strong interaction experiments at FNAL, strong interaction experiments at BNL, particle data center, Barrelet moment analysis of πN scattering data, astrophysics and astronomy, earth sciences, and instrument development and engineering for high energy physics. In theoretical physics research, studies included particle physics and accelerator physics. Computer science and mathematics research included analytical and numerical methods, information analysis techniques, advanced computer concepts, and environmental and epidemiological studies
Physics, Computer Science and Mathematics Division. Annual report, January 1-December 31, 1980
Energy Technology Data Exchange (ETDEWEB)
Birge, R.W.
1981-12-01
Research in the physics, computer science, and mathematics division is described for the year 1980. While the division's major effort remains in high energy particle physics, there is a continually growing program in computer science and applied mathematics. Experimental programs are reported in e/sup +/e/sup -/ annihilation, muon and neutrino reactions at FNAL, search for effects of a right-handed gauge boson, limits on neutrino oscillations from muon-decay neutrinos, strong interaction experiments at FNAL, strong interaction experiments at BNL, particle data center, Barrelet moment analysis of ..pi..N scattering data, astrophysics and astronomy, earth sciences, and instrument development and engineering for high energy physics. In theoretical physics research, studies included particle physics and accelerator physics. Computer science and mathematics research included analytical and numerical methods, information analysis techniques, advanced computer concepts, and environmental and epidemiological studies. (GHT)
Teaching Secondary School Mathematics and Statistics: Evidence-Based Practice. Volume 1
Averill, Robin; Harvey, Roger
2009-01-01
"Mathematics is more than skills... it is also the excitement of discovery." This is how Derek Holton, one of the contributing authors to this book, defines mathematics. His enthusiasm and energy are echoed throughout by many of the other writers. This is a book to delight mathematics teachers at all stages: experienced and inexperienced;…
Teaching Secondary School Mathematics and Statistics: Evidence-Based Practice. Volume 2
Averill, Robin; Harvey, Roger
2009-01-01
"We can never be sure that there is not some wild, untamed piece of mathematics ready to spring out on us... This is what keeps mathematics enchanting." This is how Jim Neyland, one of the contributing authors to this book, describes mathematics. His enthusiasm and energy are echoed throughout by many of the other writers. This is a book to…
Physics, Computer Science and Mathematics Division annual report, January 1--December 31, 1976
Energy Technology Data Exchange (ETDEWEB)
Lepore, J.V. (ed.)
1977-01-01
This annual report of the Physics, Computer Science and Mathematics Division describes the scientific research and other work carried out within the Division during the calendar year 1976. The Division is concerned with work in experimental and theoretical physics, with computer science and applied mathematics, and with the operation of a computer center. The major physics research activity is in high-energy physics; a vigorous program is maintained in this pioneering field. The high-energy physics research program in the Division now focuses on experiments with e/sup +/e/sup -/ colliding beams using advanced techniques and developments initiated and perfected at the Laboratory. The Division continues its work in medium energy physics, with experimental work carried out at the Bevatron and at the Los Alamos Pi-Meson Facility. Work in computer science and applied mathematics includes construction of data bases, computer graphics, computational physics and data analysis, mathematical modeling, and mathematical analysis of differential and integral equations resulting from physical problems. The computer center serves the Laboratory by constantly upgrading its facility and by providing day-to-day service. This report is descriptive in nature; references to detailed publications are given. (RWR)
Physics, Computer Science and Mathematics Division annual report, January 1--December 31, 1976
International Nuclear Information System (INIS)
Lepore, J.V.
1977-01-01
This annual report of the Physics, Computer Science and Mathematics Division describes the scientific research and other work carried out within the Division during the calendar year 1976. The Division is concerned with work in experimental and theoretical physics, with computer science and applied mathematics, and with the operation of a computer center. The major physics research activity is in high-energy physics; a vigorous program is maintained in this pioneering field. The high-energy physics research program in the Division now focuses on experiments with e + e - colliding beams using advanced techniques and developments initiated and perfected at the Laboratory. The Division continues its work in medium energy physics, with experimental work carried out at the Bevatron and at the Los Alamos Pi-Meson Facility. Work in computer science and applied mathematics includes construction of data bases, computer graphics, computational physics and data analysis, mathematical modeling, and mathematical analysis of differential and integral equations resulting from physical problems. The computer center serves the Laboratory by constantly upgrading its facility and by providing day-to-day service. This report is descriptive in nature; references to detailed publications are given
International Nuclear Information System (INIS)
Tokuyama, M.; Stanley, H.E.
