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Geometry Of The Semigroup Z 0n And Its Applications To Combinatorics Algebra And Differential Equations
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Book Synopsis Geometry of the Semigroup Z_(≥0)^n and its Applications to Combinatorics, Algebra and Differential Equations by : Sergey Chulkov
Download or read book Geometry of the Semigroup Z_(≥0)^n and its Applications to Combinatorics, Algebra and Differential Equations written by Sergey Chulkov and published by Springer. This book was released on 2016-07-10 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This vital contribution to the mathematical literature on combinatorics, algebra and differential equations develops two fundamental finiteness properties of the semigroup Z_(≥0)^n that elucidate key aspects of theories propounded by, among others, Hilbert and Kouchnirenko. The authors provide explanations for numerous results in the field that appear at first glance to be unrelated. The first finiteness property relates to the fact that Z_(≥0)^n can be represented in the form of a finite union of shifted n-dimensional octants, while the second asserts that any co-ideal of the semigroup can be represented as a finite, disjoint union of shifted co-ordinate octants. The applications of their work include proof that Hilbert’s implication that dimension d of the affine variety X equals the degree of Hilbert’s polynomial can be developed until its degree X equates to the leading coefficient of the Hilbert polynomial multiplied by d. The volume is a major forward step in this field.
Book Synopsis Structured Ring Spectra by : Andrew Baker
Download or read book Structured Ring Spectra written by Andrew Baker and published by Cambridge University Press. This book was released on 2004-11-18 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains some important new contributions to the theory of structured ring spectra.
Book Synopsis Combinatorial Geometry with Applications to Field Theory, Second Edition, graduate textbook in mathematics by : Linfan Mao
Download or read book Combinatorial Geometry with Applications to Field Theory, Second Edition, graduate textbook in mathematics written by Linfan Mao and published by Infinite Study. This book was released on 2011 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Singularities and Computer Algebra by : Christoph Lossen
Download or read book Singularities and Computer Algebra written by Christoph Lossen and published by Cambridge University Press. This book was released on 2006-04-06 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of articles giving overviews and open questions in singularities and their computational aspects.
Book Synopsis Combinatorial Geometry with Applications to Field Theory by : Linfan Mao
Download or read book Combinatorial Geometry with Applications to Field Theory written by Linfan Mao and published by Infinite Study. This book was released on 2009 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is motivated with surveying mathematics and physics by CC conjecture, i.e., a mathematical science can be reconstructed from or made by combinatorialization. Topics covered in this book include fundamental of mathematical combinatorics, differential Smarandache n-manifolds, combinatorial or differentiable manifolds and submanifolds, Lie multi-groups, combinatorial principal fiber bundles, gravitational field, quantum fields with their combinatorial generalization, also with discussions on fundamental questions in epistemology. All of these are valuable for researchers in combinatorics, topology, differential geometry, gravitational or quantum fields.
Book Synopsis Algebraic, Analytic, and Geometric Notions of Largeness for Subsets of Zd and Their Applications by : Daniel G. Glasscock
Download or read book Algebraic, Analytic, and Geometric Notions of Largeness for Subsets of Zd and Their Applications written by Daniel G. Glasscock and published by . This book was released on 2017 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we investigate the relationships between and applications of several different notions of largeness for subsets of Zd, the d-dimensional integer lattice, and, more generally, groups and semigroups. The various meanings of the word "large" appearing here are inspired by ideas in algebra, analysis, and geometry and are significant for their historical influence and usefulness in applications to combinatorics and number theory. This work is comprised of three main parts. In the first, we study the relationships between several naturally occurring notions of additive and multiplicative largeness in rings and semirings. We harness these relationships and the ideas behind them to give a number of novel applications at the intersection of Ramsey theory and number theory. In the second part, we introduce the mass and counting measures and dimensions for subsets of Zd and explore the properties of large fractal subsets of the lattice. In particular, we prove analogues of Marstrand’s projection theorem and derive applications concerning the size of sumsets of dilated subsets of Z. We then show how to derive the classic projection theorems of Marstrand and Kaufman, along with an open conjecture of Oberlin, from their discrete analogues. In the third part, we study the existence of certain combinatorial configurations in members of a family of fractal subsets of the natural numbers, the Piatetski-Shapiro sets. We provide a metrical solution to the problem of determining which Piatetski-Shapiro sets contain infinitely many solutions to bivariate linear equations.
