The aim of this book is to introduce the simulation of various physical fields and their applications for biomedical engineering, which will provide a base for researchers in the biomedical field to conduct further investigation. The entire book is classified into three levels. It starts with the first level, which presents the single physical fields including structural analysis, fluid simulation, thermal analysis, and acoustic modeling. Then, the second level consists of various couplings between two physical fields covering structural thermal coupling, porous media, fluid structural interaction (FSI), and acoustic FSI. The third level focuses on multi-coupling that coupling with more than two physical fields in the model. Each part in all levels is organized as the physical feature, finite element implementation, modeling procedure in ANSYS, and the specific applications for biomedical engineering like the FSI study of Abdominal Aortic Aneurysm (AAA), acoustic wave transmission in the ear, and heat generation of the breast tumor. The book should help for the researchers and graduate students conduct numerical simulation of various biomedical coupling problems. It should also provide all readers with a better understanding of various couplings.

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;
methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and
methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.
As a result, the book represents a blend of new methods in general computational analysis,
and specific, but also generic, techniques for study of systems theory ant its particular
branches, such as optimal filtering and information compression.
- Best operator approximation,
- Non-Lagrange interpolation,
- Generic Karhunen-Loeve transform
- Generalised low-rank matrix approximation
- Optimal data compression
- Optimal nonlinear filtering

Many large mathematical models, not only models arising and used in environmental studies, are described by systems of partial differential equations. The discretization of the spatial derivatives in such models leads to the solution of very large systems of ordinary differential equations. These systems contain many millions of equations and have to be handled over large time intervals by applying many time-steps (up to several hundred thousand time-steps). Furthermore, many scenarios are as a rule to be run. This explains the fact that the computational tasks in this situation are enormous. Therefore, it is necessary to select fast numerical methods; to develop parallel codes and, what is most important when the problems solved are very large to organize the computational process in a proper way.
The last item (which is very often underestimated but, let us re-iterate, which is very important) is the major topic of this book. In fact, the proper organization of the computational process can be viewed as a preparation of templates which can be used with different numerical methods and different parallel devices. The development of such templates is described in the book. It is also demonstrated that many comprehensive environmental studies can successfully be carried out when the computations are correctly organized. Thus, this book will help the reader to understand better that, while (a) it is very important to select fast numerical methods as well as (b) it is very important to develop parallel codes, this will not be sufficient when the problems solved are really very large. In the latter case, it is also crucial to exploit better the computer architecture by organizing properly the computational process.
- Use of templates in connection with the treatment of very large models
- Performance of comprehensive environmental studies
- Obtaining reliable and robust information about pollution levels
- Studying the impact of future climatic changes on high pollution levels
- Investigating trends related to critical levels of pollution

Numbers alone are enough to describe the importance of DC/DC converters in modern power engineering. There are more than 500 recognized topologies, with more added each year. In their groundbreaking book Advanced DC/DC Converters, expert researchers Luo and Ye organized these technologies into six generations and illustrated their principles and operation through examples of over 100 original topologies. In chapters carefully drawn from that work, Synchronous and Resonant DC/DC Conversion Technology, Energy Factor, and Mathematical Modeling provides a focused, concise overview of synchronous and multiple-element resonant power converters. This reference carefully examines the topologies of more than 50 synchronous and resonant converters by illustrating the design of several prototypes developed by the authors. Using more than 100 diagrams as illustration, the book supplies insight into the fundamental concepts, design, and applications of the fifth (synchronous) and sixth (multiple-element resonant) converters as well as DC power sources and control circuits. The authors also discuss EMI/EMC problems and include a new chapter that introduces the new concept of Energy Factor (EF) and its importance in mathematical modeling as well as analyzing the transient process and impulse response of DC/DC converters. Synchronous and Resonant DC/DC Conversion Technology, Energy Factor, and Mathematical Modeling supplies a quick and accessible guide for anyone in need of specialized information on synchronous and resonant DC/DC converter technologies.

Climate change mitigation and sustainable practices are now at the top of political and technical agendas. Environmental system modelling provides a way of appraising options and this book will make a significant contribution to the uptake of such systems. It provides knowledge of the principles involved in modelling systems, builds confidence amongst designers and offers a broad perspective of the potential of these new technologies.

The aim of the book is to provide an understanding of the concepts and principles behind predictive modelling methods; review progress in the development of the modelling software available; and explore modelling in building design through international case studies based on real design problems.

