Search results for ""birkhäuser""

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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These two volumes present the collected works of James Serrin. He did seminal work on a number of the basic tools needed for the study of solutions of partial differential equations. Many of them have been and are being applied to solving problems in science and engineering. Among the areas which he studied are maximum principle methods and related phenomena such as Harnack's inequality, the compact support principle, dead cores and bursts, free boundary problems, phase transitions, the symmetry of solutions, boundary layer theory, singularities and fine regularity properties. The volumes include commentaries by leading mathematicians to indicate the significance of the articles and to discuss further developments along the lines of these articles.

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This book provides a systematic introduction to functions of one complex variable. Its novel feature is the consistent use of special color representations – so-called phase portraits – which visualize functions as images on their domains.Reading Visual Complex Functions requires no prerequisites except some basic knowledge of real calculus and plane geometry. The text is self-contained and covers all the main topics usually treated in a first course on complex analysis. With separate chapters on various construction principles, conformal mappings and Riemann surfaces it goes somewhat beyond a standard programme and leads the reader to more advanced themes.In a second storyline, running parallel to the course outlined above, one learns how properties of complex functions are reflected in and can be read off from phase portraits. The book contains more than 200 of these pictorial representations which endow individual faces to analytic functions. Phase portraits enhance the intuitive understanding of concepts in complex analysis and are expected to be useful tools for anybody working with special functions – even experienced researchers may be inspired by the pictures to new and challenging questions.Visual Complex Functions may also serve as a companion to other texts or as a reference work for advanced readers who wish to know more about phase portraits.

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The seminar focuses on a recent solution, by the authors, of a long standing problem concerning the stable module category (of not necessarily finite dimensional representations) of a finite group. The proof draws on ideas from commutative algebra, cohomology of groups, and stable homotopy theory. The unifying theme is a notion of support which provides a geometric approach for studying various algebraic structures. The prototype for this has been Daniel Quillen’s description of the algebraic variety corresponding to the cohomology ring of a finite group, based on which Jon Carlson introduced support varieties for modular representations. This has made it possible to apply methods of algebraic geometry to obtain representation theoretic information. Their work has inspired the development of analogous theories in various contexts, notably modules over commutative complete intersection rings and over cocommutative Hopf algebras. One of the threads in this development has been the classification of thick or localizing subcategories of various triangulated categories of representations. This story started with Mike Hopkins’ classification of thick subcategories of the perfect complexes over a commutative Noetherian ring, followed by a classification of localizing subcategories of its full derived category, due to Amnon Neeman. The authors have been developing an approach to address such classification problems, based on a construction of local cohomology functors and support for triangulated categories with ring of operators. The book serves as an introduction to this circle of ideas.

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The book gives the basic results of the theory of the spaces Ap? of functions holomorphic in the unit disc, halfplane and in the finite complex plane, which depend on functional weights ? permitting any rate of growth of a function near the boundary of the domain.

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Why is the Devil thrilled when Hell gets its first mathematician? How do 6 and 27 solve the diabolical murder of 9? What are the advantages a vampire has in the math world? What happens when we run out of new math to discover? How does Dr. Frankenstein create the ideal mathematical creature? What transpires when a grad student digging for theorems strikes a rich vein on the ridge overlooking Deadwood? What happens when math students band together to foment rebellion? What will a mathematician do beyond the grave to finish that elusive proof?This is just a small subset of the questions plumbed in this collection of 45 mathematically bent stories from the fertile imagination of Colin Adams. Originally appearing in The Mathematical Intelligencer, an expository mathematics magazine, these tales give a decidedly unconventional look at the world of mathematics and mathematicians. A section of notes is provided at the end of the book that explain references that may not be familiar to all and that include additional commentary by the author.