Book Synopsis Functional Analysis, Sobolev Spaces and Partial Differential Equations by : Haim Brezis
Download or read book Functional Analysis, Sobolev Spaces and Partial Differential Equations written by Haim Brezis and published by Springer Science & Business Media. This book was released on 2010-11-02 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
Book Synopsis Semigroup Methods for Evolution Equations on Networks by : Delio Mugnolo
Download or read book Semigroup Methods for Evolution Equations on Networks written by Delio Mugnolo and published by Springer. This book was released on 2014-05-21 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise text is based on a series of lectures held only a few years ago and originally intended as an introduction to known results on linear hyperbolic and parabolic equations. Yet the topic of differential equations on graphs, ramified spaces, and more general network-like objects has recently gained significant momentum and, well beyond the confines of mathematics, there is a lively interdisciplinary discourse on all aspects of so-called complex networks. Such network-like structures can be found in virtually all branches of science, engineering and the humanities, and future research thus calls for solid theoretical foundations. This book is specifically devoted to the study of evolution equations – i.e., of time-dependent differential equations such as the heat equation, the wave equation, or the Schrödinger equation (quantum graphs) – bearing in mind that the majority of the literature in the last ten years on the subject of differential equations of graphs has been devoted to elliptic equations and related spectral problems. Moreover, for tackling the most general settings - e.g. encoded in the transmission conditions in the network nodes - one classical and elegant tool is that of operator semigroups. This book is simultaneously a very concise introduction to this theory and a handbook on its applications to differential equations on networks. With a more interdisciplinary readership in mind, full proofs of mathematical statements have been frequently omitted in favor of keeping the text as concise, fluid and self-contained as possible. In addition, a brief chapter devoted to the field of neurodynamics of the brain cortex provides a concrete link to ongoing applied research.
Book Synopsis Combinatorial Commutative Algebra by : Ezra Miller
Download or read book Combinatorial Commutative Algebra written by Ezra Miller and published by Springer Science & Business Media. This book was released on 2005-06-21 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs
Book Synopsis Computations in Algebraic Geometry with Macaulay 2 by : David Eisenbud
Download or read book Computations in Algebraic Geometry with Macaulay 2 written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications. The algorithmic tools presented here are designed to serve readers wishing to bring such tools to bear on their own problems. The first part of the book covers Macaulay 2 using concrete applications; the second emphasizes details of the mathematics.
Book Synopsis Cohen-Macaulay Representations by : Graham J. Leuschke
Download or read book Cohen-Macaulay Representations written by Graham J. Leuschke and published by American Mathematical Soc.. This book was released on 2012-05-02 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive treatment of the representation theory of maximal Cohen-Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative algebra, singularity theory, and representations of groups and algebras. Two introductory chapters treat the Krull-Remak-Schmidt Theorem on uniqueness of direct-sum decompositions and its failure for modules over local rings. Chapters 3-10 study the central problem of classifying the rings with only finitely many indecomposable MCM modules up to isomorphism, i.e., rings of finite CM type. The fundamental material--ADE/simple singularities, the double branched cover, Auslander-Reiten theory, and the Brauer-Thrall conjectures--is covered clearly and completely. Much of the content has never before appeared in book form. Examples include the representation theory of Artinian pairs and Burban-Drozd's related construction in dimension two, an introduction to the McKay correspondence from the point of view of maximal Cohen-Macaulay modules, Auslander-Buchweitz's MCM approximation theory, and a careful treatment of nonzero characteristic. The remaining seven chapters present results on bounded and countable CM type and on the representation theory of totally reflexive modules.
