What is econophysics? What makes an econophysicist? Why are financial economists reluctant to use results from econophysics? Can we overcome disputes concerning hypotheses used in financial economics and that make no sense for econophysicists? How can we create a profitable dialogue between financial economists and econophysicists? How do we develop a common theoretical framework allowing the creation of more efficient models for the financial industry? This book moves beyond the disciplinary frontiers in order to initiate the development of a common theoretical framework that makes sense for both traditionally trained financial economists and econophysicists. Unlike other publications dedicated to econophysics, this book is written by two financial economists and it situates econophysics in the evolution of financial economics. The major issues that concern the collaboration between the two fields are analyzed in detail. More specifically, this book explains the theoretical and methodological foundations of these two fields in an accessible vocabulary providing the first extensive analytic comparison between models and results from both fields. The book also identifies the major conceptual gate-keepers that complicate dialogue between the two communities while it provides elements to overcome them. By mixing conceptual, historical, theoretical and formal arguments our analysis bridges the current deaf dialogue between financial economists and econophysicists. This book details the recent results in econophysics that bring it closer to financial economics. So doing, it identifies what remains to be done for econophysicists to contribute significantly to financial economics. Beyond the clarification of the current situation, this book also proposes a generic model compatible with the two fields, defining minimal conditions for common models. Finally, this book provides a research agenda for a more fruitful collaboration between econophysicists and financial economists, creating new research opportunities. In this perspective, it lays the foundations for common theoretical framework and models.

This book revitalizes the relevance of the ideas of Henri Bergson (1859-1941) for current developments in exact sciences. It explores the relevance of Bergson's thought for contemporary philosophical reflections on three of the most important scientific research areas of today, namely physics, the life sciences and the neurosciences. It does so on the basis of the three interrelated topics of time, life and memory. Henri Bergson (1859-1941) was one of the most widely read philosophers of his era. The European public was seeking for answers to questions of the soul and the nature of life and fitting within a historical niche between intellectual rationalism and intuitive spiritualism, his writings drew much attention. This work focuses on the relevance of his philosophy for developments in exact sciences today. The discussion of physics in relation to the abstract and the concrete, the life sciences in relation to concepts of life in relation to new and emerging biotechnology, and the neurosciences in relation to the dual nature of human identity, focuses on one main topic: time. Time, isolated from experience, as the measure of the events in the universe in modern physics; time as the measure of emergent systems in evolution as the backdrop of the theory of evolution in biology; time in relation to memory and imagination in neuropsychological accounts of memory. The author thus discusses the ideas of Henri Bergson as a basis to unveil time as a living process, rather than as an instrument for the measure of events. This view forms the basis of a novel approach to the philosophy of technology. An exciting book for academics interested in the interplay between hard sciences and philosophy.

This book is both an introduction and a demonstration of how Visual Basic for Applications (VBA) can greatly enhance Microsoft Excel (R) by giving users the ability to create their own functions within a worksheet and to create subroutines to perform repetitive actions. The book is written so readers are encouraged to experiment with VBA programming with examples using fairly simple physics or non-complicated mathematics such as root finding and numerical integration. Tested Excel (R) workbooks are available for each chapter and there is nothing to buy or install.

This book presents a thoroughly empiricist account of physics. By providing an overview of the development of empiricism from Ockham to van Fraassen the book lays the foundation for its own version of empiricism. Empiricism for the author consists of three ideas: nominalism, i.e. dismissing second order quantification as unnecessary, epistemological naturalism, and viewing classification of things in natural kinds as a human habit not in need for any justification. The book offers views on the realism-antirealism debate as well as on the individuation of theories as a thoroughly neglected aspect of underdetermination. The book next discusses a broad range of topics, including the predicates body, spatial distance and time interval, the ontology of electromagnetism, propensities, the measurement problem and other philosophical issues in quantum theory. Discussions about the direction of time and about string theory make up the final part of the book.

