Composites have been studied for more than 150 years, and interest in their properties has been growing. This classic volume provides the foundations for understanding a broad range of composite properties, including electrical, magnetic, electromagnetic, elastic and viscoelastic, piezoelectric, thermal, fluid flow through porous materials, thermoelectric, pyroelectric, magnetoelectric, and conduction in the presence of a magnetic field (Hall effect). Exact solutions of the PDEs in model geometries provide one avenue of understanding composites; other avenues include microstructure-independent exact relations satisfied by effective moduli, for which the general theory is reviewed; approximation formulae for effective moduli; and series expansions for the fields and effective moduli that are the basis of numerical methods for computing these fields and moduli. The range of properties that composites can exhibit can be explored either through the model geometries or through microstructure-independent bounds on the properties. These bounds are obtained through variational principles, analytic methods, and Hilbert space approaches. Most interesting is when the properties of the composite are unlike those of the constituent materials, and there has been an explosion of interest in such composites, now known as metamaterials. The Theory of Composites surveys these aspects, among others, and complements the new body of literature that has emerged since the book was written. It remains relevant today by providing historical background, a compendium of numerous results, and through elucidating many of the tools still used today in the analysis of composite properties. This book is intended for applied mathematicians, physicists, and electrical and mechanical engineers. It will also be of interest to graduate students.

Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. Models naturally render to statistical description, where random processes and fields express the input parameters and solutions. The fundamental problem of stochastic dynamics is to identify the essential characteristics of the system (its state and evolution), and relate those to the input parameters of the system and initial data.

This book is a revised and more comprehensive version of "Dynamics of Stochastic Systems." Part I provides an introduction to the topic. Part II is devoted to the general theory of statistical analysis of dynamic systems with fluctuating parameters described by differential and integral equations. Part III deals with the analysis of specific physical problems associated with coherent phenomena.
A comprehensive update of "Dynamics of Stochastic Systems"Develops mathematical tools of stochastic analysis and applies them to a wide range of physical models of particles, fluids and wavesIncludes problems for the reader to solve

This book discusses significant research and study topics related to mathematical modelling and analysis of infectious diseases. It includes several models and modelling approaches with different aims, such as identifying and analysing causes of occurrence and re-occurrence, causes of spreading, treatments and control strategies. A valuable resource for researchers, students, educators, scientists, professionals and practitioners interested in gaining insights into various aspects of infectious diseases using mathematical modelling and mathematical analysis, the book will also appeal to general readers wanting to understand the dynamics of various diseases and related issues. Key Features Mathematical models that describe population prevalence or incidence of infectious diseases Mathematical tools and techniques to analyse data on the incidence of infectious diseases Early detection and risk estimate models of infectious diseases Mathematical models that describe the transmission of infectious diseases and analyse data Dynamical analysis and control strategies for infectious diseases Studies comparing the utility of particular models in describing infected diseases-related issues such as social, health and economic

Calculations for Molecular Biology and Biotechnology: A Guide to Mathematics in the Laboratory, Second Edition, provides an introduction to the myriad of laboratory calculations used in molecular biology and biotechnology. The book begins by discussing the use of scientific notation and metric prefixes, which require the use of exponents and an understanding of significant digits. It explains the mathematics involved in making solutions; the characteristics of cell growth; the multiplicity of infection; and the quantification of nucleic acids. It includes chapters that deal with the mathematics involved in the use of radioisotopes in nucleic acid research; the synthesis of oligonucleotides; the polymerase chain reaction (PCR) method; and the development of recombinant DNA technology. Protein quantification and the assessment of protein activity are also discussed, along with the centrifugation method and applications of PCR in forensics and paternity testing.

PRACTICAL MATH APPLICATIONS, 3E offers users math skills needed for business and personal applications. The text begins with a comprehensive review of the basic math functions (addition, subtraction, multiplication, and division) and progresses to fractions and decimals. Once the students have mastered the basics, they are introduced to practical applications that develop critical thinking skills. These applications include bank records, purchasing and pricing merchandise, payroll, taxes, insurance, consumer credit, and interest (simple and compound). This easy-to-follow, step-by-step approach allows students to work at their own pace. Numerous self-help tips, practice activities, and self-assessments are provided so that each student feels competent in their newly acquired skill before moving on to the next.

