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Author : Maruthi VA
Genre : Science
File Size : 76. 51 MB
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Introduction of the Universe by three immediate factors. Existence and Dynamics of the Universe by a Definition in three rapid stanzas. Simplification & Explanation of the Universe in five small paragraphs: Origin, Energy, Dynamics, Conscience, Eternity. Description of the Universe by a conjunction of five small chapters: Omniscience, Cosmology, Organics, Sociology, Theology.

Automata Languages And Programming

Author : Jos C.M. Baeten
ISBN : 9783540450610
Genre : Computers
File Size : 24. 50 MB
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The refereed proceedings of the 30th International Colloquium on Automata, Languages and Programming, ICALP 2003, held in Eindhoven, The Netherlands in June/July 2003. The 84 revised full papers presented together with six invited papers were carefully reviewed and selected from 212 submissions. The papers are organized in topical sections on algorithms, process algebra, approximation algorithms, languages and programming, complexity, data structures, graph algorithms, automata, optimization and games, graphs and bisimulation, online problems, verification, the Internet, temporal logic and model checking, graph problems, logic and lambda-calculus, data structures and algorithms, types and categories, probabilistic systems, sampling and randomness, scheduling, and geometric problems.

An Introduction To Measure Theory

Author : Terence Tao
ISBN : 9781470466404
Genre : Education
File Size : 20. 67 MB
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This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.

Embeddings In Manifolds

Author : Robert J. Daverman
ISBN : 9780821836972
Genre : Mathematics
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A topological embedding is a homeomorphism of one space onto a subspace of another. The book analyzes how and when objects like polyhedra or manifolds embed in a given higher-dimensional manifold. The main problem is to determine when two topological embeddings of the same object are equivalent in the sense of differing only by a homeomorphism of the ambient manifold. Knot theory is the special case of spheres smoothly embedded in spheres; in this book, much more general spaces and much more general embeddings are considered. A key aspect of the main problem is taming: when is a topological embedding of a polyhedron equivalent to a piecewise linear embedding? A central theme of the book is the fundamental role played by local homotopy properties of the complement in answering this taming question. The book begins with a fresh description of the various classic examples of wild embeddings (i.e., embeddings inequivalent to piecewise linear embeddings). Engulfing, the fundamental tool of the subject, is developed next. After that, the study of embeddings is organized by codimension (the difference between the ambient dimension and the dimension of the embedded space). In all codimensions greater than two, topological embeddings of compacta are approximated by nicer embeddings, nice embeddings of polyhedra are tamed, topological embeddings of polyhedra are approximated by piecewise linear embeddings, and piecewise linear embeddings are locally unknotted. Complete details of the codimension-three proofs, including the requisite piecewise linear tools, are provided. The treatment of codimension-two embeddings includes a self-contained, elementary exposition of the algebraic invariants needed to construct counterexamples to the approximation and existence of embeddings. The treatment of codimension-one embeddings includes the locally flat approximation theorem for manifolds as well as the characterization of local flatness in terms of local homotopy properties.

Aspects Topologiques De La Physique En Basse Dimension Topological Aspects Of Low Dimensional Systems

Author : A. Comtet
ISBN : 9783540669098
Genre : Science
File Size : 55. 17 MB
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Session LXIX. 7 - 31 July 1998

Brownian Motion

Author : Peter Mörters
ISBN : 9781139486576
Genre : Mathematics
File Size : 74. 14 MB
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This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.

Fractal Dimensions Of Networks

Author : Eric Rosenberg
ISBN : 9783030431693
Genre : Computers
File Size : 82. 34 MB
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Current interest in fractal dimensions of networks is the result of more than a century of previous research on dimensions. Fractal Dimensions of Networks ties the theory and methods for computing fractal dimensions of networks to the “classic” theory of dimensions of geometric objects. The goal of the book is to provide a unified treatment of fractal dimensions of sets and networks. Since almost all of the major concepts in fractal dimensions originated in the study of sets, the book achieves this goal by first clearly presenting, with an abundance of examples and illustrations, the theory and algorithms for sets, and then showing how the theory and algorithms have been applied to networks. Thus, the book presents the classical theory and algorithms for the box counting dimension for sets, and then presents the box counting dimension for networks. All the major fractal dimensions are studied, e.g., the correlation dimension, the information dimension, the Hausdorff dimension, the multifractal spectrum, as well as many lesser known dimensions. Algorithm descriptions are accompanied by worked examples, many applications of the methods are presented, and many exercises, ranging in difficulty from easy to research level, are included.

Differential Forms In Algebraic Topology

Author : Raoul Bott
ISBN : 9781475739510
Genre : Mathematics
File Size : 42. 77 MB
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Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.

