This clearly written and enlightening textbook provides a concise, introductory guide to the key mathematical concepts and techniques used by computer scientists. Topics and features: ideal for self-study, offering many pedagogical features such as chapter-opening key topics, chapter introductions and summaries, review questions, and a glossary; places our current state of knowledge within the context of the contributions made by early civilizations, such as the ancient Babylonians, Egyptians and Greeks; examines the building blocks of mathematics, including sets, relations and functions; presents an introduction to logic, formal methods and software engineering; explains the fundamentals of number theory, and its application in cryptography; describes the basics of coding theory, language theory, and graph theory; discusses the concept of computability and decideability; includes concise coverage of calculus, probability and statistics, matrices, complex numbers and quaternions.

This volume contains papers presented at the meeting Deformation Theory, Symplectic Geometry and Applications, held in Ascona, June 17-21, 1996. The contents touch upon many frontier domains of modern mathematics, mathematical physics and theoretical physics and include authoritative, state-of-the-art contributions by leading scientists. New and important developments in the fields of symplectic geometry, deformation quantization, noncommutative geometry (NCG) and Lie theory are presented. Among the subjects treated are: quantization of general Poisson manifolds; new deformations needed for the quantization of Nambu mechanics; quantization of intersection cardinalities; quantum shuffles; new types of quantum groups and applications; quantum cohomology; strong homotopy Lie algebras; finite- and infinite-dimensional Lie groups; and 2D field theories and applications of NCG to gravity coupled with the standard model. Audience: This book will be of interest to researchers and post-graduate students of mathematical physics, global analysis, analysis on manifolds, topological groups, nonassociative rings and algebras, and Lie algebras.

1 Industrial Mathematics in Linz The Johannes-Kepler-University is situated in Linz, which is the industrial center of Austria. This location provides unique opportunities for cooperation between in dustry and a university which derives its name from one of the most eminent ap plied mathematicians of all times. The mathematics department was founded in the late Sixties, the first students graduated in 1974. In these boom times, they had no problems of finding jobs in industry. However, their employers were then more interested in their general training than in their specific mathematical skills. To change this, the department decided to actively seek cooperation with industry in what we called "problem seminars," where students were trained to solve (under guidance) real-world problems from local industry. Groundwork was already laid by a curriculum with special emphasis on numerical analysis, statistics, and optim ization. This work in problem seminars usually evolved into diploma theses. Inci dentally, in all projects presented here, students were involved at some stages. While the original motivation for cooperation with industry was educational, it turned out that most problems presented to us also led to interesting mathematical problems, so that nowadays our motivation is as much scientific as educational. When cooperating with industry, one cannot expect that the problems to be solved fall into one's special mathematical interest.

Leyton's Process Grammar has been applied by scientists and engineers in many disciplines including medical diagnosis, geology, computer-aided design, meteorology, biological anatomy, neuroscience, chemical engineering, etc. This book demonstrates the following:

The Process Grammar invents several entirely new concepts in biological morphology and manufacturing design, and shows that these concepts are fundamentally important.

The Process Grammar has process-inference rules that give, to morphological transitions, powerful new "causal explanations."

Remarkably, the book gives a profound "unification" of "biological morphology" and "vehicle design."

The book invents over 30 new CAD operations that realize fundamentally important functions of a product.

A crucial fact is that the Process Grammar is an example of the laws in Leyton's Generative Theory of Shape which give the ability to recover the "design intents "for which the shape features of a CAD model were created. The book demonstrates that the Process Grammar recovers important design intents in biological morphology and manufacturing design. In large-scale manufacturing systems, the recovery of design intents is important for solving the interoperability problem and product lifecycle management.

This book is one of a series of books in Springer that elaborates Leyton's Generative Theory of Shape.

Within the Smart Grid, the combination of automation equipment, communication technology and IT is crucial. Interoperability of devices and systems can be seen as the key enabler of smart grids. Therefore, international initiatives have been started in order to identify interoperability core standards for Smart Grids. IEC 62357, the so called Seamless Integration Architecture, is one of these very core standards, which has been identified by recent Smart Grid initiatives and roadmaps to be essential for building and managing intelligent power systems. The Seamless Integration Architecture provides an overview of the interoperability and relations between further standards from IEC TC 57 like the IEC 61970/61968: Common Information Model - CIM. CIM has proven to be a mature standard for interoperability and engineering; consequently, it is a cornerstone of the IEC Smart Grid Standardization Roadmap. This book provides an overview on how the CIM developed, in which international projects and roadmaps is has already been covered and describes the basic use cases for CIM. This book has been written for both Power Engineers trying to get to know the EMS and business IT part of Smart Grid and for Computer Scientist finding out where ICT technology is applied in EMS and DMS Systems. The book is divided into two parts dealing with the theoretical foundations and a practical part describing tools and use cases for CIM.

