Books published by Birkhauser Verlag AG

From the reviews: "The style of the book reflects the author's wish to assist in the effective learning of optimal control by suitable choice of topics, the mathematical level used, and by including numerous illustrated examples.

This book studies time-dependent partial differential equations and their numerical solution, developing the analytic and the numerical theory in parallel, and placing special emphasis on the discretization of boundary conditions.

The book deals with the localization approach to the index problem for elliptic operators. Localization ideas have been widely used for solving various specific index problems for a long time, but the fact that there is actually a fundamental localization principle underlying all these solutions has mostly passed unnoticed. The ignorance of this general principle has often necessitated using various artificial tricks and hindered the solution of new important problems in index theory. So far, the localization principle has been only scarcely covered in journal papers and not covered at all in monographs. The suggested book is intended to fill the gap. So far, it is the first and only monograph dealing with the topic. Both the general localization principle and its applications to specific problems, existing and new, are covered. The book will be of interest to working mathematicians as well as graduate and postgraduate university students specializing in differential equations and related topics.

This volume provides an in-depth overview of the current state of psoriasis and its management. It reviews the clinical manifestations of psoriasis as well as psoriatic arthritis and emphasizes the evolving paradigm of therapy. Coverage includes topical and ultraviolet therapies as well as traditional systemic therapy.

one should succeed in finding and discussing those functions which play the part for any algebraic number field corresponding to that of the exponential function in the field of rational numbers and of the elliptic modular functions in the imaginary quadratic number field".

In a detailed and comprehensive introduction to the theory of plane algebraic curves, the authors examine this classical area of mathematics that both figured prominently in ancient Greek studies and remains a source of inspiration and a topic of research to this day. Arising from notes for a course given at the University of Bonn in Germany, "e;Plane Algebraic Curves"e; reflects the authorsE concern for the student audience through its emphasis on motivation, development of imagination, and understanding of basic ideas. As classical objects, curves may be viewed from many angles. This text also provides a foundation for the comprehension and exploration of modern work on singularities. --- In the first chapter one finds many special curves with very attractive geometric presentations the wealth of illustrations is a distinctive characteristic of this book and an introduction to projective geometry (over the complex numbers). In the second chapter one finds a very simple proof of Bezout's theorem and a detailed discussion of cubics. The heart of this book and how else could it be with the first author is the chapter on the resolution of singularities (always over the complex numbers). (...) Especially remarkable is the outlook to further work on the topics discussed, with numerous references to the literature. Many examples round off this successful representation of a classical and yet still very much alive subject. (Mathematical Reviews)

The journal "Aequationes Mathematicae" publishes papers in pure and applied mathematics in general and, in particular, articles focusing on functional equations, combinatorics and dynamical systems. This work contains invited survey papers to celebrate the 50th volume of this journal.

Seit Jahrtausenden versuchen wir, die Natur zu verstehen. Wir konnten einige der grossen Mysterien enträtseln, die uns umgeben, indem wir den Makro- und Mikrokosmos mit immer raffinierteren Werkzeugen untersuchen. Nicht nur, dass wir dabei eine überwältigende Vielfalt an Fakten gesammelt haben, wir enthüllten sogar Grundgesetze, welche die Struktur und Entwicklung der physikalischen Realität steuern. Insbesondere lernten wir aus diesen Beobachtungen, dass die Natur sich uns in der Sprache der Mathematik mitteilt. Die künstlichste aller Sprachen wird so zur natürlichsten. Die Gesetze stellen sich uns als Gleichungen dar, vielleicht der kompakteste und eindeutigste Ausdruck menschlichen Wissens. Dieses Buch ist ein Reiseführer zu den Gleichungen, den Meilensteinen des Wissens, die entscheidende Wendepunkte unseres Verständnises markieren.Wir wandern vom Herzstück der klassischen Physik, den Gesetzen von Newton und Maxwell, einerseits zu Einsteins scharfsinnigen Erkenntnissen über die Struktur von Raum und Zeit, und andererseits zu den Gleichungen von Schrödinger und Dirac und dem Standardmodell der Elementarteilchenphysik, das die Türen zum Mikrokosmos öffnete. Am Ende stehen wir vor den Super-Strings als mögliche Grundlage einer allumfassenden Theorie.

Die 11. Auflage dieser etablierten Einführung wurde sorgfältig überarbeitet und erweitert. Das Buch vermittelt Studierenden der Chemie im Haupt- und Nebenfach das Verständnis für die Grundprinzipien der organischen Chemie und ermöglicht darüber hinaus auch eine Vertiefung des in der Schule gebotenen Lehrstoffes. Das bewährte Konzept, die Bindungsverhältnisse in organischen Molekülen, ihren räumlichen Bau und die grundlegenden Reaktionstypen getrennt von Nomenklatur und Systematik zu behandeln, wurde beibehalten. Metallorganische Reagenzien, Methoden der asymmetrischen Synthese und die Prinzipien katalytischer Prozesse werden ebenso berücksichtigt wie die wichtigsten Methoden zur Charakterisierung organischer Verbindungen. Eine Übersicht über eine Reihe von Naturstoffklassen vermittelt die Grundlagen zum Verständnis biochemischer Prinzipien. Zahlreiche Übungen vertiefen den Stoff und erleichtern die Selbstkontrolle.

