"Advances in One-Dimensional Wave Mechanics" provides a comprehensive description of the motion of microscopic particles in one-dimensional, arbitrary-shaped potentials based on the analogy between Quantum Mechanics and Electromagnetism. Utilizing a deeper understanding of the wave nature of matter, this book introduces the concept of the scattered sub-waves and a series of new analytical results using the Analytical Transfer Matrix (ATM) method. This work will be useful for graduate students majoring in physics, mainly in basic quantum theory, as well as for academic researchers exploring electromagnetism, particle physics, and wave mechanics and for experts in the field of optical waveguide and integrated optics.

Prof. Zhuangqi Cao is a Professor of Physics at Shanghai Jiao Tong University, China.

Dr. Cheng Yin is a teacher at Jiangsu Key Laboratory of Power Transmission and Distribution Equipment Technology, Hohai University, China.

Now in its second edition, this book continues to give readers a broad mathematical basis for modelling and understanding the wide range of wave phenomena encountered in modern applications. New and expanded material includes topics such as elastoplastic waves and waves in plasmas, as well as new exercises. Comprehensive collections of models are used to illustrate the underpinning mathematical methodologies, which include the basic ideas of the relevant partial differential equations, characteristics, ray theory, asymptotic analysis, dispersion, shock waves, and weak solutions. Although the main focus is on compressible fluid flow, the authors show how intimately gasdynamic waves are related to wave phenomena in many other areas of physical science. Special emphasis is placed on the development of physical intuition to supplement and reinforce analytical thinking. Each chapter includes a complete set of carefully prepared exercises, making this a suitable textbook for students in applied mathematics, engineering, and other physical sciences. Reviews of the first edition: "This book ... is an introduction to the theory of linear and nonlinear waves in fluids, including the theory of shock waves. ... is extraordinarily accurate and free of misprints ... . I enjoyed reading this book. ... most attractive and enticing appearance, and I'm certain that many readers who browse through it will wish to buy a copy. The exercises ... are excellent. ... A beginner who worked through these exercises would not only enjoy himself or herself, but would rapidly acquire mastery of techniques used...in JFM and many other journals..." (C. J. Chapman, Journal of Fluid Mechanics, Vol. 521, 2004) "The book targets a readership of final year undergraduates and first year graduates in applied mathematics. In the reviewer's opinion, it is very well designed to catch the student's interest ... while every chapter displays essential features in some important area of fluid dynamics. Additionally, students may practice by solving 91 exercises. This volume is mainly devoted to inviscid flows. ... The book is very well written." (Denis Serre, Mathematical Reviews, 2004)

Systems with mechanical degrees of freedom containing unstable objects are analysed in this monograph and algorithms for their control are developed, discussed, and numerically tested. This is achieved by identifying unstable modes of motion and using all available resources to suppress them. By using this approach the region of states from which a stable regime can be reached is maximised. The systems discussed in this book are models for pendula and vehicles and find applications in mechatronics, robotics as well as in mechanical and automotive engineering.

This textbook provides a detailed introduction to the use of software in combination with simple and economical hardware (a sound level meter with calibrated AC output and a digital recording system) to obtain sophisticated measurements usually requiring expensive equipment. It emphasizes the use of free, open source, and multiplatform software. Many commercial acoustical measurement systems use software algorithms as an integral component; however the methods are not disclosed. This book enables the reader to develop useful algorithms and provides insight into the use of digital audio editing tools to document features in the signal. Topics covered include acoustical measurement principles, in-depth critical study of uncertainty applied to acoustical measurements, digital signal processing from the basics, and metrologically-oriented spectral and statistical analysis of signals. The student will gain a deep understanding of the use of software for measurement purposes; the ability to implement software-based measurement systems; familiarity with the hardware necessary to acquire and store signals; an appreciation for the key issue of long-term preservation of signals; and a full grasp of the often neglected issue of uncertainty in acoustical measurements. Pedagogical features include in-text worked-out examples, end-of-chapter problems, a glossary of metrology terms, and extensive appendices covering statistics, proofs, additional examples, file formats, and underlying theory.

The methods considered in the 7th conference on "Finite Volumes for Complex Applications" (Berlin, June 2014) have properties which offer distinct advantages for a number of applications. The second volume of the proceedings covers reviewed contributions reporting successful applications in the fields of fluid dynamics, magnetohydrodynamics, structural analysis, nuclear physics, semiconductor theory and other topics.