The book is written for advanced graduate students. The topics have been selected to present methods and models that have applications in both particle physics and polymer physics. The lectures may serve as a guide through more recent research activities and illustrate the applicability of joint methods in different contexts. The book deals with analytic tools (e.g. random walk models, polymer expansion), numerical tools (e.g. Langevin dynamics), and common models (the three-dimensional Gross-Neveu-Model).

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer's series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA's first funding phase, and provides an overview of SPPEXA's contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest.

Nonlinearity and Chaos in Molecular Vibrations deals systematically with a Lie algebraic approach to the study of nonlinear properties of molecular highly excited vibrations. The fundamental concepts of nonlinear dynamics such as chaos, fractals, quasiperiodicity, resonance, and the Lyapunov exponent, and their roles in the study of molecular vibrations are presented.
The 20 chapters cover the basic ideas, the concept of dynamical groups, the integrable two-mode SU(2) system, the unintegrable three-mode SU(3) system, the noncompact su(1,1) algebraic application, su(3) symmetry breaking and its application and the quantal effect of asymmetric molecular rotation. Emphasis is given to: resonance and chaos, the fractal structure of eigencoefficients, the C-H bend motion of acetylene, regular and chaotic motion of DCN, the existence of approximately conserved quantum numbers, one-electronic motion in multi-sites, the Lyapunov exponent, actions of periodic trajectories and quantization, the H function and its application in vibrational relaxation as well as the Dixon dip and its destruction and chaos in the transitional states. This approach bridges the gap between molecular vibrational spectroscopy and nonlinear dynamics.
The book presents a framework of information that readers can use to build their knowledge, and is therefore highly recommended for all those working in or studying molecular physics, molecular spectroscopy, chemical physics and theoretical physics.
* Discusses nonlinearity and chaotic phenomena in molecular vibrations
* Approaches the complicated highly excited molecular vibration
* Provides clear information for students and researchers looking to expand knowledge in this field

"Multi-finger Haptic Interaction "presents a panorama of technologies and methods for multi-finger haptic interaction, together with an analysis of the benefits and implications of adding multiple-fingers to haptic applications.

Research topics covered include: design and control of advanced haptic devices;multi-contact point simulation algorithms;interaction techniques and implications in human perception when interacting with multiple fingers.

These multi-disciplinary results are integrated into applications such as medical simulators for training manual skills, simulators for virtual prototyping and precise manipulations in remote environments.

"Multi-finger Haptic Interaction "presents the current and potential applications that can be developed with these systems, and details the systems' complexity. The research is focused on enhancing haptic interaction by providing multiple contact points to the user.

This state-of-the-art volume is oriented towards researchers who are involved in haptic device design, rendering methods and perception studies, as well as readers from different disciplines who are interested in applying multi-finger haptic technologies and methods to their field of interest.

This is the only book which encompassing the theories of Fourier transforms, wavelet transforms and their chronological geometrical ramifications including polar wavelet transforms, ridgelet transforms, curvelet transforms, contourlet transforms, shearlet transforms, bendlet transforms, taylorlet transforms and so on. There is an urgent need for a text that explains the fundamental concepts underlying the theory of wavelet transforms together with the chronological developments in research to the most contemporary ramifications in a flavor accessible to graduate students and researchers. The need for a contemporary coverage of wavelet transforms in a new textbook at the graduate level, encompassing the current research, is there. This book will address this need.

1) Includes exemplary MATLAB codes 2) Provides a comprehensive foundation in Fourier methods, essential for a mathematical approach to engineering 3) Applies MFS to hot topics in the field: multi-domain, multi- physics, and multi-scale characteristics 4) Applies Fourier method to structural vibrations, acoustics and vibro-acoustic 5) Aids engineers in solving boundary value problems and differential equations

Key features: Provides a literature-based approach with examples of cutting-edge applications and the state of the art Presents the necessary theory as needed, chapter by chapter Synthesises concepts from physics and chemistry.