2000-01-01
The main purpose of the Tohwa University International Conference on Statistical Physics is to provide an opportunity for an international group of experimentalists, theoreticians, and computational scientists who are working on various fields of statistical physics to gather together and discuss their recent advances. The conference covered six topics: complex systems, general methods of statistical physics, biological physics, cross-disciplinary physics, information science, and econophysics
Implicit Lagrangian equations and the mathematical modeling of physical systems
Moreau, Luc; van der Schaft, Arjan
2002-01-01
We introduce a class of optimal control problems on manifolds which gives rise (via the Pontryagin maximum principle) to a class of implicit Lagrangian systems (a notion which is introduced in the paper). We apply this to the mathematical modeling of interconnected mechanical systems and mechanical
Journal of the Nigerian Association of Mathematical Physics
African Journals Online (AJOL)
We modify existing mathematical models for HIV that account for observation from hemodialysis. Of particular interest are the criteria under which the disease infected equilibrium could be stable we indicate treatment that is adequate to significantly lower gp 120 levels and help T cells to recover to normal level. Journal of ...
Worldwide seismicity in view of non-extensive statistical physics
Chochlaki, Kaliopi; Vallianatos, Filippos; Michas, George
2014-05-01
In the present work we study the distribution of worldwide shallow seismic events occurred from 1981 to 2011 extracted from the CMT catalog, with magnitude equal or greater than Mw 5.0. Our analysis based on the subdivision of the Earth surface into seismic zones that are homogeneous with regards to seismic activity and orientation of the predominant stress field. To this direction we use the Flinn-Engdahl regionalization (Flinn and Engdahl, 1965), which consists of 50 seismic zones as modified by Lombardi and Marzocchi (2007), where grouped the 50 FE zones into larger tectonically homogeneous ones, utilizing the cumulative moment tensor method. As a result Lombardi and Marzocchi (2007), limit the initial 50 regions to 39 ones, in which we apply the non- extensive statistical physics approach. The non-extensive statistical physics seems to be the most adequate and promising methodological tool for analyzing complex systems, such as the Earth's interior. In this frame, we introduce the q-exponential formulation as the expression of probability distribution function that maximizes the Sq entropy as defined by Tsallis, (1988). In the present work we analyze the interevent time distribution between successive earthquakes by a q-exponential function in each of the seismic zones defined by Lombardi and Marzocchi (2007).confirming the importance of long-range interactions and the existence of a power-law approximation in the distribution of the interevent times. Our findings supports the ideas of universality within the Tsallis approach to describe Earth's seismicity and present strong evidence on temporal clustering of seismic activity in each of the tectonic zones analyzed. Our analysis as applied in worldwide seismicity with magnitude equal or greater than Mw 5.5 and 6.) is presented and the dependence of our result on the cut-off magnitude is discussed. This research has been funded by the European Union (European Social Fund) and Greek national resources under the
Directory of Open Access Journals (Sweden)
PIRVU DANIELA
2016-04-01
Full Text Available This paper proposes a framework for exploring the main research approaches of the financial markets, conducted in the past years by statistical physics specialists. It, also, presents the global financial developments in the last few years, as well as a review of the most important steps in the development of the physical and mathematical modelling of the socioeconomic phenomena. In this regard, we analysed research findings published in the notable international journals. Our research demonstrated that the econophysical models developed in the past few years for the description of the financial phenomena and processes do not provide satisfactory results for the construction of complete solutions able to answer the nowadays financial challenges. We believe that research instrumentation of statistical physics has developed significantly lately and the research approaches in this field should continue and should be enhanced.
