A Mathematical Approach to Special Relativity introduces the mathematical formalisms of special and general relativity. Developed from the author's experience teaching physics to students across all levels, the valuable resource introduces key concepts, building in complexity and using increasingly advanced mathematical tools as it progresses. Without assuming a background in calculus, the text begins with symmetry, before delving more deeply into Galilean relativity. Throughout, the book provides examples and useful "Guides to the Literature." This unique text emphasizes the experimental consequences and verifications of the underpinning theory in order to provide students with a solid foundation in this key area.

Current research results in stochastic and deterministic global optimization including single and multiple objectives are explored and presented in this book by leading specialists from various fields. Contributions include applications to multidimensional data visualization, regression, survey calibration, inventory management, timetabling, chemical engineering, energy systems, and competitive facility location. Graduate students, researchers, and scientists in computer science, numerical analysis, optimization, and applied mathematics will be fascinated by the theoretical, computational, and application-oriented aspects of stochastic and deterministic global optimization explored in this book. This volume is dedicated to the 70th birthday of Antanas Zilinskas who is a leading world expert in global optimization. Professor Zilinskas's research has concentrated on studying models for the objective function, the development and implementation of efficient algorithms for global optimization with single and multiple objectives, and application of algorithms for solving real-world practical problems.

The central subject of this thesis is the theoretical description of ultrafast dynamical processes in molecular systems of chemical interest and their control by laser pulses. This work encompasses different cutting-edge methods in quantum chemistry, quantum dynamics and for the rigorous description of the interaction of light and matter at the molecular level. It provides a general quantum mechanical framework for the description of chemical processes guided by laser pulses, in particular near conical intersections, i.e. geometries where the nuclear and electronic motions couple and the molecule undergoes non-adiabatic (or non-Born-Oppenheimer) dynamics. In close collaboration with experimentalists, the author succeeds in making a decisive step to link and to apply quantum physics to chemistry by transferring state of the art techniques and concepts developed in physics to chemistry, such as "light dressed atoms and molecules" and "adiabatic Floquet theory". He applies these techniques in three prototypic model systems (aniline, pyrazine and NHD2) using high-level electronic structure calculations. Readers will enjoy the comprehensive and accessible introduction to the topic and methodology, as well as the clear structure of the thesis.

This book offers a self-study program on how mathematics, computer science and science can be profitably and seamlessly intertwined. This book focuses on two variable ODE models, both linear and nonlinear, and highlights theoretical and computational tools using MATLAB to explain their solutions. It also shows how to solve cable models using separation of variables and the Fourier Series.

Neuronal dendritic trees are complex structures that endow the cell with powerful computing capabilities and allow for high neural interconnectivity. Studying the function of dendritic structures has a long tradition in theoretical neuroscience, starting with the pioneering work by Wilfrid Rall in the 1950s. Recent advances in experimental techniques allow us to study dendrites with a new perspective and in greater detail. The goal of this volume is to provide a resume of the state-of-the-art in experimental, computational, and mathematical investigations into the functions of dendrites in a variety of neural systems. The book first looks at morphological properties of dendrites and summarizes the approaches to measure dendrite morphology quantitatively and to actually generate synthetic dendrite morphologies in computer models. This morphological characterization ranges from the study of fractal principles to describe dendrite topologies, to the consequences of optimization principles for dendrite shape. Individual approaches are collected to study the aspects of dendrite shape that relate directly to underlying circuit constraints and computation. The second main theme focuses on how dendrites contribute to the computations that neurons perform. What role do dendritic morphology and the distributions of synapses and membrane properties over the dendritic tree have in determining the output of a neuron in response to its input? A wide range of studies is brought together, with topics ranging from general to system-specific phenomena-some having a strong experimental component, and others being fully theoretical. The studies come from many different neural systems and animal species ranging from invertebrates to mammals. With this broad focus, an overview is given of the diversity of mechanisms that dendrites can employ to shape neural computations.

This is an open access book. This course-tested text is an ideal starting point for engineers and physicists entering the field of particle accelerators. The fundamentals are comprehensively introduced, derivations of essential results are provided and a consistent notation style used throughout the book allows readers to quickly familiarize themselves with the field, providing a solid theoretical basis for further studies. Emphasis is placed on the essential features of the longitudinal motion of charged particle beams, together with the corresponding RF generation and power amplification devices for synchrotron and storage ring systems. In particular, electrical engineering aspects such as closed-loop control of system components are discussed. The book also offers a valuable resource for graduate students in physics, electronics engineering, or mathematics looking for an introductory and self-contained text on accelerator physics.

