Constructive Approximation

This book aims to give a self-contained presentation of a number of results, which relate the volume of convex bodies in n-dimensional Euclidean space and the geometry of the corresponding finite-dimensional normed spaces. The methods employ classical ideas from the theory of convex sets, probability theory, approximation theory and the local theory of Banach spaces. The book is in two parts. The first presents self-contained proofs of the quotient of the subspace theorem, the inverse Santalo inequality and the inverse Brunn-Minkowski inequality. The second part gives a detailed exposition of the recently introduced classes of Banach spaces of weak cotype 2 or weak type 2, and the intersection of the classes (weak Hilbert space). The book is based on courses given in Paris and in Texas.

Systems of conservation laws arise naturally in physics and chemistry. To understand them and their consequences (shock waves, finite velocity wave propagation) properly in mathematical terms requires, however, knowledge of a broad range of topics. This book sets up the foundations of the modern theory of conservation laws, describing the physical models and mathematical methods, leading to the Glimm scheme. Building on this the author then takes the reader to the current state of knowledge in the subject. The maximum principle is considered from the viewpoint of numerical schemes and also in terms of viscous approximation. Small waves are studied using geometrical optics methods. Finally, the initial-boundary problem is considered in depth. Throughout, the presentation is reasonably self-contained, with large numbers of exercises and full discussion of all the ideas. This will make it ideal as a text for graduate courses in the area of partial differential equations.

This eagerly awaited book by David F. Ford makes a unique and important contribution to the debate about the Christian doctrine of salvation. Using the pivotal image of the face, Professor Ford offers a constructive and contemporary account of the self being transformed. He engages with three modern thinkers (Levinas, Jüngel and Ricoeur) in order to rethink and reimagine the meaning of self. Developing the concept of a worshipping self, he explores the dimensions of salvation through the lenses of scripture, worship practices, the life, death and resurrection of Christ, and the lives of contemporary saints. He uses different genres and traditions to show how the self flourishes through engagement with God, other people, and the responsibilities and joys of ordinary living. The result is a habitable theology of salvation immersed in Christian faith, thought and practice while also being deeply involved with modern life in a pluralist world.

This eagerly awaited book by David F. Ford makes a unique and important contribution to the debate about the Christian doctrine of salvation. Using the pivotal image of the face, Professor Ford offers a constructive and contemporary account of the self being transformed. He engages with three modern thinkers (Levinas, Jüngel and Ricoeur) in order to rethink and reimagine the meaning of self. Developing the concept of a worshipping self, he explores the dimensions of salvation through the lenses of scripture, worship practices, the life, death and resurrection of Christ, and the lives of contemporary saints. He uses different genres and traditions to show how the self flourishes through engagement with God, other people, and the responsibilities and joys of ordinary living. The result is a habitable theology of salvation immersed in Christian faith, thought and practice while also being deeply involved with modern life in a pluralist world.

This book generalises the classical theory of orthogonal polynomials on the complex unit circle, or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. The first part treats the case where these poles are all outside the unit disk or in the lower half plane. Classical topics such as recurrence relations, numerical quadrature, interpolation properties, Favard theorems, convergence, asymptotics, and moment problems are generalised and treated in detail. The same topics are discussed for the different situation where the poles are located on the unit circle or on the extended real line. In the last chapter, several applications are mentioned including linear prediction, Pisarenko modelling, lossless inverse scattering, and network synthesis. This theory has many applications in theoretical real and complex analysis, approximation theory, numerical analysis, system theory, and in electrical engineering.

The devastating impact of alcohol on indigenous populations is well known, but debate often overlooks the broad context of the problem and the priorities of indigenous people themselves. This book was written with the desire to improve the level of informed debate, and lead to constructive action. It aims to provide readers with a coherent explanation of alcohol misuse among indigenous peoples in Australia, New Zealand and Canada. The extensive health, economic, social and cultural consequences of misuse are described in the words of the indigenous people themselves. The book found that patterns of indigenous alcohol consumption could not be understood in isolation from the impact of European colonialism and its continuing consequences. Its authors argue that our understanding of alcohol misuse needs to be reconceptualised and structural inequalities addressed.

