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Discrete Structures And Their Interactions

Author: Jason I. Brown
Publisher: CRC Press
ISBN: 1466579420
Size: 47.80 MB
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Discover the Connections between Different Structures and Fields Discrete Structures and Their Interactions highlights the connections among various discrete structures, including graphs, directed graphs, hypergraphs, partial orders, finite topologies, and simplicial complexes. It also explores their relationships to classical areas of mathematics, such as linear and multilinear algebra, analysis, probability, logic, and topology. The text introduces a number of discrete structures, such as hypergraphs, finite topologies, preorders, simplicial complexes, and order ideals of monomials, that most graduate students in combinatorics, and even some researchers in the field, seldom experience. The author explains how these structures have important applications in many areas inside and outside of combinatorics. He also discusses how to recognize valuable research connections through the structures. Intended for graduate and upper-level undergraduate students in mathematics who have taken an initial course in discrete mathematics or graph theory, this book shows how discrete structures offer new insights into the classical fields of mathematics. It illustrates how to use discrete structures to represent the salient features and discover the underlying combinatorial principles of seemingly unrelated areas of mathematics.

Handbook Of Discrete And Computational Geometry Third Edition

Author: Csaba D. Toth
Publisher: CRC Press
ISBN: 1498711421
Size: 77.84 MB
Format: PDF, Kindle
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The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in ?elds as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed signi?cantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young ?eld of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Handbook Of Discrete And Computational Geometry Third Edition

Author: Csaba D. Toth
Publisher: CRC Press
ISBN: 1351645919
Size: 70.94 MB
Format: PDF, Kindle
View: 537
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The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in ?elds as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed signi?cantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young ?eld of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.

Representation Theory Of Symmetric Groups

Author: Pierre-Loic Meliot
Publisher: CRC Press
ISBN: 1498719139
Size: 43.28 MB
Format: PDF, Docs
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Representation Theory of Symmetric Groups is the most up-to-date abstract algebra book on the subject of symmetric groups and representation theory. Utilizing new research and results, this book can be studied from a combinatorial, algorithmic or algebraic viewpoint. This book is an excellent way of introducing today’s students to representation theory of the symmetric groups, namely classical theory. From there, the book explains how the theory can be extended to other related combinatorial algebras like the Iwahori-Hecke algebra. In a clear and concise manner, the author presents the case that most calculations on symmetric group can be performed by utilizing appropriate algebras of functions. Thus, the book explains how some Hopf algebras (symmetric functions and generalizations) can be used to encode most of the combinatorial properties of the representations of symmetric groups. Overall, the book is an innovative introduction to representation theory of symmetric groups for graduate students and researchers seeking new ways of thought.

Algebraic And Discrete Mathematical Methods For Modern Biology

Author: Raina Robeva
Publisher: Academic Press
ISBN: 0128012714
Size: 69.59 MB
Format: PDF, Mobi
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Written by experts in both mathematics and biology, Algebraic and Discrete Mathematical Methods for Modern Biology offers a bridge between math and biology, providing a framework for simulating, analyzing, predicting, and modulating the behavior of complex biological systems. Each chapter begins with a question from modern biology, followed by the description of certain mathematical methods and theory appropriate in the search of answers. Every topic provides a fast-track pathway through the problem by presenting the biological foundation, covering the relevant mathematical theory, and highlighting connections between them. Many of the projects and exercises embedded in each chapter utilize specialized software, providing students with much-needed familiarity and experience with computing applications, critical components of the "modern biology" skill set. This book is appropriate for mathematics courses such as finite mathematics, discrete structures, linear algebra, abstract/modern algebra, graph theory, probability, bioinformatics, statistics, biostatistics, and modeling, as well as for biology courses such as genetics, cell and molecular biology, biochemistry, ecology, and evolution. Examines significant questions in modern biology and their mathematical treatments Presents important mathematical concepts and tools in the context of essential biology Features material of interest to students in both mathematics and biology Presents chapters in modular format so coverage need not follow the Table of Contents Introduces projects appropriate for undergraduate research Utilizes freely accessible software for visualization, simulation, and analysis in modern biology Requires no calculus as a prerequisite Provides a complete Solutions Manual Features a companion website with supplementary resources