Special functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality. The special functions to be discussed in this monograph vary greatly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective field characteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process. Each chapter closes with exercises that reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields of research, where special functions are essential to application. All in all, the book is an equally valuable resource for education in geomathematics and the study of applied and harmonic analysis. Students who wish to continue with further studies should consult the literature given as supplements for each topic covered in the exercises.

Finsler's papers on set theory are presented, here for the first time in English translation, in three parts, and each is preceded by an introduction to the field written by the editors.

LCA - Quo vadis? discusses overarching topics, new developments and major problems of Life Cycle Assessment (LCA), and compares LCA with site-specific environmental management. *What requirements should a software tool for LCA meet? A concept of site-specific LCA is proposed in response to criticism of the current approach of LCA.

It is fashionable in professional circles to deplore the difficulty of intellectual discourse between "academicians" - men of letters, researchers, rationalist- and "practitioners" - surgeons, radiologists, physical therapists.

This book explores Persian architecture and mathematics, including domed structures and two-dimensional patterns, elaborate geometry and complex three-dimensional structures of historic monuments, from mathematical ideas to architectonic structures.

This book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be applied to the study of parabolic problems. It presents known theorems from a novel perspective and teaches how to exploit basic techniques.

The primary objective of this monograph is to develop an elementary and se- containedapproachtothemathematicaltheoryofaviscousincompressible?uid n in a domain ? of the Euclidean spaceR , described by the equations of Navier- Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers' convenience, in the ?rst two chapters we collect, without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain ?. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n=2,3 that are also most signi?cant from the physical point of view. For mathematical generality, we will develop the l- earized theory for all n? 2. Although the functional-analytic approach developed here is, in principle, known to specialists, its systematic treatment is not available, and even the diverseaspectsavailablearespreadoutintheliterature.However,theliterature is very wide, and I did not even try to include a full list of related papers, also because this could be confusing for the student. In this regard, I would like to apologize for not quoting all the works that, directly or indirectly, have inspired this monograph.

This book presents recent results on nonlinear evolutionary fluid equations such as the compressible (radiative) magnetohydrodynamics (MHD) equations, compressible viscous micropolar fluid equations, the full non-Newtonian fluid equations and non-autonomous compressible Navier-Stokes equations. These types of partial differential equations arise in many fields of mathematics, but also in other branches of science such as physics and fluid dynamics.This book will be a valuable resource for graduate students and researchers interested in partial differential equations, and will also benefit practitioners in physics and engineering.

This is a self-contained, systematic and comprehensive introduction to all the subjects and techniques important in scientific computing. The style and presentation are readily accessible to undergraduates and graduates. A large number of examples, accompanied by complete C++ and Java code wherever possible, cover every topic.

Zoonosen sind Krankheiten bzw. Infektionen, die auf natürlichem Weg direkt oder indirekt zwischen Menschen und Tieren übertragen werden können. Als Zoonoseerreger kommen Viren, Bakterien, Pilze, Parasiten oder Prionen in Betracht. Zoonoseerreger sind in Tierpopulationen weit verbreitet und können von Nutztieren, die in der Regel selbst keine Anzeichen einer Infektion oder Erkrankung aufweisen, z. B. während der Schlachtung und Weiterverarbeitung auf das Fleisch übertragen werden. Mit Zoonoseerregern kontaminierte Lebensmittel stellen eine wichtige Infektionsquelle für den Menschen dar. Die Kontamination mit Zoonoseerregern kann auf allen Stufen der Lebensmittelkette von der Erzeugung bis zum Verzehr erfolgen. Lebensmittelbedingte Infektionen verlaufen häufig mild. Je nach Virulenz des Erregers und Alter und Immunitätslage der infizierten Person können aber auch schwere Krankheitsverläufe mit zum Teil tödlichem Ausgang auftreten. Die Eindämmung von Zoonosen durch Kontrolle und Prävention ist ein zentrales nationales und europäisches Ziel. Um geeignete Maßnahmen zur Verringerung des Vorkommens von Zoonoseerregern bei Nutztieren und in Lebensmitteln festlegen und deren Wirksamkeit überprüfen zu können, ist die Überwachung von Zoonoseerregern auf allen Stufen der Lebensmittelkette von grundlegender Bedeutung. Hierzu leistet das Zoonosen-Monitoring einen wichtigen Beitrag, indem repräsentative Daten über das Auftreten von Zoonoseerregern in Futtermitteln, lebenden Tieren und Lebensmitteln erhoben, ausgewertet und veröffentlicht werden und somit Kenntnisse über die Bedeutung verschiedener Lebensmittel als mögliche Infektionsquellen für den Menschen gewonnen werden. Mit der regelmäßigen Erfassung von Daten zu Zoonoseerregern gibt das Zoonosen-Monitoring außerdem Aufschluss über die Ausbreitungs- und Entwicklungstendenzen von Zoonosen. Antibiotikaresistente Bakterien breiten sich immer weiter aus, wodurch die erfolgreiche Behandlung vonInfektionskrankheiten zunehmend erschwert wird. Mit den Untersuchungen auf Resistenzen werden im Zoonosen-Monitoring zudem repräsentative Daten für die Bewertung der aktuellen Situation sowie der Entwicklungstendenzen der Resistenz bei Zoonoseerregern und kommensalen Bakterien gegenüber antimikrobiellen Substanzen gewonnen. Eine Eindämmung der zunehmenden Resistenz von Bakterien gegenüber Antibiotika ist sowohl für den Erhalt der Gesundheit des Menschen als auch der Tiergesundheit von großer Bedeutung.