Hodge Theory And Complex Algebraic Geometry I Volume 1

Author : Claire Voisin
ISBN : 9781139437691
Genre : Mathematics
File Size : 81. 39 MB
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The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The author then proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The book culminates with the Hodge decomposition theorem. The meanings of these results are investigated in several directions. Completely self-contained, the book is ideal for students, while its content gives an account of Hodge theory and complex algebraic geometry as has been developed by P. Griffiths and his school, by P. Deligne, and by S. Bloch. The text is complemented by exercises which provide useful results in complex algebraic geometry.

Lectures On Fractal Geometry And Dynamical Systems

Author : Ya. B. Pesin
ISBN : 9780821848890
Genre : Mathematics
File Size : 79. 38 MB
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Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets, which are in turn a source of irregular 'chaotic' motions in the system. This book is an introduction to these two fields, with an emphasis on the relationship between them. The first half of the book introduces some of the key ideas in fractal geometry and dimension theory - Cantor sets, Hausdorff dimension, box dimension - using dynamical notions whenever possible, particularly one-dimensional Markov maps and symbolic dynamics. Various techniques for computing Hausdorff dimension are shown, leading to a discussion of Bernoulli and Markov measures and of the relationship between dimension, entropy, and Lyapunov exponents. In the second half of the book some examples of dynamical systems are considered and various phenomena of chaotic behaviour are discussed, including bifurcations, hyperbolicity, attractors, horseshoes, and intermittent and persistent chaos. These phenomena are naturally revealed in the course of our study of two real models from science - the FitzHugh - Nagumo model and the Lorenz system of differential equations. This book is accessible to undergraduate students and requires only standard knowledge in calculus, linear algebra, and differential equations. Elements of point set topology and measure theory are introduced as needed. This book is a result of the MASS course in analysis at Penn State University in the fall semester of 2008.

Benoit Mandelbrot A Life In Many Dimensions

Author : Frame Michael
ISBN : 9789814635530
Genre : Mathematics
File Size : 81. 75 MB
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This is a collection of articles, many written by people who worked with Mandelbrot, memorializing the remarkable breadth and depth of his work in science and the arts. Contributors include mathematicians, physicists, biologists, economists, and engineers, as expected; and also artists, musicians, teachers, an historian, an architect, a filmmaker, and a comic. Some articles are quite technical, others entirely descriptive. All include stories about Benoit.Also included are chapters on fractals and music by Charles Wuorinen and by Harlan Brothers, on fractals and finance by Richard Hudson and by Christian Walter, on fractal invisibility cloaks by Nathan Cohen, and a personal reminiscence by Aliette Mandelbrot.While he is known most widely for his work in mathematics and in finance, Benoit influenced almost every field of modern intellectual activity. No other book captures the breadth of all of Benoit's accomplishments.

Astronomical Image And Data Analysis

Author : J.-L. Starck
ISBN : 9783540330257
Genre : Science
File Size : 30. 36 MB
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With information and scale as central themes, this comprehensive survey explains how to handle real problems in astronomical data analysis using a modern arsenal of powerful techniques. It treats those innovative methods of image, signal, and data processing that are proving to be both effective and widely relevant. The authors are leaders in this rapidly developing field and draw upon decades of experience. They have been playing leading roles in international projects such as the Virtual Observatory and the Grid. The book addresses not only students and professional astronomers and astrophysicists, but also serious amateur astronomers and specialists in earth observation, medical imaging, and data mining. The coverage includes chapters or appendices on: detection and filtering; image compression; multichannel, multiscale, and catalog data analytical methods; wavelets transforms, Picard iteration, and software tools. This second edition of Starck and Murtagh's highly appreciated reference again deals with topics that are at or beyond the state of the art. It presents material which is more algorithmically oriented than most alternatives and broaches new areas like ridgelet and curvelet transforms. Throughout the book various additions and updates have been made.

Bms Particles In Three Dimensions

Author : Blagoje Oblak
ISBN : 9783319618784
Genre : Science
File Size : 30. 56 MB
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This thesis presents the state of the art in the study of Bondi-Metzner-Sachs (BMS) symmetry and its applications in the simplified setting of three dimensions. It focuses on presenting all the background material in a pedagogical and self-contained manner to enable readers to fully appreciate the original results that have been obtained while learning a number of fundamental concepts in the field along the way. This makes it a highly rewarding read and a perfect starting point for anybody with a serious interest in the four-dimensional problem.

Dimension Theory Of Hyperbolic Flows

Author : Luís Barreira
ISBN : 9783319005485
Genre : Mathematics
File Size : 24. 30 MB
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The dimension theory of dynamical systems has progressively developed, especially over the last two decades, into an independent and extremely active field of research. Its main aim is to study the complexity of sets and measures that are invariant under the dynamics. In particular, it is essential to characterizing chaotic strange attractors. To date, some parts of the theory have either only been outlined, because they can be reduced to the case of maps, or are too technical for a wider audience. In this respect, the present monograph is intended to provide a comprehensive guide. Moreover, the text is self-contained and with the exception of some basic results in Chapters 3 and 4, all the results in the book include detailed proofs. The book is intended for researchers and graduate students specializing in dynamical systems who wish to have a sufficiently comprehensive view of the theory together with a working knowledge of its main techniques. The discussion of some open problems is also included in the hope that it may lead to further developments. Ideally, readers should have some familiarity with the basic notions and results of ergodic theory and hyperbolic dynamics at the level of an introductory course in the area, though the initial chapters also review all the necessary material.

