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Spectral Theory Of Non Commutative Harmonic Oscillators An Introduction
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Book Synopsis Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction by : Alberto Parmeggiani
Download or read book Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction written by Alberto Parmeggiani and published by Springer Science & Business Media. This book was released on 2010-04-22 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume describes the spectral theory of the Weyl quantization of systems of polynomials in phase-space variables, modelled after the harmonic oscillator. The main technique used is pseudodifferential calculus, including global and semiclassical variants. The main results concern the meromorphic continuation of the spectral zeta function associated with the spectrum, and the localization (and the multiplicity) of the eigenvalues of such systems, described in terms of “classical” invariants (such as the periods of the periodic trajectories of the bicharacteristic flow associated with the eiganvalues of the symbol). The book utilizes techniques that are very powerful and flexible and presents an approach that could also be used for a variety of other problems. It also features expositions on different results throughout the literature.
Book Synopsis Noncommutative Geometry and Physics 3 by : Giuseppe Dito
Download or read book Noncommutative Geometry and Physics 3 written by Giuseppe Dito and published by World Scientific. This book was released on 2013 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative differential geometry has many actual and potential applications to several domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field.
Book Synopsis International Symposium on Mathematics, Quantum Theory, and Cryptography by : Tsuyoshi Takagi
Download or read book International Symposium on Mathematics, Quantum Theory, and Cryptography written by Tsuyoshi Takagi and published by Springer Nature. This book was released on 2020-10-22 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography.
Book Synopsis A Mathematical Approach to Research Problems of Science and Technology by : Ryuei Nishii
Download or read book A Mathematical Approach to Research Problems of Science and Technology written by Ryuei Nishii and published by Springer. This book was released on 2014-07-14 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with one of the most novel advances in mathematical modeling for applied scientific technology, including computer graphics, public-key encryption, data visualization, statistical data analysis, symbolic calculation, encryption, error correcting codes, and risk management. It also shows that mathematics can be used to solve problems from nature, e.g., slime mold algorithms. One of the unique features of this book is that it shows readers how to use pure and applied mathematics, especially those mathematical theory/techniques developed in the twentieth century, and developing now, to solve applied problems in several fields of industry. Each chapter includes clues on how to use "mathematics" to solve concrete problems faced in industry as well as practical applications. The target audience is not limited to researchers working in applied mathematics and includes those in engineering, material sciences, economics, and life sciences.
Book Synopsis Casimir Force, Casimir Operators and the Riemann Hypothesis by : Gerrit Dijk
Download or read book Casimir Force, Casimir Operators and the Riemann Hypothesis written by Gerrit Dijk and published by Walter de Gruyter. This book was released on 2010-10-19 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference "Casimir Force, Casimir Operators and the Riemann Hypothesis – Mathematics for Innovation in Industry and Science" held in November 2009 in Fukuoka (Japan). The motive for the conference was the celebration of the 100th birthday of Casimir and the 150th birthday of the Riemann hypothesis. The conference focused on the following topics: Casimir operators in harmonic analysis and representation theory Number theory, in particular zeta functions and cryptography Casimir force in physics and its relation with nano-science Mathematical biology Importance of mathematics for innovation in industry The latter topic was inspired both by the call for innovation in industry worldwide and by the fact that Casimir, who was the director of Philips research for a long time in his career, had an outspoken opinion on the importance of fundamental science for industry. These proceedings are of interest both to research mathematicians and to those interested in the role science, and in particular mathematics, can play in innovation in industry.
Book Synopsis Mathematical Modelling for Next-Generation Cryptography by : Tsuyoshi Takagi
Download or read book Mathematical Modelling for Next-Generation Cryptography written by Tsuyoshi Takagi and published by Springer. This book was released on 2017-07-25 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematical background underlying security modeling in the context of next-generation cryptography. By introducing new mathematical results in order to strengthen information security, while simultaneously presenting fresh insights and developing the respective areas of mathematics, it is the first-ever book to focus on areas that have not yet been fully exploited for cryptographic applications such as representation theory and mathematical physics, among others. Recent advances in cryptanalysis, brought about in particular by quantum computation and physical attacks on cryptographic devices, such as side-channel analysis or power analysis, have revealed the growing security risks for state-of-the-art cryptographic schemes. To address these risks, high-performance, next-generation cryptosystems must be studied, which requires the further development of the mathematical background of modern cryptography. More specifically, in order to avoid the security risks posed by adversaries with advanced attack capabilities, cryptosystems must be upgraded, which in turn relies on a wide range of mathematical theories. This book is suitable for use in an advanced graduate course in mathematical cryptography, while also offering a valuable reference guide for experts.
