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This book contains select papers presented at the International Conference on Applied Mathematics and Computational Intelligence (ICAMCI-2020), held at the National Institute of Technology Agartala, Tripura, India, from 19–20 March 2020. It discusses the most recent breakthroughs in intelligent techniques such as fuzzy logic, neural networks, optimization algorithms, and their application in the development of intelligent information systems by using applied mathematics. The book also explains how these systems will be used in domains such as intelligent control and robotics, pattern recognition, medical diagnosis, time series prediction, and complicated problems in optimization. The book publishes new developments and advances in various areas of type-3 fuzzy, intuitionistic fuzzy, computational mathematics, block chain, creak analysis, supply chain, soft computing, fuzzy systems, hybrid intelligent systems, thermos-elasticity, etc. The book is targeted to researchers, scientists, professors, and students of mathematics, computer science, applied science and engineering, interested in the theory and applications of intelligent systems in real-world applications. It provides young researchers and students with new directions for their future study by exchanging fresh thoughts and finding new problems.

​This book comprises selected papers of the 26th International Conference on Difference Equations and Applications, ICDEA 2021, held virtually at the University of Sarajevo, Bosnia and Herzegovina, in July 2021.The book includes the latest and significant research and achievements in difference equations, discrete dynamical systems, and their applications in various scientific disciplines.The book is interesting for Ph.D. students and researchers who want to keep up to date with the latest research, developments, and achievements in difference equations, discrete dynamical systems, and their applications, the real-world problems.

Cooperation is pervasive throughout nature, but its origin remains an open question. For decades, social scientists, business leaders, and economists have struggled with an important question: why is cooperation so ubiquitous among unrelated humans? The answers would have profound effects because anything that promotes cooperation leads to more productive work environments and benefits society at large. Game theory provides an ideal framework for studying social dilemmas, or those situations in which people decide whether to cooperate with others (benefitting the group) or defect by prioritizing their self-interest (benefitting only the individual). The social dilemma is formulated as a mathematical game and then programmed into a computer model. Simulating the game allows researchers to investigate potential theories to explain how cooperation emerges and what promotes its persistence. Over the past 25 years, countless papers on social dilemma games have been published, yet arguably little progress has been made. The problem is the social dilemma game models are unrealistic in the sense they contain artificial constructs that deviate from the way humans act. This book describes the shortcomings in current social dilemma game modeling techniques and provides guidance on designing more effective models. A basic introduction to game theory is provided with an emphasis on the prisoner's dilemma, the most widely studied social dilemma game. Individual chapters are provided detailing the shortcomings of weak selection, spatial games, and the Moran process. Computer model validation is also discussed at length. The recommendations found in this book should help design more realistic social dilemma game models likely to produce a better understanding of human cooperation.

This proceedings volume gathers a selection of outstanding research papers presented at the third Conference on Isogeometric Analysis and Applications, held in Delft, The Netherlands, in April 2018. This conference series, previously held in Linz, Austria, in 2012 and Annweiler am Trifels, Germany, in 2014, has created an international forum for interaction between scientists and practitioners working in this rapidly developing field. Isogeometric analysis is a groundbreaking computational approach that aims to bridge the gap between numerical analysis and computational geometry modeling by integrating the finite element method and related numerical simulation techniques into the computer-aided design workflow, and vice versa. The methodology has matured over the last decade both in terms of our theoretical understanding, its mathematical foundation and the robustness and efficiency of its practical implementations. This development has enabled scientists andpractitioners to tackle challenging new applications at the frontiers of research in science and engineering and attracted early adopters for this his novel computer-aided design and engineering technology in industry. The IGAA 2018 conference brought together experts on isogeometric analysis theory and application, share their insights into challenging industrial applications and to discuss the latest developments as well as the directions of future research and development that are required to make isogeometric analysis an established mainstream technology.

This book highlights the mathematical depth and sophistication of techniques used in different areas of robotics. Each chapter is a peer-reviewed version of a paper presented during the 2021 IMA Conference on the Mathematics of Robotics, held online September 8–10, 2021. The conference gave a platform to researchers with fundamental contributions and for academic and to share new ideas. The book illustrates some of the current interest in advanced mathematics and robotics such as algebraic geometry, tropical geometry, monodromy and homotopy continuation methods applied to areas such as kinematics, path planning, swam robotics, dynamics and control. It is hoped that the conference and this publications will stimulate further related mathematical research in robotics.

This book features selected papers from the 5th International Conference on Mathematics and Computing (ICMC 2019), organized by the School of Computer Engineering, Kalinga Institute of Industrial Technology Bhubaneswar, India, on February 6 – 9, 2019. Covering recent advances in the field of mathematics, statistics and scientific computing, the book presents innovative work by leading academics, researchers and experts from industry.

This Festschrift volume is published in honor of Takao Terano on the occasion of his retirement. Takao Terano is a leading expert in the areas of agent-based modelling, knowledge systems, evolutionary computation, and service science.The contributions in this volume reflect the breadth and impact of his work. The volume contains 12 full papers related to Takao Terano's research. They deal with various aspects of artificial intelligence, multi-agent systems, collaborative and social computing, social networks, ubiquitous computing.

Soft computing techniques have reached a significant level of recognition and - ceptance from both the academic and industrial communities. The papers collected in this volume illustrate the depth of the current theoretical research trends and the breadth of the application areas in which soft computing methods are making c- tributions. This volume consists of forty six selected papers presented at the Fourth Inter- tional Conference on Recent Advances in Soft Computing, which was held in N- th th tingham, United Kingdom on 12 and 13 December 2002 at Nottingham Trent University. This volume is organized in five parts. The first four parts address mainly the f- damental and theoretical advances in soft computing, namely Artificial Neural Networks, Evolutionary Computing, Fuzzy Systems and Hybrid Systems. The fifth part of this volume presents papers that deal with practical issues and ind- trial applications of soft computing techniques. We would like to express our sincere gratitude to all the authors who submitted contributions for inclusion. We are also indebted to Janusz Kacprzyk for his - vices related to this volume. We hope you find the volume an interesting refl- tion of current theoretical and application based soft computing research.

