Search results for ""birkhäuser""

This monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of coherent sheaves of a compact complex manifold with values in its Bott-Chern cohomology, and the proof of a corresponding Riemann-Roch-Grothendieck theorem. One main tool used is the equivalence of categories established by Block between the derived category of bounded complexes with coherent cohomology and the homotopy category of antiholomorphic superconnections. Chern-Weil theoretic techniques are then used to construct forms that represent the Chern character. The main theorem is then established using methods of analysis, by combining local index theory with the hypoelliptic Laplacian.Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck is an important contribution to both the geometric and analytic study of complex manifolds and, as such, it will be a valuable resource for many researchers in geometry, analysis, and mathematical physics.

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This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants — including Olympiad and Putnam competitors — as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.

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This book introduces the study of knots, providing insights into recent applications in DNA research and graph theory. It sets forth fundamental facts such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials. It also covers more recent developments and special topics, such as chord diagrams and covering spaces. The author avoids advanced mathematical terminology and intricate techniques in algebraic topology and group theory. Numerous diagrams and exercises help readers understand and apply the theory. Each chapter includes a supplement with interesting historical and mathematical comments.

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This book, originating from a seminar held at Oberwolfach in 2022, introduces to state-of-the-art methods and results in the study of free boundary problems which are arising from compressible as well as from incompressible Euler's equations in general.

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This book presents, in a consistent and unified overview, results and developments in the field of today´s spherical sampling, particularly arising in mathematical geosciences. Although the book often refers to original contributions, the authors made them accessible to (graduate) students and scientists not only from mathematics but also from geosciences and geoengineering. Building a library of topics in spherical sampling theory it shows how advances in this theory lead to new discoveries in mathematical, geodetic, geophysical as well as other scientific branches like neuro-medicine. A must-to-read for everybody working in the area of spherical sampling.

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Daniel Alpay and Victor Vinnikov During the period July 9 to July 13, 2007,a conference called Characteristic fu- tions and transfer functions in operator theory and system theory: a conference dedicated to PaulFuhrmann onhis 70thanniversary and to the memory ofMoshe Livsiconhis90thanniversarywasheldattheDepartmentofMathematicsofBen- GurionUniversityoftheNegev.Thenotionsoftransferfunctionandcharacteristic functions proved to be fundamental in the last ?fty years in operator theory and in system theory. This conference was envisaged to pay tribute to our colleagues PaulFuhrmannandMosheLivsicwhoplayedacentralroleindevelopingthese- tions. Sadly, Moshe Livsic passedawayon the 30thof March,2007(11th of Nissan 5767), so the conference was dedicated to his memory. It is a pleasure to thank all the participants, who contributed to a very exciting and fruitful conference, and especially those who submitted papers to the present volume. The volume contains a selection of thirteen research papers dedicated to the memory of Moshe Livsic. The topics addressed can be divided into the following categories: Classical operator theory and its applications: This pertains to the paper Diff- ential-di?erence equations in entire functions by G. Belitskii and V. Tkachenko, the paper Bi-Isometries and Commutant Lifting by H. Bercovici, R.G. Douglas. and C. Foias and the paper Convexity of ranges and connectedness of level sets of quadratic forms by I. Feldman, N. Krupnik and A. Markus. Ergodictheoryandstochasticprocesses: We have the papersTheone-sidedergodic Hilbert transform of normal contractions by G. Cohen and M. Lin, and Integral Equations in the Theory of Levy Processes by L. Sakhnovich. Geometryofsmoothmappings:This iscoveredbythepaper ofY.Yomdinentitled ?-Spread of sets in metric spaces and critical values of smooth functions.

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This collection of selected contributions gives an account of recent developments in dynamic game theory and its applications, covering both theoretical advances and new applications of dynamic games in such areas as pursuit-evasion games, ecology, and economics. Written by experts in their respective disciplines, the chapters include stochastic and differential games; dynamic games and their applications in various areas, such as ecology and economics; pursuit-evasion games; and evolutionary game theory and applications. The work will serve as a state-of-the art account of recent advances in dynamic game theory and its applications for researchers, practitioners, and advanced students in applied mathematics, mathematical finance, and engineering.

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Villa Savoye is an icon of modern architecture. But who were Eugénie and Pierre Savoye, who had the house built between 1928 and 1930? Why did they commission Le Corbusier? And how did they live in the country house they dubbed "Villa les Heures Claires"? Their grandson Jean-Marc Savoye tells the story of the villa and its residents using rare documents and family memories. In his pictures, illustrator Jean-Philippe Delhomme – long fascinated by the building – brings to life the construction site, everyday life, the war period, its use as a barn, and its rescue from demolition. In 1965, Le Corbusier lived to see Villa Savoye declared a monument; in 2016 it earned a spot on the UNESCO World Heritage list and now welcomes 40,000 visitors each year.

