Nonlinear Approaches in Engineering Applications 2 focuses on the application of nonlinear approaches to different engineering and science problems. The selection of the topics for this book is based on the best papers presented in the ASME 2010 and 2011 in the tracks of Dynamic Systems and Control, Optimal Approaches in Nonlinear Dynamics and Acoustics, both of which were organized by the editors. For each selected topic, detailed concept development, derivations and relevant knowledge are provided for the convenience of the readers. The topics that have been selected are of great interest in the fields of engineering and physics and this book is designed to appeal to engineers and researchers working in a broad range of practical topics and approaches.

Today, virtually any advance in the life sciences requires a sophisticated mathematical approach. The methods of mathematics and computer science have emerged as critical tools to modeling biological phenomena, understanding patterns, and making sense of large data sets, such as those generated by the human genome project. An Invitation to Biomathematics provides a comprehensive, yet easily digested entry into the diverse world of mathematical biology--the union of biology, mathematics, and computer science.
This textbook, expertly written by a team of experienced educators, is divided into two parts. The first section presents core principles as elucidated by classical problems such as population growth, predator-prey interactions, epidemic models, and population genetics, while the second applies these principles to modern biomedical research. In addition, the supplementary work Laboratory Manual of Biomathematics (available separately) is designed to enable hands-on exploration of model development, model validation, and model refinement.
* Provides a complete guide for development of quantification skills crucial for applying mathematical methods to biological problems.
* Includes well-known examples from across disciplines in the life sciences including modern biomedical research.
* Explains how to use data sets or dynamical processes to build mathematical models.
* Offers extensive illustrative materials.
* Written in clear and easy-to-follow language without assuming a background in math or biology.
* A laboratory manual is available for hands-on, computer-assisted projects based on material covered in the text.

This contemporary first course focuses on concepts and ideas of Measure Theory, highlighting the theoretical side of the subject. Its primary intention is to introduce Measure Theory to a new generation of students, whether in mathematics or in one of the sciences, by offering them on the one hand a text with complete, rigorous and detailed proofs--sketchy proofs have been a perpetual complaint, as demonstrated in the many Amazon reader reviews critical of authors who "omit 'trivial' steps" and "make not-so-obvious 'it is obvious' remarks." On the other hand, Kubrusly offers a unique collection of fully hinted problems. On the other hand, Kubrusly offers a unique collection of fully hinted problems. The author invites the readers to take an active part in the theory construction, thereby offering them a real chance to acquire a firmer grasp on the theory they helped to build. These problems, at the end of each chapter, comprise complements and extensions of the theory, further examples and counterexamples, or auxiliary results. They are an integral part of the main text, which sets them apart from the traditional classroom or homework exercises.
JARGON BUSTER:
measure theory
Measure theory investigates the conditions under which integration can take place.
It considers various ways in which the "size" of a set can be estimated.
This topic is studied in pure mathematics programs but the theory is also foundational for students of statistics and probability, engineering, and financial engineering.
Key Features
* Designed with a minimum of prerequisites (intro analysis, and for Ch 5, linear algebra)
* Includes 140 classical measure-theory problems
* Carefully crafted to present essential elements of the theory in compact form

Mathematical Problems for Chemistry Students has been compiled and written (a) to help chemistry
students in their mathematical studies by providing them with mathematical problems really occurring in chemistry (b) to help practising chemists to activate their applied mathematical skills and (c) to introduce students and specialists
of the chemistry-related fields (physicists, mathematicians, biologists, etc.) into
the world of the chemical applications.
Some problems of the collection are mathematical reformulations of those in the standard textbooks of chemistry, others were taken from theoretical chemistry journals. All major fields of chemistry are covered, and each problem is given a solution.
This problem collection is intended for beginners and users at an intermediate level. It can be used as a companion to virtually all textbooks dealing with scientific and engineering mathematics or specifically mathematics for chemists.
* Covers a wide range of applications of the most essential tools in applied mathematics
* A new approach to a number of classical textbook-problems
* A number of non-classical problems are included

New Edition of a Classic Guide to Statistical Applications in the Biomedical Sciences

In the last decade, there have been significant changes in the way statistics is incorporated into biostatistical, medical, and public health research. Addressing the need for a modernized treatment of these statistical applications, Basic Statistics, Fourth Edition presents relevant, up-to-date coverage of research methodology using careful explanations of basic statistics and how they are used to address practical problems that arise in the medical and public health settings. Through concise and easy-to-follow presentations, readers will learn to interpret and examine data by applying common statistical tools, such as sampling, random assignment, and survival analysis.

