In diamond alluvial deposits, the information about the spatial distribution of stone size is of crucial importance for the quantitative characterisation of the different areas of the deposit. In fact, the value of the diamond reserves depends strongly on the distribution of stone sizes: between two areas with the same grade, the most valuable is the one with larger stones. The geological genesis of the mineralization, related with the transport and deposition of stones in trapsites, can create separated spatial areas, corresponding to different stone size. To characterise these distinct areas, the non smooth transitions between them should be accounted for, in the estimation of internal properties. An extended version of zonal control of geostatistical estimation (Soares et ai, 1995) proposed in this paper, aims to characterising the classes of size histogram for each geological unit, avoiding the smooth effect. For this purpose the morphology of each geological unit is obtained by using two distinct criteria: i) first, the points of each unit are classified according to the local and global probabilities of belonging to each unit (Soares, 1992); ii) in a second classification, the optimization technique of Simulated Annealing is used to rearrange the pre-classified points in order to impose, in the final morphological maps, the spatial variability of experimental samples (Goovaerts, 1994). A case study of a diamond alluvial deposit with two geological units with distinct stone size histograms is presented.

This book contains a systematic study of ecological communities of two or three interacting populations. Starting from the Lotka-Volterra system, various regulating factors are considered, such as rates of birth and death, predation and competition. The different factors can have a stabilizing or a destabilizing effect on the community, and their interplay leads to increasingly complicated behavior. Studying and understanding this path to greater dynamical complexity of ecological systems constitutes the backbone of this book. On the mathematical side, the tool of choice is the qualitative theory of dynamical systems - most importantly bifurcation theory, which describes the dependence of a system on the parameters. This approach allows one to find general patterns of behavior that are expected to be observed in ecological models. Of special interest is the reaction of a given model to disturbances of its present state, as well as to changes in the external conditions. This leads to the general idea of "dangerous boundaries" in the state and parameter space of an ecological system. The study of these boundaries allows one to analyze and predict qualitative and often sudden changes of the dynamics - a much-needed tool, given the increasing antropogenic load on the biosphere.As a spin-off from this approach, the book can be used as a guided tour of bifurcation theory from the viewpoint of application. The interested reader will find a wealth of intriguing examples of how known bifurcations occur in applications. The book can in fact be seen as bridging the gap between mathematical biology and bifurcation theory.

A beautiful interplay between probability theory (Markov processes, martingale theory) on the one hand and operator and spectral theory on the other yields a uniform treatment of several kinds of Hamiltonians such as the Laplace operator, relativistic Hamiltonian, Laplace-Beltrami operator, and generators of Ornstein-Uhlenbeck processes. For such operators regular and singular perturbations of order zero and their spectral properties are investigated.
A complete treatment of the Feynman-Kac formula is given. The theory is applied to such topics as compactness or trace class properties of differences of Feynman-Kac semigroups, preservation of absolutely continuous and/or essential spectra and completeness of scattering systems.
The unified approach provides a new viewpoint of and a deeper insight into the subject. The book is aimed at advanced students and researchers in mathematical physics and mathematics with an interest in quantum physics, scattering theory, heat equation, operator theory, probability theory and spectral theory.

This monograph is the first to present the recently discovered renormalization techniques for the Schr dinger and Dirac equations, providing a mathematically rigorous, yet simple and clear introduction to the subject. It develops field-theoretic techniques such as Feynman graph expansions and renormalization, taking pains to make all proofs as simple as possible by using generating function techniques throughout. Renormalization is performed by using an exact renormalization group differential equation, a technique that provides simple but complete proofs of the theorems.

The Complex Variable Boundary Element Method (CVBEM) has an important role to play in a number of technical engineering situations and can be a tremendous help to scholars and practitioners preoccupied with solving problems in areas such as heat transport, structural mechanics and river hydraulics. As well as describing the extremely useful applications of this method, the authors explain the mathematical background to the CVBEM, which is vital to understanding the subject as a whole. Advances in the Complex Variable Boundary Element Method is the most comprehensive of books on this subject, bringing together ten years of work and boasting the latest news in CVBEM technology. It will be of particular interest to those concerned with solving technical engineering problems - scientists, graduate students, computer programmers and those working in industry may all find the book helpful.