Book Synopsis Combinatorial Algebra: Syntax and Semantics by : Mark V. Sapir
Download or read book Combinatorial Algebra: Syntax and Semantics written by Mark V. Sapir and published by Springer. This book was released on 2014-10-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial Algebra: Syntax and Semantics provides comprehensive account of many areas of combinatorial algebra. It contains self-contained proofs of more than 20 fundamental results, both classical and modern. This includes Golod–Shafarevich and Olshanskii's solutions of Burnside problems, Shirshov's solution of Kurosh's problem for PI rings, Belov's solution of Specht's problem for varieties of rings, Grigorchuk's solution of Milnor's problem, Bass–Guivarc'h theorem about growth of nilpotent groups, Kleiman's solution of Hanna Neumann's problem for varieties of groups, Adian's solution of von Neumann-Day's problem, Trahtman's solution of the road coloring problem of Adler, Goodwyn and Weiss. The book emphasize several ``universal" tools, such as trees, subshifts, uniformly recurrent words, diagrams and automata. With over 350 exercises at various levels of difficulty and with hints for the more difficult problems, this book can be used as a textbook, and aims to reach a wide and diversified audience. No prerequisites beyond standard courses in linear and abstract algebra are required. The broad appeal of this textbook extends to a variety of student levels: from advanced high-schoolers to undergraduates and graduate students, including those in search of a Ph.D. thesis who will benefit from the “Further reading and open problems” sections at the end of Chapters 2 –5. The book can also be used for self-study, engaging those beyond t he classroom setting: researchers, instructors, students, virtually anyone who wishes to learn and better understand this important area of mathematics.
Book Synopsis Partial Differential Equations by : Lawrence C. Evans
Download or read book Partial Differential Equations written by Lawrence C. Evans and published by American Mathematical Society. This book was released on 2022-03-22 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE. For this edition, the author has made numerous changes, including a new chapter on nonlinear wave equations, more than 80 new exercises, several new sections, a significantly expanded bibliography. About the First Edition: I have used this book for both regular PDE and topics courses. It has a wonderful combination of insight and technical detail. … Evans' book is evidence of his mastering of the field and the clarity of presentation. —Luis Caffarelli, University of Texas It is fun to teach from Evans' book. It explains many of the essential ideas and techniques of partial differential equations … Every graduate student in analysis should read it. —David Jerison, MIT I usePartial Differential Equationsto prepare my students for their Topic exam, which is a requirement before starting working on their dissertation. The book provides an excellent account of PDE's … I am very happy with the preparation it provides my students. —Carlos Kenig, University of Chicago Evans' book has already attained the status of a classic. It is a clear choice for students just learning the subject, as well as for experts who wish to broaden their knowledge … An outstanding reference for many aspects of the field. —Rafe Mazzeo, Stanford University
Book Synopsis Clifford Algebras And Zeons: Geometry To Combinatorics And Beyond by : George Stacey Staples
Download or read book Clifford Algebras And Zeons: Geometry To Combinatorics And Beyond written by George Stacey Staples and published by World Scientific. This book was released on 2019-09-24 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clifford algebras have many well-known applications in physics, engineering, and computer graphics. Zeon algebras are subalgebras of Clifford algebras whose combinatorial properties lend them to graph-theoretic applications such as enumerating minimal cost paths in dynamic networks. This book provides a foundational working knowledge of zeon algebras, their properties, and their potential applications in an increasingly technological world.As a graduate-level or advanced undergraduate-level mathematics textbook, it is suitable for self-study by researchers interested in new approaches to existing combinatorial problems and applications (wireless networks, Boolean satisfiability, coding theory, etc.).As the first textbook to explore algebraic and combinatorial properties of zeon algebras in depth, it is suitable for interdisciplinary study in analysis, algebra, and combinatorics. The material is complemented by the CliffMath software package for Mathematica, which is freely available through the book's webpage.
Download or read book Mathematical Reviews written by and published by . This book was released on 1994 with total page 1032 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Analytic Combinatorics by : Philippe Flajolet
Download or read book Analytic Combinatorics written by Philippe Flajolet and published by Cambridge University Press. This book was released on 2009-01-15 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Book Synopsis Operator Calculus On Graphs: Theory And Applications In Computer Science by : George Stacey Staples
Download or read book Operator Calculus On Graphs: Theory And Applications In Computer Science written by George Stacey Staples and published by World Scientific. This book was released on 2012-02-23 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science.Presented in this book are new methods, built on the algebraic framework of Clifford algebras, for tackling important real world problems related, but not limited to, wireless communications, neural networks, electrical circuits, transportation, and the world wide web. Examples are put forward in Mathematica throughout the book, together with packages for performing symbolic computations.