Continuing the tradition of its predecessor, this new edition outlines a thorough discussion of different kinds of studies and guides readers through the important, related decision-making processes such as determining what information is needed and planning the collections process. The book equips readers with the knowledge to carry out these practices by explaining the various types of studies that are commonly conducted in the fields of medical and public health, and how the level of evidence varies depending on the area of research. Data screening and data entry into statistical programs is explained and accompanied by illustrations of statistical analyses and graphs. Additional features of the Fourth Edition include: A new chapter on data collection that outlines the initial steps in planning biomedical and public health studiesA new chapter on nonparametric statistics that includes a discussion and application of the Sign test, the Wilcoxon Signed Rank test, and the Wilcoxon Rank Sum test and its relationship to the Mann-Whitney U testAn updated introduction to survival analysis that includes the Kaplan Meier method for graphing the survival function and a brief introduction to tests for comparing survival functionsIncorporation of modern statistical software, such as SAS, Stata, SPSS, and Minitab into the presented discussion of data analysisUpdated references at the end of each chapter

"Basic Statistics," Fourth Edition is an ideal book for courses on biostatistics, medicine, and public health at the upper-undergraduate and graduate levels. It is also appropriate as a reference for researchers and practitioners who would like to refresh their fundamental understanding of statistical techniques.

The main purpose of this book is not only to present recent studies and advances in the field of social science research, but also to stimulate discussion on related practical issues concerning statistics, mathematics, and economics. Accordingly, a broad range of tools and techniques that can be used to solve problems on these topics are presented in detail in this book, which offers an ideal reference work for all researchers interested in effective quantitative and qualitative tools. The content is divided into three major sections. The first, which is titled "Social work", collects papers on problems related to the social sciences, e.g. social cohesion, health, and digital technologies. Papers in the second part, "Education and teaching issues," address qualitative aspects, education, learning, violence, diversity, disability, and ageing, while the book's final part, "Recent trends in qualitative and quantitative models for socio-economic systems and social work", features contributions on both qualitative and quantitative issues. The book is based on a scientific collaboration, in the social sciences, mathematics, statistics, and economics, among experts from the "Pablo de Olavide" University of Seville (Spain), the "University of Defence" of Brno (Czech Republic), the "G. D'Annunzio" University of Chieti-Pescara (Italy) and "Alexandru Ioan Cuza University" of Iasi (Romania). The contributions, which have been selected using a peer-review process, examine a wide variety of topics related to the social sciences in general, while also highlighting new and intriguing empirical research conducted in various countries. Given its scope, the book will appeal, in equal measure, to sociologists, mathematicians, statisticians and philosophers, and more generally to scholars and specialists in related fields.