There are many good AI books. Usually they consecrate at most one or two chapters to the imprecision knowledge processing. To our knowledge this is among the few books to be entirely dedicated to the treatment of knowledge imperfection when bui- ing intelligent systems. We consider that an entire book should be focused on this important aspect of knowledge processing. The expected audience for this book - cludes undergraduate students in computer science, IT&C, mathematics, business, medicine, etc. , graduates, specialists and researchers in these fields. The subjects treated in the book include expert systems, knowledge representation, reasoning under knowledge Imperfection (Probability Theory, Possibility Theory, Belief Theory, and Approximate Reasoning). Most of the examples discussed in details throughout the book are from the medical domain. Each chapter ends with a set of carefully pe- gogically chosen exercises, which complete solution provided. Their understanding will trigger the comprehension of the theoretical notions, concepts and results. Chapter 1 is dedicated to the review of expert systems. Hence are briefly discussed production rules, structure of ES, reasoning in an ES, and conflict resolution. Chapter 2 treats knowledge representation. That includes the study of the differences between data, information and knowledge, logical systems with focus on predicate calculus, inference rules in classical logic, semantic nets and frames.

The Centre de recherches mathCmatiques (CRM) was created in 1968 by the Universite de Montreal to promote research in the mathematical sci- ences. It is now a national institute that hosts several groups, holds special theme years, summer schools, workshops, postdoctoral program. The focus of its scientific activities ranges from pure to applied mathematics, and includes satistics, theoretical computer science, mathematical methods in biology and life sciences, and mathematical and theoretical physics. The CRM also promotes collaboration between mathematicians and industry. It is subsidized by the Natural Sciences and Engineering Research Council of Canada, the Fonds FCAR od the Province of Quebec, the Canadian Institute for Advanced Research and has private endowments. Current ac- tivities, fellowships, and annual reports can be found on the CRM web page at http://www . CRM. UMontreal. CAl. The CRM Series in Mathematical Physics will publish monographs, lec- ture notes, and proceedings base on research pursued and events held at the Centre de recherches mathematiques. Yvan Saint-Aubin Montreal Preface The subject of this three-week school was the explicit integration, that is, analytical as opposed to numerical, of all kinds of nonlinear differential equations (ordinary differential, partial differential, finite difference). The result of such integration is ideally the "general solution," but there are numerous physical systems for which only a particular solution is accessible, for instance the solitary wave of the equation of Kuramoto and Sivashinsky in turbulence.

The 1996 Carg se Summer Institute on Frontiers in Particle Physics was organized by the Universite Pierre et Marie Curie, Paris (M. Levy), the Ecole Nonnale SupCrieure, Paris (J. lliopoulos), the Katholieke Universiteit Leuven (R. Gastmans), and the Universite Catholique de Louvain (J.-M. Gerard), which, since 1975, have joined their efforts and worked in common. It was the twelfth Sunnner Institute on High Energy Physics organized jointly at Carg se by three of these universities. The Standard Model for fundamental interactions is constructed on two essential ingredients: the gauge symmetry and the mass generation mechanism. Now that the gauge theory aspect has been finnly established, the new challenge for the young researchers in elementary particle physics is the understanding of the origin of the masses. The standard Higgs mechanism is believed to be responsible for generating the masses of ALL fundamental particles. Professor D. Treille discussed the prospects for Higgs boson search and described the experimental determinations of the gauge boson masses. The influence of the top quark mass on electroweak processes has been emphasized by Professor J.L. Rosner, while Professor M. Neubert introduced the heavy-quark effective theory which allows you to get rid of heavy-quark masses. The theoretical determinations of the light quark masses have been critically analyzed by Professor H. Leutwyler. Professor A. Pich presented the various experimental tests on lepton universality and Professor R.L. MBssbauer reviewed our present knowledge on the neutrino masses."

This volume is a textbook for a year-long graduate level course in All research universities have applied mathematics for scientists and engineers. such a course, which could be taught in different departments, such as mathematics, physics, or engineering. I volunteered to teach this course when I realized that my own research students did not learn much in this course at my university. Then I learned that the available textbooks were too introduc tory. While teaching this course without an assigned text, I wrote up my lecture notes and gave them to the students. This textbook is a result of that endeavor. When I took this course many, many, years ago, the primary references were the two volumes of P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953). The present text returns the contents to a similar level, although the syllabus is quite different than given in this venerable pair of books."

