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Approximation Theory. Tampa: Proceedings of a Seminar held in Tampa, Florida, 1985 - 1986 (Lecture Notes in Mathematics #1287)

Arbeitslosigkeit und Arbeitsangebot in Österreich (Linzer Universitätsschriften #12)

Der vorliegende Band enthiilt die Referate und Koreferate, die im Oktober 1986 auf einem zweitllgigen Symposium Uber "Arbeitslosigkeit und Arbeits­ angebot in Osterreich" an der Universitiit Linz vorgetragen wurden. Die Be- trage basieren auf !aufenden Arbeiten und Zwischenergebnissen aus dem Fo- schungsschwerpunkt "Dynamik der Arbeitslosigkeit und Beschaftigung", einem auf fUnf Jahre geplanten Forschungsprogramm, das im Januar 1985 yom Fonds zur Forderung der wissenschaftlichen Forschung bewilligt und Mitte 1985 begonnen wurde. Das Projekt ist von dem Gedanken getragen, daB Fragen der Arbeitslosigkeit und Beschaftigung, die lange Zeit nieht sehr dringlich erschienen, nun intensiver Beachtung erfordem, da sie sich in allen Landem und nun auch in Osterreich als besonders hartnackiges Problem erweisen. 1m letzten Jahrzehnt hat die Arbeitsmarktforschung in Osterreich rasch an Umfang zugenommen, wobei vor allem Arbeiten aus dem Oste- reichischen Institut fUr Wirtschaftsforschung, dem Osterreichischen Statist- schen Zentralamt, dem Institut fUr Hohere Studien, dem Institut fUr Arbeit- marktpolitik an der Universitat Linz und okonomische und soziologische Untersuchungen an der Universitiit Graz zu erwahnen sind. Durch diese wissenschaftlichen Aktivitiiten, aber auch durch wichtige theoretische AnstoBe aus dem Ausland sowie durch eine wesentliche Ausweitung der yom Sozia- ministerium und den Arbeitsamtem zur VerfUgung gestellten Daten haben sich neue Moglichkeiten entwickelt, das Arbeitsmarktgeschehen in groBerem Detail zu analysieren. Wir sind dem Fonds zur Forderung der wissenschaf- lichen Forschung zu Dank verpflichtet, daB er durch Bewilligung des Schwe- punkts eine grUndliche Bearbeitung einiger dieser Themen ermoglicht hat.

An Architectonic for Science: The Structuralist Program (Synthese Library #186)

This book has grown out of eight years of close collaboration among its authors. From the very beginning we decided that its content should come out as the result of a truly common effort. That is, we did not "distribute" parts of the text planned to each one of us. On the contrary, we made a point that each single paragraph be the product of a common reflection. Genuine team-work is not as usual in philosophy as it is in other academic disciplines. We think, however, that this is more due to the idiosyncrasy of philosophers than to the nature of their subject. Close collaboration with positive results is as rewarding as anything can be, but it may also prove to be quite difficult to implement. In our case, part of the difficulties came from purely geographic separation. This caused unsuspected delays in coordinating the work. But more than this, as time passed, the accumulation of particular results and ideas outran our ability to fit them into an organic unity. Different styles of exposition, different ways of formalization, different levels of complexity were simultaneously present in a voluminous manuscript that had become completely unmanageable. In particular, a portion of the text had been conceived in the language of category theory and employed ideas of a rather abstract nature, while another part was expounded in the more conventional set-theoretic style, stressing intui­ tivity and concreteness.