A statistical physics of stationary and metastable states
International Nuclear Information System (INIS)
Cabo, A; González, A; Curilef, S; Cabo-Bizet, N G; Vera, C A
2011-01-01
We present a generalization of Gibbs statistical mechanics designed to describe a general class of stationary and metastable equilibrium states. It is assumed that the physical system maximizes the entropy functional S subject to the standard conditions plus an extra conserved constraint function F, imposed to force the system to remain in the metastable configuration. After requiring additivity for two quasi-independent subsystems, and the commutation of the new constraint with the density matrix ρ, it is argued that F should be a homogeneous function of ρ, at least for systems in which the spectrum is sufficiently dense to be considered as continuous. Therefore, surprisingly, the analytic form of F turns out to be of the kind F(p i ) = p i q , where the p i are the eigenvalues of the density matrix and q is a real number to be determined. Thus, the discussion identifies the physical relevance of Lagrange multiplier constraints of the Tsallis kind and their q parameter, as enforced by the additivity of the constraint F which fixes the metastable state. An approximate analytic solution for the probability density is found for q close to unity. The procedure is applied to describe the results from the plasma experiment of Huang and Driscoll. For small and medium values of the radial distance, the measured density is predicted with a precision similar to that achieved by minimal enstrophy and Tsallis procedures. Also, the particle density is predicted at all the radial positions. Thus, the discussion gives a solution to the conceptual difficulties of the two above mentioned approaches as applied to this problem, which both predict a non-analytic abrupt vanishing of the density above a critical radial distance
ACER: A framework on the use of mathematics in upper-division physics
Caballero, Marcos D.; Wilcox, Bethany R.; Pepper, Rachel E.; Pollock, Steven J.
2013-01-01
At the University of Colorado Boulder, as part of our broader efforts to transform middle- and upper-division physics courses, we research students' difficulties with particular concepts, methods, and tools in classical mechanics, electromagnetism, and quantum mechanics. Unsurprisingly, a number of difficulties are related to students' use of mathematical tools (e.g., approximation methods). Previous work has documented a number of challenges that students must overcome to use mathematical tools fluently in introductory physics (e.g., mapping meaning onto mathematical symbols). We have developed a theoretical framework to facilitate connecting students' difficulties to challenges with specific mathematical and physical concepts. In this paper, we motivate the need for this framework and demonstrate its utility for both researchers and course instructors by applying it to frame results from interview data on students' use of Taylor approximations.
International School and Workshop on Nonlinear Mathematical Physics and Natural Hazards
Kouteva-Guentcheva, Mihaela
2015-01-01
This book is devoted to current advances in the field of nonlinear mathematical physics and modeling of critical phenomena that can lead to catastrophic events. Pursuing a multidisciplinary approach, it gathers the work of scientists who are developing mathematical and computational methods for the study and analysis of nonlinear phenomena and who are working actively to apply these tools and create conditions to mitigate and reduce the negative consequences of natural and socio-economic disaster risk. This book summarizes the contributions of the International School and Workshop on Nonlinear Mathematical Physics and Natural Hazards, organized within the framework of the South East Europe Network in Mathematical and Theoretical Physics (SEENET MTP) and supported by UNESCO. It was held at the Bulgarian Academy of Sciences from November 28 to December 2, 2013. The contributions are divided into two major parts in keeping with the scientific program of the meeting. Among the topics covered in Part I (Nonlinear...
DeVaul, Lina
2017-01-01
A professional development program (PSPD) was implemented to improve in-service secondary mathematics teachers' content knowledge, pedagogical knowledge, and self-efficacy in teaching secondary school statistics and probability. Participants generated a teaching resource website at the conclusion of the PSPD program. Participants' content…
Nonlinear optical and atomic systems at the interface of physics and mathematics
Garreau, Jean-Claude
2015-01-01
Focusing on the interface between mathematics and physics, this book offers an introduction to the physics, the mathematics, and the numerical simulation of nonlinear systems in optics and atomic physics. The text covers a wide spectrum of current research on the subject, which is an extremely active field in physics and mathematical physics, with a very broad range of implications, both for fundamental science and technological applications: light propagation in microstructured optical fibers, Bose-Einstein condensates, disordered systems, and the newly emerging field of nonlinear quantum mechanics. Accessible to PhD students, this book will also be of interest to post-doctoral researchers and seasoned academics.