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This textbook provides a thorough overview of mathematical physics, highlighting classical topics as well as recent developments. Readers will be introduced to a variety of methods that reflect current trends in research, including the Bergman kernel approach for solving boundary value and spectral problems for PDEs with variable coefficients. With its careful treatment of the fundamentals as well as coverage of topics not often encountered in textbooks, this will be an ideal text for both introductory and more specialized courses.The first five chapters present standard material, including the classification of PDEs, an introduction to boundary value and initial value problems, and an introduction to the Fourier method of separation of variables. More advanced material and specialized treatments follow, including practical methods for solving direct and inverse Sturm-Liouville problems; the theory of parabolic equations, harmonic functions, potential theory, integral equations and the method of non-orthogonal series.Methods of Mathematical Physics is ideal for undergraduate students and can serve as a textbook for a regular course in equations of mathematical physics as well as for more advanced courses on selected topics.

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This volume is dedicated to Ciro Ciliberto on the occasion of his 70th birthday and contains refereed papers, offering an overview of important parts of current research in algebraic geometry and related research in the history of mathematics. It presents original research as well as surveys, both providing a valuable overview of the current state of the art of the covered topics and reflecting the versatility of the scientific interests of Ciro Ciliberto.

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This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham’s theorem on simplicial complexes. In addition, Sullivan’s results on computing the rational homotopy type from forms is presented. New to the Second Edition: *Fully-revised appendices including an expanded discussion of the Hirsch lemma*Presentation of a natural proof of a Serre spectral sequence result *Updated content throughout the book, reflecting advances in the area of homotopy theoryWith its modern approach and timely revisions, this second edition of Rational Homotopy Theory and Differential Forms will be a valuable resource for graduate students and researchers in algebraic topology, differential forms, and homotopy theory.

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Riemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese) for first-year graduate students in mathematics and physics. The author's treatment goes very directly to the basic language of Riemannian geometry and immediately presents some of its most fundamental theorems. It is elementary, assuming only a modest background from readers, making it suitable for a wide variety of students and course structures. Its selection of topics has been deemed "superb" by teachers who have used the text. A significant feature of the book is its powerful and revealing structure, beginning simply with the definition of a differentiable manifold and ending with one of the most important results in Riemannian geometry, a proof of the Sphere Theorem. The text abounds with basic definitions and theorems, examples, applications, and numerous exercises to test the student's understanding and extend knowledge and insight into the subject. Instructors and students alike will find the work to be a significant contribution to this highly applicable and stimulating subject.

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This book is about algebra. This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 Exchange of terms in addition Let's add 3 and 5: 3+5=8. And now change the order: 5+3=8. We get the same result. Adding three apples to five apples is the same as adding five apples to three - apples do not disappear and we get eight of them in both cases. 3 Exchange of terms in multiplication Multiplication has a similar property. But let us first agree on notation.

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This graphic novel is both a historical novel as well as an entertaining way of using mathematics to solve a crime. The plot, the possible motive of every suspect, and the elements of his or her character are based on actual historical figures.The 2nd International Congress of Mathematicians is being held in Paris in 1900. The main speaker, the renowned Professor X, is found dead in the hotel dining room. Foul play is suspected. The greatest mathematicians of all time (who are attending the Congress) are called in for questioning. Their statements to the police, however, take the form of mathematical problems. The Chief Inspector enlists the aid of a young mathematician to help solve the crime. Do numbers always tell the truth? Or don’t they?

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This book explains and helps readers to develop geometric intuition as it relates to differential forms. It includes over 250 figures to aid understanding and enable readers to visualize the concepts being discussed. The author gradually builds up to the basic ideas and concepts so that definitions, when made, do not appear out of nowhere, and both the importance and role that theorems play is evident as or before they are presented. With a clear writing style and easy-to- understand motivations for each topic, this book is primarily aimed at second- or third-year undergraduate math and physics students with a basic knowledge of vector calculus and linear algebra.

