This book introduces recent developments in the study of algebras defined by quadratic relations. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, non commutative geometry, $K$-theory, number theory, and non commutative linear algebra.The authors give a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincare-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes. The book can be used by graduate students and researchers working in algebra and any of the above-mentioned areas of mathematics.
This book is a modern treatment of the theory of theta functions in the context of algebraic geometry. The novelty of its approach lies in the systematic use of the Fourier-Mukai transform. Alexander Polishchuk starts by discussing the classical theory of theta functions from the viewpoint of the representation theory of the Heisenberg group (in which the usual Fourier transform plays the prominent role). He then shows that in the algebraic approach to this theory (originally due to Mumford) the Fourier-Mukai transform can often be used to simplify the existing proofs or to provide completely new proofs of many important theorems. This incisive volume is for graduate students and researchers with strong interest in algebraic geometry.
This book introduces recent developments in the study of algebras defined by quadratic relations. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, non commutative geometry, $K$-theory, number theory, and non commutative linear algebra.The authors give a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincare-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes. The book can be used by graduate students and researchers working in algebra and any of the above-mentioned areas of mathematics.
This book contains a systematic study of ecological communities of two or three interacting populations. Starting from the Lotka-Volterra system, various regulating factors are considered, such as rates of birth and death, predation and competition. The different factors can have a stabilizing or a destabilizing effect on the community, and their interplay leads to increasingly complicated behavior. Studying and understanding this path to greater dynamical complexity of ecological systems constitutes the backbone of this book. On the mathematical side, the tool of choice is the qualitative theory of dynamical systems — most importantly bifurcation theory, which describes the dependence of a system on the parameters. This approach allows one to find general patterns of behavior that are expected to be observed in ecological models. Of special interest is the reaction of a given model to disturbances of its present state, as well as to changes in the external conditions. This leads to the general idea of “dangerous boundaries” in the state and parameter space of an ecological system. The study of these boundaries allows one to analyze and predict qualitative and often sudden changes of the dynamics — a much-needed tool, given the increasing antropogenic load on the biosphere.As a spin-off from this approach, the book can be used as a guided tour of bifurcation theory from the viewpoint of application. The interested reader will find a wealth of intriguing examples of how known bifurcations occur in applications. The book can in fact be seen as bridging the gap between mathematical biology and bifurcation theory.
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
In recent decades, the regions of Russia have taken different paths of regime transition. Despite the consolidation of an autocratic regime at national level and the centralization steered by Vladimir Putin’s government, the variation across sub-national regimes persists. Using an innovative theoretical framework, this book explores both causes and consequences of democratization in the regions of Russia. It is the first study in the field to systematically integrate structural and agency approaches in order to account for economic, social, historical and international causes of democratization and to trace its consequences. By focusing on the challenging and under-studied topic of sub-national regimes, the book provides a unique perspective on regime transition and the new theoretical framework contributes to a better understanding of democratization world-wide. The book will be of key interest to scholars and students of democratization, sub-national regimes, East European politics, comparative politics, post-communism, and international relations.
This monograph discusses fire hazard and fire resistance in wooden structures with a long duration of operation. Aside from its increasing importance for modern architecture, wood has been the most important building material in the past. It has a distinct aesthetic, high mechanical strength, and resistance against many environmental changes. These properties are evident in structures like the still standing Grinstead Chuch, which has been built in 1045. Readers will however learn about the decreasing fire resistance in wooden buildings with a long service live. Considering the cultural value of medieval wood buildings, this topic becomes increasingly relevant. The chapters discuss the mechanical, physico-chemical and thermophysical properties of wooden structures over different lifespans. Many factors contributing to the changing fire resistance in the ageing process of wooden structures, are explained. This book is a valuable resource for students, teachers and scientists in the areas of wood science, fire research and forestry.
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
The book offers a comparative analysis of center-region relations in Russia and in China. The authors focus in particular on fiscal ties and incentives, bureaucratic and local government practices, flows of information, and the determinants of divergence between both countries. The book is based on a synthesis of a large body of empirical and theoretical evidence, and will appeal to scholars in public economics, political economy and comparative politics, as well as to students and policy analysts.
This book summarizes the state of the art in combustion synthesis of advanced materials. It is a first attempt to summarize and critically review in one monograph the mechanisms of combustion and product structure formation for a variety of systems, including nanosystems. The authors discuss a wide range of topics including phenomenology, theory, and modern in-situ experimental approaches to investigate the heterogeneous self-sustained reactions, as well as properties of the product synthesized, and methods for large-scale materials production.
Libman and Obydenkova reveal how legacies of the Communist Party of the Soviet Union (CPSU) have survived in the politics, economic development, culture, and society of post-Communist regions in the 21st Century. The authors show how this impact is not driven by Communist ideology but by the clientelistic practices, opportunism and cynicism prevalent in the CPSU. Their study is built on a novel dataset of the CPSU membership rates in Russian regions in the 1950s-1980s, alongside case studies, interviews and an analysis of mass media previously only available in Russian and discussed here in English for the first time. It will appeal to students and scholars of Russian and Eastern European politics and history, and anyone who wants to better understand countries which live or have lived through Communism: from Eastern Europe to China and East Asian Communist states.
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.
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.
The classical sampling problem is to reconstruct entire functions with given spectrum S from their values on a discrete set L. From the geometric point of view, the possibility of such reconstruction is equivalent to determining for which sets L the exponential system with frequencies in L forms a frame in the space L2(S). The book also treats the problem of interpolation of discrete functions by analytic ones with spectrum in S and the problem of completeness of discrete translates. The size and arithmetic structure of both the spectrum S and the discrete set L play a crucial role in these problems. After an elementary introduction, the authors give a new presentation of classical results due to Beurling, Kahane, and Landau. The main part of the book focuses on recent progress in the area, such as construction of universal sampling sets, high-dimensional and non-analytic phenomena. The reader will see how methods of harmonic and complex analysis interplay with various important concepts in different areas, such as Minkowski's lattice, Kolmogorov's width, and Meyer's quasicrystals. The book is addressed to graduate students and researchers interested in analysis and its applications. Due to its many exercises, mostly given with hints, the book could be useful for undergraduates.
The representation theory of symmetric groups is one of the most beautiful, popular and important parts of algebra, with many deep relations to other areas of mathematics. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski and Brundan, as well as his own
The contents included in this book are: Preface; Spin Probes for the Study of Intact and Cancer Cell Membranes; Sulphur as a Stabiliser of Polyvinylchloride; Universality of Free Energies Linearity Principle in Solution Chemistry; The KBr Action on the rate of H2O2 Decomposition in Alkaline Medium; Fireproof Materials containing Nanostructures: Principles of Formation; Fireproof Intumescent Coating Foamcoke Structure Regulation by Carbon Metal-containing Nanostructures; Upholstery Fire Barriers based on Natural Fibres; Structural Criterion on Change of a Kinetic Curves Type in the Process of a Thermooxidative Degradation; and Alternative View at the Universe. It also includes: Effect of the Cationic Polyelectrolyte Molecular Mass on the Flocculation Kinetics and the Efficiency of Polymer Precipitation from Latexes; Co-polymers with Cyclic Fragments in Dimethylsiloxane Backbone(O; Fractal Physics of the Polycondensation Processes; The Problem of Structural-Physical Organisation of Polymeric Non-Crystalline Phase; and Physical and Semi-Empirical Methods of Solvent Influence on Solute Behaviour.
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