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceara, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbanski, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Reservation procedures constitute the core of many popular data transmission protocols. They consist of two steps: A request phase in which a station reserves the communication channel and a transmission phase in which the actual data transmission takes place. Such procedures are often applied in communication networks that are characterised by a shared communication channel with large round-trip times.

In this book, we propose queuing models for situations that require a reservation procedure and validate their applicability in the context of cable networks.

We offer various mathematical models to better understand the performance of these reservation procedures. The book covers four key performance models, and modifications to these: Contention trees, the repairman model, the bulk service queue, and tandem queues.

The relevance of this book is not limited to reservation procedures and cable networks, and performance analysts from a variety of areas may benefit, as all models have found application in other fields as well.

Proceedings of the International Symposium organized by the Mathematical Institute of the Polish Academy of Sciences, The Institute for Nuclear Research, Warsaw, 25-30 March 1974

This book addresses a range of aging intensity functions, which make it possible to measure and compare aging trends for lifetime random variables. Moreover, they can be used for the characterization of lifetime distributions, also with bounded support. Stochastic orders based on the aging intensities, and their connections with some other orders, are also discussed. To demonstrate the applicability of aging intensity in reliability practice, the book analyzes both real and generated data. The estimated, properly chosen, aging intensity function is mainly recommended to identify data's lifetime distribution, and secondly, to estimate some of the parameters of the identified distribution. Both reliability researchers and practitioners will find the book a valuable guide and source of inspiration.

'Et moi, ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematicsis a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics seIVe as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One seIVice topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

This monograph is focused on control law design methods for asymptotic tracking and disturbance rejection in the presence of uncertainties. The methods are based on adaptive implementation of the Internal Model Principle (IMP). The monograph shows how this principle can be applied to the problems of asymptotic rejection/tracking of a priori uncertain exogenous signals for linear and nonlinear plants with known and unknown parameters. The book begins by introducing the problems of adaptive control, the challenges that are faced, modern methods and an overview of the IMP. It then introduces special observers for uncertain exogeneous signals affecting linear and nonlinear systems with known and unknown parameters. The basic algorithms of adaptation applied to the canonical closed-loop error models are presented. The authors then address the systematic design of adaptive systems for asymptotic rejection/tracking of a priori uncertain exosignals. The monograph also discusses the adaptive rejection/tracking of a priori uncertain exogenous signals in systems with input delay, the problems of performance improvement in disturbance rejection and reference tracking and the issue of robustness of closed-loop systems. Adaptive Regulation provides a systematic discussion of the IMP applied to a variety of control problems, making it of interest to researchers and industrial practitioners.

Advances in science and technology necessitate the use of increasingly-complicated dynamic control processes. Undoubtedly, sophisticated mathematical models are also concurrently elaborated for these processes. In particular, linear dynamic control systems iJ = Ay + Bu, y E M C ]Rn, U E ]RT, (1) where A and B are constants, are often abandoned in favor of nonlinear dynamic control systems (2) which, in addition, contain a large number of equations. The solution of problems for multidimensional nonlinear control systems en counters serious difficulties, which are both mathematical and technical in nature. Therefore it is imperative to develop methods of reduction of nonlinear systems to a simpler form, for example, decomposition into systems of lesser dimension. Approaches to reduction are diverse, in particular, techniques based on approxi mation methods. In this monograph, we elaborate the most natural and obvious (in our opinion) approach, which is essentially inherent in any theory of math ematical entities, for instance, in the theory of linear spaces, theory of groups, etc. Reduction in our interpretation is based on assigning to the initial object an isomorphic object, a quotient object, and a subobject. In the theory of linear spaces, for instance, reduction consists in reducing to an isomorphic linear space, quotient space, and subspace. Strictly speaking, the exposition of any mathemat ical theory essentially begins with the introduction of these reduced objects and determination of their basic properties in relation to the initial object."

The topics of this set of student-oriented books are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to help students feel comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.