The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications.

Researchers, PhD and masters level students in numerical analysis, scientific computing and related fields such as partial differential equations will find this volume useful, as will engineers working in numerical modeling and simulations.

This book highlights recent compelling research results and trends in various aspects of contemporary mathematics, emphasizing applicabilitions to real-world situations. The chapters present exciting new findings and developments in situations where mathematical rigor is combined with common sense. A multi-disciplinary approach, both within each chapter and in the volume as a whole, leads to practical insights that may result in a more synthetic understanding of specific global issues as well as their possible solutions. The volume will be of interest not only to experts in mathematics, but also to graduate students, scientists, and practitioners from other fields including physics, biology, geology, management, and medicine.

This book shows cognitive scientists in training how mathematics, computer science and science can be usefully and seamlessly intertwined. It is a follow-up to the first two volumes on mathematics for cognitive scientists, and includes the mathematics and computational tools needed to understand how to compute the terms in the Fourier series expansions that solve the cable equation. The latter is derived from first principles by going back to cellular biology and the relevant biophysics. A detailed discussion of ion movement through cellular membranes, and an explanation of how the equations that govern such ion movement leading to the standard transient cable equation are included. There are also solutions for the cable model using separation of variables, as well an explanation of why Fourier series converge and a description of the implementation of MatLab tools to compute the solutions. Finally, the standard Hodgkin - Huxley model is developed for an excitable neuron and is solved using MatLab.

This book gathers threads that have evolved across different mathematical disciplines into seamless narrative. It deals with condition as a main aspect in the understanding of the performance ---regarding both stability and complexity--- of numerical algorithms. While the role of condition was shaped in the last half-century, so far there has not been a monograph treating this subject in a uniform and systematic way. The book puts special emphasis on the probabilistic analysis of numerical algorithms via the analysis of the corresponding condition. The exposition's level increases along the book, starting in the context of linear algebra at an undergraduate level and reaching in its third part the recent developments and partial solutions for Smale's 17th problem which can be explained within a graduate course. Its middle part contains a condition-based course on linear programming that fills a gap between the current elementary expositions of the subject based on the simplex method and those focusing on convex programming.

Broadly organized around the applications of Fourier analysis, "Methods of Applied Mathematics with a MATLAB Overview" covers both classical applications in partial differential equations and boundary value problems, as well as the concepts and methods associated to the Laplace, Fourier, and discrete transforms. Transform inversion problems are also examined, along with the necessary background in complex variables. A final chapter treats wavelets, short-time Fourier analysis, and geometrically-based transforms. The computer program MATLAB is emphasized throughout, and an introduction to MATLAB is provided in an appendix. Rich in examples, illustrations, and exercises of varying difficulty, this text can be used for a one- or two-semester course and is ideal for students in pure and applied mathematics, physics, and engineering.

This Festschrift resulted from a workshop on "Advanced Modelling in Mathematical Finance" held in honour of Ernst Eberlein's 70th birthday, from 20 to 22 May 2015 in Kiel, Germany. It includes contributions by several invited speakers at the workshop, including several of Ernst Eberlein's long-standing collaborators and former students. Advanced mathematical techniques play an ever-increasing role in modern quantitative finance. Written by leading experts from academia and financial practice, this book offers state-of-the-art papers on the application of jump processes in mathematical finance, on term-structure modelling, and on statistical aspects of financial modelling. It is aimed at graduate students and researchers interested in mathematical finance, as well as practitioners wishing to learn about the latest developments.

This book contains papers presented at the 2014 MICCAI Workshop on Computational Diffusion MRI, CDMRI'14. Detailing new computational methods applied to diffusion magnetic resonance imaging data, it offers readers a snapshot of the current state of the art and covers a wide range of topics from fundamental theoretical work on mathematical modeling to the development and evaluation of robust algorithms and applications in neuroscientific studies and clinical practice. Inside, readers will find information on brain network analysis, mathematical modeling for clinical applications, tissue microstructure imaging, super-resolution methods, signal reconstruction, visualization, and more. Contributions include both careful mathematical derivations and a large number of rich full-color visualizations. Computational techniques are key to the continued success and development of diffusion MRI and to its widespread transfer into the clinic. This volume will offer a valuable starting point for anyone interested in learning computational diffusion MRI. It also offers new perspectives and insights on current research challenges for those currently in the field. The book will be of interest to researchers and practitioners in computer science, MR physics, and applied mathematics.