This textbook for advanced undergraduate and postgraduate students of Evolutionary Game Theory covers recent developments in the field, with an emphasis on economic contexts and applications. It begins with the basic ideas as they originated within the field of theoretical biology and then proceeds to the formulation of a theoretical framework that is suitable for the study of social and economic phenomena from an evolutionary perspective. Core topics include the Evolutionary Stable Strategy (EES) and Replicator Dynamics (RD), deterministic dynamic models, and stochastic perturbations. A set of short appendices presents some of the technical material referred to in the main text. Evolutionary theory is widely viewed as one of the most promising appraoches to understanding bounded rationality, learning, and change in complex social environments. New avenues of research are suggested by Vega-Redondo, and plentiful exmples illustrate the theory's potential applications. The recent boom experienced by this dscipline makes the book's systematic presentation of its essential contributions vital reading for newcomer to the field.

"Progress in Expressive Image Synthesis" (MEIS2015), was held in Fukuoka, Japan, September 25-27, 2015. The aim of the symposium was to provide a unique venue where various issues in computer graphics (CG) application fields could be discussed by mathematicians, CG researchers, and practitioners. Through the previous symposiums MEIS2013 and MEIS2014, mathematicians as well as CG researchers have recognized that CG is a specific and practical activity derived from mathematical theories. Issues found in CG broaden the field of mathematics and vice versa, and CG visualizes mathematical theories in an aesthetic manner. In this volume, the editors aim to provoke interdisciplinary research projects through the peer-reviewed papers and poster presentations at the this year's symposium. This book captures interactions among mathematicians, CG researchers, and practitioners sharing important, state-of-the-art issues in graphics and visual perception. The book is suitable for all CG researchers seeking open problem areas and especially for those entering the field who have not yet selected a research direction.

This thesis presents fundamental work that explains two mysteries concerning the trajectory of interplanetary spacecraft. For the first problem, the so-called Pioneer anomaly, a wholly new and innovative method was developed for computing all contributions to the acceleration due to onboard thermal sources. Through a careful analysis of all parts of the spacecraft Pioneer 10 and 11, the application of this methodology has yielded the observed anomalous acceleration. This marks a major achievement, given that this problem remained unsolved for more than a decade. For the second anomaly, the flyby anomaly, a tiny glitch in the velocity of spacecraft that perform gravity assisting maneuvers on Earth, no definitive answer is put forward; however a quite promising strategy for examining the problem is provided and a new mission is proposed. The proposal largely consists in using the Galileo Navigational Satellite System to track approaching spacecraft, and in considering a small test body that approaches Earth from a highly elliptic trajectory.

This thesis focuses on the study and characterization of entanglement and nonlocal correlations constrained under symmetries. It includes original results as well as detailed methods and explanations for a number of different threads of research: positive partial transpose (PPT) entanglement in the symmetric states; a novel, experimentally friendly method to detect nonlocal correlations in many-body systems; the non-equivalence between entanglement and nonlocality; and elemental monogamies of correlations. Entanglement and nonlocal correlations constitute two fundamental resources for quantum information processing, as they allow novel tasks that are otherwise impossible in a classical scenario. However, their elusive characterization is still a central problem in quantum information theory. The main reason why such a fundamental issue remains a formidable challenge lies in the exponential growth in complexity of the Hilbert space as well as the space of multipartite correlations. Physical systems of interest, on the other hand, display symmetries that can be exploited to reduce this complexity, opening the possibility that some of these questions become tractable for such systems.

In How Language Informs Mathematics Dirk Damsma shows how Hegel's and Marx's systematic dialectical analysis of mathematical and economic language helps us understand the structure and nature of mathematical and capitalist systems. More importantly, Damsma shows how knowledge of the latter can inform model assumptions and help improve models. His book provides a blueprint for an approach to economic model building that does away with arbitrarily chosen assumptions and is sensitive to the institutional structures of capitalism. In light of the failure of mainstream economics to understand systemic failures like the financial crisis and given the arbitrary character of most assumptions in mainstream models, such an approach is desperately needed.

This volume highlights problems from a range of biological and medical applications that can be interpreted as questions about system behavior or control. Topics include drug resistance in cancer and malaria, biological fluid dynamics, auto-regulation in the kidney, anti-coagulation therapy, evolutionary diversification and photo-transduction. Mathematical techniques used to describe and investigate these biological and medical problems include ordinary, partial and stochastic differentiation equations, hybrid discrete-continuous approaches, as well as 2 and 3D numerical simulation.

Comprehensive and thorough, this monograph emphasizes the main role differential geometry and convex analysis play in the understanding of physical, chemical, and mechanical notions. Central focus is placed on specifying the agreement between the functional framework and its physical necessity and on making clear the intrinsic character of physical elements, independent from specific charts or frames. The book is divided into four sections, covering thermostructure, classical mechanics, fluid mechanics modelling, and behavior laws. An extensive appendix provides notations and definitions as well as brief explanation of integral manifolds, symplectic structure, and contact structure. Plenty of examples are provided throughout the book, and reviews of basic principles in differential geometry and convex analysis are presented as needed. This book is a useful resource for graduate students and researchers in the field.