The mystique of biologically inspired (or bioinspired) paradigms is their ability to describe and solve complex relationships from intrinsically very simple initial conditions and with little or no knowledge of the search space. Edited by two prominent, well-respected researchers, the Handbook of Bioinspired Algorithms and Applications reveals the connections between bioinspired techniques and the development of solutions to problems that arise in diverse problem domains. A repository of the theory and fundamentals as well as a manual for practical implementation, this authoritative handbook provides broad coverage in a single source along with numerous references to the available literature for more in-depth information. The book's two sections serve to balance coverage of theory and practical applications. The first section explains the fundamentals of techniques, such as evolutionary algorithms, swarm intelligence, cellular automata, and others. Detailed examples and case studies in the second section illustrate how to apply the theory in actually developing solutions to a particular problem based on a bioinspired technique. Emphasizing the importance of understanding and harnessing the robust capabilities of bioinspired techniques for solving computationally intractable optimizations and decision-making applications, the Handbook of Bioinspired Algorithms and Applications is an absolute must-read for anyone who is serious about advancing the next generation of computing.

Due to its ubiquity across a variety of fields in science and engineering, fractional calculus has gained momentum in industry and academia. While a number of books and papers introduce either fractional calculus or numerical approximations, no current literature provides a comprehensive collection of both topics. This monograph introduces fundamental information on fractional calculus and provides a detailed treatment of existing numerical approximations. Theory and Numerical Approximations of Fractional Integrals and Derivatives presents an inclusive review of fractional calculus in terms of theory and numerical methods and systematically examines almost all existing numerical approximations for fractional integrals and derivatives. The authors consider the relationship between the fractional Laplacian and the Riesz derivative, a key component absent from other related texts, and highlight recent developments, including their own research and results. The book's core audience spans several fractional communities, including those interested in fractional partial differential equations, the fractional Laplacian, and applied and computational mathematics. Advanced undergraduate and graduate students will find the material suitable as a primary or supplementary resource for their studies.

This book presents peer-reviewed articles and recent advances on the potential applications of Science and Mathematics for future technologies, from the 7th International Conference on the Applications of Science and Mathematics (SCIEMATHIC 2021), held in Malaysia. It provides an insight about the leading trends in sustainable Science and Technology. The world is looking for sustainable solutions to problems more than ever. The synergistic approach of mathematicians, scientists and engineers has undeniable importance for future technologies. With this viewpoint, SCIEMATHIC 2021 has the theme "Quest for Sustainable Science and Mathematics for Future Technologies". The conference brings together physicists, mathematicians, statisticians and data scientists, providing a platform to find sustainable solutions to major problems around us. The works presented here are suitable for professionals and researchers globally in making the world a better and sustainable place.

Discusses replacement, repair, and inspection Offers estimation and statistical tests Covers accelerated life testing Explores warranty analysis manufacturing Includes service reliability

This title was first published in 2003. India's tax revenues depend on manufacturing while agriculture and services generate employment. WTO's Uruguay and Doha rounds imply large tariff cuts. This affects the competitiveness of the Indian manufacturing sector and has implications for government deficits. Excessive dependence on indirect taxes and subsidies to regulate markets introduces distortions and is incompatible with free market principles. The book analyses welfare implications of fiscal and trade policies for India. To put the results in perspective, developments in trade theory, public finance and Computable General Equilibrium (CGE) modelling are covered. Theoretical results are juxtaposed with empirical findings from these models. Methodology to construct CGE models is also covered. The trade model covers tariff cuts under various assumptions besides incorporating "new trade theory". As tax reforms and tariff cuts are independent, past tax reforms like MODVAT (MODified VAT) and proposed reforms like VAT, elimination/reduction of subsidies are covered using a separate tax model.

The book consists of 29 extended chapters which have been selected and invited from the submissions to the "1st International Conference on Computer Science, Applied Mathematics and Applications" (ICCSAMA 2013) held on 9-10 May, 2013 in Warsaw, Poland. The book is organized into five parts, which are: Advanced Optimization Methods and Their Applications, Queuing Theory and Applications, Computational Methods for Knowledge Engineering, Knowledge Engineering with Cloud and Grid Computing, and Logic Based Methods for Decision Making and Data Mining, respectively. All chapters in the book discuss theoretical and practical issues connected with computational methods and optimization methods for knowledge engineering.

Mathematical Analysis for Modeling is intended for those who want to understand the substance of mathematics, rather than just having familiarity with its techniques. It provides a thorough understanding of how mathematics is developed for and applies to solving scientific and engineering problems. The authors stress the construction of mathematical descriptions of scientific and engineering situations, rather than rote memorizations of proofs and formulas. Emphasis is placed on algorithms as solutions to problems and on insight rather than formal derivations.