The papers in this volume represent the most timely and advanced contributions to the 2014 Joint Applied Statistics Symposium of the International Chinese Statistical Association (ICSA) and the Korean International Statistical Society (KISS), held in Portland, Oregon. The contributions cover new developments in statistical modeling and clinical research: including model development, model checking, and innovative clinical trial design and analysis. Each paper was peer-reviewed by at least two referees and also by an editor. The conference was attended by over 400 participants from academia, industry, and government agencies around the world, including from North America, Asia, and Europe. It offered 3 keynote speeches, 7 short courses, 76 parallel scientific sessions, student paper sessions, and social events.

This book describes an effective framework for setting the right process parameters and new mold design to reduce the current plastic defects in injection molding. It presents a new approach for the optimization of injection molding process via (i) a new mold runner design which leads to 20 percent reduction in scrap rate, 2.5 percent reduction in manufacturing time, and easier ejection of injected part, (ii) a new mold gate design which leads to less plastic defects; and (iii) the introduction of a number of promising alternatives with high moldability indices. Besides presenting important developments of relevance academic research, the book also includes useful information for people working in the injection molding industry, especially in the green manufacturing field.

The author defines "Geometric Algebra Computing" as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applications in computer vision, computer graphics, and robotics. This book is organized into three parts: in Part I the author focuses on the mathematical foundations; in Part II he explains the interactive handling of geometric algebra; and in Part III he deals with computing technology for high-performance implementations based on geometric algebra as a domain-specific language in standard programming languages such as C++ and OpenCL. The book is written in a tutorial style and readers should gain experience with the associated freely available software packages and applications. The book is suitable for students, engineers, and researchers in computer science, computational engineering, and mathematics.

Evolutionary algorithms constitute a class of well-known algorithms, which are designed based on the Darwinian theory of evolution and Mendelian theory of heritage. They are partly based on random and partly based on deterministic principles. Due to this nature, it is challenging to predict and control its performance in solving complex nonlinear problems. Recently, the study of evolutionary dynamics is focused not only on the traditional investigations but also on the understanding and analyzing new principles, with the intention of controlling and utilizing their properties and performances toward more effective real-world applications. In this book, based on many years of intensive research of the authors, is proposing novel ideas about advancing evolutionary dynamics towards new phenomena including many new topics, even the dynamics of equivalent social networks. In fact, it includes more advanced complex networks and incorporates them with the CMLs (coupled map lattices), which are usually used for spatiotemporal complex systems simulation and analysis, based on the observation that chaos in CML can be controlled, so does evolution dynamics. All the chapter authors are, to the best of our knowledge, originators of the ideas mentioned above and researchers on evolutionary algorithms and chaotic dynamics as well as complex networks, who will provide benefits to the readers regarding modern scientific research on related subjects.

Computational complexity is a serious bottleneck for the design process in virtually any engineering area. While migration from prototyping and experimental-based design validation to verification using computer simulation models is inevitable and has a number of advantages, high computational costs of accurate, high-fidelity simulations can be a major issue that slows down the development of computer-aided design methodologies, particularly those exploiting automated design improvement procedures, e.g., numerical optimization. The continuous increase of available computational resources does not always translate into shortening of the design cycle because of the growing demand for higher accuracy and necessity to simulate larger and more complex systems. Accurate simulation of a single design of a given system may be as long as several hours, days or even weeks, which often makes design automation using conventional methods impractical or even prohibitive. Additional problems include numerical noise often present in the simulation data, possible presence of multiple locally optimum designs, as well as multiple conflicting objectives. In this edited book, various techniques that can alleviate solving computationally expensive engineering design problems are presented. One of the most promising approaches is the use of fast replacement models, so-called surrogates, that reliably represent the expensive, simulation-based model of the system/device of interest but they are much cheaper and analytically tractable. Here, a group of international experts summarize recent developments in the area and demonstrate applications in various disciplines of engineering and science. The main purpose of the work is to provide the basic concepts and formulations of the surrogate-based modeling and optimization paradigm, as well as discuss relevant modeling techniques, optimization algorithms and design procedures. Therefore, this book should be useful to researchers and engineers from any discipline where computationally heavy simulations are used on daily basis in the design process.

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.