Birkhäuser Basel

This is a collection of exercises in the theory of analytic functions, with completed and detailed solutions. We wish to introduce the student to applications and aspects of the theory of analytic functions not always touched upon in a first course. Using appropriate exercises show the students some aspects of what lies beyond a first course in complex variables. We also discuss topics of interest for electrical engineering students (for instance, the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). Examples of  important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space) are given. The book also includes a part where relevant facts from topology, functional analysis and Lebesgue integration are reviewed.

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This second special issue of Pure and Applied Geophysics in honor of Keiiti Aki focuses on recent advances in quantifying and interpreting heterogeneities in lithospheric structures and earthquake behavior. The volume provides a combination of reviews, methodological studies and applications on topics related to Aki's pioneering contributions. It also includes material on Keiiti Aki and a list of his publications. The discussed subjects include research associated with dynamic earthquake rupture, studies on imaging earthquake locations and structures using P and S seismic phases, and studies associated with imaging source and structure properties using scattered coda waves. The volume will be useful to students and researchers alike, who are interested in the nature of large- and small-scale heterogeneities in the earth's lithosphere and earthquake properties.

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I Resolution of Singularities.- Désingularisation en dimension 3 et caractéristique p.- Sur l'espace des courbes tracées sur une singularité.- Blowing up acyclic graphs and geometrical configurations.- On a Newton polygon approach to the uniformization of singularities of characteristic p.- Geometry of plane curves via toroidal resolution.- to the algorithm of resolution.- II Complex Singularities and Differential Systems.- Polarity with respect to a foliation.- On moduli spaces of semiquasihomogeneous singularities.- Stratification Properties of Constructible Sets.- On the linearization problem and some questions for webs in ?2.- Globalization of Admissible Deformations.- Caractérisation géométrique de l'existence du polynôme de Bernstein relatif.- Le Polygone de Newton d'un DX-module.- How good are real pictures?.- Weighted homogeneous complete intersections.- III Curves and Surfaces.- Degree 8 and genus 5 curves in ?3 and the Horrocks-Mumford bundle.- Irreducible Polynomials of k((X))[Y].- Examples of Abelian Surfaces with Polarization type (1,3).- Semigroups and Clusters at Infinity.- Cubic surfaces with double points in positive characteristic.- On the classification of reducible curve singularities.

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The past decade has witnessed a dramatic and widespread expansion of interest and activity in sub-Riemannian (Carnot-Caratheodory) geometry, motivated both internally by its role as a basic model in the modern theory of analysis on metric spaces, and externally through the continuous development of applications (both classical and emerging) in areas such as control theory, robotic path planning, neurobiology and digital image reconstruction. The quintessential example of a sub Riemannian structure is the Heisenberg group, which is a nexus for all of the aforementioned applications as well as a point of contact between CR geometry, Gromov hyperbolic geometry of complex hyperbolic space, subelliptic PDE, jet spaces, and quantum mechanics. This book provides an introduction to the basics of sub-Riemannian differential geometry and geometric analysis in the Heisenberg group, focusing primarily on the current state of knowledge regarding Pierre Pansu's celebrated 1982 conjecture regarding the sub-Riemannian isoperimetric profile. It presents a detailed description of Heisenberg submanifold geometry and geometric measure theory, which provides an opportunity to collect for the first time in one location the various known partial results and methods of attack on Pansu's problem. As such it serves simultaneously as an introduction to the area for graduate students and beginning researchers, and as a research monograph focused on the isoperimetric problem suitable for experts in the area.

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The past decade has witnessed a dramatic and widespread expansion of interest and activity in sub-Riemannian (Carnot-Caratheodory) geometry, motivated both internally by its role as a basic model in the modern theory of analysis on metric spaces, and externally through the continuous development of applications (both classical and emerging) in areas such as control theory, robotic path planning, neurobiology and digital image reconstruction. The quintessential example of a sub Riemannian structure is the Heisenberg group, which is a nexus for all of the aforementioned applications as well as a point of contact between CR geometry, Gromov hyperbolic geometry of complex hyperbolic space, subelliptic PDE, jet spaces, and quantum mechanics. This book provides an introduction to the basics of sub-Riemannian differential geometry and geometric analysis in the Heisenberg group, focusing primarily on the current state of knowledge regarding Pierre Pansu's celebrated 1982 conjecture regarding the sub-Riemannian isoperimetric profile. It presents a detailed description of Heisenberg submanifold geometry and geometric measure theory, which provides an opportunity to collect for the first time in one location the various known partial results and methods of attack on Pansu's problem. As such it serves simultaneously as an introduction to the area for graduate students and beginning researchers, and as a research monograph focused on the isoperimetric problem suitable for experts in the area.

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This volume collects the contributions of a Conference held in June 2005 at the laboratoire Paul Painleve (UMR CNRS 8524) in Lille, France. The meeting was intended to review hot topics and future trends in fluid dynamics, with the objective to foster exchanges of various viewpoints (e.g. theoretical, and numerical) on the addressed questions. It comprises a collection of research articles on recent advances in the analysis and simulation of fluid dynamics.

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Logical thinking, the analysis of complex relationships, the recognition of und- lying simple structures which are common to a multitude of problems ¿ these are the skills which are needed to do mathematics, and their development is the main goal of mathematics education. Of course, these skills cannot be learned ¿in a vacuum¿. Only a continuous struggle with concrete problems and a striving for deep understanding leads to success. A good measure of abstraction is needed to allow one to concentrate on the essential, without being distracted by appearances and irrelevancies. The present book strives for clarity and transparency. Right from the beg- ning, it requires from the reader a willingness to deal with abstract concepts, as well as a considerable measure of self-initiative. For these e?orts, the reader will be richly rewarded in his or her mathematical thinking abilities, and will possess the foundation needed for a deeper penetration into mathematics and its applications. Thisbookisthe?rstvolumeofathreevolumeintroductiontoanalysis.It- veloped from courses that the authors have taught over the last twenty six years at theUniversitiesofBochum,Kiel,Zurich,BaselandKassel.Sincewehopethatthis book will be used also for self-study and supplementary reading, we have included far more material than can be covered in a three semester sequence. This allows us to provide a wide overview of the subject and to present the many beautiful and important applications of the theory. We also demonstrate that mathematics possesses, not only elegance and inner beauty, but also provides e?cient methods for the solution of concrete problems.

