Alexandrov spaces are defined via axioms similar to those of the Euclid axioms but where certain equalities are replaced with inequalities. Depending on the signs of the inequalities, we obtain Alexandrov spaces with curvature bounded above (CBA) and curvature bounded below (CBB). Even though the definitions of the two classes of spaces are similar, their properties and known applications are quite different. The goal of this book is to give a comprehensive exposition of the structure theory of Alexandrov spaces with curvature bounded above and below. It includes all the basic material as well as selected topics inspired by considering Alexandrov spaces with CBA and with CBB simultaneously. The book also includes an extensive problem list with solutions indicated for every problem.
Aimed toward graduate students and research mathematicians, with minimal prerequisites this book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory. Beginning with an overview of fundamentals, definitions, and conventions, this book quickly moves forward to discuss the Reshetnyak gluing theorem and applies it to the billiards problems. The Hadamard–Cartan globalization theorem is explored and applied to construct exotic aspherical manifolds.
Postwar Nuremberg is set to host a historically unprecedented trial of the leaders of the defeated Third Reich. The whole world is awaiting a just verdict, but it is here where Soviet counterintelligence must wage a secret war against forces that seek to prevent that from happening at any cost. Nuremberg, having been nearly wiped from the face of the earth during the harsh fighting, becomes an arena for ruthless struggles in both hidden and overt operations. Nazis are still operating underground, spies weave their intrigues, politicians and diplomats make bargains, and movie stars dazzle the public. The enormous efforts led by the USSR’s chief prosecutor Roman Rudenko to expose the Nazi atrocities are threatened. It is here where counterintelligence officer Major Denis Rebrov must operate: he has been tasked with a matter of special state importance. But in this old imperial city, the ruins of which are home to people who would do anything for a pack of cigarettes or a loaf of bread, where revelations about unimaginable crimes come out daily, Rebrov meets Princess Irina Kurakina, born to an aristocratic family of Russian emigres. The pages of this novel abound with real historical figures. Besides the USSR chief prosecutor Rudenko and his American analogue Robert Jackson, readers will be introduced to Nazi bosses Goering, Ribbentrop, Hess and Kaltenbrunner, film stars Olga Chekhov (Hitler’s favorite actress) and Marlene Dietrich, as well as the “great leader” Stalin and his closest companions Molotov, Beria and Vyshinsky. The Nuremberg Trials is based upon real facts that were hitherto unknown and details that the author, who spent many years studying the trials, learned from participants and witnesses. Translated from the Russian by Christopher Culver. Published with the support of the Institute for Literary Translation, Russia. Publishers Maxim Hodak and Max Mendor.
Volume I, entitled Russian Mathematics Education: History and World Significance, consists of several chapters written by distinguished authorities from Russia, the United States and other nations. It Examines the hostory of mathematics education in Russia and its relevance to mathematics education throughout the world. The second volume, entitled Russian Mathematics education is highly respected for its achievements and was once very influential internationally, it has never been explored in depth. This publication does just that. --Book Jacket.
Unparalleled in scope compared to the literature currently available, the Handbook of Integral Equations, Second Edition contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equa
This biography of the famous Soviet physicist Leonid Isaakovich Mandelstam (1889-1944), who became a Professor at Moscow State University in 1925, describes his contributions to both physics and technology, as well as discussing the scientific community which formed around him, usually called the Mandelstam school. Mandelstam’s life story is thereby placed in its proper cultural context. The following more general issues are taken under consideration: the impact of German scientific culture on Russian science; the problems and fates of Russian intellectuals during the revolutionary and post-revolutionary years; the formation of the Soviet Academy of Sciences; and transformation of the system of higher education in the USSR during the 1920's and 1930's.The author shows that Mandelstam’s fundamental writings and his lectures notes allow to reconstruct his philosophy of science and his approach to the social and ethical functions of science and science education. That reconstruction is enhanced through extensive use of hitherto unpublished archival material as well as the transcripts of personal interviews conducted by the author.
An astounding personal document and unique autobiography—the life story of a Russian now living in America who was once soldier, industrialist, and diplomat under the Red Star.