This collection of papers is dedicated to the memory of Gaetano Fichera, a great mathematician and also a good friend to the editors. Regrettably it took an unusual amount of time to bring this collection out. This was primarily due to the fact that the main editor who had collected all of the materials, for this volume, P. D. Panagiotopoulos, died unexpectedly during the period when we were editing the manuscript. The other two editors in appreciation of Panagiotopoulos'contribution to this field, believe it is therefore fitting that this collection be dedicated to his memory also. The theme of the collection is centered around the seminal research of G. Fichera on the Signorini problem. Variants on this idea enter in different ways. For example, by bringing in friction the problem is no longer self-adjoint and the minimization formulation is not valid. A large portion of this collection is devoted to survey papers concerning hemivariational methods, with a main point of its application to nonsmooth mechanics. Hemivariational inequali­ ties, which are a generalization of variational inequalities, were pioneered by Panagiotopoulos. There are many applications of this theory to the study of non convex energy functionals occurring in many branches of mechanics. An area of concentration concerns contact problems, in particular, quasistatic and dynamic contact problems with friction and damage. Nonsmooth optimization methods which may be divided into the main groups of subgradient methods and bundle methods are also discussed in this collection.

This volume contains 44 papers presented at the Third Contact Mechanics International Symposium (CMIS 2001) held in Praia da Consola9ao, Peniche (portugal), June 17-21,2001. This Symposium was the direct continuation of the first two CMIS held in Lausanne (1992) and in Carry-Le-Rouet (1994). Other related meetings, in what concerns scientific topics and participants, took place in the nineties at La Grande Motte (1990), Vadstena (1996), Ferrara (1997), Munich (1998) and Grenoble (1999). The Symposium aimed at gathering researchers with interests in a wide range of topics in theoretical, computational and experimental contact mechanics. The call for papers mentioned topics in tribology, mathematical formulations and analysis, numerical methods in non-smooth mechanics, impact problems, instabilities and technological problems. The total number of participants was 102, from Universities and Research Institutes of 19 countries. The Scientific Committee reviewed 102 submitted abstracts, and the final program consisted of 6 main lectures, 43 oral communications and 36 poster presentations (see Appendix A). The papers in this book correspond to almost all the main lectures and oral communications, and they are assembled in 5 chapters: • Dynamics and Impact • Instabilities, Oscillations and Waves • Contact Models, Results and Applications • Mathematical Analysis • Numerical Methods. We thank all the authors for their valuable contributions to this volume. We are indebted to the members of the Scientific Committee for their help in refereeing the submitted abstracts and manuscripts. We also thank the Series editor, Prof. Graham Gladwell, for his assistance in the revision process.

This volume presents state-of-the-art complementarity applications, algorithms, extensions and theory in the form of eighteen papers. These at the International Conference on Com­ invited papers were presented plementarity 99 (ICCP99) held in Madison, Wisconsin during June 9-12, 1999 with support from the National Science Foundation under Grant DMS-9970102. Complementarity is becoming more widely used in a variety of appli­ cation areas. In this volume, there are papers studying the impact of complementarity in such diverse fields as deregulation of electricity mar­ kets, engineering mechanics, optimal control and asset pricing. Further­ more, application of complementarity and optimization ideas to related problems in the burgeoning fields of machine learning and data mining are also covered in a series of three articles. In order to effectively process the complementarity problems that arise in such applications, various algorithmic, theoretical and computational extensions are covered in this volume. Nonsmooth analysis has an im­ portant role to play in this area as can be seen from articles using these tools to develop Newton and path following methods for constrained nonlinear systems and complementarity problems. Convergence issues are covered in the context of active set methods, global algorithms for pseudomonotone variational inequalities, successive convex relaxation and proximal point algorithms. Theoretical contributions to the connectedness of solution sets and constraint qualifications in the growing area of mathematical programs with equilibrium constraints are also presented. A relaxation approach is given for solving such problems. Finally, computational issues related to preprocessing mixed complementarity problems are addressed.

Evolving agents to play games is a promising technology. It can provide entertaining opponents for games like Chess or Checkers, matched to a human opponent as an alternative to the perfect and unbeatable opponents embodied by current artifical intelligences. Evolved agents also permit us to explore the strategy space of mathematical games like Prisoner's Dilemma and Rock-Paper-Scissors. This book summarizes, explores, and extends recent work showing that there are many unsuspected factors that must be controlled in order to create a plausible or useful set of agents for modeling cooperation and conflict, deal making, or other social behaviors. The book also provides a proposal for an agent training protocol that is intended as a step toward being able to train humaniform agents—in other words, agents that plausibly model human behavior.

The historical and epistemological reflection on the applications of mathematical techniques to the Sciences of Nature - physics, biology, chemistry, and geology - today generates attention and interest because of the increasing use of mathematical models in all sciences and their high level of sophistication. The goal of the meeting and the papers collected in this proceedings volume is to give physicists, biologists, mathematicians, and historians of science the opportunity to share information on their work and reflect on the and mathematical models are used in the natural sciences today and in way mathematics the past. The program of the workshop combines the experience of those working on current scientific research in many different fields with the historical analysis of previous results. We hope that some novel interdisciplinary, philosophical, and epistemological considerations will follow from the two aspects of the workshop, the historical and the scientific· This proceedings includes papers presented at the meeting and some of the results of the discussions that took place during the workshop. We wish to express our gratitude to Sergio Monteiro for all his work, which has been essential for the successful publication of these proceedings. We also want to thank the editors of Kluwer AcademidPlenum Publishers for their patience and constant help, and in particular Beth Kuhne and Roberta Klarreich. Our thanks to the fallowing institutions: -Amministrazione Comunale di Arcidosso -Comunita Montana del Monte Amiata ·Center for the History of Physics, UCLA -Centre F.

