Normal Forms

Exposition for advanced undergraduates and graduate students covers the method of normal forms and its application to ordinary differential equations through perturbation analysis. Numerous examples o

This book is concerned with the bifurcation theory, the study of the changes in the structures of the solution of ordinary differential equations as parameters of the model vary. The theory has developed rapidly over the past two decades. Chapters 1 and 2 of the book introduce two systematic methods of simplifying equations: centre manifold theory and normal form theory, by which the dimension of equations may be reduced and the forms changed so that they are as simple as possible. Chapters 3–5 of the book study in considerable detail the bifurcation of those one- or two-dimensional equations with one, two or several parameters. This book is aimed at mathematicians and graduate students interested in dynamical systems, ordinary differential equations and/or bifurcation theory. The basic knowledge required by this book is advanced calculus, functional analysis and qualitative theory of ordinary differential equations.

This text bridges the gap existing in the field of set theoretical topology between the introductory texts and the more specialised monographs. The authors review fit developments in general topology and discuss important new areas of research and the importance of defining a methodology applicable to this active field of mathematics. The concept of normal cover and related ideas is considered in detail, as are the characterisations of normal spaces, collectionwise normal spaces and their interrelationships with paracompact spaces (and other weaker forms of compactness). Various methods of embedding subspaces are studied, before considering newer concepts such as M-spaces and their relationships with established ideas. These ideas are applied to give new results pertaining to the extension of continuous vector-valued functions. Wallman–Frink compactifications and realcompactifications are also studied to assist in unifying the ideas through the use of the more general L-filter.

《Civil Society》是一部探討公民自發行動與公共生活的經典著作，也是理解「公民社會」不可或缺的重要文本。面對近年來席捲全球的抗議運動與社會動盪，本書提醒我們：真正能長期塑造社會的力量，往往並不只存在於街頭或新聞焦點中，而是深植於人們日常參與的志願組織、社群與公民網絡之中。Civil Society has become a standard work of reference for anyone seeking to understand the role of voluntary citizen action in shaping society.Recent waves of global unrest have highlighted the visibility and impact of social movements and street protests in world politics. Yet, as this lucid and accessible book demonstrates, the real power of citizens more often flows through everyday participation in voluntary associations, community groups, and civic networks—forms of “normal” civic life that rarely make headlines. This is the deeper, underlying story of civil society.In this updated edition, Michael Edwards examines key developments that have rapidly transformed the civic landscape in recent years. These include the growing intersections between civil society and the market, such as social enterprises and “venture philanthropy,” as well as the

Paradigmatic gaps ('missing' inflected forms) have traditionally been considered to be the random detritus of a language's history and marginal exceptions to the normal functioning of its inflectional system. Arguing that this is a misperception, Inflectional Defectiveness demonstrates that paradigmatic gaps are in fact normal and expected products of inflectional structure. Sims offers an accessible exploration of how and why inflectional defectiveness arises, why it persists, and how it is learned. The book presents a theory of morphology which is rooted in the implicative structure of the paradigm. This systematic exploration of the topic also addresses questions of inflection class organization, the morphology-syntax interface, the structure of the lexicon, and the nature of productivity. Presenting a novel synthesis of established research and new empirical data, this work is significant for researchers and graduate students in all fields of linguistics.

Oxygen has had extraordinary effects on life. Three hundred million years ago, in Carboniferous times, dragonflies grew as big as seagulls, with wingspans ofnearly a metre. Researchers claim they could have flown only if the air had contained more oxygen than today -probably as much as 35 per cent. Giant spiders, tree-ferns, marine rock formations and fossil charcoalsall tell the same story. High oxygen levels may also explain the global firestorm that contributed to thedemise of the dinosaurs after the asteroid impact.The strange and profound effects that oxygen has had on the evolution of life pose a riddle, which this booksets out to answer. Oxygen is a toxic gas. Divers breathing pure oxygen at depth suffer from convulsionsand lung injury. Fruit flies raised at twice normal atmospheric levels of oxygen live half as long as theirsiblings. Reactive forms of oxygen, known as free radicals, are thought to cause ageing in people. Yet ifatmospheric oxygen reached 35 per cent in the Carbo

This thesis deals with specific featuresof the theory of holomorphic dynamics in dimension 2 and then sets out to studyanalogous questions in higher dimensions, e.g. dealing with normal forms forrigid

At first sight, finitely generated abelian groups and canonical forms of matrices appear to have little in common. However, reduction to Smith normal form, named after its originator H.J.S.Smith in 1

This book provides a comprehensive view of research in lens developmental biology, emphasising technical and molecular breakthroughs. Elucidation of the mechanisms that govern lens development has enabled us to understand how the normal lens forms and how developmental processes are involved in the maintenance of its normal structure, function and growth throughout life. This knowledge is fundamental to our understanding of many lens disorders. The ocular lens has also become a model for understanding the developmental biology of more complex organ systems. In this 2004 book, leading experts in lens cell biology and development discuss lens evolution, induction, morphology, the regulation of the lens cell cycle and fiber cell differentiation, as well as lens regeneration. This book is an authoritative treatment of the subject that will serve as a reference for graduate students and research scientists in developmental biology and in the visual sciences, as well as for ophthalmologists.