Asymptotic Methods for Relaxation Oscillations and Applications (Applied Mathematical Sciences #63)

In various fields of science, notably in physics and biology, one is con­ fronted with periodic phenomena having a remarkable temporal structure: it is as if certain systems are periodically reset in an initial state. A paper of Van der Pol in the Philosophical Magazine of 1926 started up the investigation of this highly nonlinear type of oscillation for which Van der Pol coined the name "relaxation oscillation". The study of relaxation oscillations requires a mathematical analysis which differs strongly from the well-known theory of almost linear oscillations. In this monograph the method of matched asymptotic expansions is employed to approximate the periodic orbit of a relaxation oscillator. As an introduction, in chapter 2 the asymptotic analysis of Van der Pol's equation is carried out in all detail. The problem exhibits all features characteristic for a relaxation oscillation. From this case study one may learn how to handle other or more generally formulated relaxation oscillations. In the survey special attention is given to biological and chemical relaxation oscillators. In chapter 2 a general definition of a relaxation oscillation is formulated.

Asymptotics for Orthogonal Polynomials (Lecture Notes in Mathematics #1265)

Recently there has been a great deal of interest in the theory of orthogonal polynomials. The number of books treating the subject, however, is limited. This monograph brings together some results involving the asymptotic behaviour of orthogonal polynomials when the degree tends to infinity, assuming only a basic knowledge of real and complex analysis. An extensive treatment, starting with special knowledge of the orthogonality measure, is given for orthogonal polynomials on a compact set and on an unbounded set. Another possible approach is to start from properties of the coefficients in the three-term recurrence relation for orthogonal polynomials. This is done using the methods of (discrete) scattering theory. A new method, based on limit theorems in probability theory, to obtain asymptotic formulas for some polynomials is also given. Various consequences of all the results are described and applications are given ranging from random matrices and birth-death processes to discrete Schrödinger operators, illustrating the close interaction with different branches of applied mathematics.

Ausländerberichterstattung in der Kommune: Inhaltsanalyse Bielefelder Tageszeitungen unter Berücksichtigung ‘ausländerfeindlicher’ Alltagstheorien (Forschungsberichte des Landes Nordrhein-Westfalen #3222)

Auswirkungen von Fehlern in den Daten auf Parameterschätzungen und Prognosen (Arbeiten zur Angewandten Statistik #30)

Größe und Komplexität empirischer ökonometrischer Modelle haben in den letzten Jahrzehnten immer mehr zugenommen. Die Zuverlässigkeit des zugrundeliegenden Datenmaterials hat sich dagegen kaum verbessert, und eine Fehlspezifizierung von Meßfehlermodellen zur Schließung der Lücke zwischen theoretischen ökonomischen Variablen und den verfügbaren Daten erscheint schon wegen der unglücklichen Trennung zwischen Datenproduzenten und Datennutzern kaum vermeidbar. In dieser Arbeit werden die Auswirkungen solcher Fehlspezifizierungen auf Parameterschätzungen und Prognosen in Modellen wachsender Komplexität bis hin zu nichtlinearen interdependenten dynamischen Modellen analysiert mit Hilfe von asymptotischen Aussagen und Monte-Carlo-Simulationen. Für ein makroökonomisches Modell für die BRD werden außerdem Methoden diskutiert zur Beschaffung von Informationen über Art und Größe von Meßfehlern. Die Simulationsrechnungen basieren auf der Zuverlässigkeit und Schnelligkeit des zugrundeliegenden numerischen Algorithmus zur Full-Information-Maximum-Likelihood-Schätzung in nichtlinearen interdependenten Modellen. Darstellung und Diskussion eines für diesen Zweck entwickelten Algorithmus (trust-region-Verfahren mit automatischer Skalierung) bilden den zweiten Schwerpunkt der Arbeit.

Automated Theorem Proving (Künstliche Intelligenz)

Since both the coments and the structure of the book appeared to be successful, only minor changes were made. In particular, some recent work in ATP has been incorporated so that the book continues to reflect the state of the art in the field. The most significant change is in the quality of the layout including the removal of a number of inaccuracies and typing errors. R. Caferra, E. Eder, F. van der Linden, and J. Muller have caught vanous minor errors. P. Haddawy and S.T. Pope have provided many stilistic improvements of the English text. Last not least, A. Bentrup and W. Fischer have produced the beautiful layout. The extensive work of typesetting was financally supported within ESPRIT pro­ ject 415. Munchen, September 1986 W. Bibel PREFACE Among the dreams of mankind is the one dealing with the mechanization of human thought. As the world today has become so complex that humans apparently fail to manage it properly with their intellectual gifts, the realization of this dream might be regarded even as something like a necessity. On the other hand, the incredi­ ble advances in computer technology let it appear as a real possibility.