Lotfi Zadeh introduced the notion of a fuzzy subset of a set in 1965. Ris seminal paper has opened up new insights and applications in a wide range of scientific fields. Azriel Rosenfeld used the notion of a fuzzy subset to put forth cornerstone papers in several areas of mathematics, among other discplines. Rosenfeld is the father of fuzzy abstract algebra. Kuroki is re­ sponsible for much of fuzzy ideal theory of semigroups. Others who worked on fuzzy semigroup theory, such as Xie, are mentioned in the bibliogra­ phy. The purpose of this book is to present an up to date account of fuzzy subsemigroups and fuzzy ideals of a semigroup. We concentrate mainly on theoretical aspects, but we do include applications. The applications are in the areas of fuzzy coding theory, fuzzy finite state machines, and fuzzy languages. An extensive account of fuzzy automata and fuzzy languages is given in [100]. Consequently, we only consider results in these areas that have not appeared in [100] and that pertain to semigroups. In Chapter 1, we review some basic results on fuzzy subsets, semigroups, codes, finite state machines, and languages. The purpose of this chapter is to present basic results that are needed in the remainder of the book. In Chapter 2, we introduce certain fuzzy ideals of a semigroup, namely, fuzzy two-sided ideals, fuzzy bi-ideals, fuzzy interior ideals, fuzzy quasi­ ideals, and fuzzy generalized bi-ideals.

The idea of this book originated in the works presented at the First Latinamerican Conference on Mathematics in Industry and Medicine, held in Buenos Aires, Argentina, from November 27 to December 1, 1995. A variety of topics were discussed at this meeting. A large percentage of the papers focused on Wavelet and Harmonic Analysis. The theory and applications of this topic shown at the Conference were interesting enough to be published. Based on that we selected some works which make the core of this book. Other papers are contributions written by invited experts in the field to complete the presentation. All the works were written after the Conference. The purpose of this book is to present recent results as well as theo­ retical applied aspects of the subject. We have decided not to include a section devoted to the theoretical foundations of wavelet methods for non­ specialists. There are excellent introductions already available, for example, Chapter one in Wavelets in Medicine and Biology, edited by A. Aldroubi and M. Unser, 1996, or some of the references cited in the chapter.

This book focuses mainly on fractional Brownian fields and their extensions. It has been used to teach graduate students at Grenoble and Toulouse's Universities. It is as self-contained as possible and contains numerous exercises, with solutions in an appendix. After a foreword by Stéphane Jaffard, a long first chapter is devoted to classical results from stochastic fields and fractal analysis. A central notion throughout this book is self-similarity, which is dealt with in a second chapter with a particular emphasis on the celebrated Gaussian self-similar fields, called fractional Brownian fields after Mandelbrot and Van Ness's seminal paper. Fundamental properties of fractional Brownian fields are then stated and proved. The second central notion of this book is the so-called local asymptotic self-similarity (in short lass), which is a local version of self-similarity, defined in the third chapter. A lengthy study is devoted to lass fields with finite variance. Among these lass fields, we find both Gaussian fields and non-Gaussian fields, called Lévy fields. The Lévy fields can be viewed as bridges between fractional Brownian fields and stable self-similar fields. A further key issue concerns the identification of fractional parameters. This is the raison d'être of the statistics chapter, where generalized quadratic variations methods are mainly used for estimating fractional parameters. Last but not least, the simulation is addressed in the last chapter. Unlike the previous issues, the simulation of fractional fields is still an area of ongoing research. The algorithms presented in this chapter are efficient but do not claim to close the debate.

ISDA'03 General Chair's Message On behalf of the ISDA'03 organizing committee, I wish to extend a very warm welcome to the conference and Tulsa in August 2003. The conference program committee has organized an exciting and invigorating program comprising pres­ entations from distinguished experts in the field, and important and wide-ranging contributions on state-of-the-art research that provide new insights into'Current Innovations in Intelligent Systems Design and Applications'. ISDA'03 builds on the success of last years. ISDA'02 was held in Atlanta, USA, August 07-08,2002 and attracted participants from over 25 countries. ISDA'03, the Third International Conference on Intelligent Systems Design and Applications, held during August 10-13, 2003, in Tulsa, USA presents a rich and exciting program. The main themes addressed by this conference are: Architectures of intelligent systems Image, speech and signal processing Internet modeling Data mining Business and management applications Control and automation Software agents Knowledge management ISDA'03 is hosted by the College of Arts and Sciences, Oklahoma State Univer­ sity, USA. ISDA'03 is technically sponsored by IEEE Systems Man and Cyber­ netics Society, World Federation on Soft Computing, European Society for Fuzzy Logic and Technology, Springer Verlag- Germany, Center of Excellence in In­ formation Technology and Telecommunications (COEITT) and Oklahoma State University. ISDA'03 received 117 technical paper submissions from over 28 countries, 7 tutorials, 3 special technical sessions and 1 workshop proposal.

