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Multiplicative Invariant Fields Of Dimension Leq 6
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Book Synopsis Multiplicative Invariant Fields of Dimension $leq 6$ by : Akinari Hoshi
Download or read book Multiplicative Invariant Fields of Dimension $leq 6$ written by Akinari Hoshi and published by American Mathematical Society. This book was released on 2023-03-09 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Algebraic Complexity Theory by : Peter Bürgisser
Download or read book Algebraic Complexity Theory written by Peter Bürgisser and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under standing of the intrinsic computational difficulty of problems.
Book Synopsis H Ring Spectra and Their Applications by : Robert R. Bruner
Download or read book H Ring Spectra and Their Applications written by Robert R. Bruner and published by Springer. This book was released on 2006-11-14 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Amenability by : Alan L. T. Paterson
Download or read book Amenability written by Alan L. T. Paterson and published by American Mathematical Soc.. This book was released on 1988 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of amenability has its roots in the work of Lebesgue at the turn of the century. In the 1940s, the subject began to shift from finitely additive measures to means. This shift is of fundamental importance, for it makes the substantial resources of functional analysis and abstract harmonic analysis available to the study of amenability. The ubiquity of amenability ideas and the depth of the mathematics involved points to the fundamental importance of the subject. This book presents a comprehensive and coherent account of amenability as it has been developed in the large and varied literature during this century. The book has a broad appeal, for it presents an account of the subject based on harmonic and functional analysis. In addition, the analytic techniques should be of considerable interest to analysts in all areas. In addition, the book contains applications of amenability to a number of areas: combinatorial group theory, semigroup theory, statistics, differential geometry, Lie groups, ergodic theory, cohomology, and operator algebras. The main objectives of the book are to provide an introduction to the subject as a whole and to go into many of its topics in some depth. The book begins with an informal, nontechnical account of amenability from its origins in the work of Lebesgue. The initial chapters establish the basic theory of amenability and provide a detailed treatment of invariant, finitely additive measures (i.e., invariant means) on locally compact groups. The author then discusses amenability for Lie groups, "almost invariant" properties of certain subsets of an amenable group, amenability and ergodic theorems, polynomial growth, and invariant mean cardinalities. Also included are detailed discussions of the two most important achievements in amenability in the 1980s: the solutions to von Neumann's conjecture and the Banach-Ruziewicz Problem. The main prerequisites for this book are a sound understanding of undergraduate-level mathematics and a knowledge of abstract harmonic analysis and functional analysis. The book is suitable for use in graduate courses, and the lists of problems in each chapter may be useful as student exercises.
Book Synopsis Systolic Geometry and Topology by : Mikhail Gersh Katz
Download or read book Systolic Geometry and Topology written by Mikhail Gersh Katz and published by American Mathematical Soc.. This book was released on 2007 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: The systole of a compact metric space $X$ is a metric invariant of $X$, defined as the least length of a noncontractible loop in $X$. When $X$ is a graph, the invariant is usually referred to as the girth, ever since the 1947 article by W. Tutte. The first nontrivial results for systoles of surfaces are the two classical inequalities of C. Loewner and P. Pu, relying on integral-geometric identities, in the case of the two-dimensional torus and real projective plane, respectively. Currently, systolic geometry is a rapidly developing field, which studies systolic invariants in their relation to other geometric invariants of a manifold. This book presents the systolic geometry of manifolds and polyhedra, starting with the two classical inequalities, and then proceeding to recent results, including a proof of M. Gromov's filling area conjecture in a hyperelliptic setting. It then presents Gromov's inequalities and their generalisations, as well as asymptotic phenomena for systoles of surfaces of large genus, revealing a link both to ergodic theory and to properties of congruence subgroups of arithmetic groups. The author includes results on the systolic manifestations of Massey products, as well as of the classical Lusternik-Schnirelmann category.
Download or read book Differential Algebraic Groups written by and published by Academic Press. This book was released on 1985-01-25 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Algebraic Groups
Book Synopsis Class Field Theory by : Georges Gras
Download or read book Class Field Theory written by Georges Gras and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Global class field theory is a major achievement of algebraic number theory based on the functorial properties of the reciprocity map and the existence theorem. This book explores the consequences and the practical use of these results in detailed studies and illustrations of classical subjects. In the corrected second printing 2005, the author improves many details all through the book.
Book Synopsis The Arithmetic of Elliptic Curves by : Joseph H. Silverman
Download or read book The Arithmetic of Elliptic Curves written by Joseph H. Silverman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.
Book Synopsis Introduction to Lie Algebras by : K. Erdmann
Download or read book Introduction to Lie Algebras written by K. Erdmann and published by Springer Science & Business Media. This book was released on 2006-09-28 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous worked examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions. Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.
Book Synopsis Representations and Nilpotent Orbits of Lie Algebraic Systems by : Maria Gorelik
Download or read book Representations and Nilpotent Orbits of Lie Algebraic Systems written by Maria Gorelik and published by Springer Nature. This book was released on 2019-10-18 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.