This guide provides a comprehensive overview of High Performance Computing (HPC) to equip students with a full skill set including cluster setup, network selection, and a background of supercomputing competitions. It covers the system, architecture, evaluating approaches, and other practical supercomputing techniques. As the world's largest supercomputing hackathon, the ASC Student Supercomputer Challenge has attracted a growing number of new talent to supercomputing and has greatly promoted communications in the global HPC community. Enclosed in this book, readers will also find how to analyze and optimize supercomputing systems and applications in real science and engineering cases.

Nonlinear Systems and Methods For Mechanical, Electrical and Biosystems presents topics observed at the 3rd Conference on Nonlinear Science and Complexity(NSC), focusing on energy transfer and synchronization in hybrid nonlinear systems. The studies focus on fundamental theories and principles, analytical and symbolic approaches, computational techniques in nonlinear physical science and mathematics. Broken into three parts, the text covers: Parametrical excited pendulum, nonlinear dynamics in hybrid systems, dynamical system synchronization and (N+1) body dynamics as well as new views different from the existing results in nonlinear dynamics, mathematical methods for dynamical systems including conservation laws, dynamical symmetry in nonlinear differential equations and invex energies and nonlinear phenomena in physical problems such as solutions, complex flows, chemical kinetics, Toda lattices and parallel manipulator.

This book is useful to scholars, researchers and advanced technical members of industrial laboratory facilities developing new tools and products.

Complexity science has been a source of new insight in physical and social systems and has demonstrated that unpredictability and surprise are fundamental aspects of the world around us. This book is the outcome of a discussion meeting of leading scholars and critical thinkers with expertise in complex systems sciences and leaders from a variety of organizations, sponsored by the Prigogine Center at The University of Texas at Austin and the Plexus Institute, to explore strategies for understanding uncertainty and surprise. Besides contributions to the conference, it includes a key digest by the editors as well as a commentary by the late nobel laureate Ilya Prigogine, "Surprises in half of a century." The book is intended for researchers and scientists in complexity science, as well as for a broad interdisciplinary audience of both practitioners and scholars. It will well serve those interested in the research issues and in the application of complexity science to physical and social systems.

* Provides an elegant introduction to the geometric concepts that are important to applications in robotics

* Includes significant state-of-the art material that reflects important advances, connecting robotics back to mathematical fundamentals in group theory and geometry

* An invaluable reference that serves a wide audience of grad students and researchers in mechanical engineering, computer science, and applied mathematics

This book concentrates on the topic of evaluation of Jacobians in some specific linear as well as nonlinear matrix transformations, in the real and complex cases, which are widely applied in the statistical, physical, engineering, biological and social sciences. It aims to develop some techniques systematically so that anyone with a little exposure to multivariable calculus can easily follow the steps and understand the various methods by which the Jacobians in complicated matrix transformations are evaluated. The material is developed slowly, with lots of worked examples, aimed at self-study. Some exercises are also given, at the end of each section.The book is a valuable reference for statisticians, engineers, physicists, econometricians, applied mathematicians and people working in many other areas. It can be used for a one-semester graduate level course on Jacobians and functions of matrix argument.

New ideas on the mathematical foundations of quantum mechanics, related to the theory of quantum measurement, as well as the emergence of quantum optics, quantum electronics and optical communications have shown that the statistical structure of quantum mechanics deserves special investigation. In the meantime it has become a mature subject. In this book, the author, himself a leading researcher in this field, surveys the basic principles and results of the theory, concentrating on mathematically precise formulations. Special attention is given to the measurement dynamics. The presentation is pragmatic, concentrating on the ideas and their motivation. For detailed proofs, the readers, researchers and graduate students, are referred to the extensively documented literature.

ECMI has a brand name in Industrial Mathematics and organises successful biannual conferences. This time, the conference on Industrial Mathematics held in Eindhoven in June 2004 Mathematics focused on Aerospace, Electronic Industry, Chemical Technology, Life Sciences, Materials, Geophysics, Financial Mathematics and Water flow. The majority of the invited talks on these topics can be found in these proceedings. Apart from these lectures, a large number of contributed papers and minisymposium papers are included here. They give an interesting (and impressive) overview of the important place mathematics has achieved in solving all kinds of problems met in industry, and commerce in particular.

