Basic Noncommutative Geometry

Author: Masoud Khalkhali

Publisher: European Mathematical Society

ISBN: 9783037190616

Category: Mathematics

Page: 223

View: 1361

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"Basic Noncommutative Geometry provides an introduction to noncommutative geometry and some of its applications. The book can be used either as a textbook for a graduate course on the subject or for self-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject. One feature of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis, algebraic topology, differential geometry and homological algebra at a first year graduate level is helpful. Developed by Alain Connes since the late 1970s, noncommutative geometry has found many applications to long-standing conjectures in topology and geometry and has recently made headways in theoretical physics and number theory. The book starts with a detailed description of some of the most pertinent algebra-geometry correspondences by casting geometric notions in algebraic terms, then proceeds in the second chapter to the idea of a noncommutative space and how it is constructed. The last two chapters deal with homological tools: cyclic cohomology and Connes-Chern characters in K-theory and K-homology, culminating in one commutative diagram expressing the equality of topological and analytic index in a noncommutative setting. Applications to integrality of noncommutative topological invariants are given as well."--Publisher's description.

Novikov Conjectures, Index Theorems, and Rigidity: Volume 1

Oberwolfach 1993

Author: Steven C. Ferry,Andrew Ranicki,Jonathan M. Rosenberg

Publisher: Cambridge University Press

ISBN: 9780521497961

Category: Mathematics

Page: 384

View: 9824

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The Novikov conjecture is the single most important unsolved problem in the topology of high-dimensional non-simply connected manifolds. These two volumes give a snapshot of the status of work on the Novikov conjecture and related topics from many points of view: geometric topology, homotopy theory, algebra, geometry, and analysis. Volume 1 contains a detailed historical survey and bibliography of the Novikov conjecture and of related subsequent developments, including an annotated reprint (both in the original Russian and in English translation) of Novikov's original 1970 statement of his conjecture; an annotated problem list; the texts of several important unpublished classic papers by Milnor, Browder, and Kasparov; and research/survey papers on the Novikov conjecture by Ferry/Weinberger, Gromov, Mishchenko, Quinn, Ranicki, and Rosenberg. Volume 2 contains fundamental long research papers by G. Carlsson on "Bounded K-theory and the assembly map in algebraic K-theory" and by S. Ferry and E. Pedersen on "Epsilon surgery theory"; and shorter research and survey papers on various topics related to the Novikov conjecture, by Bekka, Cherix, Valette, Eichhorn, and others. These volumes will appeal to researchers interested in learning more about this intriguing area.

Fractals in Engineering

From Theory to Industrial Applications

Author: Jacques Levy Vehel,Evelyne Lutton,Claude Tricot

Publisher: Springer Science & Business Media

ISBN: 1447109953

Category: Computers

Page: 402

View: 1989

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Fractal analysis research is expanding into a variety of engineering domains. The strong potential of this work is now beginning to be seen in important applications in real industrial situations. Recent research progress has already led to new developments in domains such as signal processing and chemical engineering, and the major advances in fractal theory that underlie such developments are detailed here. New domains of applications are also presented, among them environmental science and rough surface analysis. Sections include multifractal analysis, iterated function systems, random processes, network traffic analysis, fractals and waves, image compression, and applications in physics. Fractals in Engineering emphasizes the connection between fractal analysis research and applications to industry. It is an important volume that illustrates the scientific and industrial value of this exciting field.

The Finiteness Obstruction of C. T. C. Wall

Author: Kalathoor Varadarajan

Publisher: Wiley-Interscience

ISBN: N.A

Category: Mathematics

Page: 194

View: 1499

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This monograph gives an account of C. T. C. Wall's work on finiteness conditions on CW-complexes. Varadarayan recasts Wall's obstruction proofs in algebraic terms (the proofs depending upon results from algebraic number theory and on K-theoretic induction theorems), and ends with a study of finitely-dominated nilpotent spaces. Most of the material in this volume appears for the first time in book form.

Bayesian Networks and Decision Graphs

Author: Thomas Dyhre Nielsen,FINN VERNER JENSEN

Publisher: Springer Science & Business Media

ISBN: 9780387682815

Category: Science

Page: 448

View: 8896

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This is a brand new edition of an essential work on Bayesian networks and decision graphs. It is an introduction to probabilistic graphical models including Bayesian networks and influence diagrams. The reader is guided through the two types of frameworks with examples and exercises, which also give instruction on how to build these models. Structured in two parts, the first section focuses on probabilistic graphical models, while the second part deals with decision graphs, and in addition to the frameworks described in the previous edition, it also introduces Markov decision process and partially ordered decision problems.