Recent instances of bioinvasion, such as the emergence of the zebra mussel in the American Great Lakes, generated a demand among marine biologists and ecologists for groundbreaking new references that detail how organisms colonize hard substrates, and how to prevent damaging biomass concentrations. Marine Biofouling: Colonization Processes a
One of the rapidly developing areas of modern experimental nuclear physics is non-accelerator experiments using low-background detectors. Such experiments, as a rule, are aimed at solving problems that are of fundamental importance for understanding the structure of the Universe, checking the Standard Model of elementary particles, and looking for new physics behind the observable world. The most interesting tasks include the search for dark matter in the form of new weakly interacting particles, the search for neutrinoless double beta decay, the determination of the magnetic moment of the neutrino, the study of neutrino oscillation and new types of interaction of elementary particles, such as coherent neutrino scattering off heavy nuclei.All these processes, occurring with extremely low cross sections, require the development of efficient large-mass detectors capable of detecting small energy releases down to individual ionization electrons. An effective method to do this is the emission method of detecting ionizing particles in two-phase media, which has been proposed at Moscow Engineering Physics Institute (MEPhI) 50 years ago. The origin of this technique can be traced to the research headed by Prof. Boris A Dolgoshein, whose study focus on the properties of condensed noble gases as a means to develop a tracking streamer chamber with a high-density working medium.This monograph, devoted exclusively to two-phase emission detectors, considers the technology's basic features while taking into account new developments introduced into experimental practice in the last ten years since the publication of its predecessor, Emission Detectors (Bolozdynya, 2010).
This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics. The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Historical foreword on the centenary after Felix Hausdorff’s classic Set Theory Fundamentals of the theory of functions Fundamentals of the measure theory Historical notes on the Riesz – Radon – Frechet problem of characterization of Radon integrals as linear functionals
This book presents the most recent results in the area of bulk nanostructured materials and new trends in their severe plastic deformation (SPD) processing, where these techniques are now emerging from the domain of laboratory-scale research into the commercial production of various bulk nanomaterials. Special emphasis is placed on an analysis of the effect of nanostructures in materials fabricated by SPD on mechanical properties (strength and ductility, fatigue strength and life, superplasticity) and functional behavior (shape memory effects, magnetic and electric properties), as well as the numerous examples of their innovative applications. There is a high innovation potential for industrial applications of bulk nanomaterials for structural use (materials with extreme strength) as well as for functional applications such as nanomagnets, materials for hydrogen storage, thermoelectric materials, superconductors, catalysts, and biomedical implants.
Plasma plays an important role in a wide variety of industrial processes, including material processing, environmental control, electronic chip manufacturing, light sources, and green energy, not to mention fuel conversion and hydrogen production, biomedicine, flow control, catalysis, and space propulsion. Following the general outline of the bests
Written for health professionals and managers involved in the planning or provision of stroke care, this book provides a comprehensive, state-of-the-art overview of the evidence and practices that underpin high quality stroke care. It sets the scene by describing the epidemiology, trends and needs of stroke patients, followed by chapters on the prevention of stroke, investigation and management of TIAs (transient ischaemic attack), early management and thrombolysis, clinical management of acute stroke patients and rehabilitation. Each chapter is thematically-linked and provides a complete, up-to-date review of evidence, its implications for clinical practice, proven multidisciplinary models of delivering high quality care, organisation of services for greatest impact within cost constraints and emerging areas for future management of stroke patients. This book is unique as it covers areas such as palliative and end-of-life care for stroke patients, planning and provision of stroke services, benchmarking for quality of services and management of stroke patients in community settings. It will be a unique resource for anyone caring for stroke patients, regardless of discipline or level of expertise, and provides a quick and friendly compendium of evidence, good practice and practical hints on organising care.
This book constitutes the refereed proceedings of the 7th International Conference on Computational Linguistics and Intelligent Text Processing, held in February 2006. The 43 revised full papers and 16 revised short papers presented together with three invited papers were carefully reviewed and selected from 176 submissions. The papers are structured into two parts and organized in topical sections on computational linguistics research.
Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial structure of complicated systems. The main focus of the book is on efficient ways to compute (approximate) various partition functions, such as permanents, hafnians and their higher-dimensional versions, graph and hypergraph matching polynomials, the independence polynomial of a graph and partition functions enumerating 0-1 and integer points in polyhedra, which allows one to make algorithmic advances in otherwise intractable problems. The book unifies various, often quite recent, results scattered in the literature, concentrating on the three main approaches: scaling, interpolation and correlation decay. The prerequisites include moderate amounts of real and complex analysis and linear algebra, making the book accessible to advanced math and physics undergraduates.
Set Theoretical Aspects of Real Analysis is built around a number of questions in real analysis and classical measure theory, which are of a set theoretic flavor. Accessible to graduate students, and researchers the beginning of the book presents introductory topics on real analysis and Lebesgue measure theory. These topics highlight the boundary b
This book provides an exciting history of the discovery of Ramsey Theory, and contains new research along with rare photographs of the mathematicians who developed this theory, including Paul Erdös, B.L. van der Waerden, and Henry Baudet.
Superplasticity and Grain Boundaries in Ultrafine-Grained Materials, Second Edition, provides cutting-edge modeling solutions surrounding the role of grain boundaries in processes such as grain boundary diffusion, relaxation and grain growth. In addition, the book's authors explore the formation and evolution of the microstructure, texture and ensembles of grain boundaries in materials produced by severe plastic deformation. This updated edition, written by leading experts in the field, has been revised to include new chapters on the basics of nanostructure processing, the influence of deformation mechanisms on grain refinement, processing techniques for ultrafine-grained and nanostructured materials, and much more. - Provides practical applications and methods for the proper implementation of models, allowing for more effective complex metal forming processes - Features new chapters on the microstructure, mechanical behavior and functional properties of HCP metals, processing ultrafine-grained and nanostructured materials, and more - Covers experimental assessment and computational modeling techniques for adiabatic heating and saturation of grain refinement during SPD of metals and alloys
Zvi Alexander was a member of a small group that established the oil industry in Israel, providing the State with this vital fluid, and searching for oil in Israel and other countries. 'Oil', Alexander's personal story, is also the story of the Israeli oil industry; how Alexander was the first to bring to Israel non-Jewish oil businessmen from the USA; how these businessmen, along with Israel's 'National Oil Company' under Alexander's management, funded and executed oil drilling in Israel; and how Alexander's activities brought 'Signal', an international oil company based in the USA, to invest a large amount of money in Israel's 'National Oil Company', despite the Arab embargo. After the Yom Kippur War, Alexander sold the company for $16.5 million
An emerging field of discrete differential geometry aims at the development of discrete equivalents of notions and methods of classical differential geometry. The latter appears as a limit of a refinement of the discretization. Current interest in discrete differential geometry derives not only from its importance in pure mathematics but also from its applications in computer graphics, theoretical physics, architecture, and numerics. Rather unexpectedly, the very basic structures of discrete differential geometry turn out to be related to the theory of integrable systems. One of the main goals of this book is to reveal this integrable structure of discrete differential geometry. For a given smooth geometry one can suggest many different discretizations. Which one is the best? This book answers this question by providing fundamental discretization principles and applying them to numerous concrete problems. It turns out that intelligent theoretical discretizations are distinguished also by their good performance in applications. The intended audience of this book is threefold. It is a textbook on discrete differential geometry and integrable systems suitable for a one semester graduate course. On the other hand, it is addressed to specialists in geometry and mathematical physics. It reflects the recent progress in discrete differential geometry and contains many original results. The third group of readers at which this book is targeted is formed by specialists in geometry processing, computer graphics, architectural design, numerical simulations, and animation. They may find here answers to the question “How do we discretize differential geometry?” arising in their specific field. Prerequisites for reading this book include standard undergraduate background (calculus and linear algebra). No knowledge of differential geometry is expected, although some familiarity with curves and surfaces can be helpful.