PREFACE: X Workshop of the Gravitation and Mathematical Physics Division, Mexican Physical Society
2014-11-01
The collection of papers in this volume was presented during the X Workshop of the Gravitation and Mathematical Physics Division of the Mexican Physical Society (DGFM-SMF), which was held in Pachuca, Hidalgo, México, December 2-6, 2013. The Workshop is a bi-annual series of conferences sponsored by the DGFM-SMF that started in 1993 with the purposes of discussing and exchanging the research and experience of the gravitational and mathematical physics communities in Mexico. Each Mexican Workshop has been devoted to subjects of broad interest, so that students, in particular, can have access to specialized courses and talks that allow them to raise up their qualifications as professional researchers. Recurrent topics in the Mexican Workshop are supergravity, branes, black holes, the early Universe, observational cosmology, quantum gravity and cosmology and numerical relativity. Following our previous Workshops, distinguished researchers in the field, working in Mexico, were invited to give courses, whereas young researchers were invited for plenary lectures. More specialized talks were also presented in parallel sessions, with ample participation of researchers, and graduate and undergraduate students; most of the presentations have been included in these proceedings. The contributions in this volume have been peer-reviewed, and they represent most of the courses, plenary talks and contributed talks presented during our Workshop. We are indebted to the contributors of these proceedings, as well as to the other participants and organizers, all for making the event a complete success. We acknowledge the professionalism of our reviewers, who helped us to keep high quality standards in all manuscripts. Acknowledgments The organizing committee would like to acknowledge the financial support of the Mexican National Science and Technology Council (CONACyT), the Mexican Physical Society (SMF), as well as several Institutions including: Centro de Investigación y Estudios
Mathematical and statistical modeling for emerging and re-emerging infectious diseases
Hyman, James
2016-01-01
The contributions by epidemic modeling experts describe how mathematical models and statistical forecasting are created to capture the most important aspects of an emerging epidemic.Readers will discover a broad range of approaches to address questions, such as Can we control Ebola via ring vaccination strategies? How quickly should we detect Ebola cases to ensure epidemic control? What is the likelihood that an Ebola epidemic in West Africa leads to secondary outbreaks in other parts of the world? When does it matter to incorporate the role of disease-induced mortality on epidemic models? What is the role of behavior changes on Ebola dynamics? How can we better understand the control of cholera or Ebola using optimal control theory? How should a population be structured in order to mimic the transmission dynamics of diseases such as chlamydia, Ebola, or cholera? How can we objectively determine the end of an epidemic? How can we use metapopulation models to understand the role of movement restrictions and mi...
Statistical physics of medical diagnostics: Study of a probabilistic model.
Mashaghi, Alireza; Ramezanpour, Abolfazl
2018-03-01
We study a diagnostic strategy which is based on the anticipation of the diagnostic process by simulation of the dynamical process starting from the initial findings. We show that such a strategy could result in more accurate diagnoses compared to a strategy that is solely based on the direct implications of the initial observations. We demonstrate this by employing the mean-field approximation of statistical physics to compute the posterior disease probabilities for a given subset of observed signs (symptoms) in a probabilistic model of signs and diseases. A Monte Carlo optimization algorithm is then used to maximize an objective function of the sequence of observations, which favors the more decisive observations resulting in more polarized disease probabilities. We see how the observed signs change the nature of the macroscopic (Gibbs) states of the sign and disease probability distributions. The structure of these macroscopic states in the configuration space of the variables affects the quality of any approximate inference algorithm (so the diagnostic performance) which tries to estimate the sign-disease marginal probabilities. In particular, we find that the simulation (or extrapolation) of the diagnostic process is helpful when the disease landscape is not trivial and the system undergoes a phase transition to an ordered phase.
Statistical physics of medical diagnostics: Study of a probabilistic model
Mashaghi, Alireza; Ramezanpour, Abolfazl
2018-03-01
We study a diagnostic strategy which is based on the anticipation of the diagnostic process by simulation of the dynamical process starting from the initial findings. We show that such a strategy could result in more accurate diagnoses compared to a strategy that is solely based on the direct implications of the initial observations. We demonstrate this by employing the mean-field approximation of statistical physics to compute the posterior disease probabilities for a given subset of observed signs (symptoms) in a probabilistic model of signs and diseases. A Monte Carlo optimization algorithm is then used to maximize an objective function of the sequence of observations, which favors the more decisive observations resulting in more polarized disease probabilities. We see how the observed signs change the nature of the macroscopic (Gibbs) states of the sign and disease probability distributions. The structure of these macroscopic states in the configuration space of the variables affects the quality of any approximate inference algorithm (so the diagnostic performance) which tries to estimate the sign-disease marginal probabilities. In particular, we find that the simulation (or extrapolation) of the diagnostic process is helpful when the disease landscape is not trivial and the system undergoes a phase transition to an ordered phase.