The papers in this volume were selected for presentation at the 16th Int- national Meshing Roundtable (IMR), held October 14–17, 2007 in Seattle, Washington, USA. The conference was started by Sandia National Labora- riesin1992asasmallmeetingoforganizationsstrivingtoestablishacommon focus for research and development in the?eld of mesh generation. Now after 16 consecutive years, the International Meshing Roundtable has become r- ognized as an international focal point annually attended by researchers and developers from dozens of countries around the world. The 16th International Meshing Roundtable consists of technical pres- tations from contributed papers, keynote and invited talks, short course p- sentations, and a poster session and competition. The Program Committee would like to express its appreciation to all who participate to make the IMR a successful and enriching experience. The papers in these proceedings were selected from among 41 submissions by the Program Committee. Based on input from peer reviews, the committee selected these papers for their perceived quality, originality, and appropria- ness to the theme of the International Meshing Roundtable. We would like to thank all who submitted papers. We would also like to thank the colleagues who provided reviews of the submitted papers. The names of the reviewers are acknowledged in the following pages. We extend special thanks to Lynn Washburn, Bernadette Watts, and Jacqueline Finley for their time and e?ort to make the 16th IMR another outstanding conference.

The papers in this volume were selected for presentation at the 17th International Meshing Roundtable (IMR), held October 12–15, 2008 in Pittsburgh, Pennsylvania, USA. The conference was started by Sandia National Laboratories in 1992 as a small meeting of organizations striving to establish a common focus for research and dev- opment in the field of mesh generation. Now after 17 consecutive years, the Inter- tional Meshing Roundtable has become recognized as an international focal point annually attended by researchers and developers from dozens of countries around the world. The 17th International Meshing Roundtable consists of technical presentations from contributed papers, research notes, keynote and invited talks, short course pr- entations, and a poster session and competition. The Program Committee would like to express its appreciation to all who participate to make the IMR a successful and enriching experience. The papers in these proceedings were selected from more than 50 paper subm- sions. Based on input from peer reviews, the committee selected these papers for their perceived quality, originality, and appropriateness to the theme of the International Meshing Roundtable. We would like to thank all who submitted papers. We would also like to thank the colleagues who provided reviews of the submitted papers. The names of the reviewers are acknowledged in the following pages. We extend special thanks to Jacqueline Hunter and Bernadette Watts for their time and effort to make the 17th IMR another outstanding conference. August 2008 17th IMR Program Committee Organization

In his paper Theory of Communication [Gab46], D. Gabor proposed the use of a family of functions obtained from one Gaussian by time-and frequency­ shifts. Each of these is well concentrated in time and frequency; together they are meant to constitute a complete collection of building blocks into which more complicated time-depending functions can be decomposed. The application to communication proposed by Gabor was to send the coeffi­ cients of the decomposition into this family of a signal, rather than the signal itself. This remained a proposal-as far as I know there were no seri­ ous attempts to implement it for communication purposes in practice, and in fact, at the critical time-frequency density proposed originally, there is a mathematical obstruction; as was understood later, the family of shifted and modulated Gaussians spans the space of square integrable functions [BBGK71, Per71] (it even has one function to spare [BGZ75]...) but it does not constitute what we now call a frame, leading to numerical insta­ bilities. The Balian-Low theorem (about which the reader can find more in some of the contributions in this book) and its extensions showed that a similar mishap occurs if the Gaussian is replaced by any other function that is'reasonably'smooth and localized. One is thus led naturally to considering a higher time-frequency density.

In the mid-1960's I had the pleasure of attending a talk by Lotfi Zadeh at which he presented some of his basic (and at the time, recent) work on fuzzy sets. Lotfi's algebra of fuzzy subsets of a set struck me as very nice; in fact, as a graduate student in the mid-1950's, I had suggested similar ideas about continuous-truth-valued propositional calculus (inffor'and', sup for'or') to my advisor, but he didn't go for it (and in fact, confused it with the foundations of probability theory), so I ended up writing a thesis in a more conventional area of mathematics (differential algebra). I especially enjoyed Lotfi's discussion of fuzzy convexity; I remember talking to him about possible ways of extending this work, but I didn't pursue this at the time. I have elsewhere told the story of how, when I saw C. L. Chang's 1968 paper on fuzzy topological spaces, I was impelled to try my hand at fuzzi­ fying algebra. This led to my 1971 paper'Fuzzy groups', which became the starting point of an entire literature on fuzzy algebraic structures. In 1974 King-Sun Fu invited me to speak at a U. S. -Japan seminar on Fuzzy Sets and their Applications, which was to be held that summer in Berkeley.

This is the seventh volume in the series'Mathematics in Industrial Prob­ lems.'The motivation for these volumes is to foster interaction between Industry and Mathematics at the'grass roots level;'that is, at the level of specific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufacture of new or improved products. At the same time, these prob­ lems have the potential for mathematical challenge and novelty. To identify such problems, I have visited industries and had discussions with their scientists. Some of the scientists have subsequently presented their problems in the IMA Seminar on Industrial Problems. The book is based on the seminar presentations and on questions raised in subse­ quent discussions. Each chapter is devoted to one of the talks and is self­ contained. The chapters usually provide references to the mathematical literature and a list of open problems which are of interest to the industrial scientists. For some problems a partial solution is indicated briefly. The last chapter of the book contains a short description of solutions to some of the problems raised in previous volumes, as well as references to papers in which such solutions have been published. The speakers in the Seminar on Industrial Problems have given us at the IMA hours of delight and discovery. My thanks to David K. Lambert (Gen­ eral Motors Research and Development), David S.

This is the fourth volume in the series'Mathematics in Industrial Prob­ lems.'The motivation for these volumes is to foster interaction between Industry and Mathematics at the'grass roots'; that is, at the level of spe­ cific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufac­ ture of new or improved products. At the same time, these problems have the potential for mathematical challenge and novelty. To identify such problems, I have visited industries and had discussions with their scientists. Some of the scientists have subsequently presented their problems in the IMA Seminar on Industrial Problems. The book is based on questions raised in the seminar and subsequent discussions. Each chapter is devoted to one of the talks and is self-contained. The chap­ ters usually provide references to the mathematical literature and a list of open problems which are of interest to the industrial scientists. For some problems partial solution is indicated briefly. The last chapter of the book contains a short description of solutions to some of the problems raised in the third volume, as well as references to papers in which such solutions have been published.

