Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately.
This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1984.
This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1988.
The Putin and Bush presidencies, the 9/11 attack, and the war in Iraq have changed the dynamics of Russian-European-US relations and strained the Western alliance. Featuring contributions by leading experts in the field, this work is the first systematic effort to reassess the status of Russia's modernization efforts in this context. Part I examines political, economic, legal, and cultural developments in Russia for evidence of convergence with Western norms. In Part II, the contributors systematically analyze Russia's relations with the European Union, Eastern Europe, Central Asia, and the United States in light of new security concerns and changing economic and power relationships.
This book addresses the issue of cognitive semantics’ aspects that cannot be represented by traditional digital and logical means. The problem of creating cognitive semantics can be resolved in an indirect way. The electromagnetic waves, quantum fields, beam of light, chaos control, relativistic theory, cosmic string recognition, category theory, group theory, and so on can be used for this aim. Since the term artificial intelligence (AI) appeared, various versions of logic have been created; many heuristics for neural networks deep learning have been made; new nature-like algorithms have been suggested. At the same time, the initial digital, logical, and neural network principles of representation of knowledge in AI systems have not changed a lot. The researches of these aspects of cognitive semantics of AI are based on the author's convergent methodology, which provides the necessary conditions for purposeful and sustainable convergence of decision-making.
This monograph provides both an introduction to and a thorough exposition of the theory of rate-independent systems, which the authors have been working on with a lot of collaborators over 15 years. The focus is mostly on fully rate-independent systems, first on an abstract level either with or even without a linear structure, discussing various concepts of solutions with full mathematical rigor. Then, usefulness of the abstract concepts is demonstrated on the level of various applications primarily in continuum mechanics of solids, including suitable approximation strategies with guaranteed numerical stability and convergence. Particular applications concern inelastic processes such as plasticity, damage, phase transformations, or adhesive-type contacts both at small strains and at finite strains. A few other physical systems, e.g. magnetic or ferroelectric materials, and couplings to rate-dependent thermodynamic models are considered as well. Selected applications are accompanied by numerical simulations illustrating both the models and the efficiency of computational algorithms. In this book, the mathematical framework for a rigorous mathematical treatment of "rate-independent systems" is presented in a comprehensive form for the first time. Researchers and graduate students in applied mathematics, engineering, and computational physics will find this timely and well written book useful.
Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.
The book presents a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a priori differential structure (Whitney problems). The account covers development of the area from the initial classical works of the first half of the 20th century to the flourishing period of the last decade. Seemingly very specific these problems have been from the very beginning a powerful source of ideas, concepts and methods that essentially influenced and in some cases even transformed considerable areas of analysis. Aside from the material linked by the aforementioned problems the book also is unified by geometric analysis approach used in the proofs of basic results. This requires a variety of geometric tools from convex and combinatorial geometry to geometry of metric space theory to Riemannian and coarse geometry and more. The necessary facts are presented mostly with detailed proofs to make the book accessible to a wide audience.
This book focuses on organization and mechanisms of expert decision-making support using modern information and communication technologies, as well as information analysis and collective intelligence technologies (electronic expertise or simply e-expertise). Chapter 1 (E-Expertise) discusses the role of e-expertise in decision-making processes. The procedures of e-expertise are classified, their benefits and shortcomings are identified and the efficiency conditions are considered. Chapter 2 (Expert Technologies and Principles) provides a comprehensive overview of modern expert technologies. A special emphasis is placed on the specifics of e-expertise. Moreover, the authors study the feasibility and reasonability of employing well-known methods and approaches in e-expertise. Chapter 3 (E-Expertise: Organization and Technologies) describes some examples of up-to-date technologies to perform e-expertise. Chapter 4 (Trust Networks and Competence Networks) deals with the problems of expert finding and grouping by information and communication technologies. Chapter 5 (Active Expertise) treats the problem of expertise stability against any strategic manipulation by experts or coordinators pursuing individual goals. The book addresses a wide range of readers interested in management, decision-making and expert activity in political, economic, social and industrial spheres.
This book addresses the issue of cognitive semantics’ aspects that cannot be represented by traditional digital and logical means. The problem of creating cognitive semantics can be resolved in an indirect way. The electromagnetic waves, quantum fields, beam of light, chaos control, relativistic theory, cosmic string recognition, category theory, group theory, and so on can be used for this aim. Since the term artificial intelligence (AI) appeared, various versions of logic have been created; many heuristics for neural networks deep learning have been made; new nature-like algorithms have been suggested. At the same time, the initial digital, logical, and neural network principles of representation of knowledge in AI systems have not changed a lot. The researches of these aspects of cognitive semantics of AI are based on the author's convergent methodology, which provides the necessary conditions for purposeful and sustainable convergence of decision-making.