The book mainly deals with basic concepts and examples about integral calculus such as indefinite integral, definite integral, improper integrals, integrals dependent on parameters, lines integrals, double and triple integrals, and surface integrals. These basic elements of integral calculus are well presented in this book, and they are indispensable for students in higher technical education to successfully approach other theoretical or technical disciplines.

This book presents established and new approaches to perform calculations of electrostatic interactions at the nanoscale, with particular focus on molecular biology applications. It is based on the proceedings of the Computational Electrostatics for Biological Applications international meeting, which brought together researchers in computational disciplines to discuss and explore diverse methods to improve electrostatic calculations. Fostering an interdisciplinary approach to the description of complex physical and biological problems, this book encompasses contributions originating in the fields of geometry processing, shape modeling, applied mathematics, and computational biology and chemistry. The main topics covered are theoretical and numerical aspects of the solution of the Poisson-Boltzmann equation, surveys and comparison among geometric approaches to the modelling of molecular surfaces and related discretization and computational issues. It also includes a number of contributions addressing applications in biology, biophysics and nanotechnology. The book is primarily intended as a reference for researchers in the computational molecular biology and chemistry fields. As such, it also aims at becoming a key source of information for a wide range of scientists who need to know how modeling and computing at the molecular level may influence the design and interpretation of their experiments.

This book presents theories and the main useful techniques of the Finite Element Method (FEM), with an introduction to FEM and many case studies of its use in engineering practice. It supports engineers and students to solve primarily linear problems in mechanical engineering, with a main focus on static and dynamic structural problems. Readers of this text are encouraged to discover the proper relationship between theory and practice, within the finite element method: Practice without theory is blind, but theory without practice is sterile. Beginning with elasticity basic concepts and the classical theories of stressed materials, the work goes on to apply the relationship between forces, displacements, stresses and strains on the process of modeling, simulating and designing engineered technical systems. Chapters discuss the finite element equations for static, eigenvalue analysis, as well as transient analyses. Students and practitioners using commercial FEM software will find this book very helpful. It uses straightforward examples to demonstrate a complete and detailed finite element procedure, emphasizing the differences between exact and numerical procedures.

Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems explores how Newton's equation for the motion of one particle in classical mechanics combined with finite difference methods allows creation of a mechanical scenario to solve basic problems in linear algebra and programming. The authors present a novel, unified numerical and mechanical approach and an important analysis method of optimization.

A comprehensive exposition on analytic methods for solving science and engineering problems, written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important to practioners and researchers. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise.

This textbook presents a concise comparison of catalytic and biocatalytic systems outlining their catalytic properties and peculiarities. Moreover, it presents a brief introduction to the science of catalysis and attempts to unify different catalytic systems into a single, conceptually coherent structure. In fact, molecular dynamics and complexity may occur in both catalysts and biocatalysts, with many similarities in both their structural configuration and operational mechanisms. Moreover, the interactions between the different components of the catalytic system that are important in defining the overall activity, including the nature of active sites are discussed. Each chapter includes end of chapter questions supported by an online instructor solution manual. This textbook will be useful for undergraduate and graduate chemistry and biochemistry students.

Modern image processing techniques are based on multiresolution geometrical methods of image representation. These methods are efficient in sparse approximation of digital images. There is a wide family of functions called simply X-lets, and these methods can be divided into two groups: the adaptive and the nonadaptive. This book is devoted to the adaptive methods of image approximation, especially to multismoothlets.

Besides multismoothlets, several other new ideas are also covered. Current literature considers the black and white images with smooth horizon function as the model for sparse approximation but here, the class of blurred multihorizon is introduced, which is then used in the approximation of images with multiedges. Additionally, the semi-anisotropic model of multiedge representation, the introduction of the shift invariant multismoothlet transform and sliding multismoothlets are also covered.

"Geometrical Multiresolution Adaptive Transforms" should be accessible to both mathematicians and computer scientists. It is suitable as a professional reference for students, researchers and engineers, containing many open problems and will be an excellent starting point for those who are beginning new research in the area or who want to use geometrical multiresolution adaptive methods in image processing, analysis or compression."

Logic plays a central conceptual role in modern mathematics. However, mathematical logic has grown into one of the most recondite areas of mathematics. As a result, most of modern logic is inaccessible to all but the specialist. This new book is a resource that provides a quick introduction and review of the key topics in logic for the computer scientist, engineer, or mathematician.