This book addresses the experimental calibration of best-estimate numerical simulation models. The results of measurements and computations are never exact. Therefore, knowing only the nominal values of experimentally measured or computed quantities is insufficient for applications, particularly since the respective experimental and computed nominal values seldom coincide. In the author's view, the objective of predictive modeling is to extract "best estimate" values for model parameters and predicted results, together with "best estimate" uncertainties for these parameters and results. To achieve this goal, predictive modeling combines imprecisely known experimental and computational data, which calls for reasoning on the basis of incomplete, error-rich, and occasionally discrepant information. The customary methods used for data assimilation combine experimental and computational information by minimizing an a priori, user-chosen, "cost functional" (usually a quadratic functional that represents the weighted errors between measured and computed responses). In contrast to these user-influenced methods, the BERRU (Best Estimate Results with Reduced Uncertainties) Predictive Modeling methodology developed by the author relies on the thermodynamics-based maximum entropy principle to eliminate the need for relying on minimizing user-chosen functionals, thus generalizing the "data adjustment" and/or the "4D-VAR" data assimilation procedures used in the geophysical sciences. The BERRU predictive modeling methodology also provides a "model validation metric" which quantifies the consistency (agreement/disagreement) between measurements and computations. This "model validation metric" (or "consistency indicator") is constructed from parameter covariance matrices, response covariance matrices (measured and computed), and response sensitivities to model parameters. Traditional methods for computing response sensitivities are hampered by the "curse of dimensionality," which makes them impractical for applications to large-scale systems that involve many imprecisely known parameters. Reducing the computational effort required for precisely calculating the response sensitivities is paramount, and the comprehensive adjoint sensitivity analysis methodology developed by the author shows great promise in this regard, as shown in this book. After discarding inconsistent data (if any) using the consistency indicator, the BERRU predictive modeling methodology provides best-estimate values for predicted parameters and responses along with best-estimate reduced uncertainties (i.e., smaller predicted standard deviations) for the predicted quantities. Applying the BERRU methodology yields optimal, experimentally validated, "best estimate" predictive modeling tools for designing new technologies and facilities, while also improving on existing ones.

This book addresses the concepts of unstable flow solutions, convective instability and absolute instability, with reference to simple (or toy) mathematical models, which are mathematically simple despite their purely abstract character. Within this paradigm, the book introduces the basic mathematical tools, Fourier transform, normal modes, wavepackets and their dynamics, before reviewing the fundamental ideas behind the mathematical modelling of fluid flow and heat transfer in porous media. The author goes on to discuss the fundamentals of the Rayleigh-Benard instability and other thermal instabilities of convective flows in porous media, and then analyses various examples of transition from convective to absolute instability in detail, with an emphasis on the formulation, deduction of the dispersion relation and study of the numerical data regarding the threshold of absolute instability. The clear descriptions of the analytical and numerical methods needed to obtain these parametric threshold data enable readers to apply them in different or more general cases. This book is of interest to postgraduates and researchers in mechanical and thermal engineering, civil engineering, geophysics, applied mathematics, fluid mechanics, and energy technology.

This volume gathers selected contributions from the participants of the Banff International Research Station (BIRS) workshop Coupled Mathematical Models for Physical and Biological Nanoscale Systems and their Applications, who explore various aspects of the analysis, modeling and applications of nanoscale systems, with a particular focus on low dimensional nanostructures and coupled mathematical models for their description. Due to the vastness, novelty and complexity of the interfaces between mathematical modeling and nanoscience and nanotechnology, many important areas in these disciplines remain largely unexplored. In their efforts to move forward, multidisciplinary research communities have come to a clear understanding that, along with experimental techniques, mathematical modeling and analysis have become crucial to the study, development and application of systems at the nanoscale. The conference, held at BIRS in autumn 2016, brought together experts from three different communities working in fields where coupled mathematical models for nanoscale and biosystems are especially relevant: mathematicians, physicists (both theorists and experimentalists), and computational scientists, including those dealing with biological nanostructures. Its objectives: summarize the state-of-the-art; identify and prioritize critical problems of major importance that require solutions; analyze existing methodologies; and explore promising approaches to addressing the challenges identified. The contributions offer up-to-date introductions to a range of topics in nano and biosystems, identify important challenges, assess current methodologies and explore promising approaches. As such, this book will benefit researchers in applied mathematics, as well as physicists and biologists interested in coupled mathematical models and their analysis for physical and biological nanoscale systems that concern applications in biotechnology and medicine, quantum information processing and optoelectronics.

Blast Mitigation: Experimental and Numerical Studies covers both experimental and numerical aspects of material and structural response to dynamic blast loads and its mitigation. The authors present the most up-to-date understanding from laboratory studies and computational analysis for researchers working in the field of blast loadings and their effect on material and structural failure, develop designs for lighter and highly efficient structural members for blast energy absorption, discuss vulnerability of underground structures, present methods for dampening blast overpressures, discuss structural post blast collapse and give attention to underwater explosion and implosion effects on submerged infrastructure and mitigation measures for this environment.