This book presents topics in module theory and ring theory: some, such as Goldie dimension and semiperfect rings are now considered classical and others more specialized, such as dual Goldie dimension, semilocal endomorphism rings, serial rings and modules.

Combining algebraic groups and number theory, this volume gathers material from the representation theory of this group for the first time, doing so for both local (Archimedean and non-Archimedean) cases as well as for the global number field case.

Starting with an overview of the disease and its current political, financial and technical context, this Milestones in Drug Therapy volume describes the history, chemistry, mechanisms of action and resistance, preclinical and clinical use, pharmacokinetics and safety and tolerability of the current range of antimalarial drugs.

Der Begriff der Splinefunktionen wurde von I. J. Schoenberg 1946 eingefUhrt. "Spline" ist der Name eines Zeichengerates, welches auf mechanischem Weg Interpolatio- aufgaben lost. Dieses Gerat besteht aus einer flexiblen, oft mehrere Meter langen Latte, die auf dem Zeichenbrett aufliegt und dort an bestimmten Stellen durch Gewichte festgehalten wird. Die Form, die die Latte annimmt, hangt von den Elastizitatseigenschaften der Latte abo -, " , , , , , , \ , \ \ I , , , ," -"', , , , , J::>----" , I I , I I I , , , , , , , , , , , " ) Fig. 1: Latteninterpo1ation Po1ynominterpo1ation _ - - - - - - - --0 Wir konnen natUrlich versuchen, ein mathematisches Modell fUr dieses mechanische Zeichengerat zu machen, d. h. die Gestalt solcher Kurven mathematisch zu erfassen. - 2 - Die Theorie der Balkenbiegung verlangt, dass die mittlere 2 K quadratische KrUmmung, ("strain energy", Spannungs- J energie) minimiert wird. Lasst sich die Kurve als Graph einer Funktion f auf dem Intervall [a,b] schreiben, so erhalt man mit dem bekannten Ausdruck fUr die Krlimmung K [f" (t) P --------------dt ~ min (1) t [1 +f' (t)2J5/2 a Statt dieses schwierige Extremalproblem zu losen, begnUgt man sich damit, (2) zu minimieren. Die Extremalfunktion fUr das Funktional (2) ist stUckweise ein kubisches Polynom; die Polyn- stUcke gehen an den Bruchstellen so glatt ineinander Uber, dass die Funktion zweimal stetig differenzierbar ist.

This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 - 2013.

This book is a collection of essays on the reception of Leibniz's thinking in the sciences and in the philosophy of science in the 19th and 20th centuries.

This is the first comprehensive study about the non-mathematical writings and activities of the Russian algebraic geometer and number theorist Igor Shafarevich (b. 1923). In the 1970s Shafarevich was a prominent member of the dissidents' human rights movement and a noted author of clandestine anti-communist literature in the Soviet Union. Shafarevich's public image suffered a terrible blow around 1989 when he was decried as a dangerous ideologue of anti-Semitism due to his newly-surfaced old manuscript Russophobia. The scandal culminated when the President of the National Academy of Sciences of the United States suggested that Shafarevich, an honorary member, resign. The present study establishes that the allegations about anti-Semitism in Shafarevich's texts were unfounded and that Shafarevich's terrible reputation was cemented on a false basis.

This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as of partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results which then can be applied to mathematical models of the real world. The problem class includes initial value problems (IVP) for first order differential equations with constant and variable unbounded operator coefficients in a Banach space (the heat equation is a simple example), boundary value problems for the second order elliptic differential equation with an operator coefficient (e.g. the Laplace equation), IVPs for the second order strongly damped differential equation as well as exponentially convergent methods to IVPs for the first order nonlinear differential equation with unbounded operator coefficients. For researchers and students of numerical functional analysis, engineering and other sciences this book provides highly efficient algorithms for the numerical solution of differential equations and applied problems.