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This text provides a comprehensive, state-of-the art review of this field, and will serve as a valuable resource for pathologists and clinical hematologists/oncologists with an interest in chronic lymphocytic leukemia. This book is designed to provide a concise yet comprehensive summary of the traditional and new definitions, prognostic markers, the pathobiology and newer hierarchal classification based on molecular genetics/chromosomal abnormalities. It will include the most up-to-date scientific and clinical information and bring together subject matter that is usually covered separately in various specialties of hematopathology, molecular pathology, basic science and immunology. The book is written in an easy to comprehend format with emphasis on the science and illustrations to explain the same. It is therefore intended to intrigue, the junior resident and the senior pathologists/clinical oncologists and anyone who would like to keep up with this rapidly growing field.

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This book provides a road map for the efficient and successful management of atrial fibrillation (AF) in the short stay unit. It describes the problem, defines the measures of successful treatment, elucidates interventions, and supplies the tools for achieving quality care. Organized in four parts, it covers the impact of AF on patient populations; the presentation and management of AF; the transition to the outpatient environment; and systems management. Topics include the economic consequences of AF; cardioversion and cardiac implantable electronic devices in AF management; education of the AF patient and discharge planning; and quality metrics in AF. The book also provides order sheets and process criteria with which institutions can successfully manage the AF patient in the short stay unit, thus optimizing patient outcomes, patient satisfaction, and operational efficiencies. Short Stay Management of Atrial Fibrillation is a valuable resource for cardiologists, emergency medicine physicians, electrophysiologists, and other healthcare professionals involved in AF management.

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La géométrie rigide est devenue, au fil des ans, un outil indispensable dans un grand nombre de questions en géométrie arithmétique. Depuis ses premières fondations, posées par J. Tate en 1961, la théorie s'est développée dans des directions variées. Ce livre est le premier volume d'un traité qui expose un développement systématique de la géométrie rigide suivant l'approche de M. Raynaud, basée sur les schémas formels à éclatements admissibles près. Ce volume est consacré à la construction des espaces rigides dans une situation relative et à l'étude de leurs propriétés géométriques. L'accent est particulièrement mis sur l'étude de la topologie admissible d'un espace rigide cohérent, analogue de la topologie de Zariski d'un schéma. Parmi les sujets traités figurent l'étude des faisceaux cohérents et de leur cohomologie, le théorème de platification par éclatements admissibles qui généralise au cadre formel-rigide un théorème de Raynaud-Gruson dans le cadre algébrique, et le théorème de comparaison du type GAGA pour les faisceaux cohérents. Ce volume contient aussi de larges rappels et compléments de la théorie des schémas formels de Grothendieck. Ce traité est destiné tout autant aux étudiants ayant une bonne connaissance de la géométrie algébrique et souhaitant apprendre la géométrie rigide qu'aux experts en géométrie algébrique et en théorie des nombres comme source de références.

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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.

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Mathematics research opportunities for undergraduate students have grown significantly in recent years, but accessible research topics for first- and second-year students with minimal experience beyond high school mathematics are still hard to find. To address this need, this volume provides beginning students with specific research projects and the tools required to tackle them. Most of these projects are accessible to students who have not yet taken Calculus, but students who know some Calculus will find plenty to do here as well. Chapters are self-contained, presenting projects students can pursue, along with essential background material and suggestions for further reading. Suggested prerequisites are noted at the beginning of each chapter. Some topics covered include: games on graphs modeling of biological systems mosaics and virtual knots mathematics for sustainable humanity mathematical epidemiology Mathematics Research for the Beginning Student, Volume 1 will appeal to undergraduate students at two- and four-year colleges who are interested in pursuing mathematics research projects. Faculty members interested in serving as advisors to these students will find ideas and guidance as well. This volume will also be of interest to advanced high school students interested in exploring mathematics research for the first time. A separate volume with research projects for students who have already studied calculus is also available.