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The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows.​

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This thesis deals with specific features of the theory of holomorphic dynamics in dimension 2 and then sets out to study analogous questions in higher dimensions, e.g. dealing with normal forms for rigid germs, and examples of Kato 3-folds.The local dynamics of holomorphic maps around critical points is still not completely understood, in dimension 2 or higher, due to the richness of the geometry of the critical set for all iterates.In dimension 2, the study of the dynamics induced on a suitable functional space (the valuative tree) allows a classification of such maps up to birational conjugacy, reducing the problem to the special class of rigid germs, where the geometry of the critical set is simple. In some cases, from such dynamical data one can construct special compact complex surfaces, called Kato surfaces, related to some conjectures in complex geometry.

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This book describes the searches that lead to the discovery of a Higgs boson performed at CMS, one of the two main experiments at the CERN LHC. After an overview of the theory and of the CMS experiment, all search channels are described, with emphasis on the ones with the best sensitivity. The statistical methodology used to analyse and the outcomes of the searches and the discovery results are then presented in detail.

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This book consists mainly of the translation, by C. Fuchs, of the 1929 landmark paper "Über einige Anwendungen diophantischer Approximationen" by C.L. Siegel. The paper contains proofs of most important results in transcendence theory and diophantine analysis, notably Siegel’s celebrated theorem on integral points on algebraic curves. Many modern versions of Siegel’s proof have appeared, but none seem to faithfully reproduce all features of the original one. This translation makes Siegel’s original ideas and proofs available for the first time in English. The volume also contains the original version of the paper (in German) and an article by the translator and U. Zannier, commenting on some aspects of the evolution of this field following Siegel’s paper. To end, it presents three modern proofs of Siegel’s theorem on integral points.

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This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.

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The book deals with some questions related to the boundary problem in complex geometry and CR geometry. After a brief introduction summarizing the main results on the extension of CR functions, it is shown in chapters 2 and 3 that, employing the classical Harvey-Lawson theorem and under suitable conditions, the boundary problem for non-compact maximally complex real submanifolds of Cn, n=3 is solvable. In chapter 4, the regularity of Levi flat hypersurfaces Cn (n=3) with assigned boundaries is studied in the graph case, in relation to the existence theorem proved by Dolbeault, Tomassini and Zaitsev. Finally, in the last two chapters the structure properties of non-compact Levi-flat submanifolds of Cn are discussed; in particular, using the theory of the analytic multifunctions, a Liouville theorem for Levi flat submanifolds of Cn is proved.

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In this thesis I study the untwisted affine quantum algebras and their specialization at a primitive l-th root of unity. In particular my goal is the complete description of the center, when l is odd. The center of the specialization of the quantum algebra at odd roots of unity is already known in the finite case, that is for finite dimensional semisimple Lie algebras. In this thesis I prove that analogous results hold in the affine untwisted case.

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Electron gas theory is one of the broadest fields in theoretical condensed matter physics, and even its most elementary application to the study of collective excitations and screening in the simpe metals poses interesting questions. Recent Electron Energy Loss and Inelastic X-Ray Scattering experiments have shown that traditional electron gas theories are unable to account for the measured plasmon dispersion relation. While it has become clear that neither correlation nor band structure alone can explain those results, the recently developed Time Dependent Density Functional Theory provides a general framework which can account for both.

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The subject of the present thesis is a study on bipolaron formation in heavily doped and polar materials. The study is applied to the physics of superconducting compounds with high transition temperature. In particular this thesis addresses the problem of the formation and superconducting properties of real space electron (hole) pairs in these systems and their dependence on the carrier density. The pairing mechanism results from the dynamical cooperation of photonic and electronic degrees of freedom which characterize the heavily doped polar material. We call these pairs biplasmapolarons (BBP) because they can be thought as quasi-particles composed by two electrons (holes) and their cloud of virtual photons and plasmons. In the present work we extend the theory to the calculation of both BPP binding energy and effective mass and we discuss the features of the effective electron-electron interaction.

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The main goal of these lectures is to get students acquainted with a glossary of nonlinear physics. I try to present the material of the lectures (delivered at SNS Pisa in April -- June 1999) in such a way that the students do not need to use additional literature during the first reading. The lectures focus on the following arguments: discussion of nonlinear problems in classical physics; the use of the multiple time scale expansion method to solve problems of nonlinear oscillations; description of nonlinear wave steepening and shock wave formation using the Lagrange variables; solution of nonlinear elliptic equations considering the Liouville equation; soliton solutions of the Korteweg de Vries, Sine-Gordon and Nonlinear Schrödinger equations; the use of the Backlund transformation; self-similarity of nonlinear systems.