Statistical Physics of Neural Systems with Nonadditive Dendritic Coupling
Directory of Open Access Journals (Sweden)
David Breuer
2014-03-01
Full Text Available How neurons process their inputs crucially determines the dynamics of biological and artificial neural networks. In such neural and neural-like systems, synaptic input is typically considered to be merely transmitted linearly or sublinearly by the dendritic compartments. Yet, single-neuron experiments report pronounced supralinear dendritic summation of sufficiently synchronous and spatially close-by inputs. Here, we provide a statistical physics approach to study the impact of such nonadditive dendritic processing on single-neuron responses and the performance of associative-memory tasks in artificial neural networks. First, we compute the effect of random input to a neuron incorporating nonlinear dendrites. This approach is independent of the details of the neuronal dynamics. Second, we use those results to study the impact of dendritic nonlinearities on the network dynamics in a paradigmatic model for associative memory, both numerically and analytically. We find that dendritic nonlinearities maintain network convergence and increase the robustness of memory performance against noise. Interestingly, an intermediate number of dendritic branches is optimal for memory functionality.
On the Formal-Logical Analysis of the Foundations of Mathematics Applied to Problems in Physics
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.
Methods of Approximation Theory in Complex Analysis and Mathematical Physics
Saff, Edward
1993-01-01
The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. ...
Measurement and the mathematical apparatus of quantum physics
International Nuclear Information System (INIS)
Slavnov, D.A.
2007-01-01
A scheme for constructing quantum mechanics in which the Hilbert space and linear operators are not primary elements on the theory is described. Some variant of the algebraic approach is instead considered. The elements of a noncommutative algebra (observables) and functionals in this algebra serve as the primary components of the theory. Such a scheme allows one to use the formalism of the classical (Kolmogorovian) theory of probability, and to reproduce the mathematical formalism of standard quantum mechanics and to specify borders of its applicability. A brief review of necessary data from the theory of algebras and probability theory is given. The manner is described in which the considered mathematical scheme agrees with the theory of quantum measurements and allows one to avoid quantum paradoxes [ru
Quantization, geometry and noncommutative structures in mathematics and physics
Morales, Pedro; Ocampo, Hernán; Paycha, Sylvie; Lega, Andrés
2017-01-01
This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics. The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics. A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt. The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf a...
[On the founders of the Institute of Mathematics and Physics, University of Bahia].
Dias, A L
The reduced number of female students of mathematics at the University of Bahia School of Philosophy (Faculdade de Filosofia, Universidade da Bahia - FF/UBa) is quite surprising. To date, they are concentrated in areas traditionally viewed as feminine whereas men predominate in the mathematical fields. I have examined interview data from a few women who graduated in mathematics and went on to teach at the University of Bahia School of Mathematics (Faculdade de Filosofia - FF) and at the Institute of Mathematics and Physics (Instituto de Matemática e Física - IMF), where they were soon to outnumber men and constitute the majority of the mathematics teaching staff. In this study, I have investigated the course of their careers over time: from their early student days, through their time as teaching assistants and professors, and finally as founders of the Institute of Mathematics and Physics, in 1960. Special reference is made to Martha Maria de Souza Dantas, organizer of the I Brazilian Conference on Mathematics Teaching, an event which has provided the groundwork for what was to become the Institute (IMF); and to Arlete Cerqueira Lima, the mastermind behind its creation.
Mathematical and physical modeling of rainfall in centrifuge
CAICEDO, Bernardo; THOREL, Luc; TRISTANCHO, Julian
2015-01-01
Rainfall simulation in centrifuge models is important for modelling soil-atmosphere interactions. However, the presence of Coriolis force, drag forces, evaporation and wind within the centrifuge may affect the distribution of rainfall over the model. As a result, development of appropriate centrifuge rain simulators requires a demanding process of experimental trial and error. This paper highlights the key factors involved in controlling rainfall in centrifuge simulations, develops a mathemat...
Physics, Computer Science and Mathematics Division annual report, 1 January-31 December 1983
International Nuclear Information System (INIS)
Jackson, J.D.
1984-08-01
This report summarizes the research performed in the Physics, Computer Science and Mathematics Division of the Lawrence Berkeley Laboratory during calendar year 1983. The major activity of the Division is research in high-energy physics, both experimental and theoretical, and research and development in associated technologies. A smaller, but still significant, program is in computer science and applied mathematics. During 1983 there were approximately 160 people in the Division active in or supporting high-energy physics research, including about 40 graduate students. In computer science and mathematics, the total staff, including students and faculty, was roughly 50. Because of the creation in late 1983 of a Computing Division at LBL and the transfer of the Computer Science activities to the new Division, this annual report is the last from the Physics, Computer Science and Mathematics Division. In December 1983 the Division reverted to its historic name, the Physics Division. Its future annual reports will document high energy physics activities and also those of its Mathematics Department
Physics, Computer Science and Mathematics Division annual report, 1 January-31 December 1983
Energy Technology Data Exchange (ETDEWEB)
Jackson, J.D.