Presenting the latest findings in topics from across the mathematical spectrum, this volume includes results in pure mathematics along with a range of new advances and novel applications to other fields such as probability, statistics, biology, and computer science. All contributions feature authors who attended the Association for Women in Mathematics Research Symposium in 2015: this conference, the third in a series of biennial conferences organized by the Association, attracted over 330 participants and showcased the research of women mathematicians from academia, industry, and government.

This collection of original articles and surveys addresses the recent advances in linear and nonlinear aspects of the theory of partial differential equations. The key topics include operators as "sums of squares" of real and complex vector fields, nonlinear evolution equations, local solvability, and hyperbolic questions.

This book presents an authoritative collection of contributions by researchers from 16 different countries (Austria, Chile, Georgia, Germany, Mexico, Norway, P.R. of China, Poland, North Macedonia, Romania, Russia, Spain, Turkey, Ukraine, the United Kingdom and United States) that report on recent developments and new directions in advanced control systems, together with new theoretical findings, industrial applications and case studies on complex engineering systems. This book is dedicated to Professor Vsevolod Mykhailovych Kuntsevich, an Academician of the National Academy of Sciences of Ukraine, and President of the National Committee of the Ukrainian Association on Automatic Control, in recognition of his pioneering works, his great scientific and scholarly achievements, and his years of service to many scientific and professional communities, notably those involved in automation, cybernetics, control, management and, more specifically, the fundamentals and applications of tools and techniques for dealing with uncertain information, robustness, non-linearity, extremal systems, discrete control systems, adaptive control systems and others. Covering essential theories, methods and new challenges in control systems design, the book is not only a timely reference guide but also a source of new ideas and inspirations for graduate students and researchers alike. Its 15 chapters are grouped into four sections: (a) fundamental theoretical issues in complex engineering systems, (b) artificial intelligence and soft computing for control and decision-making systems, (c) advanced control techniques for industrial and collaborative automation, and (d) modern applications for management and information processing in complex systems. All chapters are intended to provide an easy-to-follow introduction to the topics addressed, including the most relevant references. At the same time, they reflect various aspects of the latest research work being conducted around the world and, therefore, provide information on the state of the art.

"Creative Environments" is a follow-up on the book Creative Space in the same series and by the same authors, serving this time as editors of a broader book on computational intelligence and knowledge engineering tools for supporting knowledge creation. This book contains four parts. The first part presents a further development of models of knowledge creation presented already in Creative Space, in particular the Triple Helix of normal academic knowledge creation and a new, integrated model of normal academic and organizational knowledge creation, called Nanatsudaki (seven waterfalls) Model. The second part presents computational intelligence tools for knowledge acquisition by machine learning and data mining, for debating, brainstorming, for roadmapping and for integrated support of academic creativity. The third part presents the use of statistics for creativity support, virtual laboratories, gaming and role playing for creativity support, methods of knowledge representation and multiple criteria aggregation, distance and electronic learning. The last part addresses knowledge management and philosophical issues and contains chapters: on management of technology and knowledge management for academic R and D; on knowledge management and creative holism or systems thinking in the knowledge age; on technology and change or the role of technology in knowledge civilisation; on the emergence of complex concepts in science; and the final chapter on summary and conclusions, including a proposal of an integrated episteme of constructive evolutionary objectivism, necessary for the knowledge civilization age.

na broad sense Design Science is the grammar of a language of images Irather than of words. Modern communication techniques enable us to transmit and reconstitute images without needing to know a specific verbal sequence language such as the Morse code or Hungarian. International traffic signs use international image symbols which are not specific to any particular verbal language. An image language differs from a verbal one in that the latter uses a linear string of symbols, whereas the former is multi dimensional. Architectural renderings commonly show projections onto three mutual ly perpendicular planes, or consist of cross sections at different altitudes capa ble of being stacked and representing different floor plans. Such renderings make it difficult to imagine buildings comprising ramps and other features which disguise the separation between floors, and consequently limit the cre ative process of the architect. Analogously, we tend to analyze natural struc tures as if nature had used similar stacked renderings, rather than, for instance, a system of packed spheres, with the result that we fail to perceive the system of organization determining the form of such structures. Perception is a complex process. Our senses record; they are analogous to audio or video devices. We cannot, however, claim that such devices perceive."