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Dieses Lehrbuch ist der erste Band einer dreiteiligen Einführung in die Analysis. Es ist durch einen modernen und klaren Aufbau geprägt, der versucht den Blick auf das Wesentliche zu richten. Anders als in den üblichen Lehrbüchern wird keine künstliche Trennung zwischen der Theorie einer Variablen und derjenigen mehrerer Veränderlicher vorgenommen. Der Leser soll in dem Erkennen der wesentlichen Inhalte und Ideen der Analysis geschult werden und sich ein solides Fundament für das Studium tieferliegender Theorien erwerben. Das Werk richtet sich an Hörer und Dozenten der Anfängervorlesung der Analysis. Durch zahlreiche Beispiele, Übungsaufgaben und Ergänzungen zum üblichen Vorlesungsstoff ist der Text ausserdem zum Selbststudium, als Vorlage für vertiefende Seminare und als Grundlage für das gesamte Mathematik- bzw. Physikstudium geeignet.

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"This textbook provides an outstanding introduction to analysis. It is distinguished by its high level of presentation and its focus on the essential.'' (Zeitschrift für Analysis und ihre Anwendung 18, No. 4 - G. Berger, review of the first German edition)

"One advantage of this presentation is that the power of the abstract concepts are convincingly demonstrated using concrete applications.'' (W. Grölz, review of the first German edition)

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Dieses Lehrbuch ist der erste Band einer dreiteiligen Einführung in die Analysis. Der moderne und klare Aufbau richtet seinen Blick auf das Wesentliche. Anders als übliche Lehrbücher trennt es nicht zwischen der Theorie einer Variablen und derjenigen mehrerer Veränderlicher. Leser erkennen wesentliche Inhalte und Ideen der Analysis und erwerben sich so ein solides Fundament für das Studium tieferliegender Theorien. Das Werk richtet sich an Hörer und Dozenten der Anfängervorlesung der Analysis. Zahlreiche Beispiele, Übungsaufgaben und Ergänzungen empfehlen es zum Selbststudium und als Grundlage für vertiefende Seminare und das gesamte Studium.

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Der zweite Band dieser Einführung in die Analysis behandelt die Integrationstheorie von Funktionen einer Variablen, die mehrdimensionale Differentialrechnung und die Theorie der Kurven und Kurvenintegrale. Der im ersten Band begonnene moderne und klare Aufbau wird konsequent fortgesetzt. Dadurch wird ein tragfähiges Fundament geschaffen, das es erlaubt, interessante Anwendungen zu behandeln, die zum Teil weit über den in der üblichen Lehrbuchliteratur behandelten Stoff hinausgehen. Zahlreiche Übungsaufgaben von unterschiedlichem Schwierigkeitsgrad und viele informative Abbildungen runden dieses Lehrbuch ab.

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Der zweite Band dieser Einführung in die Analysis behandelt die Integrationstheorie von Funktionen einer Variablen, die mehrdimensionale Differentialrechnung und die Theorie der Kurven und Kurvenintegrale. Der im ersten Band begonnene moderne und klare Aufbau wird konsequent fortgesetzt. Dadurch wird ein tragfähiges Fundament geschaffen, das es erlaubt, interessante Anwendungen zu behandeln, die zum Teil weit über den in der üblichen Lehrbuchliteratur behandelten Stoff hinausgehen.

Dies betrifft beispielsweise die Behandlung von Nemytskiioperatoren, welche eine transparente Einführung in die Variationsrechnung und Herleitung der Euler-Lagrangeschen Gleichungen ermöglicht. Ein weiteres Beispiel stellt die Darstellung der lokalen Theorie der Untermannigfaltigkeiten des Rⁿ dar.

Als Anwendungen der Theorie der Kurvenintegrale werden die Cauchyschen Integralsätze und die Theorie der holomorphen Funktionen bis einschließlich der Homologieversion des Residuensatzes entwickelt. Neben der Berechnung wichtiger bestimmter Integrale der Mathematik und der Physik, werden funktionentheoretische Eigenschaften der Gamma- und der Riemannschen Zetafunktionen besprochen.

Zahlreiche Übungsaufgaben von unterschiedlichem Schwierigkeitsgrad und viele informative Abbildungen runden dieses Lehrbuch ab.

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This third volume concludes our introduction to analysis, wherein we ?nish laying the groundwork needed for further study of the subject. As with the ?rst two, this volume contains more material than can treated in a single course. It is therefore important in preparing lectures to choose a suitable subset of its content; the remainder can be treated in seminars or left to independent study. For a quick overview of this content, consult the table of contents and the chapter introductions. Thisbookisalsosuitableasbackgroundforothercoursesorforselfstudy. We hope that its numerous glimpses into more advanced analysis will arouse curiosity and so invite students to further explore the beauty and scope of this branch of mathematics. In writing this volume, we counted on the invaluable help of friends, c- leagues, sta?, and students. Special thanks go to Georg Prokert, Pavol Quittner, Olivier Steiger, and Christoph Walker, who worked through the entire text cr- ically and so helped us removeerrors and make substantial improvements. Our thanks also goes out to Carlheinz Kneisel and Bea Wollenmann, who likewise read the majority of the manuscript and pointed out various inconsistencies. Without the inestimable e?ortofour ¿typesetting perfectionist¿, this volume could not have reached its present form: her tirelessness and patience with T X E and other software brought not only the end product, but also numerous previous versions,to a high degree of perfection. For this contribution, she has our greatest thanks.