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Mathematics research opportunities for undergraduate students have grown significantly in recent years, but accessible research topics for first- and second-year students are still hard to find. To address this need, this volume provides beginning students who have already had some exposure to calculus with specific research projects and the tools required to tackle them. Chapters are self-contained, presenting projects students can pursue, along with essential background material and suggestions for further reading. In addition to calculus, some of the later chapters require prerequisites such as linear algebra and statistics. Suggested prerequisites are noted at the beginning of each chapter. Some topics covered include: lattice walks in the plane statistical modeling of survival data building blocks and geometry modeling of weather and climate change mathematics of risk and insurance Mathematics Research for the Beginning Student, Volume 2 will appeal to undergraduate students at two- and four-year colleges who are interested in pursuing mathematics research projects. Faculty members interested in serving as advisors to these students will find ideas and guidance as well. This volume will also be of interest to advanced high school students interested in exploring mathematics research for the first time. A separate volume with research projects for students who have not yet studied calculus is also available.

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This innovative textbook presents material for a course on modern statistics that incorporates Python as a pedagogical and practical resource. Drawing on many years of teaching and conducting research in various applied and industrial settings, the authors have carefully tailored the text to provide an ideal balance of theory and practical applications. Numerous examples and case studies are incorporated throughout, and comprehensive Python applications are illustrated in detail. A custom Python package is available for download, allowing students to reproduce these examples and explore others.The first chapters of the text focus on analyzing variability, probability models, and distribution functions. Next, the authors introduce statistical inference and bootstrapping, and variability in several dimensions and regression models. The text then goes on to cover sampling for estimation of finite population quantities and time series analysis and prediction, concluding with two chapters on modern data analytic methods. Each chapter includes exercises, data sets, and applications to supplement learning.Modern Statistics: A Computer-Based Approach with Python is intended for a one- or two-semester advanced undergraduate or graduate course. Because of the foundational nature of the text, it can be combined with any program requiring data analysis in its curriculum, such as courses on data science, industrial statistics, physical and social sciences, and engineering. Researchers, practitioners, and data scientists will also find it to be a useful resource with the numerous applications and case studies that are included. A second, closely related textbook is titled Industrial Statistics: A Computer-Based Approach with Python. It covers topics such as statistical process control, including multivariate methods, the design of experiments, including computer experiments and reliability methods, including Bayesian reliability. These texts can be used independently or for consecutive courses.The mistat Python package can be accessed at https://gedeck.github.io/mistat-code-solutions/ModernStatistics/"In this book on Modern Statistics, the last two chapters on modern analytic methods contain what is very popular at the moment, especially in Machine Learning, such as classifiers, clustering methods and text analytics. But I also appreciate the previous chapters since I believe that people using machine learning methods should be aware that they rely heavily on statistical ones. I very much appreciate the many worked out cases, based on the longstanding experience of the authors. They are very useful to better understand, and then apply, the methods presented in the book. The use of Python corresponds to the best programming experience nowadays. For all these reasons, I think the book has also a brilliant and impactful future and I commend the authors for that."Professor Fabrizio RuggeriResearch Director at the National Research Council, ItalyPresident of the International Society for Business and Industrial Statistics (ISBIS)Editor-in-Chief of Applied Stochastic Models in Business and Industry (ASMBI)

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This book presents the notes from the seminar on wave phenomena given in 2019 at the Mathematical Research Center in Oberwolfach.The research on wave-type problems is a fascinating and emerging field in mathematical research with many challenging applications in sciences and engineering. Profound investigations on waves require a strong interaction of several mathematical disciplines including functional analysis, partial differential equations, mathematical modeling, mathematical physics, numerical analysis, and scientific computing.The goal of this book is to present a comprehensive introduction to the research on wave phenomena. Starting with basic models for acoustic, elastic, and electro-magnetic waves, topics such as the existence of solutions for linear and some nonlinear material laws, efficient discretizations and solution methods in space and time, and the application to inverse parameter identification problems are covered. The aim of this book is to intertwine analysis and numerical mathematics for wave-type problems promoting thus cooperative research projects in this field.