Handbook of Logic and Proof Techniques for Computer Science presents the elements of modern logic, including many current topics, to the reader having only basic mathematical literacy. Computer scientists will find specific examples and important ideas such as axiomatics, recursion theory, decidability, independence, completeness, consistency, model theory, and P/NP completeness. The book contains definitions, examples and discussion of all of the key ideas in basic logic, but also makes a special effort to cut through the mathematical formalism, difficult notation, and esoteric terminology that is typical of modern mathematical logic. T

This handbook delivers cogent and self-contained introductions to critical advanced topics, including:

* Godels completeness and incompleteness theorems

* Methods of proof, cardinal and ordinal numbers, the continuum hypothesis, the axiom of choice, model theory, and number systems and their construction

* Extensive treatment of complexity theory and programming applications

* Applications to algorithms in Boolean algebra

* Discussion of set theory and applications of logic

The book is an excellent resource for the working mathematical scientist. The graduate student or professional in computer science and engineering or the systems scientist whoneeds to have a quick sketch of a key idea from logic will find it here in this self-contained, accessible, and easy-to-use reference.

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."

Practical Asymptotics is an effective tool for reducing the complexity of large-scale applied-mathematical models arising in engineering, physics, chemistry, and industry, without compromising their accuracy. It exploits the full potential of the dimensionless representation of these models by considering the special nature of the characteristic dimensionless quantities. It can be argued that these dimensionless quantities mostly assume extreme values, particularly for practical parameter settings. Thus, otherwise complicated models can be rendered far less complex and the numerical effort to solve them is greatly reduced. In this book the effectiveness of Practical Asymptotics is demonstrated by fifteen papers devoted to widely differing fields of applied science, such as glass-bottle production, semiconductors, surface-tension-driven flows, microwaving joining, heat generation in foodstuff production, chemical-clock reactions, low-Mach-number flows, to name a few. A strong plea is made for making asymptotics teaching an integral part of any numerics curriculum. Not only will asymptotics reduce the computational effort, it also provides a fuller understanding of the underlying problems.

Queueing theory applications can be discovered in many walks of life including; transportation, manufacturing, telecommunications, computer systems and more. However, the most prevalent applications of queueing theory are in the telecommunications field. Queueing Theory for Telecommunications: Discrete Time Modelling of a Single Node System focuses on discrete time modeling and illustrates that most queueing systems encountered in real life can be set up as a Markov chain. This feature is very unique because the models are set in such a way that matrix-analytic methods are used to analyze them. Queueing Theory for Telecommunications: Discrete Time Modelling of a Single Node System is the most relevant book available on queueing models designed for applications to telecommunications. This book presents clear concise theories behind how to model and analyze key single node queues in discrete time using special tools that were presented in the second chapter. The text also delves into the types of single node queues that are very frequently encountered in telecommunication systems modeling, and provides simple methods for analyzing them. Where appropriate, alternative analysis methods are also presented. This book is for advanced-level students and researchers concentrating on engineering, computer science and mathematics as a secondary text or reference book. Professionals who work in the related industries of telecommunications, industrial engineering and communications engineering will find this book useful as well.

This book shows that evolutionary game theory can unravel how mutual cooperation, trust, and credit in a group emerge in organizations and institutions. Some organizations and institutions, such as insurance unions, credit unions, and banks, originated from very simple mutual-aid groups. Members in these early-stage mutual-aid groups help each other, making rules to promote cooperation, and suppressing free riders. Then, they come to "trust" not only each other but also the group they belong to, itself. The division of labor occurs when the society comes to have diversity and complexity in a larger group, and the division of labor also requires mutual cooperation and trust among different social roles. In a larger group, people cannot directly interact with each other, and the reputation of unknown people helps other decide who is a trustworthy person. However, if gossip spreads untruths about a reputation, trust and cooperation are destroyed. Therefore, how to suppress untrue gossip is also important for trust and cooperation in a larger group. If trustworthiness and credibility can be established, these groups are successfully sustainable. Some develop and evolve and then mature into larger organizations and institutions. Finally, these organizations and institutions become what they are now. Therefore, not only cooperation but also trust and credit are keys to understanding these organizations and institutions. The evolution of cooperation, a topic of research in evolutionary ecology and evolutionary game theory, can be applied to understanding how to make institutions and organizations sustainable, trustworthy, and credible. It provides us with the idea that evolutionary game theory is a good mathematical tool to analyze trust and credit. This kind of research can be applied to current hot topics such as microfinance and the sustainable use of ecosystems.