This book gives an overview ofthe current state of nonlinear wave mechanics with emphasis on strong discontinuities (shock waves) and localized self­ preserving shapes (solitons) in both elastic and fluid media. The exposition is intentionallyat a detailed mathematical and physical level, our expectation being that the reader will enjoy coming to grips in a concrete manner with advances in this fascinating subject. Historically, modern research in nonlinear wave mechanics began with the famous 1858 piston problem paper of Riemann on shock waves and con­ tinued into the early part of the last century with the work of Hadamard, Rankine, and Hugoniot. After WWII, research into nonlinear propagation of dispersive waves rapidly accelerated with the advent of computers. Works of particular importance in the immediate post-war years include those of von Neumann, Fermi, and Lax. Later, additional contributions were made by Lighthill, Glimm, Strauss, Wendroff, and Bishop. Dispersion alone leads to shock fronts of the propagating waves. That the nonlinearity can com­ pensate for the dispersion, leading to propagation with a stable wave having constant velocity and shape (solitons) came as a surprise. A solitary wave was first discussed by J. Scott Russell in 1845 in'Report of British Asso­ ciations for the Advancement of Science.'He had, while horseback riding, observed a solitary wave travelling along a water channel and followed its unbroken progress for over a mile.

The nature of the physical Universe has been increasingly better understood in recent years, and cosmological concepts have undergone a rapid evolution (see, e.g., [11], [2],or [5]). Although there are alternate theories, it is generally believed that the large-scale relationships and homogeneities that we see can only be explainedby having the universe expand suddenlyin a very early “in?ationary” period. Subsequent evolution of the Universe is described by the Hubble expansion, the observation that the galaxies are?ying away from each other. We can attribute di?erent rates of this expansion to domination of di?erent cosmological processes, beginning with radiation, evolving to matter domination, and, relatively recently, to vacuum domination (the Cosmological Constant term)[4]. We assume throughout that we will be relying as much as possible on observational data, with simulations used only for limited purposes, e.g., the appearance of the Milky Wayfrom nearbyintergalactic viewpoints. The visualization of large-scale astronomical data sets using?xed, non-interactive animations has a long history. Several books and?lms exist, ranging from “Cosmic View: The Universe in Forty Jumps” [3] by Kees Boeke to “Powers of 10” [6,13] by Charles and Ray Eames, and the recent Imax?lm “Cosmic Voyage” [15]. We have added our own contribution [9], “Cosmic Clock,” which is an animation based entirely on the concepts and implementation described in this paper.

Computational mechanics, as a science employed for the numerical model­ ing of processes in nature and engineering, has over the last few decades developed two strands. The first concerns the putting of more and more powerful software packages into computational practice, using increas­ ingly high-performance computers with increasingly large memory. The traditional finite element and finite difference approaches are still preva­ lent. Over the years however, researchers have met with new problems; their solutions on the basis of traditional methods are at best difficult and at worst impossible to obtain. Such problems provided a powerful impetus in the development of the second strand, resulting in the development of es­ sentially new approaches for numerical modeling, for example meshless methods,'molecular'dynamics, neuron networks. The current state of the art formed the basis of many papers presented at the Fifth World Congress on Computational Mechanics, Vienna 2002. It is within the framework of the second strand that this book has been written.

The workshop on Applications and Computation of Orthogonal Polynomials took place March 22-28, 1998 at the Oberwolfach Mathematical Research Institute. It was the first workshop on this topic ever held at Oberwolfach. There were 46 participants from 13 countries, more than half coming from Germany and the United States, and a substantial number from Italy. A total of 23 plenary lectures were presented and 4 short informal talks. Open problems were discussed during an evening session. This volume contains refereed versions of 18 papers presented at, or submitted to, the conference. The theory of orthogonal polynomials, as a branch of classical analysis, is well established. But orthogonal polynomials play also an important role in many areas of scientific computing, such as least squares fitting, numerical integration, and solving linear algebraic systems. Though the basic tenets have their roots in 19th­ century mathematics, the use of modern computers has required the development and study of new algorithms that are accurate and robust. The computational methods and applications represented in this volume, of necessity, are incomplete, yet sufficiently varied to convey an impression of current activities in this area.

This volume consists of papers presented at the Variational Analysis and Aerospace Engineering Workshop II held in Erice, Italy in September 2010 at the International School of Mathematics'Guido Stampacchia'. The workshop provided a platform for aerospace engineers and mathematicians (from universities, research centers and industry) to discuss the advanced problems requiring an extensive application of mathematics. The presentations were dedicated to the most advanced subjects in engineering and, in particular to computational fluid dynamics methods, introduction of new materials, optimization in aerodynamics, structural optimization, space missions, flight mechanics, control theory and optimization, variational methods and applications, etc. This book will capture the interest of researchers from both academia and industry.