The book presents nine mini-courses from a summer school, Dynamics of Biological Systems, held at the University of Alberta in 2016, as part of the prestigious seminar series: Seminaire de Mathematiques Superieures (SMS). It includes new and significant contributions in the field of Dynamical Systems and their applications in Biology, Ecology, and Medicine. The chapters of this book cover a wide range of mathematical methods and biological applications. They - explain the process of mathematical modelling of biological systems with many examples, - introduce advanced methods from dynamical systems theory, - present many examples of the use of mathematical modelling to gain biological insight - discuss innovative methods for the analysis of biological processes, - contain extensive lists of references, which allow interested readers to continue the research on their own. Integrating the theory of dynamical systems with biological modelling, the book will appeal to researchers and graduate students in Applied Mathematics and Life Sciences.

Rooted in a pedagogically successful problem-solving approach to linear algebra, this work fills a gap in the literature that is sharply divided between, on the one end, elementary texts with only limited exercises and examples, and, at the other end, books too advanced in prerequisites and too specialized in focus to appeal to a wide audience. Instead, it clearly develops the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality, while simultaneously emphasizing applications to fields such as biology, economics, computer graphics, electrical engineering, cryptography, and political science.Key features: * Intertwined discussion of linear algebra and geometry* Example-driven exposition; each section starts with a concise overview of important concepts, followed by a selection of fully-solved problems* Over 500 problems are carefully selected for instructive appeal, elegance, and theoretical importance; roughly half include complete solutions* Two or more solutions provided to many of the problems; paired solutions range from step-by-step, elementary methods whose purpose is to strengthen basic comprehension to more sophisticated, self-study manual for professional scientists and mathematicians. Complete with bibliography and index, this work is a natural bridge between pure/ applied mathematics and the natural/social sciences, appropriate for any student or researcher who needs a strong footing in the theory, problem-solving, and model-building that are the subject's hallmark. I

The Generator Coordinate Method (GCM) is a mathematical tool for the understanding of stable atomic nuclei. Electronic, Atomic and Molecular Calculations is designed to assist scientists applying GCM in the analysis of the electronic structure of atoms and molecules. There have been numerous publications covering nuclear physics and electronic structure of atoms and molecules, but this book is unique in the sense that it specifically addresses the application of GCM for such purposes. Using this book, researchers will be able to understand and calculate the electronic structure in a novel manner.
* Only book that covers the Generator Coordinate Method and applications for atoms, molecules and nuclei
* Clearly describes how the GCM can be used as a powerful tool for design of atomic basis sets
* Reviews current literature on GCM in atomic and molecular fields and a large part of the literature of the method in nuclear physics

This book is designed to supplement standard texts and teaching material in the areas of differential equations in engineering such as in Electrical ,Mechanical and Biomedical engineering. Emphasis is placed on the Boundary Value Problems that are often met in these fields.This keeps the the spectrum of the book rather focussed .The book has basically emerged from the need in the authors lectures on "Advanced Numerical Methods in Biomedical Engineering" at Yeditepe University and it is aimed to assist the students in solving general and application specific problems in Science and Engineering at upper-undergraduate and graduate level.Majority of the problems given in this book are self-contained and have varying levels of difficulty to encourage the student. Problems that deal with MATLAB simulations are particularly intended to guide the student to understand the nature and demystify theoretical aspects of these problems. Relevant references are included at the end of each chapter. Here one will also find large number of software that supplements this book in the form of MATLAB script (.m files). The name of the files used for the solution of a problem are indicated at the end of each corresponding problem statement.There are also some exercises left to students as homework assignments in the book. An outstanding feature of the book is the large number and variety of the solved problems that are included in it. Some of these problems can be found relatively simple, while others are more challenging and used for research projects. All solutions to the problems and script files included in the book have been tested using recent MATLAB software.The features and the content of this book will be most useful to the students studying in Engineering fields, at different levels of their education (upper undergraduate-graduate).

