Download or read book Kolmogorov s Heritage in Mathematics written by Eric Charpentier and published by Springer Science & Business Media. This book was released on 2007-09-13 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, several world experts present (one part of) the mathematical heritage of Kolmogorov. Each chapter treats one of his research themes or a subject invented as a consequence of his discoveries. The authors present his contributions, his methods, the perspectives he opened to us, and the way in which this research has evolved up to now. Coverage also includes examples of recent applications and a presentation of the modern prospects.
Download or read book Introduction to Arnold s Proof of the Kolmogorov Arnold Moser Theorem written by Achim Feldmeier and published by CRC Press. This book was released on 2022-07-08 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: INTRODUCTION TO ARNOLD’S PROOF OF THE KOLMOGOROV–ARNOLD–MOSER THEOREM This book provides an accessible step-by-step account of Arnold’s classical proof of the Kolmogorov–Arnold–Moser (KAM) Theorem. It begins with a general background of the theorem, proves the famous Liouville–Arnold theorem for integrable systems and introduces Kneser’s tori in four-dimensional phase space. It then introduces and discusses the ideas and techniques used in Arnold’s proof, before the second half of the book walks the reader through a detailed account of Arnold’s proof with all the required steps. It will be a useful guide for advanced students of mathematical physics, in addition to researchers and professionals. Features • Applies concepts and theorems from real and complex analysis (e.g., Fourier series and implicit function theorem) and topology in the framework of this key theorem from mathematical physics. • Covers all aspects of Arnold’s proof, including those often left out in more general or simplifi ed presentations. • Discusses in detail the ideas used in the proof of the KAM theorem and puts them in historical context (e.g., mapping degree from algebraic topology).
Download or read book Kolmogorov in Perspective written by London Mathematical Society and published by . This book was released on 2000 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The editorial board for the History of Mathematics series has selected for this volume a series of translations from two Russian publications, Kolmogorov in Remembrance and Mathematics and its Historical Development. This book, Kolmogorov in Perspective, includes articles written by Kolmogorov's students and colleagues and his personal accounts of shared experiences and lifelong mathematical friendships. The articles combine to give an excellent personal and scientific biography of this important mathematician. There is also an extensive bibliography with the complete list of Kolmogorov's work.
Download or read book Constructivity and Computability in Historical and Philosophical Perspective written by Jacques Dubucs and published by Springer. This book was released on 2014-08-27 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ranging from Alan Turing’s seminal 1936 paper to the latest work on Kolmogorov complexity and linear logic, this comprehensive new work clarifies the relationship between computability on the one hand and constructivity on the other. The authors argue that even though constructivists have largely shed Brouwer’s solipsistic attitude to logic, there remain points of disagreement to this day. Focusing on the growing pains computability experienced as it was forced to address the demands of rapidly expanding applications, the content maps the developments following Turing’s ground-breaking linkage of computation and the machine, the resulting birth of complexity theory, the innovations of Kolmogorov complexity and resolving the dissonances between proof theoretical semantics and canonical proof feasibility. Finally, it explores one of the most fundamental questions concerning the interface between constructivity and computability: whether the theory of recursive functions is needed for a rigorous development of constructive mathematics. This volume contributes to the unity of science by overcoming disunities rather than offering an overarching framework. It posits that computability’s adoption of a classical, ontological point of view kept these imperatives separated. In studying the relationship between the two, it is a vital step forward in overcoming the disagreements and misunderstandings which stand in the way of a unifying view of logic.
Download or read book Electron Model Based on Helmholtz s Electron Vortex Theory Kolmogorov s Theory of Turbulence written by Victor Christianto and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we explore a new electron model based on Helmholtz’s electron vortex and Kolmogorov theory of turbulence. We also discuss a new model of origination of charge and matter.