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Der dritte und letzte Band dieser Reihe ist der Integrationstheorie und den Grundlagen der globalen Analysis gewidmet. Klarer Aufbau, eine strukturierte Darstellung der Theorie und zahlreiche Beispiele sowie konkrete Rechnungen und Übungsaufgaben erleichtern die Einübung des Stoffes. Sie machen dieses Lehrbuch zu einem verlässlichen Begleiter durch das gesamte Studium. Die Autoren geben ihren Lesern geeignete Werkzeuge für die weitere Beschäftigung mit der Mathematik an die Hand und liefern zahlreiche Ausblicke auf weiterführende Theorien.

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Das Waringsche Problem.- Kongruenzen und p-Adische Dichte.- Exponentialsummen, Kongruenzen und Gleichungen.- Beweis des Hauptsatzes über die Invariante h.

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We bring into full light some excerpts on musical subjects which were until now scattered throughout the most famous scientific texts. The main scientific and musical cultures outside of Europe are also taken into consideration. The first and most important property to underline in the scientific texts examined here is the language they are written in. This means that our multicultural history of the sciences necessarily also becomes a review of the various dominant languages used in the different historical contexts. In this volume, the history of the development of the sciences is told as it happened in real contexts, not in an alienated ideal world.
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We bring into full light some excerpts on musical subjects which were until now scattered throughout the most famous scientific texts. The main scientific and musical cultures outside of Europe are also taken into consideration. The first and most important property to underline in the scientific texts examined here is the language they are written in. This means that our multicultural history of the sciences necessarily also becomes a review of the various dominant languages used in the different historical contexts. In this volume, the history of the development of the sciences is told as it happened in real contexts, not in an alienated ideal world.
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Introductories.- Morphology.- Molecular Biology.- Chemical Engineering.- Cell Biology and Dynamics.- Assays and Models.- Biomedical Technology.- Pharmacology and Medicine.- Notes.- Acknowledgement.- Index of Authors.

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Development of HIV protease inhibitors: A survey.- Anti-influenza drugs and neuraminidase inhibitors.- Recent advances in prevention and treatment of hepatitis C virus infections.- Drug discovery and development of antiviral agents for the treatment of chronic hepatitis B virus infection.- Current and potential therapies for the treatment of herpesvirus infections.- Protease inhibitors as potential antiviral agents for the treatment of picornaviral infections.

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This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009-2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a number of applications to L-functions of t-motives), gamma and zeta functions in characteristic p, and the binomial theorem. The other two are focused on topics closer to the classical theory of abelian varieties over number fields: they give respectively a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the construction of Mordell-Weil groups of high rank) and a state of the art survey of Geometric Iwasawa Theory explaining the recent proofs of various versions of the Main Conjecture, in the commutative and non-commutative settings.

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Boundary problems constitute an essential field of common mathematical interest, they lie in the center of research activities both in analysis and geometry. This book encompasses material from both disciplines, and focuses on their interactions which are particularly apparent in this field. Moreover, the survey style of the contributions makes the topics accessible to a broad audience with a background in analysis or geometry, and enables the reader to get a quick overview.

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The construction of mathematical models is an essential scientific activity. Mathematics has long been associated with developments in the exact sciences and engineering, but more recently mathematical modelling has been used to investigate complex systems that arise in many other fields. The contributors to this book demonstrate the application of mathematics to modern research topics in ecology and environmental science, health and medicine, phylogenetics and neural networks, theoretical chemistry, economics and management.

The reader will find some review papers outlining current research directions in hot topics such as pattern formation and applications to medicine, and more targeted research papers on current developments in the various disciplines included. Both should provide insight and inspiration for further work on these subjects. The extensive relevant literature cited in some of the survey expository articles is another feature.

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Reprint from Pure and Applied Geophysics (PAGEOPH), Volume 135 (1991), No. 2

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Reprint from Pure and Applied Geophysics (PAGEOPH), Volume 135 (1991), No. 2

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Bioelectrochemistry: Principles and Practice provides a comprehensive compilation of all the physicochemical aspects of the different biochemical and physiological processes. The role of electric and magnetic fields in biological systems forms the focus of this second volume in the Bioelectrochemistry series. The most prominent use of electric fields is found in some fish. These species generate fields of different strengths and patterns serving either as weapons, or for the purpose of location and communication. Electrical phenomena involved in signal transduction are discussed by means of two examples, namely excitation-contraction coupling in muscles and light transduction in photoreceptors. Also examined is the role of electrical potential differences in energy metabolism and its control. Temporal and spatial changes of the potential difference across the membranes of nerve cells are carefully evaluated, since they are the basis of the spreading and processing of information in the nervous system. The dielectric properties of cells and their responses to electric fields, such as electrophoresis and electrorotation, are dealt with in detail. Finally, the effects of magnetic fields on living systems and of low-frequency electromagnetic fields on cell metabolism are also considered. Further volumes will be added to the series, which is intended as a set of source books for graduate and postgraduate students as well as research workers at all levels in bioelectrochemistry.

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Bioelectrochemistry of Membranes is the last volume in the book series "Bioelectrochemistry: Principles and Practice" that provides a comprehensive compilation of physicochemical aspects of different biochemical and physiological processes. This sixth volume introduces basic knowledge and important electrochemical and biophysical aspects of membrane potentials, lipid bilayers and cell membranes.

The volumes of this book series serve as source books for advanced students and researchers at all levels of bioelectrochemistry.