The Legacy of Alladi Ramakrishnan in the Mathematical Sciences

Author: Krishnaswami Alladi,John R. Klauder,Calyampudi R. Rao

Publisher: Springer Science & Business Media

ISBN: 9781441962638

Category: Mathematics

Page: 575

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In the spirit of Alladi Ramakrishnan’s profound interest and contributions to three fields of science — Mathematics, Statistics, and Physics — this volume contains invited surveys and research articles from prominent members of these communities who also knew Ramakrishnan personally and greatly respected his influence in these areas of science. Historical photos, telegrams, and biographical narratives of Alladi Ramakrishnan’s illustrious career of special interest are included as well.

Multiscale Modeling in Epitaxial Growth

Author: Axel Voigt

Publisher: Springer Science & Business Media

ISBN: 3764373431

Category: Mathematics

Page: 240

View: 8948

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Epitaxy is relevant for thin film growth and is a very active area of theoretical research since several years. Recently powerful numerical techniques have been used to link atomistic effects at the film's surface to its macroscopic morphology. This book also serves as an introduction into this highly active interdisciplinary field of research for applied mathematicians, theoretical physicists and computational materials scientists.

Multivariate Approximation and Splines

Author: Günther Nürnberger,Jochen W. Schmidt,Guido Walz

Publisher: Birkhäuser

ISBN: 3034888716

Category: Mathematics

Page: 326

View: 1109

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This book contains the refereed papers which were presented at the interna tional conference on "Multivariate Approximation and Splines" held in Mannheim, Germany, on September 7-10,1996. Fifty experts from Bulgaria, England, France, Israel, Netherlands, Norway, Poland, Switzerland, Ukraine, USA and Germany participated in the symposium. It was the aim of the conference to give an overview of recent developments in multivariate approximation with special emphasis on spline methods. The field is characterized by rapidly developing branches such as approximation, data fit ting, interpolation, splines, radial basis functions, neural networks, computer aided design methods, subdivision algorithms and wavelets. The research has applications in areas like industrial production, visualization, pattern recognition, image and signal processing, cognitive systems and modeling in geology, physics, biology and medicine. In the following, we briefly describe the contents of the papers. Exact inequalities of Kolmogorov type which estimate the derivatives of mul the paper of BABENKO, KOFANovand tivariate periodic functions are derived in PICHUGOV. These inequalities are applied to the approximation of classes of mul tivariate periodic functions and to the approximation by quasi-polynomials. BAINOV, DISHLIEV and HRISTOVA investigate initial value problems for non linear impulse differential-difference equations which have many applications in simulating real processes. By applying iterative techniques, sequences of lower and upper solutions are constructed which converge to a solution of the initial value problem.

Scientific Computing in Electrical Engineering

SCEE 2016, St. Wolfgang, Austria, October 2016

Author: Ulrich Langer,Wolfgang Amrhein,Walter Zulehner

Publisher: Springer

ISBN: 3319755382

Category: Mathematics

Page: 266

View: 842

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This collection of selected papers presented at the 11th International Conference on Scientific Computing in Electrical Engineering (SCEE), held in St. Wolfgang, Austria, in 2016, showcases the state of the art in SCEE. The aim of the SCEE 2016 conference was to bring together scientists from academia and industry, mathematicians, electrical engineers, computer scientists, and physicists, and to promote intensive discussions on industrially relevant mathematical problems, with an emphasis on the modeling and numerical simulation of electronic circuits and devices, electromagnetic fields, and coupled problems. The focus in methodology was on model order reduction and uncertainty quantification. This extensive reference work is divided into six parts: Computational Electromagnetics, Circuit and Device Modeling and Simulation, Coupled Problems and Multi‐Scale Approaches in Space and Time, Mathematical and Computational Methods Including Uncertainty Quantification, Model Order Reduction, and Industrial Applications. Each part starts with a general introduction, followed by the respective contributions. This book will appeal to mathematicians and electrical engineers. Further, it introduces algorithm and program developers to recent advances in the other fields, while industry experts will be introduced to new programming tools and mathematical methods.

Novikov Conjectures, Index Theorems, and Rigidity:

Author: Steven C. Ferry,Andrew Ranicki,Jonathan M. Rosenberg

Publisher: Cambridge University Press

ISBN: 9780521497954

Category: Mathematics

Page: 376

View: 7725

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These volumes are the outgrowth of a conference held at the Mathematisches Forschungsinstitut Oberwolfach (Germany) on the subject of `Novikov conjectures, index theorems and rigidity'.