Download or read book The Splendors and Miseries of Martingales written by Laurent Mazliak and published by Springer Nature. This book was released on 2022-10-17 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past eighty years, martingales have become central in the mathematics of randomness. They appear in the general theory of stochastic processes, in the algorithmic theory of randomness, and in some branches of mathematical statistics. Yet little has been written about the history of this evolution. This book explores some of the territory that the history of the concept of martingales has transformed. The historian of martingales faces an immense task. We can find traces of martingale thinking at the very beginning of probability theory, because this theory was related to gambling, and the evolution of a gambler’s holdings as a result of following a particular strategy can always be understood as a martingale. More recently, in the second half of the twentieth century, martingales became important in the theory of stochastic processes at the very same time that stochastic processes were becoming increasingly important in probability, statistics and more generally in various applied situations. Moreover, a history of martingales, like a history of any other branch of mathematics, must go far beyond an account of mathematical ideas and techniques. It must explore the context in which the evolution of ideas took place: the broader intellectual milieux of the actors, the networks that already existed or were created by the research, even the social and political conditions that favored or hampered the circulation and adoption of certain ideas. This books presents a stroll through this history, in part a guided tour, in part a random walk. First, historical studies on the period from 1920 to 1950 are presented, when martingales emerged as a distinct mathematical concept. Then insights on the period from 1950 into the 1980s are offered, when the concept showed its value in stochastic processes, mathematical statistics, algorithmic randomness and various applications.
Download or read book Kolmogorov in Perspective written by American Mathematical Society and published by Amer Mathematical Society. This book was released on 2000 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The editorial board for the History of Mathematics series has selected for this volume a series of translations from two Russian publications, Kolmogorov in Remembrance and Mathematics and its Historical Development. This book, Kolmogorov in Perspective, includes articles written by Kolmogorov's students and colleagues and his personal accounts of shared experiences and lifelong mathematical friendships. Specifically, the article, "Andrei? Nikolaevich Kolmogorov. A Biographical Sketch of His Life and Creative Paths" by A. N. Shiryaev, gives an excellent personal and scientific biography of Kolmogorov. The volume also includes the following articles: "On A. N. Kolmogorov" by V. I. Arnol'd, "In Memory of A. N. Kolmogorov" by S. M. Nikol'skii?, "Remembrances of A. N. Kolmogorov" by Ya. G. Sinai?, "The Influence of Andrei? Nikolaevich Kolmogorov on My Life" by P. L. Ul'yanov, "A Few Words on A. N. Kolmogorov" by P. S. Aleksandrov, "Memories of P. S. Aleksandrov" by A. N. Kolmogorov, "Newton and Contemporary Mathematical Thought" by A. N. Kolmogorov, and an extensive bibliography with the complete list of Kolmogorov's works-including the articles written for encyclopedias and newspapers. The book is illustrated with photographs and includes quotations from Kolmogorov's letters and conversations, uniquely reflecting his mathematical tastes and opinions. Co-published with the London Mathematical Society. Members of the LMS may order directly from the AMS at the AMS member price.
Download or read book Selected Works of A N Kolmogorov written by Vladimir M. Tikhomirov and published by Springer Science & Business Media. This book was released on 1991-06-30 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Praesidium of the USSR Academy of Sciences has decided to publish three volumes of Selected Works of A.N. Kolmogorov, one of the most prominent mathematicians of the 20th century. The creative work of A.N. Kolmogorov is exceptionally versatile. In his studies on trigonometric and orthogonal series, theory of measure and inte gral, mathematical logic, approximation theory, geometry, topology, functional analysis, classical mechanics, ergodic theory, superposition of functions, and in formation theory, many conceptual and fundamental problems were solved and new questions were posed which gave rise to a great number of investigations. A.N. Kolmogorov is one of the founders of the Soviet school of probability theory, mathematical statistics, and the theory of turbulence. In these areas he obtained a number of basic results, with many applications to mechanics, geophysics, linguistics, biology and other branches of knowledge. This edition includes the most important papers by A.N. Kolmogorov on mathematics and natural science. It does not include philosophical and ped agogical studies of A.N. Kolmogorov, his articles written for the "Bol'shaya Sov'etskaya Entsiklopediya", papers on prosody and various applications of mathematics and publications on general questions. The material of this edition was selected and grouped by A.N. Kolmogorov.
Download or read book Complexity and Evolution of Dissipative Systems written by Sergey Vakulenko and published by Walter de Gruyter. This book was released on 2013-11-27 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the dynamic complexity of neural, genetic networks, and reaction diffusion systems. The author shows that all robust attractors can be realized in dynamics of such systems. In particular, a positive solution of the Ruelle-Takens hypothesis for on chaos existence for large class of reaction-diffusion systems is given. The book considers viability problems for such systems - viability under extreme random perturbations - and discusses an interesting hypothesis of M. Gromov and A. Carbone on biological evolution. There appears a connection with the Kolmogorov complexity theory. As applications, transcription-factors-microRNA networks are considered, patterning in biology, a new approach to estimate the computational power of neural and genetic networks, social and economical networks, and a connection with the hard combinatorial problems.