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Die präzise Überwachung von Bioprozessen ist eine der wichtigsten Voraussetzungen für ihre Systemanalyse, mathematische Modellierung, Regelung und Dokumentation. Die Umsetzung von Ausgangsprodukten mit Hilfe von Biokatalysatoren muss genau verfolgt werden, um hohe Produktivität und Produktqualität zu erreichen. Dieses Buch fasst erstmals die allgemeinen und speziellen Messmethoden, die für die Prozessüberwachung von zentraler Bedeutung sind, zusammen. Das Spektrum der vorgestellten Methoden umfasst verschiedene in-situ Techniken für die Überwachung von Zustand- und Kontrollvariablen, sterile on-line-Probeentnahmetechniken, Probekonditionierung, sowie moderne on-line- und die wichtigsten off-line-Analysemethoden für die Prozessüberwachung unter Berücksichtigung der neuesten Entwicklungen auf diesem Gebiet. Die Anwendungen dieser Methoden werden an typischen Bioprozessen beispielhaft aufgezeigt. Darüber hinaus werden Beispiele für die anaerobe Abwasserbehandlung beschrieben und die wirtschaftlichen, ökologischen und Sicherheitsaspekte dieser Prozesse berücksichtigt.

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This volume provides an up-to-date account of the achievements pertaining to the application of capsaicin and capsaicin-like molecules in the therapy of various human ailments such as pain, non-allergic rhinitis, obesity, tumors, and gastrointestinal, dermatologic, and urologic disorders. It discusses the basic functions  of  the capsaicin receptor (TRPV1), its mechanisms of action, and its role in physiological and pathological processes. The text focuses on the most recent progress in the use of capsaicin and capsaicin-like molecules as a therapeutic agent and highlights potential pharmaceutical implications of further TRPV1 research. The chapters are written by noted experts in their fields of endeavor. This book offers both clinicians and researchers valuable resource and reference material  on the subject that will stimulate future research.

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George Britton, Synnl/Jve Liaaen-Jensen and Hanspeter Pfander This book, Volume 2 in the series Carotenoids, is the first book to be published that is devoted entirely to the total synthesis of carotenoids, but it is timely in view of the rapid development and the growing diversification of the carotenoid field. The 1971 Carotenoids book contained a major chapter of 250 pages on total synthesis by H. Mayer and O. Isler. That comprehensive and authoritative review described systematically the construction of many synthons and the synthesis of many natural and unnatural carotenoids and related compounds. Twenty five years on, that chapter remains an essential reference work and source of information, with its extensive collection of tabulated data and lists of references to the original literature. Surveys of progress since 1971 have been presented at the IUPAC International Symposia on Carotenoids and are included in the published proceedings of these symposia. The history of major publications in the carotenoid field, leading to the development of this series, was outlined in the preface to the series published in Vol. IA. The general philo­ sophy outlined in that preface, with emphasis on practical guidance and the inclusion of worked examples of some of the most useful procedures, is maintained in Vol. 2. In kceping with this philosophy, Vol. 2 is not intended to be an exhaustive review of the literature, but is planned as a practical book, as well as a source of information.

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With the number of natural carotenoid structures reported rising above 700, there is a clear need for a single reference work containing data on all these compounds. A previous work, the Key to Carotenoids (1987, 2nd edition, Birkhäuser Publishing), listed complete literature references to 563 carotenoids obtained from natural sources up to 1982; this list was extended in an appendix to Carotenoids Vol. 1A. The forthcoming Handbook expands this coverage to include all natural carotenoids and common isolation artefacts for which structures have been assigned up to the end of 2001. For each compound, it provides selected key references and critically assessed information about natural occurrence and isolation, and spectroscopic data for identification.

Though the Handbook serves as a unique comprehensive reference book on the known carotenoids, it is designed to be used in conjunction with the Carotenoids series. The numbering of carotenoids in the Handbook is the same as that used throughout the Carotenoids volumes. The factual information and practical guidance given in this well received book series ideally complements the informations given in the Handbook. It is highly advisable to be familiar with the general methods and precautions for handling carotenoids, and with the isolation and purification strategies and methods as described and evaluated in Vol. 1A, and the principles, application and interpretation of the spectroscopic techniques as described in Vol. 1B, to ensure that the identifications and analyses on which carotenoid work is based are accurate and reliable.

The Handbook of Carotenoids is an important source of information for both specialists and non-specialists. It will be of great value not only to chemists and biochemists, but to all researchers whose work and interests bring them into the diverse field of carotenoids, especially those from areas of biology, food science, nutrition, medicine, horticulture,agriculture, aquaculture, ecology, and biotechnology.

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George Britton, Synnl/Jve Liaaen-Jensen and Hanspeter Pfander This book, Volume 2 in the series Carotenoids, is the first book to be published that is devoted entirely to the total synthesis of carotenoids, but it is timely in view of the rapid development and the growing diversification of the carotenoid field. The 1971 Carotenoids book contained a major chapter of 250 pages on total synthesis by H. Mayer and O. Isler. That comprehensive and authoritative review described systematically the construction of many synthons and the synthesis of many natural and unnatural carotenoids and related compounds. Twenty five years on, that chapter remains an essential reference work and source of information, with its extensive collection of tabulated data and lists of references to the original literature. Surveys of progress since 1971 have been presented at the IUPAC International Symposia on Carotenoids and are included in the published proceedings of these symposia. The history of major publications in the carotenoid field, leading to the development of this series, was outlined in the preface to the series published in Vol. IA. The general philo­ sophy outlined in that preface, with emphasis on practical guidance and the inclusion of worked examples of some of the most useful procedures, is maintained in Vol. 2. In kceping with this philosophy, Vol. 2 is not intended to be an exhaustive review of the literature, but is planned as a practical book, as well as a source of information.