After 20 years of pursuing rough set theory and its applications a look on its present state and further prospects is badly needed. The monograph Rough Set Theory and Granular Computing edited by Masahiro Inuiguchi, Shoji Hirano and Shusaku Tsumoto meets this demand. It presents the newest developments in this area and gives fair picture of the state of the art in this domain. Firstly, in the keynote papers by Zdzislaw Pawlak, Andrzej Skowron and Sankar K. Pal the relationship of rough sets with other important methods of data analysis -Bayes theorem, neuro computing and pattern recognitio- is thoroughly examined. Next, several interesting generalizations of the the­ ory and new directions of research are presented. Furthermore application of rough sets in data mining, in particular, rule induction methods based on rough set theory is presented and discussed. Further important issue dis­ cussed in the monograph is rough set based data analysis, including study of decisions making in conflict situations. Last but not least, some recent engi­ neering applications of rough set theory are given. They include a proposal of rough set processor architecture organization for fast implementation of ba­ sic rough set operations and discussion of results concerning advanced image processing for unmanned aerial vehicle. Thus the monograph beside presenting wide spectrum of ongoing research in this area also points out new emerging areas of study and applications, which makes it a valuable source of information to all interested in this do­ main.

This volume covers the fields of measurement and information acqulSltlon. It contains a collection of papers representing the current research trends in these areas. What are those trends? The first one is the enormous growth in the amount of information and the amazing technologies, which make this information available anywhere and anytime. The second one is a substantial development of methods of the information presentation including, to name just a few, multimedia, virtual environment, computer animation. The third one is the all-time boosting demand for improving the quality of decisions made on the base of this information in various applications ranging from engineering to business. Nowadays information acquisition should not only provide more information but also provide it in such a way as to assure effective and efficient processing of this information. And here comes a relatively new methodology of soft computing. Application of soft computing in measurement and information acquisition is considered in this volume.

This volume provides a general overview of discrete- and continuous-time Markov control processes and stochastic games, along with a look at the range of applications of stochastic control and some of its recent theoretical developments. These topics include various aspects of dynamic programming, approximation algorithms, and infinite-dimensional linear programming. In all, the work comprises 18 carefully selected papers written by experts in their respective fields. Optimization, Control, and Applications of Stochastic Systems will be a valuable resource for all practitioners, researchers, and professionals in applied mathematics and operations research who work in the areas of stochastic control, mathematical finance, queueing theory, and inventory systems. It may also serve as a supplemental text for graduate courses in optimal control and dynamic games.

The papers in this volume were selected for presentation at the 15th International Meshing Roundtable, held September 17–20, 2006 in Birmingham, Alabama, U.S.A.. The conference was started by Sandia National Laboratories in 1992 as a small meeting of organizations striving to establish a common focus for research and development in the field of mesh generation. Now after 15 consecutive years, the International Meshing Roundtable has become recognized as an international focal point annually attended by researchers and developers from dozens of countries around the world. The 15th International Meshing Roundtable consists of technical presentations from contributed papers, keynote and invited talks, short course presentations, and a poster session and competition. The Program Committee would like to express its appreciation to all who participate to make the IMR a successful and enriching experience. The papers in these proceedings were selected from among 42 submissions by the Program Committee. Based on input from peer reviews, the committee selected these papers for their perceived quality, originality, and appropriateness to the theme of the International Meshing Roundtable. The Program Committee would like to thank all who submitted papers. We would also like to thank the colleagues who provided reviews of the submitted papers. The names of the reviewers are acknowledged in the following pages. As Program Chair, I would like to extend special thanks to the Program Committee and to the Conference Coordinators for their time and effort to make the 15th IMR another outstanding conference.

This volume is a collection of papers presented at the international conference on Nonlinear Mathematics for Uncertainty and Its Applications (NLMUA2011), held at Beijing University of Technology during the week of September 7--9, 2011. The conference brought together leading researchers and practitioners involved with all aspects of nonlinear mathematics for uncertainty and its applications.Over the last fifty years there have been many attempts in extending the theory of classical probability and statistical models to the generalized one which can cope with problems of inference and decision making when the model-related information is scarce, vague, ambiguous, or incomplete. Such attempts include the study of nonadditive measures and their integrals, imprecise probabilities and random sets, and their applications in information sciences, economics, finance, insurance, engineering, and social sciences.The book presents topics including nonadditive measures and nonlinear integrals, Choquet, Sugeno and other types of integrals, possibility theory, Dempster-Shafer theory, random sets, fuzzy random sets and related statistics, set-valued and fuzzy stochastic processes, imprecise probability theory and related statistical models, fuzzy mathematics, nonlinear functional analysis, information theory, mathematical finance and risk managements, decision making under various types of uncertainty, and others.

This new edition includes three new chapters, 7 through 9, that have very broad, practical applications in engineering and science. In addition, the author's latest research results incorporated into the new textbook demonstrates better performance than the popular METIS software for partitioning graphs, partitioning finite element meshes, and producing fill-reducing orderings for sparse matrices. The new Chapter 8, and its pre-requisite, Chapter 7, present a state-of-the-art algorithm for computing the shortest paths for real-life (large-scale) transportation networks with minimum computational time. This approach has not yet appeared in any existing textbooks and it could open the doors for other transportation engineering applications. Chapter 9 vastly expands the scope of the previous edition by including sensitivity (gradient) computation and MATLAB's built-in function “fmincon” for obtaining the optimum (or best) solution for general engineering problems.

This book focuses on stability analysis and control design approaches for multi-agent systems under network-induced constraints. A hybrid system approach is introduced to address the cooperative control problem of networked multi-agent systems, and several important topics such as asynchronous sampled data cooperative control, hybrid event-triggered cooperative control, and reset-based cooperative control are studied under the hybrid system framework. The special feature of this book is that a hybrid systems approach is proposed for the cooperative control of multi-agent systems, which is beneficial for relaxing the conservativeness of stability analysis and network parameter computation. Interested readers can learn a novel approach to cooperative control of multi-agent systems, and this book can benefit researchers, engineers, and graduate students in the fields of multi-robot cooperation, unmanned aerial vehicle formation, control engineering, etc.