Vector algebra is a particularly weak point in undergraduate mathematics but seminal to understanding more advanced algebra topics. The book is meant as a primary book but might also be used as a supplement to courses in linear algebra and multivariable or vector calculus. There are no direct, current competitors at this level (undergraduate)

This volume contains the best papers presented at the 2nd ECCOMAS International Conference on Multiscale Computations for Solids and Fluids, held June 10-12, 2015. Topics dealt with include multiscale strategy for efficient development of scientific software for large-scale computations, coupled probability-nonlinear-mechanics problems and solution methods, and modern mathematical and computational setting for multi-phase flows and fluid-structure interaction. The papers consist of contributions by six experts who taught short courses prior to the conference, along with several selected articles from other participants dealing with complementary issues, covering both solid mechanics and applied mathematics.

The prize-winning essays in this book address the fascinating but sometimes uncomfortable relationship between physics and mathematics. Is mathematics merely another natural science? Or is it the result of human creativity? Does physics simply wear mathematics like a costume, or is math the lifeblood of physical reality? The nineteen wide-ranging, highly imaginative and often entertaining essays are enhanced versions of the prize-winning entries to the FQXi essay competition "Trick or Truth", which attracted over 200 submissions. The Foundational Questions Institute, FQXi, catalyzes, supports, and disseminates research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality, but unlikely to be supported by conventional funding sources.

Now in its third edition, Mathematical Concepts in the Physical Sciences provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference.

Mathematics and Music: Composition, Perception, and Performance, Second Edition includes many new sections and more consistent expectations of a student's experience. The new edition of this popular text is more accessible for students with limited musical backgrounds and only high school mathematics is required. The new edition includes more illustrations than the previous one and the added sections deal with the XronoMorph rhythm generator, musical composition, and analyzing personal performance. The text teaches the basics of reading music, explaining how various patterns in music can be described with mathematics, providing mathematical explanations for musical scales, harmony, and rhythm. The book gives students a deeper appreciation showing how music is informed by both its mathematical and aesthetic structures. Highlights of the Second Edition: Now updated for more consistent expectations of students' backgrounds More accessible for students with limited musical backgrounds Full-color presentation Includes more thorough coverage of spectrograms for analyzing recorded music Provides a basic introduction to reading music Features new coverage of building and evaluating rhythms

This book highlights the benefits of Non-Destructive Testing (NDT) methods and their applications on several cultural heritage sites including the Holy Selphuchre Monitoring System in Jerusalem. This book demonstrates Nondestructive sensing technologies and inspection modules as main tools for documentation, diagnosis, characterization, preservation planning, monitoring and quality of restoration, assessment and evaluation of material and preservation work.

This book is a substantially revised and expanded edition reflecting major developments in stochastic numerics since the first edition was published in 2004. The new topics, in particular, include mean-square and weak approximations in the case of nonglobally Lipschitz coefficients of Stochastic Differential Equations (SDEs) including the concept of rejecting trajectories; conditional probabilistic representations and their application to practical variance reduction using regression methods; multi-level Monte Carlo method; computing ergodic limits and additional classes of geometric integrators used in molecular dynamics; numerical methods for FBSDEs; approximation of parabolic SPDEs and nonlinear filtering problem based on the method of characteristics. SDEs have many applications in the natural sciences and in finance. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce the solution of multi-dimensional problems for partial differential equations to the integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. Many special schemes for SDEs are presented. In the second part of the book numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear, are constructed. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, applied probability, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.

* Written by an interdisciplinary group of specialists from the arts, humanities and sciences at Oxford University * Suitable for a wide non-academic readership, and will appeal to anyone with an interest in mathematics, science and philosophy.