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These volumes collect the lecture notes of the course “An introduction to computational physics” held in the academic year 2000/01 for students of the University of Pisa and Scuola Normale Superiore at the level of the last two-year undergraduates in physics and chemistry. Grid methods are the tool of the trade for the solution of ordinary and partial differential equations and consequently they represent a “must” for anyone dealing with computational science. With grid methods, a major distinction is made between methods which do not require matrix algebra and those which do.

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The papers published here have been written by friends, former students and colleagues of Luigi Radicati di Bronzolo on the occasion of his 70th birthday to express the affection and deep esteem he induced in them with his considerateness, intelligence, knowledge and culture. The papers appear in two volumes; on the basis of their titles it is easy to recognize that they may be grouped according to the following subjects: 1) Atomic, molecular and nuclear physics; 2) Astrophysics; 3) Elementary particles; 4) Mathematics; 5) Physical and biological ordered and disordered states; 6) Principles of quantum mechanics and of field theory.

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During the academic year 1995/96, I was invited by the Scuola Normale Superiore to give a series of lectures. The purpose of these notes is to make the underlying economic problems and the mathematical theory of exterior differential systems accessible to a larger number of people. It is the purpose of these notes to go over these results at a more leisurely pace, keeping in mind that mathematicians are not familiar with economic theory and that very few people have read Elie Cartan.

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These are the informal notes of two seminars held at the Università di Roma “La Sapienza”, and at the Scuola Normale Superiore in Pisa in spring and autumn 1997. We discuss in detail the content of the parts of a paper by Givental dealing with mirror symmetry for projective complete intersections.

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The lectures concentrate on some old and new relations between quasiderivatives of solutions to Ito stochastic equations and interior smoothness of harmonic functions associated with degenerate elliptic equations. Recent progress in the case of constant coefficients is discussed in full detail.

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This is a written version of the Cattedra Galileiana lectures, presented in 2002 at the Scuola Normale in Pisa. The objective is to combine an orientation to credit-risk modeling (emphasizing the valuation of corporate debt and credit derivatives) with an introduction to the analytical tractability and richness of affine state processes. This is not a general survey of either topic, but rather is designed to introduce researchers with some background in mathematics to a useful set of modeling techniques and an interesting set of applications.

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The achievement of Bose-Einstein condensation in ultra-cold vapours of alkali atoms has given enormous impulse to the study of dilute atomic gases in condensed quantum states inside magnetic traps and optical lattices. High purity and easy optical access make them ideal candidates to investigate fundamental issues on interacting quantum systems. This review presents some theoretical issues which have been addressed in this area and the numerical techniques which have been developed and used to describe them, from mean-field models to classical and quantum simulations for equilibrium and dynamical properties. The attention given in this article to methods beyond standard mean-field approaches should make it a useful reference point for future advances in these areas.

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The notes are based on lectures on stochastic processes given at Scuola Normale Superiore in 1999 and 2000. Some new material was added and only selected, less standard results were presented. We did not include several applications to statistical mechanics and mathematical finance, covered in the lectures, as we hope to write part two of the notes devoted to applications of stochastic processes in modelling. The main themes of the notes are constructions of stochastic processes. We present different approaches to the existence question proposed by Kolmogorov, Wiener, Ito and Prohorov. Special attention is also paid to Levy processes. The lectures are basically self-contained and rely only on elementary measure theory and functional analysis. They might be used for more advanced courses on stochastic processes.

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This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions. The book further contains many original PDE problems originating in biosciences.

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This second volume on technology is mainly devoted to three prize-winning memoirs, answering questions related to ship-building which were proposed by the French Académie Royale des Sciences in the years 1737, 1755, and 1757. The volume hosts two further items: a popularizing text on astronomy from 1723, and the theory of the spiral pump, a technical item from 1772. In the introductory part of the volume every memoir is analysed and extensively summarized, so the reader should obtain a clear view of the content in modern terms.

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The subject of these notes is counting and related topics, viewed from a computational perspective. A major theme of the book is the idea of accumulating information about a set of combinatorial structures by performing a random walk on those structures. These notes will be of value not only to teachers of postgraduate courses on these topics, but also to established researchers. For the first time this body of knowledge has been brought together in a single volume.

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Correction to the text about C.S. Roero printed on the inside front cover page: Clara Silvia Roero began her research with Tullio Viola, full Professor of Analysis at Turin University. From 1987 to 2000 she was associate professor of Matematiche Complementari and of History of Mathematics at the University of Cagliari (1987-1990) and at the University of Turin (1990-2000). From 2000 she is full professor of History of Mathematics at Turin University, Faculty of Mathematical and Physical Sciences. She is currently President of the Italian Society of History of Mathematics (Società Italiana di Storia delle Matematiche). She is author of several articles and books on the history of mathematics from antiquity to 20th century, in particular on the history of the Leibnizian Calculus; and she is a member of the editorial board of the Bollettino di Storia delle Scienze Matematiche.