This new edition presents the essential topics in probability and statistics from a rigorous standpoint. Any discipline involving randomness, including medicine, engineering, and any area of scientific research, must have a way of analyzing or even predicting the outcomes of an experiment. The authors focus on the tools for doing so in a thorough, yet introductory way. After providing an overview of the basics of probability, the authors cover essential topics such as confidence intervals, hypothesis testing, and linear regression. These subjects are presented in a one semester format, suitable for engineers, scientists, and STEM students with a solid understanding of calculus. There are problems and exercises included in each chapter allowing readers to practice the applications of the concepts.

This is a personal story about being involved in the study of nonlinear phenomena for more than half a century. The focus is on the development of ideas and the resulting knowledge. This is the visible part of research, but much is usually hidden. The author describes how the ideas were generated and how an “invisible college” of friends and colleagues has emerged. The presentation is spiced by thoughts about the beauty of science and philosophical considerations on the complex world, where nonlinear interactions play an important role. The book is in some sense a biography but not so much about the personal life of the author – it is about science and its actors. Based on the author's experience in many European research centres and science policy institutions, it reflects on the development of knowledge in nonlinear dynamics as well as science policy actions over the second half of the 20th century and the first quarter of the 21st century. Graduates and postgraduates interested in the progress of research will find the book particularly engaging.

This book constitutes the refereed proceedings of the 9th Dortmund Fuzzy Days, held in Dortmund, Germany, 2006. The Fuzzy Days conference has established itself as an international forum for the discussion of new results in the field of Computational Intelligence. All the papers had to undergo a thorough review guaranteeing a solid quality of the programme. The papers are devoted to foundational and practical issues in fuzzy systems, neural networks, evolutionary algorithms, and machine learning and thus cover the whole range of computational intelligence.

This book tells the story of the probability integral, the approaches to analyzing it throughout history, and the many areas of science where it arises. The so-called probability integral, the integral over the real line of a Gaussian function, occurs ubiquitously in mathematics, physics, engineering and probability theory. Stubbornly resistant to the undergraduate toolkit for handling integrals, calculating its value and investigating its properties occupied such mathematical luminaries as De Moivre, Laplace, Poisson, and Liouville. This book introduces the probability integral, puts it into a historical context, and describes the different approaches throughout history to evaluate and analyze it. The author also takes entertaining diversions into areas of math, science, and engineering where the probability integral arises: as well as being indispensable to probability theory and statistics, it also shows up naturally in thermodynamics and signal processing. Designed to be accessible to anyone at the undergraduate level and above, this book will appeal to anyone interested in integration techniques, as well as historians of math, science, and statistics.

This book examines the most fundamental parts of convex analysis and its applications to optimization and location problems. Accessible techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and to build a theory of generalized differentiation for convex functions and sets in finite dimensions. The book serves as a bridge for the readers who have just started using convex analysis to reach deeper topics in the field. Detailed proofs are presented for most of the results in the book and also included are many figures and exercises for better understanding the material. Applications provided include both the classical topics of convex optimization and important problems of modern convex optimization, convex geometry, and facility location.

This book provides a complete framework for the fundamental concepts and results of texture spaces and its applications. The principal aim is to present a comprehensive arguments due to connections among the textures, fuzzy sets and rough sets. In this context, direlations, fuzzy direlations and fuzzy relations constitute a bridge for the remarkable observations on rough set theory. In a more general setting, the approximation operators are also inspected for fuzzy rough set models with two domains of discourse. Since the book is self-contained and reader-friendly, the respected researchers may utilize this source for further investigations of the necessary results for their studies on rough set theory using textures. Therefore, prospective readers are not only mathematicians who interest in purely mathematical theories related to textures, but also engineers of information sciences who need more information for their interdisciplinary studies with respect to rough sets and fuzzy sets.

This book develops the core proposition that systems theory is an attempt to construct an “exact and scientific metaphysics,” a system of general ideas central to science that can be expressed mathematically. Collectively, these ideas would constitute a nonreductionist “theory of everything” unlike what is being sought in physics. Inherently transdisciplinary, systems theory offers ideas and methods that are relevant to all of the sciences and also to professional fields such as systems engineering, public policy, business, and social work. To demonstrate the generality and importance of the systems project, the book structures its content in three parts: Essay, Notes, and Commentary. The Essay section is a short distillation of systems ideas that illuminate the problems that many types of systems face. Commentary explains systems thinking, its value, and its relation to mainstream scientific knowledge. It shows how systems ideas revise our understanding of science and how theyimpact our views on religion, politics, and history. Finally, Notes contains all the mathematics in the book, as well as scientific, philosophical, and poetic content that is accessible to readers without a strong mathematical background. Elements and Relations is intended for researchers and students in the systems (complexity) field as well as related fields of social science modeling, systems biology and ecology, and cognitive science. It can be used as a textbook in systems courses at the undergraduate or graduate level and for STEM education. As much of the book does not require a background in mathematics, it is also suitable for general readers in the natural and social sciences as well as in the humanities, especially philosophy.

This textbook offers a comprehensive coverage of the fundamentals of calculus, linear algebra and analytic geometry. Intended for bachelor's students in science, engineering, architecture, economics, the presentation is self-contained, and supported by numerous graphs, to facilitate visualization and also to stimulate readers'intuition. The proofs of the theorems are rigorous, yet presented in straightforward and comprehensive way. With a good balance between algebra, geometry and analysis, this book guides readers to apply the theory to solve differential equations. Many problems and solved exercises are included. Students are expected to gain a solid background and a versatile attitude towards calculus, algebra and geometry, which can be later used to acquire new skills in more advanced scientific disciplines, such as bioinformatics, process engineering, and finance. At the same time, instructors are provided with extensive information and inspiration for the preparationof their own courses.