This book focuses on organization and mechanisms of expert decision-making support using modern information and communication technologies, as well as information analysis and collective intelligence technologies (electronic expertise or simply e-expertise). Chapter 1 (E-Expertise) discusses the role of e-expertise in decision-making processes. The procedures of e-expertise are classified, their benefits and shortcomings are identified and the efficiency conditions are considered. Chapter 2 (Expert Technologies and Principles) provides a comprehensive overview of modern expert technologies. A special emphasis is placed on the specifics of e-expertise. Moreover, the authors study the feasibility and reasonability of employing well-known methods and approaches in e-expertise. Chapter 3 (E-Expertise: Organization and Technologies) describes some examples of up-to-date technologies to perform e-expertise. Chapter 4 (Trust Networks and Competence Networks) deals with the problems of expert finding and grouping by information and communication technologies. Chapter 5 (Active Expertise) treats the problem of expertise stability against any strategic manipulation by experts or coordinators pursuing individual goals. The book addresses a wide range of readers interested in management, decision-making and expert activity in political, economic, social and industrial spheres.
Alexander “Sasha” Sergeeff è nato a Mosca, Russia, nel 1968. Ha cominciato a dipingere all'età di 5 anni. Ha frequentato Liceo Artistico di Mosca. Ha studiato e lavorato in Accademia di Belle Arti di Mosca. Dal 1993 vive e lavora a Roma. Le sue opere sono state esposte nelle numerose mostre tra Mosca, Roma, Milano, Parigi, New York ed altri città del mondo. Suo modo di lavorare rimasto rigorosamente ottocentesco: su commissione privata.
Once a Grand Duke" is a 1931 work by former Duke Alexander Mikhailovich of Russia (1866 - 1933), a dynast of the Russian Empire, author, explorer, naval officer, and the brother-in-law of Emperor Nicholas II. Within these pages, he gives a fascinating and unique account of the last fifty years of the Russian Empire, concentrating of course on the Romanov Family and the events leading up to the fated February Revolution. This volume will appeal to those with an interest in Russian history and in particular the final years of the Romanov dynasty. Contents include: "Our Friends of December the Fourteenth," "A Grand Duke is Born," "My First War," "An Emperor in Love," "The Windless Afternoons," "A Grand Duke Comes of Age," "A Grand Duke at Large," "A Grand Duke Settles Down," "My Relatives," "Millions That Were," "Nicholas II," "Tin Gods," "Drifting," etc. Many vintage book such as this are increasingly scarce and expensive. It is with this in mind that we are republishing this volume now in an affordable, modern edition complete with the original text and artwork.
The tsars of Russia reigned as absolute monarchs long past the time when the authority of other sovereigns had been curtailed. Here, historian Alexander Ivanov reveals their fears and betrayals, privilege and debauchery, conspiracies and rivalries, love and tragedy as they forged Russia into one of the world's greatest empires. No ruler in history has embodied the oppressive domination of these rulers more vividly than Alexander Ivanov's opening subject, Tsar Ivan IV, the first of all the Russian tsars, known to history as Ivan the Terrible. Although a gifted ruler who did much to unite and improve the conditions in his primitive country, Ivan was also a notorious sadist who delighted in torturing and murdering anyone who displeased him. Ivan's death in 1584 ushered in the Time of Troubles, thirty-five years of famine, plague, and war that crippled the nation. A series of rulers attempted to cope with the devastation, beginning with Ivan's successor Boris Godunov. Finally, grasping for stability, Russia's nobles begged young Michael Romanov, the great-nephew of Ivan's beloved wife Anastasia, to take the throne. Michael successfully united the war-torn and ravaged nation and founded a dynasty that would rule for 300 years. The Romanov line produced Russia's most brilliant yet most unconventional sovereign: Peter the Great, a towering figure of a man whose restless, creative mind led him on an inexorable quest to modernize and civilize the still backward nation. The reforms he enacted so enraged nobles and peasants alike that Peter had to quash a series of rebellions to keep his crown. Ruthlessly stifling dissent and massacring rebels, he ultimately cowed the Russian people into submission, achieving a legacy that nearly equaled his ambitions. It was left to a woman - and a foreigner, at that - to lead the nation further out of the darkness. German princess Sophie Friederike Auguste of Anhalt-Zerbst, known to the world as Catherine the Great, absorbed the principles of the eighteenth-century Enlightenment and applied them to a country built on the backs of millions of serfs. However ineffective some of her policies, in the end, she made Russia a major player on the European stage. Serfdom was finally abolished in the nineteenth century, but it would be decades before Russian peasants could own land of their own and learn to farm it productively. The boyars and tsars clung to power until the Bolshevik revolution of 1917. The sad fate of the last tsar, Nicholas II, and his family, marked the end of the absolute power that Ivan the Terrible had so exploited. The abuses would continue but under a new and drastically different form of government.
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