The calculus of variations is a classical area of mathematical analysis-300 years old-yet its myriad applications in science and technology continue to hold great interest and keep it an active area of research. These two volumes contain the referenced proceedings of the international conference on Calculus of Variations and Related Topics held at the Technion-Israel Institute of Technology in March 1998. The conference commemorated 300 years of work in the field and brought together many of its leading experts. The papers in the first volume focus on critical point theory and differential equations. The other volume deals with variational aspects of optimal control. Together they provide a unique opportunity to review the state-of-the-art of the calculus of variations, as presented by an international panel of masters in the field.
Contemplating Shostakovich marks an important new stage in the understanding of Shostakovich and his working environment. Each chapter covers aspects of the composer's output in the context of his life and cultural milieu. The contributions uncover 'outside' stimuli behind Shostakovich's works, allowing the reader to perceive the motivations behind his artistic choices; at the same time, the nature of those choices offers insights into the workings of the larger world – cultural, social, political – that he inhabited. Thus his often ostensibly quirky choices are revealed as responses – by turns sentimental, moving, sardonic and angry – to the particular conditions, with all their absurdities and contradictions, that he had to negotiate. Here we see the composer emerging from the role of tortured loner of older narratives into that of the gregarious and engaged member of his society that, for better and worse, characterized the everyday reality of his life. This invaluable collection offers remarkable new insight, in both depth and range, into the nature of Shostakovich's working circumstances and of his response to them. The collection contains the seeds for a wide range of new directions in the study of Shostakovich's works and the larger contexts of their creation and reception.
This book highlights various topics on measure theory and vividly demonstrates that the different questions of this theory are closely connected with the central measure extension problem. Several important aspects of the measure extension problem are considered separately: set-theoretical, topological and algebraic. Also, various combinations (e.g., algebraic-topological) of these aspects are discussed by stressing their specific features. Several new methods are presented for solving the above mentioned problem in concrete situations. In particular, the following new results are obtained: the measure extension problem is completely solved for invariant or quasi-invariant measures on solvable uncountable groups; non-separable extensions of invariant measures are constructed by using their ergodic components; absolutely non-measurable additive functionals are constructed for certain classes of measures; the structure of algebraic sums of measure zero sets is investigated. The material presented in this book is essentially self-contained and is oriented towards a wide audience of mathematicians (including postgraduate students). New results and facts given in the book are based on (or closely connected with) traditional topics of set theory, measure theory and general topology such as: infinite combinatorics, Martin's Axiom and the Continuum Hypothesis, Luzin and Sierpinski sets, universal measure zero sets, theorems on the existence of measurable selectors, regularity properties of Borel measures on metric spaces, and so on. Essential information on these topics is also included in the text (primarily, in the form of Appendixes or Exercises), which enables potential readers to understand the proofs and follow the constructions in full details. This not only allows the book to be used as a monograph but also as a course of lectures for students whose interests lie in set theory, real analysis, measure theory and general topology.
This book consists of extracts from key documents, along with commentary and further reading, on the ‘Great Patriotic War’ of the Soviet Union against Nazi Germany, 1941-45. Despite the historical significance of the war, few Soviet documents have been published in English. This work provides translations of a range of extracts from Soviet documents relating to the titanic struggle on the Eastern Front during World War II, with commentary. This is the only single-volume work in English to use documentary evidence to look at the Soviet war effort from military, political, economic and diplomatic perspectives. The book should not only facilitate a deeper study of the Soviet war effort, but also allow more balanced study of what is widely known in the West as the ‘Eastern Front’. This book will be of much interest to students and scholars of military history, Soviet history, and World War II history.
This monograph gives the reader an up-to-date account of the fine properties of real-valued functions and measures. The unifying theme of the book is the notion of nonmeasurability, from which one gets a full understanding of the structure of the subsets of the real line and the maps between them. The material covered in this book will be of interest to a wide audience of mathematicians, particularly to those working in the realm of real analysis, general topology, and probability theory. Set theorists interested in the foundations of real analysis will find a detailed discussion about the relationship between certain properties of the real numbers and the ZFC axioms, Martin's axiom, and the continuum hypothesis.