Book Synopsis Topics in Algebraic and Topological K-Theory by : Paul Frank Baum
Download or read book Topics in Algebraic and Topological K-Theory written by Paul Frank Baum and published by Springer Science & Business Media. This book was released on 2010-11-05 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories.
Book Synopsis Blow-up Theories for Semilinear Parabolic Equations by : Bei Hu
Download or read book Blow-up Theories for Semilinear Parabolic Equations written by Bei Hu and published by Springer Science & Business Media. This book was released on 2011-03-23 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general equations.
Download or read book Lévy Matters I written by Thomas Duquesne and published by Springer Science & Business Media. This book was released on 2010-09-05 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the breadth of the topic, this volume explores Lévy processes and applications, and presents the state-of-the-art in this evolving area of study. These expository articles help to disseminate important theoretical and applied research to those studying the field.
Book Synopsis Computational Approach to Riemann Surfaces by : Alexander I. Bobenko
Download or read book Computational Approach to Riemann Surfaces written by Alexander I. Bobenko and published by Springer Science & Business Media. This book was released on 2011-02-12 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics.
Book Synopsis Random Perturbation of PDEs and Fluid Dynamic Models by : Franco Flandoli
Download or read book Random Perturbation of PDEs and Fluid Dynamic Models written by Franco Flandoli and published by Springer Science & Business Media. This book was released on 2011-03-11 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explores the random perturbation of PDEs and fluid dynamic models. The text describes the role of additive and bilinear multiplicative noise, and includes examples of abstract parabolic evolution equations.
Author :Catherine Donati Martin Publisher :Springer Science & Business Media ISBN 13 :3642152163 Total Pages :511 pages Book Rating :4.6/5 (421 download)
Book Synopsis Séminaire de Probabilités XLIII by : Catherine Donati Martin
Download or read book Séminaire de Probabilités XLIII written by Catherine Donati Martin and published by Springer Science & Business Media. This book was released on 2010-10-28 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a new volume of the Séminaire de Probabilités which is now in its 43rd year. Following the tradition, this volume contains about 20 original research and survey articles on topics related to stochastic analysis. It contains an advanced course of J. Picard on the representation formulae for fractional Brownian motion. The regular chapters cover a wide range of themes, such as stochastic calculus and stochastic differential equations, stochastic differential geometry, filtrations, analysis on Wiener space, random matrices and free probability, as well as mathematical finance. Some of the contributions were presented at the Journées de Probabilités held in Poitiers in June 2009.
Book Synopsis Topological Complexity of Smooth Random Functions by : Robert Adler
Download or read book Topological Complexity of Smooth Random Functions written by Robert Adler and published by Springer Science & Business Media. This book was released on 2011-05-18 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors’ 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.
Book Synopsis Lebesgue and Sobolev Spaces with Variable Exponents by : Lars Diening
Download or read book Lebesgue and Sobolev Spaces with Variable Exponents written by Lars Diening and published by Springer Science & Business Media. This book was released on 2011-03-31 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.
Book Synopsis The Ricci Flow in Riemannian Geometry by : Ben Andrews
Download or read book The Ricci Flow in Riemannian Geometry written by Ben Andrews and published by Springer Science & Business Media. This book was released on 2011 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.
Book Synopsis Some Mathematical Models from Population Genetics by : Alison Etheridge
Download or read book Some Mathematical Models from Population Genetics written by Alison Etheridge and published by Springer Science & Business Media. This book was released on 2011-01-07 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work reflects sixteen hours of lectures delivered by the author at the 2009 St Flour summer school in probability. It provides a rapid introduction to a range of mathematical models that have their origins in theoretical population genetics. The models fall into two classes: forwards in time models for the evolution of frequencies of different genetic types in a population; and backwards in time (coalescent) models that trace out the genealogical relationships between individuals in a sample from the population. Some, like the classical Wright-Fisher model, date right back to the origins of the subject. Others, like the multiple merger coalescents or the spatial Lambda-Fleming-Viot process are much more recent. All share a rich mathematical structure. Biological terms are explained, the models are carefully motivated and tools for their study are presented systematically.
Book Synopsis Symmetries of Compact Riemann Surfaces by : Emilio Bujalance
Download or read book Symmetries of Compact Riemann Surfaces written by Emilio Bujalance and published by Springer Science & Business Media. This book was released on 2010-10-06 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with symmetries of compact Riemann surfaces. A symmetry of a compact Riemann surface S is an antianalytic involution of S. It is well known that Riemann surfaces exhibiting symmetry correspond to algebraic curves which can be defined over the field of real numbers. In this monograph we consider three topics related to the topology of symmetries, namely the number of conjugacy classes of symmetries, the numbers of ovals of symmetries and the symmetry types of Riemann surfaces.