This volume is the first of the new series Advances in Dynamics and Delays. It offers the latest advances in the research of analyzing and controlling dynamical systems with delays, which arise in many real-world problems. The contributions in this series are a collection across various disciplines, encompassing engineering, physics, biology, and economics, and some are extensions of those presented at the IFAC (International Federation of Automatic Control) conferences since 2011. The series is categorized in five parts covering the main themes of the contributions: * Stability Analysis and Control Design * Networks and Graphs * Time Delay and Sampled-Data Systems * Computational and Software Tools * Applications This volume will become a good reference point for researchers and PhD students in the field of delay systems, and for those willing to learn more about the field, and it will also be a resource for control engineers, who will find innovative control methodologies for relevant applications, from both theory and numerical analysis perspectives.

This book presents the state-of-the-art in various aspects of analysis and mining of online social networks. Within the broader context of online social networks, it focuses on important and upcoming topics of social network analysis and mining such as the latest in sentiment trends research and a variety of techniques for community detection and analysis. The book collects chapters that are expanded versions of the best papers presented at the IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM'2015), which was held in Paris, France in August 2015. All papers have been peer reviewed and checked carefully for overlap with the literature. The book will appeal to students and researchers in social network analysis/mining and machine learning.

Dynamical System Synchronization (DSS) meticulously presents for the first time the theory of dynamical systems synchronization based on the local singularity theory of discontinuous dynamical systems. The book details the sufficient and necessary conditions for dynamical systems synchronizations, through extensive mathematical expression. Techniques for engineering implementation of DSS are clearly presented compared with the existing techniques.

This volume presents the latest advances and trends in stochastic models and related statistical procedures. Selected peer-reviewed contributions focus on statistical inference, quality control, change-point analysis and detection, empirical processes, time series analysis, survival analysis and reliability, statistics for stochastic processes, big data in technology and the sciences, statistical genetics, experiment design, and stochastic models in engineering. Stochastic models and related statistical procedures play an important part in furthering our understanding of the challenging problems currently arising in areas of application such as the natural sciences, information technology, engineering, image analysis, genetics, energy and finance, to name but a few. This collection arises from the 12th Workshop on Stochastic Models, Statistics and Their Applications, Wroclaw, Poland.

This book presents the latest algorithmic developments in the cell-mapping method for the global analysis of nonlinear dynamic systems, global solutions for multi-objective optimization problems, and global solutions for zeros of complex algebraic equations. It also discusses related engineering and scientific applications, including the nonlinear design of structures for better vibration resistance and reliability; multi-objective, structural-acoustic design for sound abatement; optimal multi-objective design of airfoils for better lift; and optimal multi-objective design of linear and nonlinear controls with or without time delay. The first book on the subject to include extensive Matlab and C++ codes, it presents various implementation algorithms of the cell-mapping method, enabling readers to understand how the method works and its programming aspects. A link to the codes on the Springer website will be provided to the readers.

Focused on recent advances, this book covers theoretical foundations as well as various applications. It presents modern mathematical modeling approaches to the qualitative and numerical analysis of solutions for complex engineering problems in physics, mechanics, biochemistry, geophysics, biology and climatology. Contributions by an international team of respected authors bridge the gap between abstract mathematical approaches, such as applied methods of modern analysis, algebra, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems on the one hand, and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. As such, the book will be of interest to mathematicians and engineers working at the interface of these fields.

The book shows how eastern and western perspectives and conceptions can be used to addresses recent topics laying at the crossroad between philosophy and cognitive science. It reports on new points of view and conceptions discussed during the International Conference on Philosophy and Cognitive Science (PCS2013), held at the Sun Yat-sen University, in Guangzhou, China, and the 2013 Workshop on Abductive Visual Cognition, which took place at KAIST, in Deajeon, South Korea. The book emphasizes an ever-growing cultural exchange between academics and intellectuals coming from different fields. It juxtaposes research works investigating new facets on key issues between philosophy and cognitive science, such as the role of models and causal representations in science; the status of theoretical concepts and quantum principles; abductive cognition, vision, and visualization in science from an eco-cognitive perspective. Further topics are: ignorance immunization in reasoning; moral cognition, violence, and epistemology; and models and biomorphism. The book, which presents a unique and timely account of the current state-of-the art on various aspects in philosophy and cognitive science, is expected to inspire philosophers, cognitive scientists and social scientists, and to generate fruitful exchanges and collaboration among them.