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Quantitative Methods for Finance and Investments" ensures that readers will gain a reasonable degree of comfort and proficiency in applying elementary mathematics to financial analysis in a variety of areas. All of the methodology in this book is geared toward the development, implementation, and analysis of financial models to solve problems encountered by both finance students and practitioners. The book:
analyzes theoretical and practitioner-oriented models long with the mathematics required to construct them
presents the most essential mathematical techniques and their applications to financial analysis
provides dozens of practical applications, examples, and end-of-chapter exercises with detailed solutions
demonstrates key spreadsheet applications of the mathematical models in chapter appendices
emphasizes practical applications of modeling technique.

First published in 1992, AY's Neuroanatomy of C. elegans for Computation provides the neural circuitry database of the nematode Caenorhabditis elegans, both in printed form and in ASCII files on 5.25-inch diskettes (for use on IBM (R) and compatible personal computers, Macintosh (R) computers, and higher level machines). Tables of connections among neuron classes, synapses among individual neurons, gap junctions among neurons, worm cells and their embryonic origin, and synthetically derived neuromuscular connections are presented together with the references from which the data were compiled and edited. Sample data files and source codes of FORTRAN and BASIC programs are provided to illustrate the use of mathematical tools for any researcher or student interested in examining a natural neural network and discovering what makes it tick.

"If Augustin Cournot had still been alive, he could have won the Nobel Memorial Prize in Economics on at least three different occasions", exclaimed Nobel Laureate Robert Aumann during the 2005 Cournot Centre conference. From his earliest publications, Cournot broke from tradition with his predecessors in applying mathematical modelling to the social sphere. Consequently, he was the first to affirm the mathematization of social phenomena as an essential principle. The fecundity of Cournot's works stems not only from this departure, but also from a richness that irrigated the social sciences of the twentieth century. In this collection, the contributors - including two Nobel laureates in economics - highlight Cournot's profound innovativeness and continued relevance in the areas of industrial economics, mathematical economics, market competition, game theory and epistemology of probability and statistics. Each of the seven authors reminds us of the force and modernity of Cournot's thought as a mathematician, historian of the sciences, philosopher and, not least, as an economist. Combining an epistemological perspective with a theoretical one, this book will be of great interest to researchers and students in the fields of economics, the history of economic thought, and epistemology.

Originally published in 1984. Since the logic underlying economic theory can only be grasped fully by a thorough understanding of the mathematics, this book will be invaluable to economists wishing to understand vast areas of important research. It provides a basic introduction to the fundamental mathematical ideas of topology and calculus, and uses these to present modern singularity theory and recent results on the generic existence of isolated price equilibria in exchange economies.

This special issue of Mathematical Thinking and Learning describes models and modeling perspectives toward mathematics problem solving, learning, and teaching. The concern is not only the mature forms of models and modeling in communities of scientists and mathematicians, but also the need to initiate students in these forms of thought. The contributions of this issue suggest a variety of ways that students (children through adults) can be introduced to highly productive forms of modeling practices. Collectively, they illustrate how modeling activities often lead to remarkable mathematical achievements by students formerly judged to be too young or too lacking in ability for such sophisticated and powerful forms of mathematical thinking. The papers also illustrate how modeling activities often create productive interdisciplinary niches for mathematical thinking, learning, and problem solving that involve simulations of similar situations that occur when mathematics is useful beyond school.

This book focuses on the development of a new simulation paradigm allowing for the solution of models that up to now have never been resolved and which result in spectacular CPU time savings (in the order of millions) that, combined with supercomputing, could revolutionize future ICT (information and communication technologies) at the heart of science and technology. The authors have recently proposed a new paradigm for simulation-based engineering sciences called Proper Generalized Decomposition, PGD, which has proved a tremendous potential in many aspects of forming process simulation. In this book a review of the basics of the technique is made, together with different examples of application.

This sequel to volume 19 of Handbook on Statistics on Stochastic Processes: Modelling and Simulation is concerned mainly with the theme of reviewing and, in some cases, unifying with new ideas the different lines of research and developments in stochastic processes of applied flavour. This volume consists of 23 chapters addressing various topics in stochastic processes. These include, among others, those on manufacturing systems, random graphs, reliability, epidemic modelling, self-similar processes, empirical processes, time series models, extreme value therapy, applications of Markov chains, modelling with Monte Carlo techniques, and stochastic processes in subjects such as engineering, telecommunications, biology, astronomy and chemistry. particular with modelling, simulation techniques and numerical methods concerned with stochastic processes. The scope of the project involving this volume as well as volume 19 is already clarified in the preface of volume 19. The present volume completes the aim of the project and should serve as an aid to students, teachers, researchers and practitioners interested in applied stochastic processes.

