The present volume contains the Proceedings of the International Conference on Spectral Theory and Mathematical Physics held in Santiago de Chile in November 2014. Main topics are: Ergodic Quantum Hamiltonians, Magnetic Schroedinger Operators, Quantum Field Theory, Quantum Integrable Systems, Scattering Theory, Semiclassical and Microlocal Analysis, Spectral Shift Function and Quantum Resonances. The book presents survey articles as well as original research papers on these topics. It will be of interest to researchers and graduate students in Mathematics and Mathematical Physics.

This workbook is designed to supplement optics textbooks and covers all the traditional topics of geometrical optics. Terms, equations, definitions, and concepts are discussed briefly and explained through a series of problems that are worked out in a step-by-step manner which simplifies the problem-solving process. Additional practice problems are provided at the end of each chapter. * - An indispensable tool when studying for the state and National Boards * - An ideal supplement to optics textbooks * - Covers the traditional topics of geometrical optics.

This monograph investigates the existence of higher order sliding mode in discrete-time systems and propounds a new concept of discrete-time higher order sliding mode. The authors propose a definition of discrete-time higher order sliding mode and a control law is designed by means of a concept for an uncertain linear-time invariant system, as well as the behavior of the closed-loop system is analyzed. Moreover, the book includes a thorough treatment of the probabilistic and non-deterministic case, i.e. stochastic discrete-time higher order sliding mode. The target audience primarily comprises research experts in control theory but the book may also be beneficial for graduate students alike.

The book presents eight well-known and often used algorithms besides nine newly developed algorithms by the first author and his students in a practical implementation framework. Matlab codes and some benchmark structural optimization problems are provided. The aim is to provide an efficient context for experienced researchers or readers not familiar with theory, applications and computational developments of the considered metaheuristics. The information will also be of interest to readers interested in application of metaheuristics for hard optimization, comparing conceptually different metaheuristics and designing new metaheuristics.

In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.

This work uses techniques of optimization and operations research to develop the first comprehensive survey of the entire field of the optimization of resource, production, and distribution systems. Sten Thore proposes an "economic logistics" that is similar to the well-known concept of military logistics, but which is expanded to include such features as the optimal location of plants, inventories and retail outlets, and the management of hierarchical multi-echelon production, inventory, and distribution systems. The study of individual features of this supply process is familiar from operations research, but Thore joins these elements together into larger analytic structures encompassing the production and distribution system in an entire industry. Following an introductory chapter and a review of the saddle-point theory, coauthored with W. W. Cooper, Thore explores the three dimensions of the supply process synthesis: the spatial dimension (as in simple transportation systems), the vertical dimension (extending from resources to finished consumer goods, as in activity analysis), and the time dimension (as in inventory accumulation and investment). The combination of these then leads to models of such diverse subjects as regional warehouse systems, activity analysis and activity networks, multi-stage warehouse systems of intermediate goods, distribution networks, and spatial equilibrium. Each chapter contains its own exercises which are solved numerically and discussed in great detail, and illustrate such optimization techniques as linear and nonlinear programming, goal programming and goal focusing, chance-constrained programming, and infinite games. This work is designed for use ingraduate courses in economics and mathematics modeling, and will also be a useful addition to college and university library collections.

This book provides the mathematical foundations for Feynman's operator calculus and for the Feynman path integral formulation of quantum mechanics as a natural extension of analysis and functional analysis to the infinite-dimensional setting. In one application, the results are used to prove the last two remaining conjectures of Freeman Dyson for quantum electrodynamics. In another application, the results are used to unify methods and weaken domain requirements for non-autonomous evolution equations. Other applications include a general theory of Lebesgue measure on Banach spaces with a Schauder basis and a new approach to the structure theory of operators on uniformly convex Banach spaces. This book is intended for advanced graduate students and researchers.

This book focuses on the latest applications of nonlinear approaches in engineering and addresses a range of scientific problems. Examples focus on issues in automotive technology, including automotive dynamics, control for electric and hybrid vehicles, and autodriver algorithm for autonomous vehicles. Also included are discussions on renewable energy plants, data modeling, driver-aid methods, and low-frequency vibration. Chapters are based on invited contributions from world-class experts who advance the future of engineering by discussing the development of more optimal, accurate, efficient, cost, and energy effective systems. This book is appropriate for researchers, students, and practising engineers who are interested in the applications of nonlinear approaches to solving engineering and science problems. Presents a broad range of practical topics and approaches; Explains approaches to better, safer, and cheaper systems; Emphasises automotive applications, physical meaning, and methodologies.