This is a book on how to gain control of one's emotions. It is a serious book that contains a theory of automatic processing it presents and its implications for controlling emotions. Epstein is a pro

This book provides a first course on quantum mechanics and describes simple applications to physical phenomena that are of immediate and everyday interest. The first five chapters introduce the fundamentals of quantum mechanics and are followed by a revision quiz with which readers may test their understanding. The remaining chapters describe applications, including the physics of lasers, molecular binding, simple properties of crystalline solids arising from their band structure, and the operation of junction transistors. This new edition (first edition entitled Simple Quantum Physics) has been expanded to include a chapter on the theory of spin and its application to magnetic resonance imaging, as well as a description of the WKB approximation and its application to alpha decay. Ideal either as a course text or a self-study text, the book contains nearly 100 exercises and hints to their solution.

This book provides the most comprehensive analysis of one of the most important issues in China today: the tensions between the Chinese Communist Party and the Chinese state legislative, judicial, administrative, and military institutions. Taking the 'neo-institutionalist' approach, the author suggests that the Communist Party in post-1949 China faces an institutional dilemma: the Party cannot live with the state, and it cannot live without the state. Zheng demonstrates that it is not only conceptually constructive, but analytically imperative to distinguish the state from the Communist Party. Secondly, he integrates detailed study with broader generalizations about Chinese politics, thus making efforts to overcome the tendency toward specialized scholarship at the expense of comparative and systemic understanding of China. He also opens a new dimension of Chinese politics - the uncertain and conflictual relationship between the Communist Party and the Chinese state.

Recognizing that clients are unique and resourceful creators of their own realities, this hands-on guide promotes skills that help clinicians meet the demands of the current health care environment. C

In this book Jonathan Hall seeks to demonstrate that the ethnic groups of ancient Greece, like many ethnic groups throughout the world today, were not ultimately racial, linguistic, religious or cultural groups, but social groups whose 'origins' in extraneous territories were just as often imagined as they were real. Adopting an explicitly anthropological point of view, he examines the evidence of literature, archaeology and linguistics to elucidate the nature of ethnic identity in ancient Greece. Rather than treating Greek ethnic groups as 'natural' or 'essential' - let alone 'racial' - entities, he emphasises the active, constructive and dynamic role of ethnography, genealogy, material culture and language in shaping ethnic consciousness. An introductory chapter outlines the history of the study of ethnicity in Greek antiquity.

This book presents a comprehensive and coherent account of the theory of quantum fields on a lattice, an essential technique for the study of the strong and electroweak nuclear interactions. Quantum field theory describes basic physical phenomena over an extremely wide range of length or energy scales. Quantum fields exist in space and time, which can be approximated by a set of lattice points. This approximation allows the application of powerful analytical and numerical techniques, and has provided a powerful tool for the study of both the strong and the electroweak interaction. After introductory chapters on scalar fields, gauge fields and fermion fields, the book studies quarks and gluons in QCD and fermions and bosons in the electroweak theory. The last chapter is devoted to numerical simulation algorithms which have been used in recent large-scale numerical simulations. The book will be valuable for graduate students and researchers in theoretical physics, elementary particle phy

What differences do welfare state variations make for women? How do women and men fare in different welfare states? Diane Sainsbury answers these questions by analysing the situation in countries whose welfare state policies differ in significant ways: the United States, the United Kingdom, Sweden, and the Netherlands. Building on feminist criticisms of mainstream research, Professor Sainsbury reconceptualises the crucial dimensions of variation, notably those relevant to gender. She determines the extent to which legislation reflects and perpetuates the gendered division of labour in the family and society, as well as what types of policy alter gender relations in social provision. She thereby increases our understanding of how policy mechanisms, especially the bases of entitlement, exclude or incorporate women and offers constructive proposals for securing greater equality between women and men.