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"102 Combinatorial Problems" consists of carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Key features: * Provides in-depth enrichment in the important areas of combinatorics by reorganizing and enhancing problem-solving tactics and strategies * Topics include: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities The book is systematically organized, gradually building combinatorial skills and techniques and broadening the student's view of mathematics. Aside from its practical use in training teachers and students engaged in mathematical competitions, it is a source of enrichment that is bound to stimulate interest in a variety of mathematical areas that are tangential to combinatorics.

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This monograph is concerned with the interplay between the theory of operator semigroups and spectral theory. The basics on operator semigroups are concisely covered in this self-contained text. Part I deals with the Hille--Yosida and Lumer--Phillips characterizations of semigroup generators, the Trotter--Kato approximation theorem, Kato’s unified treatment of the exponential formula and the Trotter product formula, the Hille--Phillips perturbation theorem, and Stone’s representation of unitary semigroups. Part II explores generalizations of spectral theory’s connection to operator semigroups.

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Seit dem Beginn der Arbeiten zur ersten Auflage dieses Wörterbuchs sind mehr als 25 Jahre vergangen. Mein damals gehegter Wunsch, daß mit diesem Werk der botanischen Forschung und Praxis ein zuverlässigeres Mittel zur schnellen Orientierung über Etymologie, Geschichte und Aussprache der botanischen Namen in die Hand gegeben werden könnte, ist über Erwarten in Erfüllung gegangen, wie die zahlreichen Zuschriften und Rezensionen gezeigt haben. Auf der anderen Seite sind aber im vergangenen Vierteljahrhundert gerade auf dem taxonomischen Gebiet Veränderungen in einer Größenordnung von mehreren Tausenden eingetreten, die allein schon deswegen eine Neubearbeitung dieses Buches erforderlich machten. Es genügt hierfür, die von mir damals benutzte 9. Aufl. des ZANDER von 1964 mit der aktuellen 14. Aufl. von 1993 zu vergleichen, die insgesamt 27 308 Namen, darunter aber 8209 Synonyme, umfaßt. Es war also zunächst angebracht, das taxonomische Material zu aktualisieren und die Synonyme bis auf wenige, in der Forschung noch diskutierte (z. B. Pritzelago = Hutchinsia) oder aus Gewohnheit beibehaltene Relikte (z. B. Ophrys fuciflora statt regelhaftem Ophrys holoserica) zu eliminieren. Zugleich habe ich die Mate­ rialgrundlage durch die massenhafte Neuaufnahme von Gattungen und Arten der Bakterien, Algen, Flechten, Moose und Farne, aber auch der Gymnospermen und Angiospermen, erheblich erweitert. Aus konventionellen Gründen sind auch die mykologischen Taxa weiterhin in diesem Buch vertreten, selbst wenn nach neueren Erkenntnissen die Pilze nicht mehr dem Pflanzenreich zugeordnet werden können. Auf dieser Grundlage bietet das Wörterbuch jetzt mehr als 35 000 Taxa, die einer etymo­ logischen Prüfung zu unterziehen waren.

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These lecture notes are devoted to the analysis of a nonlocal equation in the whole of Euclidean space. In studying this equation, all the necessary material is introduced in the most self-contained way possible, giving precise references to the literature when necessary. The results presented are original, but no particular prerequisite or knowledge of the previous literature is needed to read this text. The work is accessible to a wide audience and can also serve as introductory research material on the topic of nonlocal nonlinear equations.

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This book presents a series of lectures on three of the best known examples of free discontinuity problems: the Mumford-Shah model for image segmentation, a variational model for the epitaxial growth of thin films, and the sharp interface limit of the Ohta-Kawasaki model for pattern formation in dyblock copolymers.

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This book contains lecture notes of a series of courses on the regularity theory of partial differential equations and variational problems, held in Pisa and Parma in the years 2009 and 2010. The contributors, Nicola Fusco, Tristan Rivière and Reiner Schätzle, provide three updated and extensive introductions to various aspects of modern Regularity Theory concerning: mathematical modelling of thin films and related free discontinuity problems, analysis of conformally invariant variational problems via conservation laws, and the analysis of the Willmore functional. Each contribution begins with a very comprehensive introduction, and is aimed to take the reader from the introductory aspects of the subject to the most recent developments of the theory.