Simulating Social Complexity

A Handbook

Author: Bruce Edmonds,Ruth Meyer

Publisher: Springer

ISBN: 3540938133

Category: Computers

Page: 754

View: 2684

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Social systems are among the most complex known. This poses particular problems for those who wish to understand them. The complexity often makes analytic approaches infeasible and natural language approaches inadequate for relating intricate cause and effect. However, individual- and agent-based computational approaches hold out the possibility of new and deeper understanding of such systems. Simulating Social Complexity examines all aspects of using agent- or individual-based simulation. This approach represents systems as individual elements having each their own set of differing states and internal processes. The interactions between elements in the simulation represent interactions in the target systems. What makes these elements "social" is that they are usefully interpretable as interacting elements of an observed society. In this, the focus is on human society, but can be extended to include social animals or artificial agents where such work enhances our understanding of human society. The phenomena of interest then result (emerge) from the dynamics of the interaction of social actors in an essential way and are usually not easily simplifiable by, for example, considering only representative actors. The introduction of accessible agent-based modelling allows the representation of social complexity in a more natural and direct manner than previous techniques. In particular, it is no longer necessary to distort a model with the introduction of overly strong assumptions simply in order to obtain analytic tractability. This makes agent-based modelling relatively accessible to a range of scientists. The outcomes of such models can be displayed and animated in ways that also make them more interpretable by experts and stakeholders. This handbook is intended to help in the process of maturation of this new field. It brings together, through the collaborative effort of many leading researchers, summaries of the best thinking and practice in this area and constitutes a reference point for standards against which future methodological advances are judged. This book will help those entering into the field to avoid "reinventing the wheel" each time, but it will also help those already in the field by providing accessible overviews of current thought. The material is divided into four sections: Introductory, Methodology, Mechanisms, and Applications. Each chapter starts with a very brief section called ‘Why read this chapter?’ followed by an abstract, which summarizes the content of the chapter. Each chapter also ends with a section of ‘Further Reading’ briefly describing three to eight items that a newcomer might read next.

Fractals in Engineering

New Trends in Theory and Applications

Author: Jacques Lévy-Véhel,Evelyne Lutton

Publisher: Springer Science & Business Media

ISBN: 1846280486

Category: Technology & Engineering

Page: 290

View: 304

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Survival and Event History Analysis

A Process Point of View

Author: Odd Aalen,Ornulf Borgan,Hakon Gjessing

Publisher: Springer Science & Business Media

ISBN: 038768560X

Category: Mathematics

Page: 540

View: 2202

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The aim of this book is to bridge the gap between standard textbook models and a range of models where the dynamic structure of the data manifests itself fully. The common denominator of such models is stochastic processes. The authors show how counting processes, martingales, and stochastic integrals fit very nicely with censored data. Beginning with standard analyses such as Kaplan-Meier plots and Cox regression, the presentation progresses to the additive hazard model and recurrent event data. Stochastic processes are also used as natural models for individual frailty; they allow sensible interpretations of a number of surprising artifacts seen in population data. The stochastic process framework is naturally connected to causality. The authors show how dynamic path analyses can incorporate many modern causality ideas in a framework that takes the time aspect seriously. To make the material accessible to the reader, a large number of practical examples, mainly from medicine, are developed in detail. Stochastic processes are introduced in an intuitive and non-technical manner. The book is aimed at investigators who use event history methods and want a better understanding of the statistical concepts. It is suitable as a textbook for graduate courses in statistics and biostatistics.

European Congress of Mathematics, Barcelona, July 10-14, 2000

Vol. 1

Author: Carles Casacuberta

Publisher: Springer Science & Business Media

ISBN: 9783764364175

Category: Mathematics

Page: 582

View: 6564

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The Third European Congress of Mathematics (3ecm) took place from July 10th to July 14th, 2000 in Barcelona. It was organised by the Societat Catalana de Matematiques (Catalan Mathematical Society), under the auspices of the Euro­ pean Mathematical Society (EMS). As foreseen by the EMS and the International Mathematical Union, this Congress was a major event in World Mathematical Year 2000. In addition to reviewing outstanding research achievements, important aspects of the life of European mathematics were discussed. Mathematics is undergoing a period of rapid changes. Effective computation and applications in science and technology go ever more hand in hand with con­ ceptual developments. It was one of the aims of 3ecm to reflect this mutual enrich­ ment, while steering present and future trends of mathematical sciences. In fact, the motto of the Congress, Shaping the 21st Century, was meant to capture these views. Nearly 1400 people from 87 countries gathered together in the Palau de Con­ gressos of Barcelona in order to take part in the activities of the 3ecm scientific programme: Nine plenary lectures, thirty invited lectures in parallel sessions, lec­ tures given by EMS prize winners, ten mini-symposia on special topics, seven round tables, poster sessions, presentations of mathematical software and video exhibitions. Twenty events were satellites of 3ecm in various countries.