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 volume presents contributions by leading experts in the field. The articles are dedicated to D.B. Fuchs on the occasion of his 60th birthday. Contributors to the book were directly influenced by Professor Fuchs, and include his students, friends, and professional colleagues. In addition to their research, they offer personal reminicences about Professor Fuchs, giving insight into the history of Russian mathematics.
Since the volume may be of interest to a broad variety of people, it is arranged in parts that require different levels of mathematical background. Part I can be assessed by those interested in the application of visualization methods in decision making. In Part II computational methods are introduced in a relatively simple form. Part III is written for readers in applied mathematics interested in the theoretical basis of modern optimization.
Light Scattering Reviews (vol.7) is aimed at the description of modern advances in radiative transfer and light scattering. The following topics will be considered: the general - purpose discrete - ordinate algorithm DISORT for radiative transfer, fast radiative transfer techniques, use of polarization in remote sensing, Markovian approach for radiative transfer in cloudy atmospheres, coherent and incoherent backscattering by turbid media and surfaces,advances in radiative transfer methods as used for luminiscence tomography, optical properties of aerosol, ice crystals, snow, and oceanic water. This volume will be a valuable addition to already published volumes 1-6 of Light Scattering Reviews.
Increasing information content is an important scientific problem in modern observation systems development. Radar, or microwave, imaging can be used for this purpose. The book provides an overview of the field and explains why a unified approach based on wave field processing techniques, including holographic and tomographic approaches, is necessary in high resolution radar design. It contains discussion of new areas in imaging radar theory, holographic radar, the questions of estimation and improving radar image quality, and finally various practical applications.
Grandmaster Alexander Panchenko (1953-2009) was one of the most successful chess trainers in the Soviet Union, and later in Russia. Panchenko ran a legendary chess school that specialised in turning promising players into masters. The secret of his success were his dedication and enthusiasm as a teacher combined with his outstanding training materials. ‘Pancha’ provided his pupils with systematic knowledge, deep understanding and the ability to take practical decisions. Now, Panchenko’s classic Mastering Chess Middlegames is for the first time available in translation, giving club-players around the world access to this unique training method. The book contains a collection of inspiring lessons on the most important middlegame topics: attack, defence, counterplay, realising the advantage, obstructing the plans of your opponent, the battle of the heavy pieces, and much more. In each chapter, Panchenko clearly identifies the various aspects of the topic, formulates easy-to-grasp rules, presents a large number of well-chosen examples and ends with a wealth of practical tests. The brilliance of Alexander Panchenko’s didactic method shines through in this book. It is hard to give better advice for ambitious chess players than to follow this tried-and-tested and highly instructive road towards mastering the chess middlegame.
As editor I want especially to thank Dr. Ernst Freese for helpful co operation in preparing these volumes, and to express my appreclatlOn to Drs. Kurt Hirschhorn and Marvin Legator, the other members of the editorial board. Alexander Hollaender January 1971 Preface The purpose of these volumes is to encourage the development and ap plication of testing and monitoring procedures to avert significant human exposure to mutagenic agents. The need for protection against exposure to possibly mutagenic chemicals is only now coming to be generally realized. The recently issued Report of the Secretary's Commission on Pesticides and Their Possible Effects on Health (the Mrak Report-U.S. Department of Health, Education and Welfare, December 1969) has made an important start. Its Panel on Mutagenicity recommends that all currently used pesticides be tested for mutagenicity in several recently developed and relatively simple systems. Whether recommendations such as these are actually put into effect will depend on convincing government, industry, and the public that the problem is important, that the proposed tests would be effective, and that they can be conducted at a cost that is not prohibitive. Why is it important to screen environmental agents for mutagenic activity? To those who will read this book, the answer is self-evident. The sine qua non of all that we value and all that we are is our genetic heritage.
This reference book for researchers working on glacial sediments provides a complete overview of the various glacial deposits in the ocean. It presents a collection of worldwide data on glacio-marine phenomena.
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