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More than twenty years after the idea of this Carotenoids book series was first discussed, we finally reach the end of the project with Volume 5, which covers the functions and actions of carotenoids in human nutrition and health. In 1971, in Isler¿s book Carotenoids, functions of carotenoids and vitamin A were covered in just two chapters. Now, thanks to technical developments and multidisciplinary approaches that make it possible to study functional processes in great detail, this subject is the most rapidly expanding area of carotenoid research, and occupies two full volumes, Volumes 4: Natural Functions and 5: Nutrition and Health. Although Volume 5 can be used as a single stand-alone volume, the two were planned as companion volumes to be used together. To understand the mechanisms of functions and actions of carotenoids, including how carotenoids may be involved in maintaining human health, requires understanding of the underlying principles, which are presented in the first part of Volume 4. The general philosophy and strategy of the series, to have expert authors review and analyse critically a particular topic and present information and give guidance on practical strategies and procedures is maintained in Volumes 4 and 5. It is also the aim that these publications should be useful for both experienced carotenoid researchers and newcomers to the field.

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More than twenty years after the idea of this Carotenoids book series was first discussed, we finally reach the end of the project with Volume 5, which covers the functions and actions of carotenoids in human nutrition and health. In 1971, in Isler's book Carotenoids, functions of carotenoids and vitamin A were covered in just two chapters. Now, thanks to technical developments and multidisciplinary approaches that make it possible to study functional processes in great detail, this subject is the most rapidly expanding area of carotenoid research, and occupies two full volumes, Volumes 4: Natural Functions and 5: Nutrition and Health. Although Volume 5 can be used as a single stand-alone volume, the two were planned as companion volumes to be used together. To understand the mechanisms of functions and actions of carotenoids, including how carotenoids may be involved in maintaining human health, requires understanding of the underlying principles, which are presented in the first part of Volume 4. The general philosophy and strategy of the series, to have expert authors review and analyse critically a particular topic and present information and give guidance on practical strategies and procedures is maintained in Volumes 4 and 5. It is also the aim that these publications should be useful for both experienced carotenoid researchers and newcomers to the field.
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The Carotenoids book series provides detailed accounts of the fundamental chemistry of carotenoids and the basic methods used in carotenoid research, and critical discussions of the biochemistry, functions and applications of these important compounds.

Volume 4 and its companion, Volume 5, deal with the functions of carotenoids in all kinds of living organisms and the actions of carotenoids in human nutrition and health. The material presented in the earlier Volumes is all relevant to studies of biological functions and actions. In particular, biological studies must be supported by a rigorous analytical base. The various analytical procedures described in Volumes 1A and 1B, supplemented by the data for individual compounds given in the Carotenoids Handbook, must be understood and applied correctly, whether they are being used for quantitative analysis, identification or in complex studies of carotenoids in situ.

In the first part of Volume 4, the structural features that are most important for determining the properties and hence the biological roles of carotenoids are emphasized. The overall molecular geometry (size, three-dimensional shape, presence of functional groups) is vital to ensure that the carotenoid fits into cellular, sub-cellular and molecular structures in the correct location and orientation to allow it to function efficiently. Specific interactions with other molecules, e.g. to form aggregates or complexes with proteins, strongly influence the properties of a carotenoid in vivo and are thus also crucial to functioning. The extended delocalized p-electron system that characterizes the central part of the structure gives the carotenoids their peculiar photochemical properties and reactivity towards oxidizing agents and free radicals.

This treatment provides a foundation for the description of the main functions of carotenoids and their breakdown products in the second part of Volume 4 and in Volume 5. Topics covered in Volume 4 include various aspects of the roles of carotenoids in colour and colouration, photosynthesis and other photofunctions, and protection. The formation and roles of carotenoid metabolites and breakdown products as perfume/aroma compounds and as vitamin A are also outlined; the latter is dealt with in more detail in Volume 5, which provides a comprehensive discussion of carotenoids in human health and nutrition..

Biologists now are not only discovering new phenomena but are striving to elucidate details of the underlying mechanisms that explain their observations. Chemistry is moving in new directions relevant to studies in vivo and new techniques are being developed to investigate structural details and interactions and to detect and interpret changes on an ever shorter timescale. Volumes 4 and 5 thus point the way to the future of carotenoid research by highlighting the importance of interdisciplinary approaches to study these complex and sophisticated systems.

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After the book "Basic Operator Theory" by Gohberg-Goldberg was pub­ lished, we, that is the present authors, intended to continue with another book which would show the readers the large variety of classes of operators and the important role they play in applications. The book was planned to be of modest size, but due to the profusion of results in this area of analysis, the number of topics grew larger than ex­ pected. Consequently, we decided to divide the material into two volumes - the first volume being presented now. During the past years, courses and seminars were given at our respective in­ stitutions based on parts of the texts. These were well received by the audience and enabled us to make appropriate choices for the topics and presentation for the two vol­ umes. We would like to thank G.J. Groenewald, A.B. Kuijper and A.C.M. Ran of the Vrije Universiteit at Amsterdam, who provided us with lists of remarks and corrections. We are now aware that the Basic Operator Theory book should be revised so that it may suitably fit in with our present volumes. This revision is planned to be the last step of an induction and not the first.