Book Synopsis Index to Theses with Abstracts Accepted for Higher Degrees by the Universities of Great Britain and Ireland and the Council for National Academic Awards by :
Download or read book Index to Theses with Abstracts Accepted for Higher Degrees by the Universities of Great Britain and Ireland and the Council for National Academic Awards written by and published by . This book was released on 2008 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Variational Analysis and Aerospace Engineering by : Giuseppe Buttazzo
Download or read book Variational Analysis and Aerospace Engineering written by Giuseppe Buttazzo and published by Springer Science & Business Media. This book was released on 2009-08-21 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Variational Analysis and Aerospace Engineering conference held in Erice, Italy in September 2007 at International School of Mathematics, Guido Stampacchia provided a platform for aerospace engineers and mathematicians to discuss the problems requiring an extensive application of mathematics. This work contains papers presented at the workshop.
Download or read book 数论导引 written by and published by . This book was released on 2007 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: 本书内容包括素数、无理数、同余、费马定理、连分数、不定方程、二次域、算术函数、分化等。
Book Synopsis Geometric Representation Theory and Gauge Theory by : Alexander Braverman
Download or read book Geometric Representation Theory and Gauge Theory written by Alexander Braverman and published by Springer Nature. This book was released on 2019-11-22 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a review of the vibrant areas of geometric representation theory and gauge theory, which are characterized by a merging of traditional techniques in representation theory with the use of powerful tools from algebraic geometry, and with strong inputs from physics. The notes are based on lectures delivered at the CIME school "Geometric Representation Theory and Gauge Theory" held in Cetraro, Italy, in June 2018. They comprise three contributions, due to Alexander Braverman and Michael Finkelberg, Andrei Negut, and Alexei Oblomkov, respectively. Braverman and Finkelberg’s notes review the mathematical theory of the Coulomb branch of 3D N=4 quantum gauge theories. The purpose of Negut’s notes is to study moduli spaces of sheaves on a surface, as well as Hecke correspondences between them. Oblomkov's notes concern matrix factorizations and knot homology. This book will appeal to both mathematicians and theoretical physicists and will be a source of inspiration for PhD students and researchers.
Book Synopsis Signal Processing Noise by : Vyacheslav Tuzlukov
Download or read book Signal Processing Noise written by Vyacheslav Tuzlukov and published by CRC Press. This book was released on 2018-10-08 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: Additive and multiplicative noise in the information signal can significantly limit the potential of complex signal processing systems, especially when those systems use signals with complex phase structure. During the last few years this problem has been the focus of much research, and its solution could lead to profound improvements in applications of complex signals and coherent signal processing. Signal Processing Noise sets forth a generalized approach to signal processing in multiplicative and additive noise that represents a remarkable advance in signal processing and detection theory. This approach extends the boundaries of the noise immunity set by classical and modern signal processing theories, and systems constructed on this basis achieve better detection performance than that of systems currently in use. Featuring the results of the author's own research, the book is filled with examples and applications, and each chapter contains an analysis of recent observations obtained by computer modelling and experiments. Tables and illustrations clearly show the superiority of the generalized approach over both classical and modern approaches to signal processing noise. Addressing a fundamental problem in complex signal processing systems, this book offers not only theoretical development, but practical recommendations for raising noise immunity in a wide range of applications.
Book Synopsis Geometric Aspects of Functional Analysis by : Bo'az Klartag
Download or read book Geometric Aspects of Functional Analysis written by Bo'az Klartag and published by Springer Nature. This book was released on 2020-07-08 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continuing the theme of the previous volumes, these seminar notes reflect general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. Two classical topics represented are the Concentration of Measure Phenomenon in the Local Theory of Banach Spaces, which has recently had triumphs in Random Matrix Theory, and the Central Limit Theorem, one of the earliest examples of regularity and order in high dimensions. Central to the text is the study of the Poincaré and log-Sobolev functional inequalities, their reverses, and other inequalities, in which a crucial role is often played by convexity assumptions such as Log-Concavity. The concept and properties of Entropy form an important subject, with Bourgain's slicing problem and its variants drawing much attention. Constructions related to Convexity Theory are proposed and revisited, as well as inequalities that go beyond the Brunn–Minkowski theory. One of the major current research directions addressed is the identification of lower-dimensional structures with remarkable properties in rather arbitrary high-dimensional objects. In addition to functional analytic results, connections to Computer Science and to Differential Geometry are also discussed.
Book Synopsis Physics and Astrophysics of Neutrinos by : Masataka Fukugita
Download or read book Physics and Astrophysics of Neutrinos written by Masataka Fukugita and published by Springer Science & Business Media. This book was released on 2013-12-14 with total page 947 pages. Available in PDF, EPUB and Kindle. Book excerpt: Observations of neutrinos being emitted by the supernova SN1987A, star neutrinos, and atmospheric neutrinos have provided new insights into astronomy, as well as new unresolved phenomena such as the solar neutrino problem, spurring investigative studies among particle physicists and astrophysicists. One of the most important features of this book is its enumeration of a number of basic properties of neutrinos and their relationship to Grand Unified Theories, focusing on the origin of the neutrino's mass and the generation mixing of neutrinos. All the kamiokande results, detector performances, and complete references are included.