This volume comprises the latest developments in both fundamental science and patient-specific applications, discussing topics such as: cellular mechanics; injury biomechanics; biomechanics of heart and vascular system; medical image analysis; and both patient-specific fluid dynamics and solid mechanics simulations. With contributions from researchers world-wide, the Computational Biomechanics for Medicine series of titles provides an opportunity for specialists in computational biomechanics to present their latest methodologies and advancements.

This thesis presents the state of the art in the study of Bondi-Metzner-Sachs (BMS) symmetry and its applications in the simplified setting of three dimensions. It focuses on presenting all the background material in a pedagogical and self-contained manner to enable readers to fully appreciate the original results that have been obtained while learning a number of fundamental concepts in the field along the way. This makes it a highly rewarding read and a perfect starting point for anybody with a serious interest in the four-dimensional problem.

This book develops a set of reference methods capable of modeling uncertainties existing in membership functions, and analyzing and synthesizing the interval type-2 fuzzy systems with desired performances. It also provides numerous simulation results for various examples, which fill certain gaps in this area of research and may serve as benchmark solutions for the readers. Interval type-2 T-S fuzzy models provide a convenient and flexible method for analysis and synthesis of complex nonlinear systems with uncertainties.

Stunning recent results by Host-Kra, Green-Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a modern foundation for introductory courses on ergodic theory, especially for students or researchers with an interest in functional analysis. While basic analytic notions and results are reviewed in several appendices, more advanced operator theoretic topics are developed in detail, even beyond their immediate connection with ergodic theory. As a consequence, the book is also suitable for advanced or special-topic courses on functional analysis with applications to ergodic theory. Topics include: * an intuitive introduction to ergodic theory * an introduction to the basic notions, constructions, and standard examples of topological dynamical systems * Koopman operators, Banach lattices, lattice and algebra homomorphisms, and the Gelfand-Naimark theorem * measure-preserving dynamical systems * von Neumann's Mean Ergodic Theorem and Birkhoff's Pointwise Ergodic Theorem * strongly and weakly mixing systems * an examination of notions of isomorphism for measure-preserving systems * Markov operators, and the related concept of a factor of a measure preserving system * compact groups and semigroups, and a powerful tool in their study, the Jacobs-de Leeuw-Glicksberg decomposition * an introduction to the spectral theory of dynamical systems, the theorems of Furstenberg and Weiss on multiple recurrence, and applications of dynamical systems to combinatorics (theorems of van der Waerden, Gallai,and Hindman, Furstenberg's Correspondence Principle, theorems of Roth and Furstenberg-Sarkoezy) Beyond its use in the classroom, Operator Theoretic Aspects of Ergodic Theory can serve as a valuable foundation for doing research at the intersection of ergodic theory and operator theory

This book concerns the mathematical modeling and computer simulation of the human stomach. It follows the four modern P's (prevention, prediction, personalization, and precision in medicine) approach in addressing the highly heterogeneous nature of processes underlying gastric motility disorders manifested as gastroparesis, functional dyspepsia, myenteric enteropathy etc. The book comprehensively guides readers through the fundamental theoretical concepts to complex physiological models of the organ. This requires a deep and thorough understanding of driving pathophysiological mechanisms as well as the collaborative effort of specialists working in fundamental and biological science. Such a multidisciplinary partnership is vital because it upholds gnostic capabilities and provides the exchange of thoughts and ideas thus offering broad perspectives into the evolution and management of diseases. The book is a valuable resource for applied mathematicians, computational biologists, bioengineers, physicians, physiologists and researchers working in various fields of biomedicine.

Spectral methods have long been popular in direct and large eddy simulation of turbulent flows, but their use in areas with complex-geometry computational domains has historically been much more limited. More recently the need to find accurate solutions to the viscous flow equations around complex configurations has led to the development of high-order discretization procedures on unstructured meshes, which are also recognized as more efficient for solution of time-dependent oscillatory solutions over long time periods. Here Karniadakis and Sherwin present a much-updated and expanded version of their successful first edition covering the recent and significant progress in multi-domain spectral methods at both the fundamental and application level. Containing over 50% new material, including discontinuous Galerkin methods, non-tensorial nodal spectral element methods in simplex domains, and stabilization and filtering techniques, this text aims to introduce a wider audience to the use of spectral/hp element methods with particular emphasis on their application to unstructured meshes. It provides a detailed explanation of the key concepts underlying the methods along with practical examples of their derivation and application, and is aimed at students, academics and practitioners in computational fluid mechanics, applied and numerical mathematics, computational mechanics, aerospace and mechanical engineering and climate/ocean modelling.