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These are the proceedings of a one-week international conference centered on asymptotic analysis and its applications. They contain major contributions dealing with: mathematical physics: PT symmetry, perturbative quantum field theory, WKB analysis, local dynamics: parabolic systems, small denominator questions, new aspects in mould calculus, with related combinatorial Hopf algebras and application to multizeta values, a new family of resurgent functions related to knot theory.

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Low energy neutrino astrophysics studies the evolutionary life of the stars via the neutrinos emitted during the quiescent phase (solar neutrinos) and during the explosive death of big mass stars (supernova neutrinos). The neutrino mean free path in matter is about twenty orders of magnitude greater than that of light; therefore neutrinos reaching us can be produced also in deep and high-density levels of stars. Since massless neutrinos are unaffected by their travel in the interstellar space, their energies and arrival directions carry information on the star history. The subject of this thesis is the search for neutrino bursts from galactic stellar gravitational collapses performed in the MACRO experiment, a large area modular detector, operating since autumn 1989.

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This set of lecture notes is the outcome of a lecture series, given in April 2000 by the author while holding the “Cattedra Galileiana” at Scuola Normale Superiore in Pisa. The purpose of the lectures was to give an overview of some recent work concerning structural properties of the evolution of the forward rate curve in an arbitrage free bond market.

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These Lecture Notes are based on a course given in June 2001 at the Cattedra Galileiana of Scuola Normale Superiore di Pisa. The course consisted of a short introduction into the basic concepts of Mathematical Finance, focusing on the notion of “no arbitrage”, and subsequently applying these concepts to portfolio optimization. To avoid technical difficulties I mainly dealt with the situation where the underlying probability space is finite and only sketched the difficulties arising in the general case. We then pass to the scheme of utility optimisation for general semi-martingale models. Some topics of this course are not standard: for example, in the treatment of the general existence theorem for the optimal portfolio, we give a direct proof which is not relying on duality theory. Similarly, the treatment of the asymptotic elasticity of utility functions and a related counter-example are original to these notes.

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His ideas turned the mathematical world on its head. As a scientist he should be placed on the same level as Newton and Einstein. This account of Euler's life and livings is embedded in the great political developments of his time, particularly in Austria, Prussia and Russia. The comic by Elena Pini (illustrations) and Alice and Andreas K. Heyne (text) follows the life of the genius from Basel, who, born 300 years ago, would set out to change the scientific world. The book is completed by a short biography of Euler and relevant data of the most important politicians and contemporaries.

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Die haptische Wahrnehmung ist von elementarer Bedeutung für die Planung, Steuerung und Ausführung alltäglicher Handlungen. Diese dem Tastsinn zugeordnete Wahrnehmungsform findet immer größere Beachtung. Mit aktuellen Ergebnissen aus interdisziplinärer Forschung und Praxis dokumentiert das Buch das zunehmende Interesse an diesem vielseitigen Forschungsgebiet. Nach einer erkenntnistheoretischen und historischen Einführung widmen sich drei Kapitel neurophysiologischen Grundlagen sowie psychologischen und klinisch-neuropsychologischen Aspekten der haptischen Wahrnehmung. Vielfältige Beispiele unter anderem aus der Automobil- und Lebensmittelindustrie sowie der Raumfahrt verdeutlichen den praktischen Nutzen der dargestellten Erkenntnisse. Das gut verständliche Buch gewährt Fachkundigen und Studenten, aber auch interessierten Laien einen Einblick in dieses faszinierende Wissensgebiet, das stets neue Herausforderungen entdeckt und innovative Lösungen präsentiert.

