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Such graphs provide semantics for various modal logics (alethic, temporal, epistemic and doxastic, dynamic, deontic, description logics) and also turned out useful for other nonclassical logics (intuitionistic, conditional, several paraconsistent and relevant logics).

The scientific personalities of Luigi Cremona, Eugenio Beltrami, Salvatore Pincherle, Federigo Enriques, Beppo Levi, Giuseppe Vitali, Beniamino Segre and of several other mathematicians who worked in Bologna in the century 1861-1960 are examined by different authors, in some cases providing different view points.

It is no longer time-consuming analysis of unknown products, but rather selective identifications of individual forms, modifications and processings, and overall analysis of global protein outputs from cells and tissues in health and disease.

As explained in the introduction, this represents a useful and important viewpoint in algebraic geometry, especially concerning the theory of algebraic curves and their function fields. of geometrical or topological nature) are often indicated, also to provide motivations and intuition for many results.

These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring.

The Poincaré Seminar is held twice a year at the Institut Henri Poincaré in Paris. This volume contains the lectures of the 2002 seminars. The main topic of the first one was the vacuum energy, in particular the Casimir effect and the nature of the cosmological constant. The second one concentrated on renormalization, giving a comprehensive account of its mathematical structure and applications to high energy physics, statistical mechanics and classical mechanics.Students will find excellent introductions to the subjects with further lectures leading to the frontiers of experimental and theoretical research, scientists will profit from contributions by outstanding experts.

It addresses classical inequalities related to means or to convexity as well as inequalities arising in the field of ordinary and partial differential equations, like Sobolev or Hardy-type inequalities, and inequalities occurring in geometrical contexts.

from the creation of a design system involving a parametric shape grammar with descriptions to generate urban block layouts within a defined spatial region, to a novel example of a kinetic shape grammar simulating human body movements.

This book discusses the theoretical foundations of Organic Computing, its methods, tools and learning techniques, architectural patterns and applications. A concluding chapter reviews new projects spawned since the original German Research Foundation program.

This textbook presents basic notions and techniques of Fourier analysis in discrete settings. Written in a concise style, it is interlaced with remarks, discussions and motivations from signal analysis. The first part is dedicated to topics related to the Fourier transform, including discrete time-frequency analysis and discrete wavelet analysis. Basic knowledge of linear algebra and calculus is the only prerequisite. The second part is built on Hilbert spaces and Fourier series and culminates in a section on pseudo-differential operators, providing a lucid introduction to this advanced topic in analysis. Some measure theory language is used, although most of this part is accessible to students familiar with an undergraduate course in real analysis. Discrete Fourier Analysis is aimed at advanced undergraduate and graduate students in mathematics and applied mathematics. Enhanced with exercises, it will be an excellent resource for the classroom as well as for self-study.

The book provides a comprehensive introduction to compact finite difference methods for solving boundary value ODEs with high accuracy. The corresponding theory is based on exact difference schemes (EDS) from which the implementable truncated difference schemes (TDS) are derived. The TDS are now competitive in terms of efficiency and accuracy with the well-studied numerical algorithms for the solution of initial value ODEs. Moreover, various a posteriori error estimators are presented which can be used in adaptive algorithms as important building blocks. The new class of EDS and TDS treated in this book can be considered as further developments of the results presented in the highly respected books of the Russian mathematician A. A. Samarskii. It is shown that the new Samarskii-like techniques open the horizon for the numerical treatment of more complicated problems.The book contains exercises and the corresponding solutions enabling the use as a course text or for self-study. Researchers and students from numerical methods, engineering and other sciences will find this book provides an accessible and self-contained introduction to numerical methods for solving boundary value ODEs.

This volume is dedicated to the fundamentals of convex functional analysis. On the one hand, a bare minimum of the theory required to understand the principles of functional, convex and set-valued analysis is presented.

This title features papers that examine issues in digital fabrication as well as different mathematical instruments applied to architecture, including geometric tracing systems, proportional systems, descriptive geometry and correspondence analysis.

This book collects the papers of the conference held in Berlin, Germany, 27-29 August 2012, on 'Space, Geometry and the Imagination from Antiquity to the Modern Age'. The conference was a joint effort by the Max Planck Institute for the History of Science (Berlin) and the Centro die Ricerca Matematica Ennio De Giorgi (Pisa).

Die Autoren beginnen mit der Primfaktorzerlegung und dem größten gemeinsamen Teiler ¿ Begriffen, die aus dem Schulunterricht bekannt sind, aber bei genauerer Betrachtung viel von ihrer Selbstverständlichkeit verlieren. Sie erörtern das Dezimalsystem, die Kongruenzrechnung, primitive Wurzeln und das Reziprozitätsgesetz für quadratische Reste. Ihr ausführliches Buch richtet sich an Dozenten, Lehrer und Studenten und ist aber für alle verständlich, die den elementaren Schulstoff beherrschen. Es eignet sich zur Vorlesungsbegleitung und zum Selbststudium. Aufgaben am Ende eines jeden Paragraphen helfen dabei, den Lehrstoff zu üben und zu vertiefen.