Autowave Processes in Kinetic Systems: Spatial and Temporal Self-Organisation in Physics, Chemistry, Biology, and Medicine (Mathematics and its Applications #11)

Probably, we are obliged to Science, more than to any other field of the human activity, for the origin of our sense that collective efforts are necessary indeed. F. Joliot-Curie The study of autowave processes is a young science. Its basic concepts and methods are still in the process of formation, and the field of its applications to various domains of natural sciences is expanding continuously. Spectacular examples of various autowave processes are observed experimentally in numerous laboratories of quite different orientations, dealing with investigations in physics, chemistry and biology. It is O1). r opinion, however, that if a history of the discovery of autowaves will he written some day its author should surely mention three fundamental phenomena which were the sources of the domain in view. "Ve mean combustion and phase transition waves, waves in chemical reactors where oxidation-reduction processes take place, and propagation of excitations in nerve fibres. The main tools of the theory of autowave processes are various methods used for investigating nonlinear discrete or distributed oscillating systems, the mathe­ matical theory of nonlinear parabolic differential equations, and methods of the theory of finite automata. It is noteworthy that the theory of autowave,. , has been greatly contributed to be work of brilliant mathematicians who anticipated the experimental discoveries in their abstract studies. One should mention R. Fishel' (1937), A. N. Kolmogorov, G. 1. Petrovskii, and N. S. Piskunov (1937), N. Wiener and A. Rosenbluth (1946), A. Turing (1952).

Beijing Lectures in Harmonic Analysis. (AM-112), Volume 112 (PDF)

Based on seven lecture series given by leading experts at a summer school at Peking University, in Beijing, in 1984. this book surveys recent developments in the areas of harmonic analysis most closely related to the theory of singular integrals, real-variable methods, and applications to several complex variables and partial differential equations. The different lecture series are closely interrelated; each contains a substantial amount of background material, as well as new results not previously published. The contributors to the volume are R. R. Coifman and Yves Meyer, Robert Fcfferman, Carlos K. Kenig, Steven G. Krantz, Alexander Nagel, E. M. Stein, and Stephen Wainger.

Bildschirmtext in der Ausbildung: Dargestellt am Beispiel der Wirtschaftsuniversität Wien (Betriebs- und Wirtschaftsinformatik #18)

Biostatistics: Advances in Statiscal Sciences Festschrift in Honor of Professor V.M. Joshi’s 70th Birthday Volume V (The Western Ontario Series in Philosophy of Science #38)

On May 27-31, 1985, a series of symposia was held at The University of Western Ontario, London, Canada, to celebrate the 70th birthday of Pro­ fessor V. M. Joshi. These symposia were chosen to reflect Professor Joshi's research interests as well as areas of expertise in statistical science among faculty in the Departments ofStatistical and Actuarial Sciences, Economics, Epidemiology and Biostatistics, and Philosophy. From these symposia, the six volumes which comprise the "Joshi Festschrift" have arisen. The 117 articles in this work reflect the broad interests and high quality of research of those who attended our conference. We would like to thank all of the contributors for their superb cooperation in helping us to complete this project. Our deepest gratitude must go to the three people who have spent so much of their time in the past year typing these volumes: Jackie Bell, Lise Constant, and Sandy Tarnowski. This work has been printed from "camera ready" copy produced by our Vax 785 computer and QMS Lasergraphix printers, using the text processing software TEX. At the initiation of this project, we were neophytes inthe use ofthis system. Thank you, Jackie, Lise, and Sandy, for having the persistence and dedication needed to complete this undertaking.