1984-08-01
This report summarizes the research performed in the Physics, Computer Science and Mathematics Division of the Lawrence Berkeley Laboratory during calendar year 1983. The major activity of the Division is research in high-energy physics, both experimental and theoretical, and research and development in associated technologies. A smaller, but still significant, program is in computer science and applied mathematics. During 1983 there were approximately 160 people in the Division active in or supporting high-energy physics research, including about 40 graduate students. In computer science and mathematics, the total staff, including students and faculty, was roughly 50. Because of the creation in late 1983 of a Computing Division at LBL and the transfer of the Computer Science activities to the new Division, this annual report is the last from the Physics, Computer Science and Mathematics Division. In December 1983 the Division reverted to its historic name, the Physics Division. Its future annual reports will document high energy physics activities and also those of its Mathematics Department.
Directory of Open Access Journals (Sweden)
Luis Rojas-Torres
2014-09-01
Full Text Available This paper summarizes a study conducted in 2013 with the purpose of predicting the failure rate of math courses taken by Pharmacy, Mathematics, Actuarial Science, Physics and Meteorology students at Universidad de Costa Rica (UCR. Using the Logistics Regression statistical techniques applied to the 2010 cohort, failure rates were predicted of students in the aforementioned programs in one of their Math introductory courses (Calculus 101 for Physics and Meteorology, Math Principles for Mathematics and Actuarial Science and Applied Differential Equations for Pharmacy. For these models, the UCR admission average, the student’s genre, and the average correct answers in the Quantitative Skills Test were used as predictor variables. The most important variable for all models was the Quantitative Skills Test, and the model with the highest correct classification rate was the Logistics Regression. For the estimated Physics-Meteorology, Pharmacy and Mathematics-Actuarial Science models, correct classifications were 89.8%, 73.6%, and 93.9%, respectively.
Some Aspects of Mathematical and Physical Approaches for Topological Quantum Computation
Directory of Open Access Journals (Sweden)
V. Kantser
2011-10-01
Full Text Available A paradigm to build a quantum computer, based on topological invariants is highlighted. The identities in the ensemble of knots, links and braids originally discovered in relation to topological quantum field theory are shown: how they define Artin braid group -- the mathematical basis of topological quantum computation (TQC. Vector spaces of TQC correspond to associated strings of particle interactions, and TQC operates its calculations on braided strings of special physical quasiparticles -- anyons -- with non-Abelian statistics. The physical platform of TQC is to use the topological quantum numbers of such small groups of anyons as qubits and to perform operations on these qubits by exchanging the anyons, both within the groups that form the qubits and, for multi-qubit gates, between groups. By braiding two or more anyons, they acquire up a topological phase or Berry phase similar to that found in the Aharonov-Bohm effect. Topological matter such as fractional quantum Hall systems and novel discovered topological insulators open the way to form system of anyons -- Majorana fermions -- with the unique property of encoding and processing quantum information in a naturally fault-tolerant way. In the topological insulators, due to its fundamental attribute of topological surface state occurrence of the bound, Majorana fermions are generated at its heterocontact with superconductors. One of the key operations of TQC -- braiding of non-Abelian anyons: it is illustrated how it can be implemented in one-dimensional topological isolator wire networks.
Developing A-level physics students' mathematical skills - a way forward?
Raw, A. J.
1999-09-01
This article outlines research that details the mathematical difficulties of physics students and it also discusses various projects to overcome these difficulties. The successes of these projects are very encouraging and show a way forward for A-level physics teaching.
Yavuz, Ahmet
2015-01-01
This study aims to investigate (1) students' trust in mathematics calculation versus intuition in a physics problem solving and (2) whether this trust is related to achievement in physics in the context of epistemic game theoretical framework. To achieve this research objective, paper-pencil and interview sessions were conducted. A paper-pencil…
de Mul, F.F.M.; Martin Batlle, C.; Martin i Batlle, Cristina; de Bruijn, Imme; Rinzema, K.; Rinzema, Kees
2003-01-01
Teaching physics to first-year university students (in the USA: junior/senior level) is often hampered by their lack of skills in the underlying mathematics, and that in turn may block their understanding of the physics and their ability to solve problems. Examples are vector algebra, differential