Everywhere In The Alpha Dimension

Author : Robert Lee Joseph
ISBN : 1588989976
Genre : Fiction
File Size : 31. 50 MB
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Action transcends galaxies and even dimensions in this fourth exciting installment of the 'Everywhere Adventure Series'. Arch Nemesis Hardison James escapes and causes problems in more than one galaxy and two dimensions.Dr. Jenny Royston Garrett works with the Quorax Epidemic Team and becomes infected with a deadly disease. Hank and his Security team become stranded in the Alpha Dimension. Meredith Royston with her children, Amber and Corey are visiting the Calliope Zoo when the planet is pulled into the Alpha Dimension by the mysterious and deadly Dimensional Rift, wreaking death and destruction on the whole planet.Can Jenny be saved in time and can the team find a way into the other dimension to save their families and teammates?Chantrelle worries about her fianc�, Chad, trapped in the Alpha Dimension with the Galactic Security Team.Find out what happens in this dramatic exciting installment in 'Everywhere in the Alpha Dimension'.


Author : Scientific American
ISBN : 9780226742731
Genre : Science
File Size : 52. 5 MB
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From the Scopes “Monkey Trial” of 1925 to the court ruling against the Dover Area School Board’s proposed intelligent design curriculum in 2005, few scientific topics have engendered as much controversy—or grabbed as many headlines—as evolution. And since the debate shows no signs of abating, there is perhaps no better time to step back and ask: What is evolution? Defined as the gradual process by which something changes into a different and usually more complex and efficient form, evolution explains the formation of the universe, the nature of viruses, and the emergence of humans. A first-rate summary of the actual science of evolution, this Scientific American reader is a timely collection that gives readers an opportunity to consider evolution’s impact in various settings. Divided into four sections that consider the evolution of the universe, cells, dinosaurs, and humans, Evolution brings together more than thirty articles written by some of the world’s most respected evolutionary scientists. As tour guides through the genesis of the universe and complex cells, P. James E. Peebles examines the evidence in support of an expanding cosmos, while Christian de Duve discusses the birth of eukaryotes. In an article that anticipated his book Full House, Stephen Jay Gould argues that chance and contingency are as important as natural selection for evolutionary change. And Ian Tatersall makes two fascinating contributions, submitting his view that the schematic of human evolution looks less like a ladder and more like a bush. With the latest on what’s being researched at every level of evolutionary studies, from prospects of life on other planets to the inner working of cells, Evolution offers general readers an opportunity to update their knowledge on this hot topic while giving students an introduction to the problems and methodologies of an entire field of inquiry.

The Pearson Guide To Objective Physics For The Iit Jee 2 E

Author : Dudeja
ISBN : 8131726770
Genre :
File Size : 59. 79 MB
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Differential Geometry

Author : Robert Geroch
ISBN : 9781927763063
Genre : Science
File Size : 38. 28 MB
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Robert Geroch's lecture notes on differential geometry reflect his original and successful style of teaching - explaining abstract concepts with the help of intuitive examples and many figures. The book introduces the most important concepts of differential geometry and can be used for self-study since each chapter contains examples and exercises, plus test and examination problems which are given in the Appendix. As these lecture notes are written by a theoretical physicist, who is an expert in general relativity, they can serve as a very helpful companion to Geroch's excellent "General Relativity: 1972 Lecture Notes."

Fracture And Complexity

Author : Alberto Carpinteri
ISBN : 9789402420265
Genre : Science
File Size : 87. 84 MB
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The book explores the two opposite natural trends of composite systems: (i) order and structure emerging from heterogeneity and randomness, and (ii) instability and chaos arising from simple nonlinear rules. Providing insights into the rapidly growing field of complexity sciences, the book focuses on the role of complexity in fracture mechanics. It firstly discusses the occurrence of self-similarity and fractal patterns in deformation, damage, fracture, and fragmentation of heterogeneous materials and the apparent scaling of the nominal mechanical properties of disordered materials, as well as of the time-to-failure after fatigue and creep loading. Then the book addresses criticality in the acoustic emissions from damaged structures and tectonic faults. Further, it examines the snap-back instability in the structural behavior of relatively large composite structures in the framework of catastrophe theory, and lastly describes the transition toward chaos in the dynamics of cracked elements.

Handbook Of Discrete And Computational Geometry Third Edition

Author : Csaba D. Toth
ISBN : 9781351645911
Genre : Computers
File Size : 75. 35 MB
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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.

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