This book distinguishes itself from much of the polemical literature on these issues by offering the most judicious and well-balanced account yet available of animals' moral standing, and related questions concerning their minds and welfare. Transcending jejune debates focused on utilitarianism versus rights, the book offers a fresh methodological approach with specific and constructive conclusions about our treatment of animals. David DeGrazia provides the most thorough discussion yet of whether equal consideration should be extended to animals' interests, and examines the issues of animal minds and animal well-being with an unparalleled combination of philosophical rigor and empirical documentation. His book is an important contribution to the field of animal ethics and will be read with special interest by all philosophers teaching such courses, as well as biologists, those professionally involved with animals, and general readers concerned about animal welfare.

This book distinguishes itself from much of the polemical literature on these issues by offering the most judicious and well-balanced account yet available of animals' moral standing, and related questions concerning their minds and welfare. Transcending jejune debates focused on utilitarianism versus rights, the book offers a fresh methodological approach with specific and constructive conclusions about our treatment of animals. David DeGrazia provides the most thorough discussion yet of whether equal consideration should be extended to animals' interests, and examines the issues of animal minds and animal well-being with an unparalleled combination of philosophical rigor and empirical documentation. His book is an important contribution to the field of animal ethics and will be read with special interest by all philosophers teaching such courses, as well as biologists, those professionally involved with animals, and general readers concerned about animal welfare.

In this volume, which was originally published in 1996, noisy information is studied in the context of computational complexity; in other words the text deals with the computational complexity of mathematical problems for which information is partial, noisy and priced. The author develops a general theory of computational complexity of continuous problems with noisy information and gives a number of applications; deterministic as well as stochastic noise is considered. He presents optimal algorithms, optimal information, and complexity bounds in different settings: worst case, average case, mixed worst-average and average-worst, and asymptotic. The book integrates the work of researchers in such areas as computational complexity, approximation theory and statistics, and includes many fresh results as well. About two hundred exercises are supplied with a view to increasing the reader's understanding of the subject. The text will be of interest to professional computer scientists, statis

"In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic num

Two of the greatest problems facing the human race today are poverty and the threat to the natural environment. Economic growth is routinely advocated as the solution to poverty, but the natural environment is already threatened by current levels of economic activity. This compelling book examines both economic and ecological approaches to this dilemma, and considers policy issues for industrial economies. It also includes a useful review of recent literature in the area. Michael Common argues that economists rarely address threats to sustainability. He suggests that, while economics cannot offer a blueprint for a sustainable society, the use of economic or price incentives can help achieve social goals and address threats to sustainability.This book is a balanced, constructive and original contribution in the rapidly emerging fields of environmental economics and policy.

This book offers a new, algebraic, approach to set theory. The authors introduce a particular kind of algebra, the Zermelo-Fraenkel algebras, which arise from the familiar axioms of Zermelo-Fraenkel set theory. Furthermore the authors explicitly construct such algebras using the theory of bisimulations. Their approach is completely constructive, and contains both intuitionistic set theory and topos theory. In particular it provides a uniform description of various constructions of the cumulative hierarchy of sets in forcing models, sheaf models and realisability models. Graduate students and researchers in mathematical logic, category theory and computer science should find this book of great interest, and it should be accessible to anyone with some background in categorical logic.

Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied mathematics and algebra, this book presents an innovative synthesis of methods used to study problems of equivalence and symmetry which arise in a variety of mathematical fields and physical applications. Systematic and constructive methods for solving equivalence problems and calculating symmetries are developed and applied to a wide variety of mathematical systems, including differential equations, variational problems, manifolds, Riemannian metrics, polynomials and differential operators. Particular emphasis is given to the construction and classification of invariants, and to the reductions of complicated objects to simple canonical forms. This book will be a valuable resource for students and researchers in geometry, analysis, algebra, mathematical physics and other related fields.

In this book, David Novak conducts an historical, philosophical and theological reflection on the central Jewish doctrine of Israel's election by God, also known as the idea of the chosen people. Historically, he analyses the great change in modern Jewish thought brought about by Spinoza's inversion of the doctrine: that it was not God who elected Israel, but Israel who elected God. The development of that inversion is illustrated by the thought of the German philosopher-theologian, Hermann Cohen. Philosophically, Novak explores the ontological implications of the two differing theologies of election. Theologically, he argues for the correlation of election and revelation, and maintains that a theology of election is required in order to deal with two central questions, namely: who are the Jews, and how are Jews to be related to the world? The constructive picture which results leads to a fresh understanding of Jewish modernity.