This volume contains the proceedings of the Arizona School of Analysis and Mathematical Physics, held from March 5-9, 2018, at the University of Arizona, Tucson, Arizona. A main goal of this school was to introduce graduate students and postdocs to exciting topics of current research that are both influenced by physical intuition and require the use of cutting-edge mathematics. The articles in this volume reflect recent progress and innovative techniques developed within mathematical physics. Two works investigate spectral gaps of quantum spin systems. Specifically, Abdul-Rahman, Lemm, Lucia, Nachtergaele, and Young consider decorated AKLT models, and Lemm demonstrates a finite-size criterion for $D$-dimensional models. Bachmann, De Roeck, and Fraas summarize a recent proof of the adiabatic theorem, while Bachmann, Bols, De Roeck, and Fraas discuss linear response for interacting Hall insulators. Models on general graphs are the topic of the articles by Fischbacher, on higher spin XXZ, and by Latushkin and Sukhtaiev, on an index theorem for Schrodinger operators. Probabilistic applications are the focus of the articles by DeMuse and Yin, on exponential random graphs, by Saenz, on KPZ universality, and by Stolz, on disordered quantum spin chains. In all, the diversity represented here is a testament to the enthusiasm this rich field of mathematical physics generates.

Theoretical foundations of atmospheric remote sensing are electromagnetic theory, radiative transfer and inversion theory. This book provides an overview of these topics in a common context, compile the results of recent research, as well as fill the gaps, where needed. The following aspects are covered: principles of remote sensing, the atmospheric physics, foundations of the radiative transfer theory, electromagnetic absorption, scattering and propagation, review of computational techniques in radiative transfer, retrieval techniques as well as regularization principles of inversion theory. As such, the book provides a valuable resource for those who work with remote sensing data and want to get a broad view of theoretical foundations of atmospheric remote sensing. The book will be also useful for students and researchers working in such diverse fields like inverse problems, atmospheric physics, electromagnetic theory, and radiative transfer.

Special numerical techniques are already needed to deal with n x n matrices for large n. Tensor data are of size n x n x...x n=nd, where nd exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. This monograph describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra.

This book presents key works of Boris Hessen, outstanding Soviet philosopher of science, available here in English for the first time. Quality translations are accompanied by an editors' introduction and annotations. Boris Hessen is known in history of science circles for his "Social and Economic Roots of Newton's Principia" presented in London (1931), which inspired new approaches in the West. As a philosopher and a physicist, he was tasked with developing a Marxist approach to science in the 1920s. He studied the history of physics to clarify issues such as reductionism and causality as they applied to new developments. With the philosophers called the "Dialecticians", his debates with the opposing "Mechanists" on the issue of emergence are still worth studying and largely ignored in the many recent works on this subject. Taken as a whole, the book is a goldmine of insights into both the foundations of physics and Soviet history.

The book discusses three classes of problems: the generalized Nash equilibrium problems, the bilevel problems and the mathematical programming with equilibrium constraints (MPEC). These problems interact through their mathematical analysis as well as their applications. The primary aim of the book is to present the modern tool of variational analysis and optimization, which are used to analyze these three classes of problems. All contributing authors are respected academicians, scientists and researchers from around the globe. These contributions are based on the lectures delivered by experts at CIMPA School, held at the University of Delhi, India, from 25 November-6 December 2013, and peer-reviewed by international experts. The book contains five chapters. Chapter 1 deals with nonsmooth, nonconvex bilevel optimization problems whose feasible set is described by using the graph of the solution set mapping of a parametric optimization problem. Chapter 2 describes a constraint qualification to MPECs considered as an application of calmness concept of multifunctions and is used to derive M-stationarity conditions for MPEC. Chapter 3 discusses the first- and second-order optimality conditions derived for a special case of a bilevel optimization problem in which the constraint set of the lower level problem is described as a general compact convex set. Chapter 4 concentrates the results of the modelization and analysis of deregulated electricity markets with a focus on auctions and mechanism design. Chapter 5 focuses on optimization approaches called reflection methods for protein conformation determination within the framework of matrix completion. The last chapter (Chap. 6) deals with the single-valuedness of quasimonotone maps by using the concept of single-directionality with a special focus on the case of the normal operator of lower semi-continuous quasiconvex functions.