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Our DMV Seminar on 'Classical Nonintegrability, Quantum Chaos' intended to introduce students and beginning researchers to the techniques applied in nonin­ tegrable classical and quantum dynamics. Several of these lectures are collected in this volume. The basic phenomenon of nonlinear dynamics is mixing in phase space, lead­ ing to a positive dynamical entropy and a loss of information about the initial state. The nonlinear motion in phase space gives rise to a linear action on phase space functions which in the case of iterated maps is given by a so-called transfer operator. Good mixing rates lead to a spectral gap for this operator. Similar to the use made of the Riemann zeta function in the investigation of the prime numbers, dynamical zeta functions are now being applied in nonlinear dynamics. In Chapter 2 V. Baladi first introduces dynamical zeta functions and transfer operators, illustrating and motivating these notions with a simple one-dimensional dynamical system. Then she presents a commented list of useful references, helping the newcomer to enter smoothly into this fast-developing field of research. Chapter 3 on irregular scattering and Chapter 4 on quantum chaos by A. Knauf deal with solutions of the Hamilton and the Schr6dinger equation. Scatter­ ing by a potential force tends to be irregular if three or more scattering centres are present, and a typical phenomenon is the occurrence of a Cantor set of bounded orbits. The presence of this set influences those scattering orbits which come close.

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Im heutigen Informationszeitalter werden täglich riesige Mengen von digitalen Daten über Kanäle wie die Atmosphäre, die Telefonleitung oder Speichermedien übertragen. Dabei treten bei der Übertragung zwei zentrale Probleme auf: einerseits die Sicherung der Daten gegenüber zufälligen Fehlern, die der Kanal verursacht (etwa durch Rauschen in der Atmosphäre oder Kratzer auf der CD), andererseits die Sicherung der Information gegenüber unerlaubtem Lesen (etwa beim Pay-TV) oder sogar der Manipulation der Daten (etwa beim Homebanking). Auf die erste Frage gibt die Codierungstheorie, auf die zweite die Kryptographie eine Antwort. Das Buch führt in die wesentlichen Methoden der beiden Themenkreise ein. Die Aufnahme von aktuellem Stoff, wie beispielsweise LDPC-Codes oder dem AKS-Algorithmus, geben dem Text eine moderne Prägung.

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This volume is devoted to some topical problems and various applications of operator theory and its interplay with modern complex analysis. 30 carefully selected surveys and research papers are united by the "operator theoretic ideology" and systematic use of modern function theoretical techniques.

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This book contains a collection of research articles and surveys on recent developments on operator theory as well as its applications covered in the IWOTA 2011 conference held at Sevilla University in the summer of 2011. The topics include spectral theory, differential operators, integral operators, composition operators, Toeplitz operators, and more. The book also presents a large number of techniques in operator theory.
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Consisting of 23 refereed contributions, this volume offers a broad and diverse view of current research in control and estimation of partial differential equations. Topics addressed include, but are not limited to - control and stability of hyperbolic systems related to elasticity, linear and nonlinear; - control and identification of nonlinear parabolic systems; - exact and approximate controllability, and observability; - Pontryagin's maximum principle and dynamic programming in PDE; and - numerics pertinent to optimal and suboptimal control problems. This volume is primarily geared toward control theorists seeking information on the latest developments in their area of expertise. It may also serve as a stimulating reader to any researcher who wants to gain an impression of activities at the forefront of a vigorously expanding area in applied mathematics.

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Es darf als gesichert gelten, dass Einstein bereits 1895-1896, während er sich an der Aargauischen Kantonsschule auf die Maturitätsprüfung vorbereitete, erste Ideen zur Relativitätstheorie entwickelte. Die Publikation befasst sich eingehend mit der Aarauer Zeit des später zu Weltruhm gelangten Physikers und bespricht die grundlegenden Ideen seiner Arbeiten von 1905, die diesen Weltruhm begründeten. Aus dem Inhalt: - Kommentierte Originalabdrucke dreier vom siebzehnjährigen Einstein verfasster Maturitätsprüfungsarbeiten - Spezielle Relativitätstheorie: Eine Übung im Überwinden von Denkgewohnheiten - Über die Herkunft der Speziellen Relativitätstheorie - Einsteins Analyse der Brownschen Bewegung - Einstein und die Begründung der Quantentheorie - Relativitätstheorie und der Friedhof der Sterne Beitragsautoren: Domenico Giulini, Herbert Hunziker, Walter Pfeifer, Heinrich Staehelin, Norbert Straumann

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The present book is the first of the two volume Proceedings of the Mark Krein International Conference on Operator Theory and Applications. This conference, which was dedicated to the 90th Anniversary of the prominent mathematician Mark Krein, was held in Odessa, Ukraine from 18-22 August, 1997. The confer­ encefocused onthemain ideas, methods, results, andachievementsofM.G. Krein. This first volume is devoted to the theory of differential operators and related topics. It opens with a description of the conference, biographical material and a number of survey papers about the work of M.G. Krein. The main part of the book consists oforiginal research papers presenting the stateofthe art in the area ofdifferential operators. The second volume of these proceedings, entitled Operator Theory and related Topics, concerns the other aspects of the conference. The two volumes will be of interest to a wide-range of readership in pure and applied mathematics, physics and engineering sciences. Table of Contents Preface............................................................. v Table of Contents VII Picture of M.G. Krein Xl About the Mark Krein International Conference . Mark Grigorevich Krein (A short biography) 5 I. Gohberg The Seminar on Ship Hydrodynamics, Organized by M.G. Krein 9 v.G. Sizov Review Papers: The Works ofM.G. Krein on Eigenfunction Expansion for Selfadjoint Operators and their Applications and Development 21 Yu.M. Berezansky M.G. Krein and the Extension Theory of Symmetric Operators.