Download or read book Commutative Algebra Constructive Methods written by Henri Lombardi and published by Springer. This book was released on 2015-07-22 with total page 1033 pages. Available in PDF, EPUB and Kindle. Book excerpt: Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra. It takes a constructive viewpoint in commutative algebra and studies algorithmic approaches alongside several abstract classical theories. Indeed, it revisits these traditional topics with a new and simplifying manner, making the subject both accessible and innovative. The algorithmic aspects of such naturally abstract topics as Galois theory, Dedekind rings, Prüfer rings, finitely generated projective modules, dimension theory of commutative rings, and others in the current treatise, are all analysed in the spirit of the great developers of constructive algebra in the nineteenth century. This updated and revised edition contains over 350 well-arranged exercises, together with their helpful hints for solution. A basic knowledge of linear algebra, group theory, elementary number theory as well as the fundamentals of ring and module theory is required. Commutative Algebra: Constructive Methods will be useful for graduate students, and also researchers, instructors and theoretical computer scientists.
Download or read book A Random Walk in Physics written by Massimo Cencini and published by Springer Nature. This book was released on 2021-06-15 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an informal, easy-to-understand account of topics in modern physics and mathematics. The focus is, in particular, on statistical mechanics, soft matter, probability, chaos, complexity, and models, as well as their interplay. The book features 28 key entries and it is carefully structured so as to allow readers to pursue different paths that reflect their interests and priorities, thereby avoiding an excessively systematic presentation that might stifle interest. While the majority of the entries concern specific topics and arguments, some relate to important protagonists of science, highlighting and explaining their contributions. Advanced mathematics is avoided, and formulas are introduced in only a few cases. The book is a user-friendly tool that nevertheless avoids scientific compromise. It is of interest to all who seek a better grasp of the world that surrounds us and of the ideas that have changed our perceptions.
Download or read book Reaction Kinetics Exercises Programs and Theorems written by János Tóth and published by Springer. This book was released on 2018-09-18 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fifty years ago, a new approach to reaction kinetics began to emerge: one based on mathematical models of reaction kinetics, or formal reaction kinetics. Since then, there has been a rapid and accelerated development in both deterministic and stochastic kinetics, primarily because mathematicians studying differential equations and algebraic geometry have taken an interest in the nonlinear differential equations of kinetics, which are relatively simple, yet capable of depicting complex behavior such as oscillation, chaos, and pattern formation. The development of stochastic models was triggered by the fact that novel methods made it possible to measure molecules individually. Now it is high time to make the results of the last half-century available to a larger audience: students of chemistry, chemical engineering and biochemistry, not to mention applied mathematics. Based on recent papers, this book presents the most important concepts and results, together with a wealth of solved exercises. The book is accompanied by the authors’ Mathematica package, ReactionKinetics, which helps both students and scholars in their everyday work, and which can be downloaded from http://extras.springer.com/ and also from the authors’ websites. Further, the large set of unsolved problems provided may serve as a springboard for individual research.
Download or read book Russian Mathematicians In The 20th Century written by Yakov Sinai and published by World Scientific. This book was released on 2003-10-08 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 20th century, many mathematicians in Russia made great contributions to the field of mathematics. This invaluable book, which presents the main achievements of Russian mathematicians in that century, is the first most comprehensive book on Russian mathematicians. It has been produced as a gesture of respect and appreciation for those mathematicians and it will serve as a good reference and an inspiration for future mathematicians. It presents differences in mathematical styles and focuses on Soviet mathematicians who often discussed “what to do” rather than “how to do it”. Thus, the book will be valued beyond historical documentation.The editor, Professor Yakov Sinai, a distinguished Russian mathematician, has taken pains to select leading Russian mathematicians — such as Lyapunov, Luzin, Egorov, Kolmogorov, Pontryagin, Vinogradov, Sobolev, Petrovski and Krein — and their most important works. One can, for example, find works of Lyapunov, which parallel those of Poincaré; and works of Luzin, whose analysis plays a very important role in the history of Russian mathematics; Kolmogorov has established the foundations of probability based on analysis. The editor has tried to provide some parity and, at the same time, included papers that are of interest even today.The original works of the great mathematicians will prove to be enjoyable to readers and useful to the many researchers who are preserving the interest in how mathematics was done in the former Soviet Union.