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This volume contains the work of the great Swiss mathematician on differential geometry, a field marked by some of his greatest achievements. Between 1690 and 1700, Jacob Bernoulli published twelve treatises in the scientific journal Acta Eruditorum on the use of infinitesimal methods to answer geometrical questions. Preparatory notes for most of these papers and on many other themes are found in Bernoulli's scientific diary Meditationes, from which twentynine texts are published here for the first time. Among the curves considered are the isochrones (lines of constant descent), the parabolic spiral, the loxodrome, the cycloid, the tractrix, and the logarithmic spiral (Bernoulli's spira mirabilis, which also adorns his tombstone). The description of these curves by differential equations and by geometrical constructions, their rectification and quadrature, and the determination of their evolutes and caustics offered Bernoulli and his colleagues a range of challenging problems, many of them relevant for mechanical or optical applications. The French mathematician André Weil, who lived in the United States until his recent death, has greatly influenced 20th century mathematics, among other things, as a founding member of the Bourbaki group. For many years he has pursued intensive studies of the history of mathematics, especially number theory and algebraic geometry. Weil's introduction to this volume places Jacob Bernoulli's contribution to differential geometry in a line of development from Descartes, Huygens and Barrow through Newton's und Leibniz's epochal innovations right up to the codification of the subject by Euler. Martin Mattmüller, secretary of the Bernoulli Edition at Basel, edited the source text. His commentaries consider particular topics in differential geometry with reference to their historical context at the end of the 17th century.

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Das Fotopraktikum vermittelt systematisch das gesamte Spektrum der heutigen angewandten Fotografie. Es wurde für Leser geschrieben, die es exakt, gründlich und ohne Umschweife wissen wollen. Für Studenten der Hoch-, Fachhoch-, Abend- und Volkshochschulen, für den Nachwuchs der Fotobranche sowie für die, denen die Fotografie im Beruf unentbehrlich ist. Und natürlich auch für ambitionierte Amateure.

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The works from Daniel Bernoulli's youth contained in this first volume of his Collected Works bear witness above all of his versatility; they deal with subjects as different as physiology, formal logic, mathematical analysis, hydrodynamics and positional astronomy. Daniel Bernoulli's contacts with Italian scientists gave rise to several controversies. The present volume documents both sides in each of these debates, which culminated with the publication of Bernoulli's first book Exercitationes mathe- maticae in 1724. The discussions with the renowned mathematician Jacopo Riccati on second-order differential equations and on the Newtonian theory of the out-flow of fluids from vessels deserve particular interest. A third group of texts goes back to the time Bernoulli spent at the newly- founded Academy of Sciences in St. Petersburg, where he had been appointed in 1725. There he worked out two more contributions to physiological research - on muscle movement and on the blind spot in the human eye - as well as his only paper in positional astronomy. This last work - suggested by a prize question of the Paris Académie des Sciences - became the occasion for a vehement conflict; the present volume documents these "Zänkereien" (squabbles) and also reproduces three competing treatises. To complete the documentation of Daniel Bernoulli's work on physiology, the volume also includes his academic ceremonial speech De Vita of 1737, where he sketches for the first time the circulation of the work done by the human heart, and its elaboration by Bernoulli's student Daniel Passavant.

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This volume, together with Volumes 22 and 23 of the same series, contains Euler's contributions to the theory of the movement of the sun and especially of the moon. Time and again Euler worked on the program of applying Newton's principles of mechanics to improve our unterstanding of the movement of the celestial bodies. Euler's monumental "Theoria motuum Lunae nova methodo pertractata" of 1772 (his "Second Theory of the Moon") forms Volume 22, whereas Volume 23 mainly contains his early Astronomical Tables and his "First Theory of the Moon" of 1753. In the present volume the reader will find early papers by Euler pertaining to the preparation of his Astronomical Tables, a series of articles written between his two Theories of the Moon, and finally three substantial essays closely related to his "Second Theory of the Moon". The texts are reprinted in the original language most commonly French or Latin.

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