Blaise Pascal 1623–1662 (Vita Mathematica #2)

Brains, Machines, and Mathematics

This is a book whose time has come-again. The first edition (published by McGraw-Hill in 1964) was written in 1962, and it celebrated a number of approaches to developing an automata theory that could provide insights into the processing of information in brainlike machines, making it accessible to readers with no more than a college freshman's knowledge of mathematics. The book introduced many readers to aspects of cybernetics-the study of computation and control in animal and machine. But by the mid-1960s, many workers abandoned the integrated study of brains and machines to pursue artificial intelligence (AI) as an end in itself-the programming of computers to exhibit some aspects of human intelligence, but with the emphasis on achieving some benchmark of performance rather than on capturing the mechanisms by which humans were themselves intelligent. Some workers tried to use concepts from AI to model human cognition using computer programs, but were so dominated by the metaphor "the mind is a computer" that many argued that the mind must share with the computers of the 1960s the property of being serial, of executing a series of operations one at a time. As the 1960s became the 1970s, this trend continued. Meanwhile, experi­ mental neuroscience saw an exploration of new data on the anatomy and physiology of neural circuitry, but little of this research placed these circuits in the context of overall behavior, and little was informed by theoretical con­ cepts beyond feedback mechanisms and feature detectors.

A Budget of Trisections

It is impossible to trisect angles with straightedge and compass alone, but many people try and think they have succeeded. This book is about angle trisections and the people who attempt them. Its purposes are to collect many trisections in one place, inform about trisectors, to amuse the reader, and, perhaps most importantly, to reduce the number of trisectors. This book includes detailed information about the personalities of trisectors and their constructions. It can be read by anyone who has taken a high school geometry course.

Calculus of Several Variables (Undergraduate Texts in Mathematics)

This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.

Cell-to-Cell Mapping: A Method of Global Analysis for Nonlinear Systems (Applied Mathematical Sciences #64)

For many years, I have been interested in global analysis of nonlinear systems. The original interest stemmed from the study of snap-through stability and jump phenomena in structures. For systems of this kind, where there exist multiple stable equilibrium states or periodic motions, it is important to examine the domains of attraction of these responses in the state space. It was through work in this direction that the cell-to-cell mapping methods were introduced. These methods have received considerable development in the last few years, and have also been applied to some concrete problems. The results look very encouraging and promising. However, up to now, the effort of developing these methods has been by a very small number of people. There was, therefore, a suggestion that the published material, scattered now in various journal articles, could perhaps be pulled together into book form, thus making it more readily available to the general audience in the field of nonlinear oscillations and nonlinear dynamical systems. Conceivably, this might facilitate getting more people interested in working on this topic. On the other hand, there is always a question as to whether a topic (a) holds enough promise for the future, and (b) has gained enough maturity to be put into book form. With regard to (a), only the future will tell. With regard to (b), I believe that, from the point of view of both foundation and methodology, the methods are far from mature.

Chaos, Noise and Fractals

The study of nonlinear dynamical systems has been gathering momentum since the late 1950s. It now constitutes one of the major research areas of modern theoretical physics. The twin themes of fractals and chaos, which are linked by attracting sets in chaotic systems that are fractal in structure, are currently generating a great deal of excitement. The degree of structure robustness in the presence of stochastic and quantum noise is thus a topic of interest. Chaos, Noise and Fractals discusses the role of fractals in quantum mechanics, the influence of phase noise in chaos and driven optical systems, and the arithmetic of chaos. The book represents a balanced overview of the field and is a worthy addition to the reading lists of researchers and students interested in any of the varied, and sometimes bizarre, aspects of this intriguing subject.