Research in computational group theory, an active subfield of computational algebra, has emphasised three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. The author emphasises the connections with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, computational number theory, and computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms from computational number theory are used to study the abelian quotients of a finitely presented group. The work of Baumslag, Cannonito and Miller on computing nonabelian polycyclic quotients is described as a generalisation of Buchberger's Gröbner basis methods to right ideals in the integral group ring of a polycyclic group. Researchers in computational group theory, mathematicians interested in finitely presented groups and theore

There might appear to be little that binds the study of order and the study of violence and conflict. Bloodshed in its multiple forms is often seen as something separate from and unrelated to the domains of 'normal' politics that constitute what we think of as order. But violence is used to create order, to maintain it, and to uphold it in the face of challenges. This volume demonstrates the myriad ways in which order and violence are inextricably intertwined. The chapters embrace such varied disciplines as political science, economics, history, sociology, philosophy, and law; employ different methodologies, from game theory to statistical modeling to in-depth historical narrative to anthropological ethnography; and focus on different units of analysis and levels of aggregation, from the state to the individual to the world system. All are essential reading for anyone who seeks to understand current trends in global conflict.

The German Democratic Republic's emergence as the key political player within the Warsaw Pact intensified debates concerning the critical East German military role in Soviet strategy for the future of Eastern Europe. Douglas Macgregor traces the origins of collaboration to earlier forms of Russo-German military alliance. He explores the development of military cooperation since the formation of the GDR National People's Army in 1956 and discusses the importance of East Germany as a military model for the Warsaw Pact's Northern Tier. German cooperation is historically as normal as one of conflict. The need for cooperation has been alternately balanced by the propensity to conflict of incompatible nationalisms. Specific historical circumstances have determined which tendency has prevailed at any given point; contemporary elites in East Berlin and Moscow do no more than revive an earlier convergence of strategic and political interests.

This volume provides a developmental perspective of the regulation and dysregulation of emotion, in particular, how children learn about feelings and how they learn to deal with both positive and negative feelings. Emotion regulation involves the interaction of physical, behavioural and cognitive processes in response to changes in one's emotional state. The changes can be brought on by factors internal to the individual (e.g. biological) or external (e.g. other people). Featuring contributions from leading researchers in developmental psychopathology, the volume concentrates on theories and data concerning the development of emotion regulation with an emphasis on both intrapersonal and interpersonal processes. Original conceptualizations of the reciprocal influences among the various response systems - neurophysiological-biochemical, behavioral-expressive, and subjective-experiential - are provided, and the individual chapters address both normal and psychopathological forms of emotio

This 2001 book provides a practical and systematic approach to the acquisition, interpretation, and reporting of physiologic responses to exercise. Pulmonologists, cardiologists, and sports physicians, as well as respiratory therapists and other allied health professionals will find this book an indispensable resource when learning to select proper instruments, identify the most appropriate test protocols, and integrate and interpret physiologic response variables. The final chapter presents clinical cases to illuminate useful strategies for exercise testing and interpretation. Useful appendices offer laboratory forms, algorithms and calculations, as well as answers to FAQs. A glossary of terms, symbols, and definitions is also included. Exercise Testing and Interpretation: A Practical Approach offers clearly defined responses (both normal and abnormal) to over thirty performance variables including aerobic, cardiovascular, ventilatory, and gas-exchange variables. Practical, portable,

Semiclassical approximation addresses the important relationship between quantum and classical mechanics. There has been a very strong development in the mathematical theory, mainly thanks to methods of microlocal analysis. This book develops the basic methods, including the WKB-method, stationary phase and h-pseudodifferential operators. The applications include results on the tunnel effect, the asymptotics of eigenvalues in relation to classical trajectories and normal forms, plus slow perturbations of periodic Schrödinger operators appearing in solid state physics. No previous specialized knowledge in quantum mechanics or microlocal analysis is assumed, and only general facts about spectral theory in Hilbert space, distributions, Fourier transforms and some differential geometry belong to the prerequisites. This book is addressed to researchers and graduate students in mathematical analysis, as well as physicists who are interested in rigorous results. A fairly large fraction can be

The Computer Algebra and Differential Equations meeting held in France in June 1992 (CADE-92) was the third of a series of biennial workshops devoted to recent developments in computer algebra systems. This book contains selected papers from that meeting. Three main topics are discussed. The first of these is the theory of D-modules. This offers an excellent way to effectively handle linear systems of partial differential equations. The second topic concerns the theoretical aspects of dynamical systems, with an introduction to Ecalle theory and perturbation analysis applied to differential equations and other nonlinear systems. The final topic is the theory of normal forms. Here recent improvements in the theory and computation of normal forms are discussed.

An elementary text that can be understood by anyone with a background in high school geometry, this text focuses on the problems inherent to coloring maps, homeomorphism, applications of Descartes' theorem, and topological polygons. Considerations of the topological classification of closed surfaces cover elementary operations, use of normal forms of polyhedra, more. Includes 108 figures. 1967 edition.