This book is intended to be a useful contribution for the modern teaching of applied mathematics, educating Industrial Mathematicians that will meet the growing demand for such experts. It covers many applications where mathematics play a fundamental role, from biology, telecommunications, medicine, physics, finance and industry. It is presented in such a way that can be useful in Modelation, Simulation and Optimization courses, targeting master and PhD students. Its content is based on many editions from the successful series of Modelling Weeks organized by the European Consortium of Mathematics in Industry (ECMI). Each chapter addresses a particular problem, and is written in a didactic way, providing the description of the problem, the particular way of approaching it and the proposed solution, along with the results obtained.

This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography.

Inverse problems such as imaging or parameter identification deal with the recovery of unknown quantities from indirect observations, connected via a model describing the underlying context. While traditionally inverse problems are formulated and investigated in a static setting, we observe a significant increase of interest in time-dependence in a growing number of important applications over the last few years. Here, time-dependence affects a) the unknown function to be recovered and / or b) the observed data and / or c) the underlying process. Challenging applications in the field of imaging and parameter identification are techniques such as photoacoustic tomography, elastography, dynamic computerized or emission tomography, dynamic magnetic resonance imaging, super-resolution in image sequences and videos, health monitoring of elastic structures, optical flow problems or magnetic particle imaging to name only a few. Such problems demand for innovation concerning their mathematical description and analysis as well as computational approaches for their solution.

This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models. It presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it includes recently developed methods, such as mixed model diagnostics, mixed model selection, and jackknife method in the context of mixed models. The book is aimed at students, researchers and other practitioners who are interested in using mixed models for statistical data analysis.

The second edition of this book brings together a cutting edge international team of contributors to critically review the current knowledge regarding the effectiveness of training interventions designed to improve cognitive functions in different target populations. Since the publication of the first volume, the field of cognitive research has rapidly evolved. There is substantial evidence that cognitive and physical training can improve cognitive performance, but these benefits seem to vary as a function of the type and the intensity of interventions and the way training-induced gains are measured and analyzed. This book will address the new topics in psychological research and aims to resolve some of the currently debated issues. This book offers a comprehensive overview of empirical findings and methodological approaches of cognitive training research in different cognitive domains (memory, executive functions, etc.), types of training (working memory training, video game training, physical training, etc.), age groups (from children to young and older adults), target populations (children with developmental disorders, aging workers, MCI patients etc.), settings (laboratory-based studies, applied studies in clinical and educational settings), and methodological approaches (behavioral studies, neuroscientific studies). Chapters feature theoretical models that describe the mechanisms underlying training-induced cognitive and neural changes. Cognitive Training: An Overview of Features and Applications, Second Edition will be of interest to researchers, practitioners, students, and professors in the fields of psychology and neuroscience.

This book introduces readers to some of the most significant advances in core computer science-based technologies. At the dawn of the 4th Industrial Revolution, the field of computer science-based technologies is growing continuously and rapidly, and is developing both in itself and in terms of its applications in many other disciplines. Written by leading experts and consisting of 18 chapters, the book is divided into seven parts: (1) Computer Science-based Technologies in Education, (2) Computer Science-based Technologies in Risk Assessment and Readiness, (3) Computer Science-based Technologies in IoT, Blockchains and Electronic Money, (4) Computer Science-based Technologies in Mobile Computing, (5) Computer Science-based Technologies in Scheduling and Transportation, (6) Computer Science-based Technologies in Medicine and Biology, and (7) Theoretical Advances in Computer Science with Significant Potential Applications in Technology. Featuring an extensive list of bibliographic references at the end of each chapter to help readers probe further into the application areas of interest to them, this book is intended for professors, researchers, scientists, engineers and students in computer science-related disciplines. It is also useful for those from other disciplines wanting to become well versed in some of the latest computer science-based technologies.

This book intends to introduce some recent results on passivity of complex dynamical networks with single weight and multiple weights. The book collects novel research ideas and some definitions in complex dynamical networks, such as passivity, output strict passivity, input strict passivity, finite-time passivity, and multiple weights. Furthermore, the research results previously published in many flagship journals are methodically edited and presented in a unified form. The book is likely to be of interest to university researchers and graduate students in Engineering and Mathematics who wish to study the passivity of complex dynamical networks.