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Research of discrete event systems is strongly motivated by applications in flex­ ible manufacturing, in traffic control and in concurrent and real-time software verification and design, just to mention a few important areas. Discrete event system theory is a promising and dynamically developing area of both control theory and computer science. Discrete event systems are systems with non-numerically-valued states, inputs, and outputs. The approaches to the modelling and control of these systems can be roughly divided into two groups. The first group is concerned with the automatic design of controllers from formal specifications of logical requirements. This re­ search owes much to the pioneering work of P.J. Ramadge and W.M. Wonham at the beginning of the eighties. The second group deals with the analysis and op­ timization of system throughput, waiting time, and other performance measures for discrete event systems. The present book contains selected papers presented at the Joint Workshop on Discrete Event Systems (WODES'92) held in Prague, Czechoslovakia, on Au­ gust 26-28, 1992 and organized by the Institute of Information Theory and Au­ tomation of the Czechoslovak Academy of Sciences, Prague, Czechoslovakia, by the Automatic Control Laboratory of the Swiss Federal Institute of Technology (ETH) , Zurich, Switzerland, and by the Department of Computing Science of the University of Groningen, Groningen, the Netherlands.

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Although much of classical ergodic theory is concerned with single transformations and one-parameter flows, the subject inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multidimensional symmetry groups. However, the wealth of concrete and natural examples which has contributed so much to the appeal and development of classical dynamics, is noticeably absent in this more general theory. The purpose of this book is to help remedy this scarcity of explicit examples by introducing a class of continuous Zd-actions diverse enough to exhibit many of the new phenomena encountered in the transition from Z to Zd, but which nevertheless lends itself to systematic study: the Zd-actions by automorphisms of compact, abelian groups. One aspect of these actions, not surprising in itself but quite striking in its extent and depth nonetheless, is the connection with commutative algebra and arithmetical algebraic geometry. The algebraic framework resulting from this connection allows the construction of examples with a variety of specified dynamical properties, and by combining algebraic and dynamical tools one obtains a quite detailed understanding of this class of Zd-actions.

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It is a marvelous display of the richness and depth of the interplay between dynamical systems on one hand and commutative algebra and number theory on the other. (...) This book is a very valuable addition to the literature on dynamical systems and ergodic theory.

(Mathematical Reviews)

This beautifully written monograph (...) is a very important addition to the literature, giving the first systematic account of the ergodic theory of algebraic Zd-actions. It will be of immense value to any researchers and graduate students interested in such multi-dimensional actions.

(Zentralblatt MATH)

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This book is a collection of essays devoted in part to new research direc­ tions in systems, networks, and control theory, and in part to the growing interaction of these disciplines with new sectors of engineering and applied sciences like coding, computer vision, and hybrid systems. These are new areas of rapid growth and of increasing importance in modern technology. The essays, written by world-leading experts in the field, reproduce and expand the plenary and minicoursejminisymposia invited lectures which were delivered at the Mathematical Theory of Networks and Systems Sym­ posium (MTNS-98), held in Padova, Italy, on July 6-10, 1998. Systems, control, and networks theory has permeated the development of much of present day technology. The impact has been visible in the past fifty years through the dramatic expansion and achievements of the aerospace and avionics industry, through process control and factory au­ tomation, robotics, communication signals analysis and synthesis, and, more recently, even finance, to name just the most visible applications. The theory has developed from the early phase of its history when the ba­ sic tools were elementary complex analysis, Laplace transform, and linear differential equations, to present day, where the mathematics ranges widely from functional analysis, PDE's, abstract algebra, stochastic processes and differential geometry. Irrespective of the particular tools, however, the ba­ sic unifying paradigms of feedback, stability, optimal control, and recursive filtering, have remained the bulk of the field and continue to be the basic motivation for the theory, coming from the real world.

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This book is a collection of essays devoted in part to new research direc­ tions in systems, networks, and control theory, and in part to the growing interaction of these disciplines with new sectors of engineering and applied sciences like coding, computer vision, and hybrid systems. These are new areas of rapid growth and of increasing importance in modern technology. The essays, written by world-leading experts in the field, reproduce and expand the plenary and minicoursejminisymposia invited lectures which were delivered at the Mathematical Theory of Networks and Systems Sym­ posium (MTNS-98), held in Padova, Italy, on July 6-10, 1998. Systems, control, and networks theory has permeated the development of much of present day technology. The impact has been visible in the past fifty years through the dramatic expansion and achievements of the aerospace and avionics industry, through process control and factory au­ tomation, robotics, communication signals analysis and synthesis, and, more recently, even finance, to name just the most visible applications. The theory has developed from the early phase of its history when the ba­ sic tools were elementary complex analysis, Laplace transform, and linear differential equations, to present day, where the mathematics ranges widely from functional analysis, PDE's, abstract algebra, stochastic processes and differential geometry. Irrespective of the particular tools, however, the ba­ sic unifying paradigms of feedback, stability, optimal control, and recursive filtering, have remained the bulk of the field and continue to be the basic motivation for the theory, coming from the real world.

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In the last decade of the 20th century, there has been great progress in the physics of earthquake generation; that is, the introduction of laboratory-based fault constitutive laws as a basic equation governing earthquake rupture, quantitative description of tectonic loading driven by plate motion, and a microscopic approach to study fault zone processes. The fault constitutive law plays the role of an interface between microscopic processes in fault zones and macroscopic processes of a fault system, and the plate motion connects diverse crustal activities with mantle dynamics. An ambitious challenge for us is to develop realistic computer simulation models for the complete earthquake process on the basis of microphysics in fault zones and macro-dynamics in the crust-mantle system. Recent advances in high performance computer technology and numerical simulation methodology are bringing this vision within reach. The book consists of two parts and presents a cross-section of cutting-edge research in the field of computational earthquake physics. Part I includes works on microphysics of rupture and fault constitutive laws, and dynamic rupture, wave propagation and strong ground motion. Part II covers earthquake cycles, crustal deformation, plate dynamics, and seismicity change and its physical interpretation. Topics covered in Part I range from the microscopic simulation and laboratory studies of rock fracture and the underlying mechanism for nucleation and catastrophic failure to the development of theoretical models of frictional behaviors of faults; as well as the simulation studies of dynamic rupture processes and seismic wave propagation in a 3-D heterogeneous medium, to the case studies of strong ground motions from the 1999 Chi-Chi earthquake and seismic hazard estimation for Cascadian subduction zone earthquakes.