It is distinguished by its high level of presentation and its focus on the essential.'' (Zeitschrift fur Analysis und ihre Anwendung 18, No. 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.

Intended for both researchers and practitioners, this book will be a valuable resource for studying and applying recent robust statistical methods. It contains up-to-date research results in the theory of robust statisticsTreats computational aspects and algorithms and shows interesting and new applications.

Das Buch ist ein Leitfaden über die modernen Fertigungsverfahren in der Triebwerktechnik. Besonderer Wert wurde hierbei auf die Darstellung der werkstofftechnischen, metallkundlichen und physikalischen Zusammenhänge gelegt, von denen sich die wesentlichen technischen Maßnahmen der Fertigung ableiten. Die Vertiefung in einzelne Sachgebiete wird mit Hilfe eines umfangreichen Literaturverzeichnisses unterstützt. Das Buch wendet sich mit seiner interdisziplinären Darstellung von Werkstofftechnik, Fertigungstechnik und Funktionalität der Maschinenkomponenten an Ingenieure und Techniker, die an der Entwicklung und Fertigung von Gasturbinen arbeiten. Ebenso sind die Studenten der Werkstofftechnik, der Fertigungstechnik, des Maschinenbaus und der ihm zugeordneten Disziplinen angesprochen. Prof. Dr.-Ing. Peter Adam ist Inhaber des Lehrstuhls für Oberflächentechnik an der Friedrich-Schiller-Universität Jena. Er arbeitete über 20 Jahre als Leiter der Fertigungsverfahrensentwicklung bei der Motoren- und Turbinen-Union München.

Carbonic anhydrase (CA) is a seemingly ubiquitous enzyme of profound physiological importance, which plays essential roles in respiration, acid-base homeostasis, bone resorption, calcification, photosynthesis, several biosynthetic pathways and a variety of processes involving ion, gas and fluid transfer.

The volume contains contributions from authors from a large variety of countries on different aspects of partial differential equations, such as evolution equations and estimates for their solutions, control theory, inverse problems, nonlinear equations, elliptic theory on singular domains, numerical approaches.

In this book the author presents a comprehensive study of Diophantos' monumental work known as Arithmetika, a highly acclaimed and unique set of books within the known Greek mathematical corpus. This allows the author to describe the structure, the contents and the mathematics of the Arithmetika in detail.

This volume collects six articles on selected topics at the frontier between partial differential equations and spectral theory, written by leading specialists in their respective field. The articles focus on topics that are in the center of attention of current research, with original contributions from the authors.

Since their discovery hundreds of years ago, people have been fascinated by the wondrous properties of Fibonacci numbers. Starting with the basic properties of Fibonacci numbers, the present book explores their relevance in number theory, the theory of continued fractions, geometry and approximation theory.

This elegantly written text includes a wealth of exercises for students as it weaves classical probability theory into the quantum framework. It deepens our understanding of classical and quantum views on the dynamics of systems subject to the laws of chance.

Kurt Goedel, together with Bertrand Russell, is the most important name in logic, and in the foundations and philosophy of mathematics of this century.

The fourth one is devoted to Entropy, giving a comprehensive account of the history and various realizations of this concept, from thermodynamics to black holes, and includes theoretical and experimental discussions of the corresponding fluctuations for mesoscopic systems near equilibrium.

Automorphic forms on the upper half plane have been studied for a long time. He extended Hecke's relation between automorphic forms and Dirichlet series to real analytic automorphic forms.

The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book "e;5000 Jahre Geometrie,"e; in which geometry is presented as a chain of developments in cultural history and their interaction with architecture, the visual arts, philosophy, science and engineering.Geometry originated in the ancient cultures along the Indus and Nile Rivers and in Mesopotamia, experiencing its first "e;Golden Age"e; in Ancient Greece. Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe. Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultures, the European approaches formed the ideas and branches of geometry we know in the modern age: coordinate methods, analytical geometry, descriptive and projective geometry in the 17th an 18th centuries, axiom systems, geometry as a theory with multiple structures and geometry in computer sciences in the 19th and 20th centuries.Each chapter of the book starts with a table of key historical and cultural dates and ends with a summary of essential contents of geometry in the respective era. Compelling examples invite the reader to further explore the problems of geometry in ancient and modern times.The book will appeal to mathematicians interested in Geometry and to all readers with an interest in cultural history.From letters to the authors for the German language editionI hope it gets a translation, as there is no comparable work.Prof. J. Grattan-Guinness (Middlesex University London)"e;Five Thousand Years of Geometry"e; - I think it is the most handsome book I have ever seen from Springer and the inclusion of so many color plates really improves its appearance dramatically!Prof. J.W. Dauben (City University of New York)An excellent book in every respect. The authors have successfully combined the history of geometry with the general development of culture and history. ...The graphic design is also excellent.Prof. Z. Nadenik (Czech Technical University in Prague)