This book provides a crash course on various methods from the bifurcation theory of Functional Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineering and the study of FDEs has been a major source of inspiration for advancement in nonlinear analysis and infinite dimensional dynamical systems. The book summarizes some practical and general approaches and frameworks for the investigation of bifurcation phenomena of FDEs depending on parameters with chap. This well illustrated book aims to be self contained so the readers will find in this book all relevant materials in bifurcation, dynamical systems with symmetry, functional differential equations, normal forms and center manifold reduction. This material was used in graduate courses on functional differential equations at Hunan University (China) and York University (Canada).

This book describes the endeavour to relate the particle spectrum with representations of operational electroweak spacetime, in analogy to the atomic spectrum as characterizing representations of hyperbolic space. The spectrum of hyperbolic position space explains the properties of the nonrelativistic atoms; the spectrum of electroweak spacetime is hoped to explain those of the basic interactions and elementary particles. In this book, the theory of operational symmetries is developed from the numbers, from Plato's and Kepler's symmetries over the simple Lie groups to their applications in nonrelativistic, special relativistic and general relativistic quantum theories with the atomic spectrum for hyperbolic position and, in first attempts, the particle spectrum for electroweak spacetime. The standard model of elementary particles and interactions is characterized by a symmetry group. In general, as initiated by Weyl and stressed by Heisenberg, quantum theory can be built as a theory of operation groups and their unitary representations. In such a framework, time, position and spacetime is modeled by equivalence classes of symmetry groups. For a unification on this road, the quest is not for a final theory with a basic equation for basic particles, but for the basic operation group and its representations.

This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the first textbook on infinite-dimensional port-Hamiltonian systems. An abstract functional analytical approach is combined with the physical approach to Hamiltonian systems. This combined approach leads to easily verifiable conditions for well-posedness and stability. The book is accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Moreover, the theory is illustrated by many worked-out examples.

This book is an elementary introduction to the basic concepts of financial mathematics with a central focus on discrete models and an aim to demonstrate simple but widely used financial derivatives for managing market risks. Only a basic knowledge of probability, real analysis, ordinary differential equations, linear algebra and some common sense are required to utilise this book. Financial mathematics is an application of advanced mathematical and statistical methods to financial management and markets, with a main objective to quantify and hedge risks. Since the book aims to present the basics of financial mathematics to the reader, only essential elements of probability and stochastic analysis are given to explain ideas on derivative pricing and hedging. To keep the reader intrigued and motivated, the book has a sandwich structure: Probability and stochastics are given on the spot, at places where mathematics can almost immediately be illustrated by an application to finance. The first part of the book introduces one of the main principles in finance - no arbitrage pricing.It also introduces main financial instruments such as forward and futures contracts, bonds and swaps, and options. This part is not mathematical. The second part deals with pricing and hedging of European- and American-type options in the discrete time setting. In addition, the concept of complete and incomplete markets is discussed. Elementary probability is briefly revised and discrete-time - discrete-space stochastic processes used in financial modelling are considered. The third part discusses stochastic analysis and introduces the Wiener process, Ito integrals, and stochastic differential equations. The main feature of this final part of the book is the famous Black - Scholes formula for pricing European options. Some guidance for further study of this exciting and rapidly changing subject is given in the last chapter. The book has approximately 100 exercises, for which most solutions have been provided.

The book "Computational Error and Complexity in Science and Engineering" pervades all the science and engineering disciplines where computation occurs. Scientific and engineering computation happens to be the interface between the mathematical model/problem and the real world application. One needs to obtain good quality numerical values for any real-world implementation. Just mathematical quantities symbols are of no use to engineers/technologists. Computational complexity of the numerical method to solve the mathematical model, also computed along with the solution, on the other hand, will tell us how much computation/computational effort has been spent to achieve that quality of result. Anyone who wants the specified physical problem to be solved has every right to know the quality of the solution as well as the resources spent for the solution. The computed error as well as the complexity provide the scientific convincing answer to these questions.
Specifically some of the disciplines in which the book will be readily useful are (i) Computational Mathematics, (ii) Applied Mathematics/Computational Engineering, Numerical and Computational Physics, Simulation and Modelling. Operations Research (both deterministic and stochastic), Computing Methodologies, Computer Applications, and Numerical Methods in Engineering.
Key Features:
- Describes precisely ready-to-use computational error and complexity
- Includes simple easy-to-grasp examples wherever necessary.
- Presents error and complexity in error-free, parallel, and probabilistic methods.
- Discusses deterministic and probabilistic methods with error and complexity.
- Points out the scope and limitation ofmathematical error-bounds.
- Provides a comprehensive up-to-date bibliography after each chapter.
- Describes precisely ready-to-use computational error and complexity
- Includes simple easy-to-grasp examples wherever necessary.
- Presents error and complexity in error-free, parallel, and probabilistic methods.
- Discusses deterministic and probabilistic methods with error and complexity.
- Points out the scope and limitation of mathematical error-bounds.
- Provides a comprehensive up-to-date bibliography after each chapter.