This book strikes a healthy balance between theory and applications, ensuring that it doesn't offer a set of tools with no mathematical roots. It is intended as a comprehensive and largely self-contained introduction to probability and statistics for university students from various faculties, with accompanying implementations of some rudimentary statistical techniques in the language R. The content is divided into three basic parts: the first includes elements of probability theory, the second introduces readers to the basics of descriptive and inferential statistics (estimation, hypothesis testing), and the third presents the elements of correlation and linear regression analysis. Thanks to examples showing how to approach real-world problems using statistics, readers will acquire stronger analytical thinking skills, which are essential for analysts and data scientists alike.

Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals is intended to help bridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The work is designed to give young, non-specialist mathematicians a solid foundation in the theory of fractals, and, in the process, to equip them with exposure to a variety of geometric, analytical, and algebraic tools with applications across other areas.

Interest rate modeling and the pricing of related derivatives remain subjects of increasing importance in financial mathematics and risk management. This book provides an accessible introduction to these topics by a step-by-step presentation of concepts with a focus on explicit calculations. Each chapter is accompanied with exercises and their complete solutions, making the book suitable for advanced undergraduate and graduate level students.This second edition retains the main features of the first edition while incorporating a complete revision of the text as well as additional exercises with their solutions, and a new introductory chapter on credit risk. The stochastic interest rate models considered range from standard short rate to forward rate models, with a treatment of the pricing of related derivatives such as caps and swaptions under forward measures. Some more advanced topics including the BGM model and an approach to its calibration are also covered.

This book presents time synchronization and its essential role as a conduit of optimized networks and as one of the key imperatives of ubiquitous connectivity. The author discusses how, without proper time synchronization, many mission critical infrastructures such as 5G mobile networks, smart grids, data centres CATV, and industrial networks would render in serious performance issues and may be subject to catastrophic failure. The book provides a thorough understanding of time synchronization from fundamental concepts to the application of time synchronization in NextGen mission critical infrastructure. Readers will find information not only on designing the optimized products for mission critical infrastructure but also on building NextGen mission critical infrastructure.

This book gives a rigorous, physics focused, introduction to set theory that is geared towards natural science majors.We present the science major with a robust introduction to set theory, focusing on the specific knowledge and skills that will unavoidably be needed in calculus topics and natural science topics in general, rather than taking a philosophical-math-fundamental oriented approach that is commonly found in set theory textbooks.

To put the world of linear algebra to advanced use, it is not enough to merely understand the theory; there is a significant gap between the theory of linear algebra and its myriad expressions in nearly every computational domain. To bridge this gap, it is essential to process the theory by solving many exercises, thus obtaining a firmer grasp of its diverse applications. Similarly, from a theoretical perspective, diving into the literature on advanced linear algebra often reveals more and more topics that are deferred to exercises instead of being treated in the main text. As exercises grow more complex and numerous, it becomes increasingly important to provide supporting material and guidelines on how to solve them, supporting students' learning process. This book provides precisely this type of supporting material for the textbook "Numerical Linear Algebra and Matrix Factorizations," published as Vol. 22 of Springer's Texts in Computational Science and Engineering series. Instead of omitting details or merely providing rough outlines, this book offers detailed proofs, and connects the solutions to the corresponding results in the textbook. For the algorithmic exercises the utmost level of detail is provided in the form of MATLAB implementations. Both the textbook and solutions are self-contained. This book and the textbook are of similar length, demonstrating that solutions should not be considered a minor aspect when learning at advanced levels.

This book provides an overview of the current advances in artificial intelligence and neural nets. Artificial intelligence (AI) methods have shown great capabilities in modelling, prediction and recognition tasks supporting human-machine interaction. At the same time, the issue of emotion has gained increasing attention due to its relevance in achieving human-like interaction with machines. The real challenge is taking advantage of the emotional characterization of humans' interactions to make computers interfacing with them emotionally and socially credible. The book assesses how and to what extent current sophisticated computational intelligence tools might support the multidisciplinary research on the characterization of appropriate system reactions to human emotions and expressions in interactive scenarios. Discussing the latest recent research trends, innovative approaches and future challenges in AI from interdisciplinary perspectives, it is a valuable resource for researchers and practitioners in academia and industry.

This is a companion textbook for an introductory course in physics. It aims to link the theories and models that students learn in class with practical problem-solving techniques. In other words, it should address the common complaint that 'I understand the concepts but I can't do the homework or tests'. The fundamentals of introductory physics courses are addressed in simple and concise terms, with emphasis on how the fundamental concepts and equations should be used to solve physics problems.