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Der Band enthält einen Teil der Abhandlungen Eulers zur Störungstheorie. Er ist der letzte von drei diesem Thema gewidmeten Bänden. Gegenstand der Untersuchungen ist das Dreikörperproblem, das heisst die Beschreibung der Bewegung eines Himmelskörpers um ein Zentralgestirn unter Berücksichtigung der Störung durch einen weiteren Himmelskörper.Dieses Problem behandelt Euler in einigen der vorliegenden Abhandlungen nicht nur für Massenpunkte, sondern erstmals auch für ausgedehnte Himmelskörper. Die so verallgemeinerte Himmelsmechanik, die er als „mechanische Astronomie“ bezeichnete, prägte er massgebend. Dazu gehört unter anderem auch das Rotationsverhalten von Himmelskörpern unter dem Einfluss äusserer Gravitationskräfte, das er mit seinen berühmten Bewegungsgleichungen der Starrkörperrotation erfolgreich zu beschreiben vermochte.

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This volume concludes the second series of Leonhard Euler's Opera Omnia. It contains Euler's contributions to cosmic physics. Most substantial is the Essay on the Tide, which shared the prize awarded by the Paris Academy of Science in 1740. Other topics are the constitution of the atmosphere, ocean currents and winds, comets, the resistance of the aether, the lunar atmosphere, and the shape of the earth. The papers collected in this volume span a period from 1727 to 1775. They show Euler's lasting interest in questions of cosmic physics.

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The thoroughly updated second edition of this key textbook provides an authoritative discussion of cardiovascular disease for the practicing primary care clinician. It examines a variety of disease states with emphasis on risk factors, risk estimation, and established cardiac disease. The book also explores the co-morbid conditions that surround cardiovascular disease. It includes key points, algorithms, case studies, recommendations on evidence-based practice, and summary boxes. A key resource for the busy practitioner, the Second Edition of Comprehensive Cardiovascular Medicine in the Primary Care Setting is designed to give residents, fellows, and primary care physicians the skills to confidently perform assessments, initiate and maintain efficacious therapy, and know when a referral to a cardiologist is advisable.

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This book addresses the unique sociocultural and historical systems of oppression that have alienated African-American and other racial minority patients within the mental healthcare system. This text aims to build a novel didactic curriculum addressing racism, justice, and community mental health as these issues intersect clinical practice. Unlike any other resource, this guide moves beyond an exploration of the problem of racism and its detrimental effects, to a practical, solution-oriented discussion of how to understand and approach the mental health consequences with a lens and sensitivity for contemporary justice issues. After establishing the historical context of racism within organized medicine and psychiatry, the text boldly examines contemporary issues, including clinical biases in diagnosis and treatment, addiction and incarceration, and perspectives on providing psychotherapy to racial minorities. The text concludes with chapters covering training and medical education within this sphere, approaches to supporting patients coping with racism and discrimination, and strategies for changing institutional practices in mental healthcare. Written by thought leaders in the field, Racism and Psychiatry is the only current tool for psychiatrists, psychologists, administrators, educators, medical students, social workers, and all clinicians working to treat patients dealing with issues of racism at the point of mental healthcare.

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Michel Desvigne ist der international profilierteste französische Landschaftsarchitekt. Ansässig in Paris, hatte er Gastprofessuren an der Architectural Association in London, an der Harvard University und anderswo inne. Desvignes Projekte haben eine starke strategische und konzeptionelle Komponente. Eine große Rolle spielen Verkehrsprojekte, die die städtebaulich-planerische Kompetenz seiner Landschaftsarchitektur unterstreichen. Das Buch dokumentiert zehn Großprojekte Desvignes aus Frankreich, den USA, Spanien und Qatar, bei denen er nicht nur für die Landschaftsarchitektur, sondern für die gesamte Projektleitung verantwortlich zeichnet. Wie lassen sich solche Projekte hoher Komplexität realisieren? Wie entwickelt sich der intellektuelle Gedankengang? Welche spezifischen Probleme stellen sich bei der Umsetzung?

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Building with straw bales is a technique pioneered a century ago in the state of Nebraska. In recent years there has been a renaissance in the use of straw as a building material largely in the American Southwest, but also in Canada, Australia, France, Holland, Germany, Austria and China. Straw is a renewable resource with excellent insulating properties. It is a cheap and easy-to-use option for self-builders, and even large-scale structures can be erected using timber framework filled with straw. This book is a practical, hands-on guide to building with straw. Fire safety, protection against moisture, damp, pests and parasites are treated in detail. Numerous on-site photos document the process of assembly and construction step by step. 30 exemplary international projects illustrate the wide spectrum of design possibilities with straw.

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