This book offers the first comprehensive presentation of measure-valued solutions for nonlinear deterministic and stochastic evolution equations on infinite dimensional Banach spaces. Unlike traditional solutions, measure-valued solutions allow for a much broader class of abstract evolution equations to be addressed, providing a broader approach.The book presents extensive results on the existence of measure-valued solutions for differential equations that have no solutions in the usual sense. It covers a range of topics, including evolution equations with continuous/discontinuous vector fields, neutral evolution equations subject to vector measures as impulsive forces, stochastic evolution equations, and optimal control of evolution equations. The optimal control problems considered cover the existence of solutions, necessary conditions of optimality, and more, significantly complementing the existing literature.This book will be of great interest to researchers in functional analysis, partial differential equations, dynamic systems and their optimal control, and their applications, advancing previous research and providing a foundation for further exploration of the field.

This book presents the modeling and scaling of physical problems, which result in normalized perturbation equations. This is followed by solving perturbation problems and evaluating the results. The author refines perturbation methods into simple, understandable elements and avoids unnecessary theorems and proofs. In addition, the results are consolidated and interpreted, and the presented examples are succinct to illustrate the essential techniques. This book is ideal and beneficial for practicing scientists and engineers who need to understand and apply perturbation methods to difficult problems with applications in mathematics, engineering, and biology. Discussions on new perspectives, simpler presentations on convergence, and the expansion of integrals are included.

The first edition of the Encyclopedia of Complexity and Systems Science (ECSS, 2009) presented a comprehensive overview of granular computing (GrC) broadly divided into several categories: Granular computing from rough set theory, Granular Computing in Database Theory, Granular Computing in Social Networks, Granular Computing and Fuzzy Set Theory, Grid/Cloud Computing, as well as general issues in granular computing. In 2011, the formal theory of GrC was established, providing an adequate infrastructure to support revolutionary new approaches to computer/data science, including the challenges presented by so-called big data. For this volume of ECSS, Second Edition, many entries have been updated to capture these new developments, together with new chapters on such topics as data clustering, outliers in data mining, qualitative fuzzy sets, and information flow analysis for security applications. Granulations can be seen as a natural and ancient methodology deeply rooted in the human mind. Many daily'things'are routinely granulated into sub'things': The topography of earth is granulated into hills, plateaus, etc., space and time are granulated into infinitesimal granules, and a circle is granulated into polygons of infinitesimal sides. Such granules led to the invention of calculus, topology and non-standard analysis. Formalization of general granulation was difficult but, as shown in this volume, great progress has been made in combing discrete and continuous mathematics under one roof for a broad range of applications in data science.

This study guide is designed for students taking a Calculus III course. The textbook includes examples, questions, and practice problems that will help students to review and sharpen their knowledge of the subject and enhance their performance in the classroom. The material covered in the book includes linear algebra and analytical geometry; lines, surfaces, and vector functions in three-dimensional coordinate systems; multiple-variable functions; multiple integrals and their applications; line integrals and their applications. Offering detailed solutions, multiple methods for solving problems, and clear explanations of concepts, this hands-on guide will improve students'problem-solving skills and foster a solid understanding of calculus, which will benefit them in all of their calculus-based courses.

This book provides fifteen computational projects aimed at numerically solving problems from a broad range of applications including Fluid Mechanics, Chemistry, Elasticity, Thermal Science, Computer Aided Design, Signal and Image Processing. For each project the reader is guided through the typical steps of scientific computing from physical and mathematical description of the problem to numerical formulation and programming and finally to critical discussion of numerical results. Considerable emphasis is placed on practical issues of computational methods. The last section of each project contains the solutions to all proposed exercises and guides the reader in using the MATLAB scripts. The mathematical framework provides a basic foundation in numerical analysis of partial differential equations and main discretization techniques, such as finite differences, finite elements, spectral methods and wavelets. The book is primarily intended as a graduate-level textin applied mathematics, but it may also be used by students in engineering or physical sciences. It will also be a useful reference for researchers and practicing engineers. The second edition builds upon its earlier material (revised and updated) with three all-new chapters intended to reinforce the presentation of mathematical aspects on numerical methods: Fourier approximation, high-order finite difference methods, and basic tools for numerical optimization. Corresponding new applications and programs concern spectral Fourier methods to solve ordinary differential equations, finite difference methods up to sixth-order to solve boundary value problems and, finally, optimization strategies to fit parameters of an epidemiological model.

This book explores boundary value problems for Riemann-Liouville fractional dynamic equations on arbitrary time scales as well as the shifting problem on the whole time scale. The author includes an introductory overview of fractional dynamic calculus on time scales. The book also introduces the Laplace transform on arbitrary time scales, including the bilateral Laplace transform, the Laplace transform of power series, and a deduction of an inverse formula. The author then discusses the generalized convolutions of functions on arbitrary time scales and the shifting problem for existence of solutions. The book moves on to cover boundary value problems and initial boundary value problems for some classes Riemann-Liouville fractional dynamic equations.

This book introduces undergraduate students of engineering and science to applied mathematics essential to the study of many problems. Topics are differential equations, power series, Laplace transforms, matrices and determinants, vector analysis, partial differential equations, complex variables, and numerical methods. Approximately, 160 examples and 1000 homework problems aid students in their study. This book presents mathematical topics using derivations rather than theorems and proofs. This textbook is uniquely qualified to apply mathematics to physical applications (spring-mass systems, electrical circuits, conduction, diffusion, etc.), in a manner that is efficient and understandable. This book is written to support a mathematics course after differential equations, to permit several topics to be covered in one semester, and to make the material comprehensible to undergraduates. An Instructor Solutions Manual, and also a Student Solutions Manual that provides solutions to select problems, is available.^