Fuzzy Logic has gained increasing acceptance as a way to deal with complexity and uncertainty in many areas of science and engineering. This book is the first to address its practical applications to chemical systems. Ten distinguished authors discuss the role of fuzzy logic in the characterization of a variety of chemical concepts, including chirality, quantum systems, molecular engineering and design, and hierarchical classification methods. Fuzzy Logic in Chemistry will appeal to both students and professionals who are seeking to learn more about theory and applications in an area of growing importance to the physical sciences.
Key Features
* The first book on the applications of fuzzy logic in chemistry
* Covers a topic relevant to many disciplines, including molecular design
* Discusses applications of fuzzy logic to the physical sciences, a rapidly growing area
* Features chapters from highly distinguished authors in the physical sciences

A clear, up-to-date presentation of the principles of flow in open channels

A fundamental knowledge of flow in open channels is essential for the planning and design of systems to manage water resources. Open-Channel Flow conveys this knowledge through the use of practical problems that can be solved either analytically or by simple numerical methods that do not require the use of computer software.

This completely up-to-date text includes several features not found in any other book on the subject. It derives one- dimensional equations of motion using both a simplified approach and a rigorous approach, and it explains the distinction between the momentum and mechanical energy equations. The author places great emphasis on identifying the types and locations of the control sections that are essential in analyzing flow profiles, and he includes a section on recently recognized nonunique flow profiles.

Offering numerous worked examples that are helpful in understanding the basic principles and their practical applications, this book:

• Presents the latest computational methods for profiling spatially varied and unsteady flow
• Includes end-of-section exercises that measure and build understanding
• Fully explains governing equations in algebraic and differential form
• Brings sluice-gate analysis completely up to date
• Covers artificial channel controls such as weirs, spillways, and gates, and special topics such as transitions in supercritical flow and flow through culverts

Written in metric units throughout, this excellent learning tool for senior- and graduate-level students in civil and environmental engineering programs is also a useful reference for practicing civil and environmental engineers.

Computational Electromagnetics is a young and growing discipline, expanding as a result of the steadily increasing demand for software for the design and analysis of electrical devices. This book introduces three of the most popular numerical methods for simulating electromagnetic fields: the finite difference method, the finite element method and the method of moments. In particular it focuses on how these methods are used to obtain valid approximations to the solutions of Maxwell's equations, using, for example, "staggered grids" and "edge elements." The main goal of the book is to make the reader aware of different sources of errors in numerical computations, and also to provide the tools for assessing the accuracy of numerical methods and their solutions. To reach this goal, convergence analysis, extrapolation, von Neumann stability analysis, and dispersion analysis are introduced and used frequently throughout the book. Another major goal of the book is to provide students with enough practical understanding of the methods so they are able to write simple programs on their own. To achieve this, the book contains several MATLAB programs and detailed description of practical issues such as assembly of finite element matrices and handling of unstructured meshes. Finally, the book aims at making the students well-aware of the strengths and weaknesses of the different methods, so they can decide which method is best for each problem.

In thissecond edition, extensive computer projects are added as well as new material throughout.

Reviews of previous edition:

"The well-written monograph is devoted to students at the undergraduate level, but is also useful for practising engineers." (Zentralblatt MATH, 2007)"

During the last two decades the boundary element method has experienced a remarkable evolution. Contemporary concepts and techniques leading to the advancements of capabilities and understanding of the mathematical and computational aspects of the method in mechanics are presented. The special emphasis on theoretical and numerical issues, as well as new formulations and approaches for special and important fields of solid and fluid mechanics are considered. Several important and new mathematical aspects are presented: singularity and hypersingular formulations, regularity, errors and error estimators, adaptive methods, Galerkin formulations, coupling of BEM-FEM and non-deterministic (stochastic and fuzzy) BEM formulations. Novel developments and applications of the boundary element method in various fields of mechanics of solids and fluids are considered: heat conduction, diffusion and radiation, non-linear problems, dynamics and time-depending problems, fracture mechanics, thermoelasticity and poroelasticity, aerodynamics and acoustics, contact problems, biomechanics, optimization and sensitivity analysis problems, ill posed and inverse problems, and identification problems.