This monograph provides a concise overview of the main theoretical and numerical tools to solve homogenization problems in solids with finite elements. Starting from simple cases (linear thermal case) the problems are progressively complexified to finish with nonlinear problems. The book is not an overview of current research in that field, but a course book, and summarizes established knowledge in this area such that students or researchers who would like to start working on this subject will acquire the basics without any preliminary knowledge about homogenization. More specifically, the book is written with the objective of practical implementation of the methodologies in simple programs such as Matlab. The presentation is kept at a level where no deep mathematics are required.

This book discusses recent advances and research in applied mathematics, statistics and their applications in computing. It features papers presented at the fourth conference in the series organized at the Indian Institute of Technology (Banaras Hindu University), Varanasi, India, on 9 - 11 January 2018 on areas of current interest, including operations research, soft computing, applied mathematical modelling, cryptology, and security analysis. The conference has emerged as a powerful forum, bringing together leading academic scientists, experts from industry, and researchers and offering a venue to discuss, interact and collaborate to stimulate the advancement of mathematics and its applications in computer science. The education of future consumers, users, producers, developers and researchers of mathematics and its applications is an important challenge in modern society, and as such, mathematics and its application in computer science are of vital significance to all spectrums of the community, as well as to mathematicians and computing professionals across different educational levels and disciplines. With contributions by leading international experts, this book motivates and creates interest among young researchers.

This book collects recent advances in the field of nonlinear dynamics in biological systems. Focusing on medical applications as well as more fundamental questions in biochemistry, it presents recent findings in areas such as control in chemically driven reaction-diffusion systems, electrical wave propagation through heart tissue, neural network growth, chiral symmetry breaking in polymers and mechanochemical pattern formation in the cytoplasm, particularly in the context of cardiac cells. It is a compilation of works, including contributions from international scientists who attended the "2nd BCAM Workshop on Nonlinear Dynamics in Biological Systems," held at the Basque Center for Applied Mathematics, Bilbao in September 2016. Embracing diverse disciplines and using multidisciplinary approaches - including theoretical concepts, simulations and experiments - these contributions highlight the nonlinear nature of biological systems in order to be able to reproduce their complex behavior. Edited by the conference organizers and featuring results that represent recent findings and not necessarily those presented at the conference, the book appeals to applied mathematicians, biophysicists and computational biologists.

This book provides a tutorial in the use of Altair Compose and Altair Activate, software packages that provide system modeling and simulation facilities. Advanced system modeling software provide multiple ways of creating models: models can be programmed in specialized languages, graphically constructed as block-diagrams and state machines, or expressed mathematically in equation-based languages. Compose and Activate are introduced in this text in two parts. The first part introduces the multi-language environment of Compose and its use for modeling, simulation and optimization. The second describes the graphical system modeling and optimization with Activate, an open-system environment providing signal-based modeling as well as physical system component-based modeling. Throughout both parts are applied examples from mechanical, biological, and electrical systems, as well as control and signal processing systems. This book will be an invaluable addition with many examples both for those just interested in OML and those doing industrial scale modeling, simulation, and design. All examples are worked using the free basic editions of Activate and Compose that are available.

This volume contains the proceedings of the Kovalevsky symposium held in Stockholm 2000. The first part is devoted to the life of S. Kovalevsky, the first female professor of mathematics, who influenced the development of European science during the last century. Historical notes by G. Mittag-Leffler and copies of official documents related to her life as well as several articles on her life and mathematics are presented. The main articles by J.-E. BjArk describe her life and professorship at Stockholm University. Part two of the volume contains 23 contributions in pure and applied mathematics, and in mathematical physics resulting from the lectures delivered within the program of the symposium.