Download or read book Physics beyond catching a mouse in the dark From Big Science to Deep Science written by Victor Christianto and published by Infinite Study. This book was released on with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Higgs particle has been detected a few years ago, that is what newspapers tell us. For many physicists, the Standard Model of particle physics has accomplished all the jobs. Or to put it simply: The game is over. Is it true? Then some physicists began to ask: can go beyond the Standard Model? Because the supersymmetric extension of the Standard Model has failed. If you feel that theoretical physics is becoming boring, you are not alone. Fortunately, there is good news: a new generation of physicists are doing table-top experiments in their basements. Can we expect new results later? If so, what will the future of physics look like? This article discusses this question, starting with a blunt look at the relationship between mathematics and physical reality, written from the perspectives of a mathematician and a cosmologist.
Download or read book The Mathematics Behind Biological Invasions written by Mark A. Lewis and published by Springer. This book was released on 2016-05-05 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates the mathematical analysis of biological invasions. Unlike purely qualitative treatments of ecology, it draws on mathematical theory and methods, equipping the reader with sharp tools and rigorous methodology. Subjects include invasion dynamics, species interactions, population spread, long-distance dispersal, stochastic effects, risk analysis, and optimal responses to invaders. While based on the theory of dynamical systems, including partial differential equations and integrodifference equations, the book also draws on information theory, machine learning, Monte Carlo methods, optimal control, statistics, and stochastic processes. Applications to real biological invasions are included throughout. Ultimately, the book imparts a powerful principle: that by bringing ecology and mathematics together, researchers can uncover new understanding of, and effective response strategies to, biological invasions. It is suitable for graduate students and established researchers in mathematical ecology.
Download or read book Paul L vy and Maurice Fr chet written by Marc Barbut and published by Springer Science & Business Media. This book was released on 2013-11-29 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fascinating correspondence between Paul Lévy and Maurice Fréchet spans an extremely active period in French mathematics during the twentieth century. The letters of these two Frenchmen show their vicissitudes of research and passionate enthusiasm for the emerging field of modern probability theory. The letters cover various topics of mathematical importance including academic careers and professional travels, issues concerning students and committees, and the difficulties both mathematicians met to be elected to the Paris Academy of Sciences. The technical questions that occupied Lévy and Fréchet on almost a daily basis are the primary focus of these letters, which are charged with elation, frustration and humour. Their mathematical victories and setbacks unfolded against the dramatic backdrop of the two World Wars and the occupation of France, during which Lévy was obliged to go into hiding. The clear and persistent desire of these mathematicians to continue their work whatever the circumstance testifies to the enlightened spirit of their discipline which was persistent against all odds. The book contains a detailed and comprehensive introduction to the central topics of the correspondence. The original text of the letters is also annotated by numerous footnotes for helpful guidance. Paul Lévy and Maurice Fréchet will be useful to anybody interested in the history of mathematics in the twentieth century and, in particular, the birth of modern probab ility theory.
Download or read book Russian Mathematicians in the 20th Century written by Yakov Sinai and published by World Scientific. This book was released on 2003 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 20th century, many mathematicians in Russia made great contributions to the field of mathematics. This invaluable book, which presents the main achievements of Russian mathematicians in that century, is the first most comprehensive book on Russian mathematicians. It has been produced as a gesture of respect and appreciation for those mathematicians and it will serve as a good reference and an inspiration for future mathematicians. It presents differences in mathematical styles and focuses on Soviet mathematicians who often discussed “what to do” rather than “how to do it”. Thus, the book will be valued beyond historical documentation.The editor, Professor Yakov Sinai, a distinguished Russian mathematician, has taken pains to select leading Russian mathematicians — such as Lyapunov, Luzin, Egorov, Kolmogorov, Pontryagin, Vinogradov, Sobolev, Petrovski and Krein — and their most important works. One can, for example, find works of Lyapunov, which parallel those of Poincaré; and works of Luzin, whose analysis plays a very important role in the history of Russian mathematics; Kolmogorov has established the foundations of probability based on analysis. The editor has tried to provide some parity and, at the same time, included papers that are of interest even today.The original works of the great mathematicians will prove to be enjoyable to readers and useful to the many researchers who are preserving the interest in how mathematics was done in the former Soviet Union.