New Trends in Mechanism Science

Analysis and Design

Author: Doina Pisla,marco ceccarelli,Manfred Husty,Burkhard Corves

Publisher: Springer Science & Business Media

ISBN: 9789048196890

Category: Technology & Engineering

Page: 710

View: 6096

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After two succesful conferences held in Innsbruck (Prof. Manfred Husty) in 2006 and Cassino in 2008 (Prof Marco Ceccarelli) with the participation of the most important well-known scientists from the European Mechanism Science Community, a further conference was held in Cluj Napoca, Romania, in 2010 (Prof. Doina Pisla) to discuss new developments in the field. This book presents the most recent research advances in Mechanism Science with different applications. Amongst the topics treated are papers on Theoretical kinematics, Computational kinematics, Mechanism design, Mechanical transmissions, Linkages and manipulators, Mechanisms for biomechanics, Micro-mechanisms, Experimental mechanics, Mechanics of robots, Dynamics of multi-body systems, Dynamics of machinery, Control issues of mechanical systems, Novel designs, History of mechanism science etc.

Space, Structure and Randomness

Contributions in Honor of Georges Matheron in the Fields of Geostatistics, Random Sets and Mathematical Morphology

Author: Michel Bilodeau,Fernand Meyer,Michel Schmitt

Publisher: Springer Science & Business Media

ISBN: 9780387291154

Category: Mathematics

Page: 398

View: 1591

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Space, structure, and randomness: these are the three key concepts underlying Georges Matheron’s scientific work. He first encountered them at the beginning of his career when working as a mining engineer, and then they resurfaced in fields ranging from meteorology to microscopy. What could these radically different types of applications possibly have in common? First, in each one only a single realisation of the phenomenon is available for study, but its features repeat themselves in space; second, the sampling pattern is rarely regular, and finally there are problems of change of scale. This volume is divided in three sections on random sets, geostatistics and mathematical morphology. They reflect his professional interests and his search for underlying unity. Some readers may be surprised to find theoretical chapters mixed with applied ones. We have done this deliberately. GM always considered that the distinction between the theory and practice was purely academic. When GM tackled practical problems, he used his skill as a physicist to extract the salient features and to select variables which could be measured meaningfully and whose values could be estimated from the available data. Then he used his outstanding ability as a mathematician to solve the problems neatly and efficiently. It was his capacity to combine a physicist’s intuition with a mathematician’s analytical skills that allowed him to produce new and innovative solutions to difficult problems. The book should appeal to graduate students and researchers working in mathematics, probability, statistics, physics, spatial data analysis, and image analysis. In addition it will be of interest to those who enjoy discovering links between scientific disciplines that seem unrelated at first glance. In writing the book the contributors have tried to put GM’s ideas into perspective. During his working life, GM was a genuinely creative scientist. He developed innovative concepts whose usefulness goes far beyond the confines of the discipline for which they were originally designed. This is why his work remains as pertinent today as it was when it was first written.

Mathematical Statistics and Probability Theory

Proceedings, Sixth International Conference, Wisła (Poland), 1978

Author: W. Klonecki,A. Kozek,J. Rosinski

Publisher: Springer Science & Business Media

ISBN: 1461573971

Category: Mathematics

Page: 373

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Since 1972 the Institute of Mathematics and the Committee of Mathematics of the Polish Academy of Sciences organize annually con ferences on mathematical statistics in Wisla. The 1978 conference, supported also by the University of Wroclaw,was held in Wisla from December 7 to December 13 and attended by around 100 participants from 11 countries. K. Urbanik, Rector of the University of Wroclaw, was the honorary chairman of the conference. Traditionally at these conferences there are presented results on mathematical statistics and related fields obtained in Poland during the year of the conference as well as results presented by invited scholars from other countries. In 1978 invitations to present talks were accepted by 20 e~inent statisticians and probabilists. The topics of the invited lectures and contributed papers included theoretical statistics with a broad cover of the theory of linear models, inferences from stochastic processes, probability theory and applications to biology and medicine. In these notes there appear papers submitted by 30 participants of the conference. During the conference, on December 9, there was held a special session of the Polish Mathematical Society on the occasion of elect ing Professor Jerzy Neyman the honorary member of the Polish Mathematical Society. At this session W. Orlicz, president of the Polish Mathematical Society, K.Krickeberg,president of the Bernoulli Society. R. Bartoszynski and K. Doksum gave talks on Neyman IS con tribution to statistics, his organizational achievements in the U.S.