How is theology liberating? In the context of a post-Gorbachev world, where many demand freedom which the Western powers seem ill-equipped to deliver, is it even possible to envisage a liberative theology? Taking as his starting point the Marxist complaint that Christianity is ideological, Peter Scott argues that it is not enough for Christian theology to talk about liberation: it must be liberative. Stressing with feminist and liberation theologies the embodied, contextual nature of theology, the constructive proposal made here locates God's liberating abundance toward society in an interpretation of resurrection as social. Only in this way, in the author's view, can a trinitarian Christian account of liberation be adequately grounded. The book will be of interest to all those who wish to know if theology may speak truthfully about the transformation of society: it offers the shape of a liberative theology pointing towards social freedom.

Combinatorics is a subject of increasing importance, owing to its links with computer science, statistics and algebra. This is a textbook aimed at second-year undergraduates to beginning graduates. It stresses common techniques (such as generating functions and recursive construction) which underlie the great variety of subject matter and also stresses the fact that a constructive or algorithmic proof is more valuable than an existence proof. The book is divided into two parts, the second at a higher level and with a wider range than the first. Historical notes are included which give a wider perspective on the subject. More advanced topics are given as projects and there are a number of exercises, some with solutions given.

Excellent graduate-level monograph investigates relationship between various structural properties of real functions and the character of possible approximations to them by polynomials and other func

This book attacks the assumption found in moral philosophy that social control as such is an intellectually and morally destructive force. It replaces this view with a richer and deeper perspective on the nature of social character aimed at showing how social freedom cannot mean immunity from social pressure. The author demonstrates how our competence as rational and social agents depends on a constructive adaptation of social control mechanisms. Our facility at achieving our goals is enhanced, rather than undermined, by social control. The author then articulates sources, contracts, and degrees of legitimate social control in different social and historical settings. Drawing on a wide range of material in moral and political philosophy, law, cognitive and social psychology, anthropology and literature, Professor Schoeman shows how the aim of moral philosophy ought to be to understand our social character, not to establish fortifications against it in the name of rationality and autono

Disjunctive Poetics examines some of the most interesting and experimental contemporary writers whose work forms a counterpoint to the mainstream writing of our time. Peter Quartermain suggests that the explosion of non-canonical modern writing is linked to the severe political, social and economic dislocation of non-English-speaking immigrants who, bringing alternative culture with them as they passed through Ellis Island in their hundreds of thousands at the turn of the century, found themselves uprooted from their traditions and dissociated from their cultures. The line of American poetry that runs from Gertrude Stein through Louis Zukofsky and the Objectivists to the Language Writers, Quartermain contends, is not the constructive but the deconstructive aspect, which emphasises the materiality and ambiguity of the linguistic medium and the arbitrariness and openness of the creative process. Providing close reading of Gertrude Stein, Louis Zukofsky, Robert Creeley, Basil Bunting, Guy

At a time when the accepted standard treatment for alcoholism is long-term and expensive, solution-focused therapy, as developed at the Brief Family Therapy Center in Milwaukee, offers a brief and cost-effective alternative. Insoo Kim Berg and Scott D. Miller believe that a focus on solutions, rather than pathology, is the most constructive strategy for working with problem drinkers; their foremost concern is with what works. To this end they don't reject traditional treatment programs; rather, they view them as one part of a flexible and multidimensional approach to alcohol abuse treatment.The authors successfully utilize solution-focused therapy in their work with problem drinkers, but it is their philosophy of working with clients-and within clients' belief systems-to encourage change that is at the heart of their model. The model, grounded in the philosophy of solution-focused brief therapy, introduces a paradigmatic change in the approach to substance abuse treatment. Rather than

Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory. Volume 2: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems. This two-volume work provides a comprehensive and timely survey of the application of the methods of quantum field theory to statistical physics, a very active and fruitful area of modern research. The first volume provides a pedagogical introduction to the subject, discussing Brownian motion, its anticommutative counterpart in the guise of Onsager's solution to the two-dimensional Ising model, the mean field or Landau approximation, scaling ideas exemplified by the Kosterlitz-Thouless theory for the XY transition, the continuous renormalization group applied to the standard phi-to the fourth theory (the simplest typical case) and lattice gauge theory as a pathway to the understanding of quark confinement in quantum chromodynamics. The second volume covers more diverse topics, including strong coupling expansions and the

Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory. Volume 2: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems. This two-volume work provides a comprehensive and timely survey of the application of the methods of quantum field theory to statistical physics, a very active and fruitful area of modern research. The first volume provides a pedagogical introduction to the subject, discussing Brownian motion, its anticommutative counterpart in the guise of Onsager's solution to the two-dimensional Ising model, the mean field or Landau approximation, scaling ideas exemplified by the Kosterlitz-Thouless theory for the XY transition, the continuous renormalization group applied to the standard phi-to the fourth theory (the simplest typical case) and lattice gauge theory as a pathway to the understanding of quark confinement in quantum chromodynamics. The second volume covers more diverse topics, including strong coupling expansions and the

This volume contains selected contributions from a very successful meeting on Number Theory and Dynamical Systems held at the University of York in 1987. There are close and surprising connections between number theory and dynamical systems. One emerged last century from the study of the stability of the solar system where problems of small divisors associated with the near resonance of planetary frequencies arose. Previously the question of the stability of the solar system was answered in more general terms by the celebrated KAM theorem, in which the relationship between near resonance (and so Diophantine approximation) and stability is of central importance. Other examples of the connections involve the work of Szemeredi and Furstenberg, and Sprindzuk. As well as containing results on the relationship between number theory and dynamical systems, the book also includes some more speculative and exploratory work which should stimulate interest in different approaches to old problems.

What does it mean today to 'think like a lawyer'? Drawing on extensive interviews with men and women attorneys, the authors explore how moral reasoning affects lawyers' understanding of justice and their own role in promoting it. This examination of personal and institutional imperatives in the legal profession, illustrated with quotations from the lawyers themselves, raises questions that transcend traditional discussions of legal ethics. The authors examine: the relationship between gender and patterns of moral thinking; the ways that personal morality affects public and professional responsibility; the legal system's response to social changes in public ethics and in women's roles. In conclusion the authors offer suggestions for constructive changes in legal education and the code of professional ethics to foster morally responsive democracy. All those concerned with moral reasoning, gender roles, and the evolution of the legal system will find this stimulating and timely reading.

This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Dr Young has stressed applications of the theory, particularly to the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. It is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). Thus it will make an excellent first course in Hilbert space theory at either undergraduate or graduate level and will also be of interest to electrical engineers and physicists, particularly those involved in control theory and filter design.

The central theme of this book is the theorem of Ambrose and Singer, which gives for a connected, complete and simply connected Riemannian manifold a necessary and sufficient condition for it to be homogeneous. This is a local condition which has to be satisfied at all points, and in this way it is a generalization of E. Cartan's method for symmetric spaces. The main aim of the authors is to use this theorem and representation theory to give a classification of homogeneous Riemannian structures on a manifold. There are eight classes, and some of these are discussed in detail. Using the constructive proof of Ambrose and Singer many examples are discussed with special attention to the natural correspondence between the homogeneous structure and the groups acting transitively and effectively as isometrics on the manifold.

This invaluable anatomical reference shows important parts of the human body, both in motion and in repose: hand, wrist, fingers, forearm, neck, thigh, leg, and more. Drawings of bone and muscle stru

When osseointegration was first introduced by Brånemark as a therapy for the replacement of the natural dentition, it was accepted as an appropriate and predictable solution for young and middle-aged edentulous patients. No one anticipated the positive results and high level of acceptability that this therapy would bring about. The decision regarding whether to save a tooth or insert an implant is one that the implant clinician makes based on previous experience, recently approved therapeutics, and the best interests of the patient. This high-quality and timely publication will serve to enhance the armamentarium of implant clinicians in this regard. The editors have engaged leading thinkers in surgery and prosthetics to share their methods, ranging from prevention to regeneration. The text provides contemporary information for achieving constructive endpoint goals and for managing solutions to peri-implantitis and should have a place in every dental library.