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In the last decade of the 20th century, there has been great progress in the physics of earthquake generation; that is, the introduction of laboratory-based fault constitutive laws as a basic equation governing earthquake rupture, quantitative description of tectonic loading driven by plate motion, and a microscopic approach to study fault zone processes. The fault constitutive law plays the role of an interface between microscopic processes in fault zones and macroscopic processes of a fault system, and the plate motion connects diverse crustal activities with mantle dynamics. An ambitious challenge for us is to develop realistic computer simulation models for the complete earthquake process on the basis of microphysics in fault zones and macro-dynamics in the crust-mantle system. Recent advances in high performance computer technology and numerical simulation methodology are bringing this vision within reach. The book consists of two parts and presents a cross-section of cutting-edge research in the field of computational earthquake physics. Part I includes works on microphysics of rupture and fault constitutive laws, and dynamic rupture, wave propagation and strong ground motion. Part II covers earthquake cycles, crustal deformation, plate dynamics, and seismicity change and its physical interpretation. Topics in Part II range from the 3-D simulations of earthquake generation cycles and interseismic crustal deformation associated with plate subduction to the development of new methods for analyzing geophysical and geodetical data and new simulation algorithms for large amplitude folding and mantle convection with viscoelastic/brittle lithosphere, as well as a theoretical study of accelerated seismic release on heterogeneous faults, simulation of long-range automaton models of earthquakes, and various approaches to earthquake predicition based on underlying physical and/or statistical models for seismicity change.

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LIST OF PARTICIPANTS 11 THERMOPHILIC HYDROLYTIC ENZYMES (PROTEINASES, AMYLASES) 17 Thermal Stability of Homologous Neutral Metalloendopeptidases in Thermo­ philic and Mesophilic Bacteria: Structural Considerations M. K. PANGBURN, P. L. LEVY, K. A. WALSH and H. NEURATH 19 The Structure and Stability of Thermolysin L. H. WEAVER, W. R. KESTER, K. F. TEN EYCK and B. W. MATTHEWS 31 Studies of the Inhibition of Thermolysin J. FEDER, N. AUFDERHEIDE and B. S. WILDI 41 Effect of EDTA on the Conformational Stability of Thermolysin A. FONTANA, E. BOCCU and F. M. VERONESE 55 Role of a Sulfhydryl Group in the Structure and Function of Alkaline Proteases from a Thermophilic Actinomycete K. MIZUSAWA and F. YOSHIDA 61 Partial Characterization of a Thermophilic Actinomycete Rennin S. LAXER, A. PINSKY and B. BARTOOV 67 Amylase Activity and Stability at High and Low Temperature Depending on Calcium and other Divalent Cations W. HEINEN and A. M. LAUWERS 77 Role of Calcium Ion in the Thermostability of a-Amylase Produced from Bacillus stearothermophilus K. YUTAN I 91 THERMOPHILIC DEHYDROGENASES 105 Thermophilic Glyceraldehyde-3-P Dehydrogenase R. E. AMELUNXEN and R. SINGLETON JR. 107 Glyceraldehyde 3-Phosphate Dehydrogenase from an Extreme Thermophile, Thermus aquaticus 121 J. D. HOCKING and J. I. HARRIS Thermal Properties of Glyceraldehyde 3-Phosphate Dehydrogenase from Escherichia coli A. FONTANA, C. GRANDI, E. BOCCU and F. M. VERONESE 135 Comparative Conformational Properties of Thermophilic and Mesophilic 6-Phosphogluconate Dehydrogenase F. M. VERONESE, C. GRANDI, E. BOCCU and A.

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Die fachgerechte Erbebensicherung von Bauwerken ist heute nicht mehr eine Frage der Erkenntnisse, sondern eine Frage der Ausbildung von Bauingenieuren und Architekten und somit der Umsetzung vorhandenen Wissens in die Praxis. Durch wenige gezielte Massnahmen konzeptioneller und konstruktiver Art sowie durch eine problemgerechte Berechnung und Bemessung kann das Schadenrisiko drastisch vermindert und ein hoher Schutzgrad gegen Einsturz erreicht werden. Das Buch ist auf die Bedürfnisse des praktisch tätigen Bauingenieurs ausgerichtet; mit seiner starken Gewichtung des erbebengerechten Entwurfs hilft es, konzeptionelle Fehler und Mängel zu vermeiden, da diese auch durch eine noch so ausgeklügelte ingenieurmässige Berechnung und Bemessung nicht kompensiert werden können. Das Buch gibt aber auch zahlreiche Hinweise zu aktuellen Forschungsthemen.

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Die fachgerechte Erbebensicherung von Bauwerken ist heute nicht mehr eine Frage der Erkenntnisse, sondern eine Frage der Ausbildung von Bauingenieuren und Architekten und somit der Umsetzung vorhandenen Wissens in die Praxis. Durch wenige gezielte Massnahmen konzeptioneller und konstruktiver Art sowie durch eine problemgerechte Berechnung und Bemessung kann das Schadenrisiko drastisch vermindert und ein hoher Schutzgrad gegen Einsturz erreicht werden. Das Buch ist auf die Bedürfnisse des praktisch tätigen Bauingenieurs ausgerichtet; mit seiner starken Gewichtung des erbebengerechten Entwurfs hilft es, konzeptionelle Fehler und Mängel zu vermeiden, da diese auch durch eine noch so ausgeklügelte ingenieurmässige Berechnung und Bemessung nicht kompensiert werden können. Das Buch gibt aber auch zahlreiche Hinweise zu aktuellen Forschungsthemen.

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