The third edition of this handbook is designed to provide a broad coverage of the concepts, implementations, and applications in metaheuristics. The book's chapters serve as stand-alone presentations giving both the necessary underpinnings as well as practical guides for implementation. The nature of metaheuristics invites an analyst to modify basic methods in response to problem characteristics, past experiences, and personal preferences, and the chapters in this handbook are designed to facilitate this process as well. This new edition has been fully revised and features new chapters on swarm intelligence and automated design of metaheuristics from flexible algorithm frameworks. The authors who have contributed to this volume represent leading figures from the metaheuristic community and are responsible for pioneering contributions to the fields they write about. Their collective work has significantly enriched the field of optimization in general and combinatorial optimization in particular.Metaheuristics are solution methods that orchestrate an interaction between local improvement procedures and higher level strategies to create a process capable of escaping from local optima and performing a robust search of a solution space. In addition, many new and exciting developments and extensions have been observed in the last few years. Hybrids of metaheuristics with other optimization techniques, like branch-and-bound, mathematical programming or constraint programming are also increasingly popular. On the front of applications, metaheuristics are now used to find high-quality solutions to an ever-growing number of complex, ill-defined real-world problems, in particular combinatorial ones. This handbook should continue to be a great reference for researchers, graduate students, as well as practitioners interested in metaheuristics.

This book presents, in a uniform way, several problems in applied mechanics, which are analysed using the matrix theory and the properties of eigenvalues and eigenvectors. It reveals that various problems and studies in mechanical engineering produce certain patterns that can be treated in a similar way. Accordingly, the same mathematical apparatus allows us to study not only mathematical structures such as quadratic forms, but also mechanics problems such as multibody rigid mechanics, continuum mechanics, vibrations, elastic and dynamic stability, and dynamic systems. In addition, the book explores a wealth of engineering applications.

This book brings together carefully selected, peer-reviewed works on mathematical biology presented at the BIOMAT International Symposium on Mathematical and Computational Biology, which was held at the Institute of Numerical Mathematics, Russian Academy of Sciences, in October 2017, in Moscow. Topics covered include, but are not limited to, the evolution of spatial patterns on metapopulations, problems related to cardiovascular diseases and modeled by boundary control techniques in hemodynamics, algebraic modeling of the genetic code, and multi-step biochemical pathways. Also, new results are presented on topics like pattern recognition of probability distribution of amino acids, somitogenesis through reaction-diffusion models, mathematical modeling of infectious diseases, and many others. Experts, scientific practitioners, graduate students and professionals working in various interdisciplinary fields will find this book a rich resource for research and applications alike.

This book includes review articles in the field of elliptic integrals, elliptic functions and modular forms intending to foster the discussion between theoretical physicists working on higher loop calculations and mathematicians working in the field of modular forms and functions and analytic solutions of higher order differential and difference equations.

The author presents current work in bond graph methodology by providing a compilation of contributions from experts across the world that covers theoretical topics, applications in various areas as well as software for bond graph modeling.
It addresses readers in academia and in industry concerned with the analysis of multidisciplinary engineering systems or control system design who are interested to see how latest developments in bond graph methodology with regard to theory and applications can serve their needs in their engineering fields.
This presentation of advanced work in bond graph modeling presents the leading edge of research in this field. It is hoped that it stimulates new ideas with regard to further progress in theory and in applications.

This book offers a complete guide to designing Linear Fresnel Reflector Systems for concentrating solar radiation. It includes theoretical analyses, computational tools and mathematical formulae to facilitate the development, design, construction and application of these systems. In addition, the book presents a concise yet thorough treatment of the theory behind these systems, and provides useful and efficient calculation procedures that can be used to model and develop their practical applications. Along with the theoretical analyses provided in the book, the physical background is explained using mathematical formulae, illustrations, graphs and tables. Methods are presented for solving the non-linear mathematical systems that describe a significant variety of cases. In addition, MATLAB codes are supplied (both in the text and online). Consequently, readers interested in applying the methodology presented here will have all the source codes at hand, allowing them to easily expand on them by introducing appropriate modifications for their respective design configuration. Given its scope, the book will be of interest to engineers and researchers, who can use their scientific background to help them develop more energy-efficient Linear Fresnel Reflector systems. It will also appeal to students studying these systems for the first time, as it supplies a comprehensive overview of their theoretical analysis and applications.