Chaos, Noise and Fractals

The study of nonlinear dynamical systems has been gathering momentum since the late 1950s. It now constitutes one of the major research areas of modern theoretical physics. The twin themes of fractals and chaos, which are linked by attracting sets in chaotic systems that are fractal in structure, are currently generating a great deal of excitement. The degree of structure robustness in the presence of stochastic and quantum noise is thus a topic of interest. Chaos, Noise and Fractals discusses the role of fractals in quantum mechanics, the influence of phase noise in chaos and driven optical systems, and the arithmetic of chaos. The book represents a balanced overview of the field and is a worthy addition to the reading lists of researchers and students interested in any of the varied, and sometimes bizarre, aspects of this intriguing subject.

Classic Papers in Combinatorics (Modern Birkhäuser Classics)

This volume surveys the development of combinatorics since 1930 by presenting in chronological order the fundamental results of the subject proved in over five decades of original papers by: T. van Aardenne-Ehrenfest.- R.L. Brooks.- N.G. de Bruijn.- G.F. Clements.- H.H. Crapo.- R.P. Dilworth.- J. Edmonds.- P. Erdös.- L.R. Ford, Jr.- D.R. Fulkerson.- D. Gale.- L. Geissinger.- I.J. Good.- R.L. Graham.- A.W. Hales.- P. Hall.- P.R. Halmos.- R.I. Jewett.- I. Kaplansky.- P.W. Kasteleyn.- G. Katona.- D.J. Kleitman.- K. Leeb.- B. Lindström.- L. Lovász.- D. Lubell.- C. St. J.A. Nash-Williams.- G. Pólya.-R. Rado.- F.P. Ramsey.- G.-C. Rota.- B.L. Rothschild.- H.J. Ryser.- C. Schensted.- M.P. Schützenberger.- R.P. Stanley.- G. Szekeres.- W.T. Tutte.- H.E. Vaughan.- H. Whitney.

Classical Principles and Optimization Problems (Mathematics and its Applications #15)

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, tbat they can't see the problem. perbaps you will find the fina\ question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van GuJik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such newemerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Classical Tessellations and Three-Manifolds (Universitext)

This unusual book, richly illustrated with 29 colour illustrations and about 200 line drawings, explores the relationship between classical tessellations and three-manifolds. In his original and entertaining style, the author provides graduate students with a source of geometrical insight into low-dimensional topology. Researchers in this field will find here an account of a theory that is on the one hand known to them but here is "clothed in a different garb" and can be used as a source for seminars on low-dimensional topology, or for preparing independent study projects for students, or again as the basis of a reading course.

Classification Theory: Proceedings of the U.S.-Israel Workshop on Model Theory in Mathematical Logic Held in Chicago, Dec. 15-19, 1985 (Lecture Notes in Mathematics #1292)

Cognition as Intuitive Statistics (Psychology Revivals)

Originally published in 1987, this title is about theory construction in psychology. Where theories come from, as opposed to how they become established, was almost a no-man’s land in the history and philosophy of science at the time. The authors argue that in the science of mind, theories are particularly likely to come from tools, and they are especially concerned with the emergence of the metaphor of the mind as an intuitive statistician. In the first chapter, the authors discuss the rise of the inference revolution, which institutionalized those statistical tools that later became theories of cognitive processes. In each of the four following chapters they treat one major topic of cognitive psychology and show to what degree statistical concepts transformed their understanding of those topics.

Cognition as Intuitive Statistics (Psychology Revivals)

Originally published in 1987, this title is about theory construction in psychology. Where theories come from, as opposed to how they become established, was almost a no-man’s land in the history and philosophy of science at the time. The authors argue that in the science of mind, theories are particularly likely to come from tools, and they are especially concerned with the emergence of the metaphor of the mind as an intuitive statistician. In the first chapter, the authors discuss the rise of the inference revolution, which institutionalized those statistical tools that later became theories of cognitive processes. In each of the four following chapters they treat one major topic of cognitive psychology and show to what degree statistical concepts transformed their understanding of those topics.