The thirty papers published in this book represent the latest developments in Discontinuous Deformation Analysis (DDA). The Numerical Manifold Method (NMM) and other numerical methods and their applications are also covered, as are the theoretical contributions of 3D DDA, modelling and visualization of 3D joint systems, and high-order NMM. Applications of these advances include the stability of underground works, rock slopes and boreholes.

Originally published in 1979. An Input/output database is an information system carrying current data on the intermediate consumption of any product or service by all the specified major firms that consume it. This book begins with a survey of how the interrelationships of an economic system can be represented in a two-dimensional model which traces the output of each economic sector to all other sectors. It talks about how the use of such databases to identify major buyers and sellers can illuminate problems of economic policy at the national, regional, and corporate level and aid in analyzing factors affecting the control of inflation, energy use, transportation, and environmental pollution. The book discusses how advances in database technology, have brought to the fore such issues as the right to individual privacy, corporate secrecy, the public's right of access to stored data, and the use of such information for national planning in a free-enterprise society.

Originally published in 1970; with a second edition in 1989. Empirical Bayes methods use some of the apparatus of the pure Bayes approach, but an actual prior distribution is assumed to generate the data sequence. It can be estimated thus producing empirical Bayes estimates or decision rules. In this second edition, details are provided of the derivation and the performance of empirical Bayes rules for a variety of special models. Attention is given to the problem of assessing the goodness of an empirical Bayes estimator for a given set of prior data. Chapters also focus on alternatives to the empirical Bayes approach and actual applications of empirical Bayes methods.

Originally published in 1984. This book brings together a reasonably complete set of results regarding the use of Constraint Item estimation procedures under the assumption of accurate specification. The analysis covers the case of all explanatory variables being non-stochastic as well as the case of identified simultaneous equations, with error terms known and unknown. Particular emphasis is given to the derivation of criteria for choosing the Constraint Item. Part 1 looks at the best CI estimators and Part 2 examines equation by equation estimation, considering forecasting accuracy.

Designing small structures necessitates an a priori understanding of various device behaviors. The way to gain such understanding is to construct, analyze, and interpret the proper mathematical model.

Through such models, Modeling MEMS and NEMS illuminates microscale and nanoscale phenomena, thereby facilitating the design and optimization of micro- and nanoscale devices. After some introductory material, a review of continuum mechanics, and a study of scaling, the book is organized around phenomena. Each chapter addresses a sequence of real devices that share a common feature. The authors abstract that feature from the devices and present the mathematical tools needed to model it. They construct, analyze, and interpret a series of models of increasing complexity, then at the end of the chapter, they return to one of the devices described, apply the model to it, and interpret the analysis.

In the beginning, the world of microdevices was dominated by experimental work and the development of fabrication techniques. As it matures, optimization and innovative designs are moving to the forefront. Modeling MEMS and NEMS not only provides the practical background and tools needed to design and optimize microdevices but it also helps develop the intuitive understanding that can lead to developing new and better designs and devices.

The 20th century saw tremendous achievements and progress in science and
technology. Undoubtedly, computers and computer-related technologies acted as
one of vital catalysts for accelerating this progress in the latter half of
the century. The contributions of mathematical sciences have been equally
profound, and the synergy between mathematics and computer science has played a
key role in accelerating the progress of both fields as well as science
and engineering.

Mathematical sciences will undoubtedly continue to play this vital role in this
new century. In particular, mathematical modeling and numerical simulation will
continue to be among the essential methodologies for solving massive and
complex problems that arise in science, engineering and manufacturing. Underpinning this all from a sound, theoretical perspective will be numerical algorithms. In recognition of this observation, this volume focuses on the
following specific topics.

(1) Fundamental numerical algorithms
(2) Applications of numerical algorithms
(3) Emerging technologies.

The articles included in this issue by experts on advanced scientific and
engineering computations from numerous countries elucidate state-of-the-art achievements in these three topics from various angles and suggest the future directions. Although we cannot hope to cover all the aspects in scientific and engineering computations, we hope that the articles will interest, inform and inspire members of the science and engineering community.