Radiative Transfer On Discrete Spaces

Author: Rudolph W. Preisendorfer
Publisher: Elsevier
ISBN: 148318529X
Size: 18.16 MB
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Pure and Applied Mathematics, Volume 74: Radiative Transfer on Discrete Spaces presents the geometrical structure of natural light fields. This book describes in detail with mathematical precision the radiometric interactions of light-scattering media in terms of a few well established principles. Organized into four parts encompassing 15 chapters, this volume begins with an overview of the derivations of the practical formulas and the arrangement of formulas leading to numerical solution procedures of radiative transfer problems in plane-parallel media. This text then constructs radiative transfer theory in three ways. Other chapters consider the development of discrete radiative transfer theory from the local interaction principle. This book discusses as well the development of continuous radiative transfer theory. The final chapter deals with the task of formulating a mathematical foundation for radiative transfer theory. This book is a valuable resource for researchers in the field of radiative transfer theory whose interests transcend the physical and numerical aspects of the interaction of light with matter.

Introduction To Random Graphs

Author: Alan Frieze
Publisher: Cambridge University Press
ISBN: 1107118506
Size: 27.44 MB
Format: PDF
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The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.

Diophantine Analysis

Author: Jörn Steuding
Publisher: Birkhäuser
ISBN: 3319488171
Size: 48.20 MB
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This collection of course notes from a number theory summer school focus on aspects of Diophantine Analysis, addressed to Master and doctoral students as well as everyone who wants to learn the subject. The topics range from Baker’s method of bounding linear forms in logarithms (authored by Sanda Bujačić and Alan Filipin), metric diophantine approximation discussing in particular the yet unsolved Littlewood conjecture (by Simon Kristensen), Minkowski’s geometry of numbers and modern variations by Bombieri and Schmidt (Tapani Matala-aho), and a historical account of related number theory(ists) at the turn of the 19th Century (Nicola M.R. Oswald). Each of these notes serves as an essentially self-contained introduction to the topic. The reader gets a thorough impression of Diophantine Analysis by its central results, relevant applications and open problems. The notes are complemented with many references and an extensive register which makes it easy to navigate through the book.

Fluid Structure Interactions

Author: Michael P. Paidoussis
Publisher: Academic Press
ISBN: 0123973139
Size: 61.96 MB
Format: PDF, ePub
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The first of two books concentrating on the dynamics of slender bodies within or containing axial flow, Fluid-Structure Interaction, Volume 1 covers the fundamentals and mechanisms giving rise to flow-induced vibration, with a particular focus on the challenges associated with pipes conveying fluid. This volume has been thoroughly updated to reference the latest developments in the field, with a continued emphasis on the understanding of dynamical behaviour and analytical methods needed to provide long-term solutions and validate the latest computational methods and codes. In this edition, Chapter 7 from Volume 2 has also been moved to Volume 1, meaning that Volume 1 now mainly treats the dynamics of systems subjected to internal flow, whereas in Volume 2 the axial flow is in most cases external to the flow or annular. Provides an in-depth review of an extensive range of fluid-structure interaction topics, with detailed real-world examples and thorough referencing throughout for additional detail Organized by structure and problem type, allowing you to dip into the sections that are relevant to the particular problem you are facing, with numerous appendices containing the equations relevant to specific problems Supports development of long-term solutions by focusing on the fundamentals and mechanisms needed to understand underlying causes and operating conditions under which apparent solutions might not prove effective

Fluid Structure Interactions

Author: Thomas Richter
Publisher: Springer
ISBN: 3319639706
Size: 10.28 MB
Format: PDF, Mobi
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This book starts by introducing the fundamental concepts of mathematical continuum mechanics for fluids and solids and their coupling. Special attention is given to the derivation of variational formulations for the subproblems describing fluid- and solid-mechanics as well as the coupled fluid-structure interaction problem. Two monolithic formulations for fluid-structure interactions are described in detail: the well-established ALE formulation and the modern Fully Eulerian formulation, which can effectively deal with problems featuring large deformation and contact. Further, the book provides details on state-of-the-art discretization schemes for fluid- and solid-mechanics and considers the special needs of coupled problems with interface-tracking and interface-capturing techniques. Lastly, advanced topics like goal-oriented error estimation, multigrid solution and gradient-based optimization schemes are discussed in the context of fluid-structure interaction problems.