This book offers a timely overview of theories and methods developed by an authoritative group of researchers to understand the link between criticality and brain functioning. Cortical information processing in particular and brain function in general rely heavily on the collective dynamics of neurons and networks distributed over many brain areas. A key concept for characterizing and understanding brain dynamics is the idea that networks operate near a critical state, which offers several potential benefits for computation and information processing. However, there is still a large gap between research on criticality and understanding brain function. For example, cortical networks are not homogeneous but highly structured, they are not in a state of spontaneous activation but strongly driven by changing external stimuli, and they process information with respect to behavioral goals. So far the questions relating to how critical dynamics may support computation in this complex setting, and whether they can outperform other information processing schemes remain open. Based on the workshop "Dynamical Network States, Criticality and Cortical Function", held in March 2017 at the Hanse Institute for Advanced Studies (HWK) in Delmenhorst, Germany, the book provides readers with extensive information on these topics, as well as tools and ideas to answer the above-mentioned questions. It is meant for physicists, computational and systems neuroscientists, and biologists.

Modern applications of logic, in mathematics, theoretical computer science, and linguistics, require combined systems involving many different logics working together. In this book the author offers a basic methodology for combining - or fibring - systems. This means that many existing complex systems can be broken down into simpler components, hence making them much easier to manipulate.

This book introduces Meaningful Purposive Interaction Analysis (MPIA) theory, which combines social network analysis (SNA) with latent semantic analysis (LSA) to help create and analyse a meaningful learning landscape from the digital traces left by a learning community in the co-construction of knowledge. The hybrid algorithm is implemented in the statistical programming language and environment R, introducing packages which capture - through matrix algebra - elements of learners' work with more knowledgeable others and resourceful content artefacts. The book provides comprehensive package-by-package application examples, and code samples that guide the reader through the MPIA model to show how the MPIA landscape can be constructed and the learner's journey mapped and analysed. This building block application will allow the reader to progress to using and building analytics to guide students and support decision-making in learning.

Computational modeling allows to reduce, refine and replace animal experimentation as well as to translate findings obtained in these experiments to the human background. However these biomedical problems are inherently complex with a myriad of influencing factors, which strongly complicates the model building and validation process. This book wants to address four main issues related to the building and validation of computational models of biomedical processes: 1. Modeling establishment under uncertainty 2. Model selection and parameter fitting 3. Sensitivity analysis and model adaptation 4. Model predictions under uncertainty In each of the abovementioned areas, the book discusses a number of key-techniques by means of a general theoretical description followed by one or more practical examples. This book is intended for graduate students and researchers active in the field of computational modeling of biomedical processes who seek to acquaint themselves with the different ways in which to study the parameter space of their model as well as its overall behavior.

This book provides an accessible introduction to the basic theory of fluid mechanics and computational fluid dynamics (CFD) from a modern perspective that unifies theory and numerical computation. Methods of scientific computing are introduced alongside with theoretical analysis and MATLAB (R) codes are presented and discussed for a broad range of topics: from interfacial shapes in hydrostatics, to vortex dynamics, to viscous flow, to turbulent flow, to panel methods for flow past airfoils. The third edition includes new topics, additional examples, solved and unsolved problems, and revised images. It adds more computational algorithms and MATLAB programs. It also incorporates discussion of the latest version of the fluid dynamics software library FDLIB, which is freely available online. FDLIB offers an extensive range of computer codes that demonstrate the implementation of elementary and advanced algorithms and provide an invaluable resource for research, teaching, classroom instruction, and self-study. This book is a must for students in all fields of engineering, computational physics, scientific computing, and applied mathematics. It can be used in both undergraduate and graduate courses in fluid mechanics, aerodynamics, and computational fluid dynamics. The audience includes not only advanced undergraduate and entry-level graduate students, but also a broad class of scientists and engineers with a general interest in scientific computing.

This book provides a comprehensive overview of different biomedical data types, including both clinical and genomic data. Thorough explanations enable readers to explore key topics ranging from electrocardiograms to Big Data health mining and EEG analysis techniques. Each chapter offers a summary of the field and a sample analysis. Also covered are telehealth infrastructure, healthcare information association rules, methods for mass spectrometry imaging, environmental biodiversity, and the global nonlinear fitness function for protein structures. Diseases are addressed in chapters on functional annotation of lncRNAs in human disease, metabolomics characterization of human diseases, disease risk factors using SNP data and Bayesian methods, and imaging informatics for diagnostic imaging marker selection. With the exploding accumulation of Electronic Health Records (EHRs), there is an urgent need for computer-aided analysis of heterogeneous biomedical datasets. Biomedical data is notorious for its diversified scales, dimensions, and volumes, and requires interdisciplinary technologies for visual illustration and digital characterization. Various computer programs and servers have been developed for these purposes by both theoreticians and engineers. This book is an essential reference for investigating the tools available for analyzing heterogeneous biomedical data. It is designed for professionals, researchers, and practitioners in biomedical engineering, diagnostics, medical electronics, and related industries.

This volume presents the proceedings of the 11th Conference on Problems and Methods in Mathematical Physics (11th TMP), held in Chemnitz, March 25-28, 1999. The conference was dedicated to the memory of Siegfried PrAssdorf, who made important contributions to the theory and numerical analysis of operator equations and their applications in mathematical physics and mechanics. The main part of the book comprises original research papers. The topics are ranging from integral and pseudodifferential equations, boundary value problems, operator theory, boundary element and wavelet methods, approximation theory and inverse problems to various concrete problems and applications in physics and engineering, and reflect PrAssdorf's broad spectrum of research activities. The volume also contains articles describing the life and mathematical achievements of Siegfried PrAssdorf and includes a list of his publications. The book is addressed to a wide audience in the mathematical and engineering sciences.

Discrete stochastics is the theory of discrete probability spaces. This undergraduate textbook gives a concise introduction into discrete stochastics in general, and into a variety of typical special topics in this field, such as information theory, fluctuation theory, and semigroups of stochastic matrices. The emphasis lies on probability theory rather than on statistical methodology. Motivations, interpretations, and numerous examples and exercises relate the mathematical theory to stochastic experience.

This book shows how to develop efficient quantitative methods to characterize neural data and extra information that reveals underlying dynamics and neurophysiological mechanisms. Written by active experts in the field, it contains an exchange of innovative ideas among researchers at both computational and experimental ends, as well as those at the interface. Authors discuss research challenges and new directions in emerging areas with two goals in mind: to collect recent advances in statistics, signal processing, modeling, and control methods in neuroscience; and to welcome and foster innovative or cross-disciplinary ideas along this line of research and discuss important research issues in neural data analysis. Making use of both tutorial and review materials, this book is written for neural, electrical, and biomedical engineers; computational neuroscientists; statisticians; computer scientists; and clinical engineers.

This book gathers outstanding papers on numerical modeling in Mechanical Engineering (Volume 2) as part of the proceedings of the 1st International Conference on Numerical Modeling in Engineering (NME 2018), which was held in Ghent, Belgium. The overall objective of the conference was to bring together international scientists and engineers in academia and industry from fields related to advanced numerical techniques, such as the finite element method (FEM), boundary element method (BEM), isogeometric analysis (IGA), etc., and their applications to a wide range of engineering disciplines. This book addresses various industrial engineering applications of numerical simulations to Mechanical and Materials Engineering, including: Aerospace applications, Acoustic analysis, Biomechanical applications, Contact problems and wear, Heat transfer analysis, Vibration and dynamics, Transient analysis, Nonlinear analysis, Composite materials, Polymers, Metal alloys, Fracture mechanics, Fatigue of materials, Creep behavior, Phase transformation, and Crystal plasticity.

Modern optimization approaches have attracted many research scientists, decision makers and practicing researchers in recent years as powerful intelligent computational techniques for solving several complex real-world problems. The Handbook of Research on Modern Optimization Algorithms and Applications in Engineering and Economics highlights the latest research innovations and applications of algorithms designed for optimization applications within the fields of engineering, IT, and economics. Focusing on a variety of methods and systems as well as practical examples, this book is a significant resource for graduate-level students, decision makers, and researchers in both public and private sectors who are seeking research-based methods for modeling uncertain real-world problems.