Böcker utgivna av Birkhauser Verlag AG

The notes in this volume correspond to advanced courses held at the Centre de Recerca Matematica as part of the research program in Arithmetic Geometry in the 2009-2010 academic year.The notes by Laurent Berger provide an introduction to p-adic Galois representations and Fontaine rings, which are especially useful for describing many local deformation rings at p that arise naturally in Galois deformation theory.The notes by Gebhard Bockle offer a comprehensive course on Galois deformation theory, starting from the foundational results of Mazur and discussing in detail the theory of pseudo-representations and their deformations, local deformations at places l = p and local deformations at p which are flat. In the last section,the results of Bockle and Kisin on presentations of global deformation rings over local ones are discussed. The notes by Mladen Dimitrov present the basics of the arithmetic theory of Hilbert modular forms and varieties, with an emphasis on the study of the images of the attached Galois representations, on modularity lifting theorems over totally real number fields, and on the cohomology of Hilbert modular varieties with integral coefficients. The notes by Lassina Dembele and John Voight describe methods for performing explicit computations in spaces of Hilbert modular forms. These methods depend on the Jacquet-Langlands correspondence and on computations in spaces of quaternionic modular forms, both for the case of definite and indefinite quaternion algebras. Several examples are given, and applications to modularity of Galois representations are discussed. The notes by Tim Dokchitser describe the proof, obtained by the author in a joint project with Vladimir Dokchitser, of the parity conjecture for elliptic curves over number fields under the assumption of finiteness of the Tate-Shafarevich group. The statement of the Birch and Swinnerton-Dyer conjecture is included, as well as a detailed study of local and global root numbers of elliptic curves and their classification.

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

Many physical processes in fields such as mechanics, thermodynamics, electricity, magnetism or optics are described by means of partial differential equations. The aim of the present book is to demontstrate the basic methods for solving the classical linear problems in mathematical physics of elliptic, parabolic and hyperbolic type. In particular, the methods of conformal mappings, Fourier analysis and Green`s functions are considered, as well as the perturbation method and integral transformation method, among others. Every chapter contains concrete examples with a detailed analysis of their solution.The book is intended as a textbook for students in mathematical physics, but will also serve as a handbook for scientists and engineers.

The book contains reproductions of the most important papers that gave birth to the first developments in nonlinear programming. The anthology includes an extensive preliminary chapter, where the editors trace out the history of mathematical programming, with special reference to linear and nonlinear programming.

The focus of this book and its geometric notions is on real vector spaces X that are finite or infinite inner product spaces of arbitrary dimension greater than or equal to 2. It characterizes both euclidean and hyperbolic geometry with respect to natural properties of (general) translations and general distances of X. Also for these spaces X, it studies the sphere geometries of Mobius and Lie as well as geometries where Lorentz transformations play the key role.Proofs of newer theorems characterizing isometries and Lorentz transformations under mild hypotheses are included, such as for instance infinite dimensional versions of famous theorems of A.D. Alexandrov on Lorentz transformations. A real benefit is the dimension-free approach to important geometrical theories. New to this third edition is a chapter dealing with a simple and great idea of Leibniz that allows us to characterize, for these same spaces X, hyperplanes of euclidean, hyperbolic geometry, or spherical geometry, the geometries of Lorentz-Minkowski and de Sitter, and this through finite or infinite dimensions greater than 1. Another new and fundamental result in this edition concerns the representation of hyperbolic motions, their form and their transformations. Further we show that the geometry (P,G) of segments based on X is isomorphic to the hyperbolic geometry over X. Here P collects all x in X of norm less than one, G is defined to be the group of bijections of P transforming segments of P onto segments.The only prerequisites for reading this book are basic linear algebra and basic 2- and 3-dimensional real geometry. This implies that mathematicians who have not so far been especially interested in geometry could study and understand some of the great ideas of classical geometries in modern and general contexts.

In dem vorliegenden Buch sind Methoden zur Bestimmung von Standorten und Einzugsbereichen zentraler Einrichtungen zusammengefaßt, um den in der Planungspraxis tätigen Stadt-, Regional- und Landesplanern eine handbuchartige Zusammenstellung über Methoden für die Standort­ bestimmung zur Verfügung zu stellen. Es sollen darüber hinaus dem wissenschaftlich orientierten Planer Ansatzpunkte für weitere For­ schungsarbeiten gezeigt werden. Das Buch ist die überarbeitete Fas­ sung meiner Dissertation, die der Abteilung Raumplanung, Universität Dortmund, im Mai 1976 vorgelegt wurde. Es ist während einer mehrjähri­ gen Lehr- und Forschungstätigkeit an der Abteilung Raumplanung, Universität Dortmund, entstanden und durch Diskussionen mit Kollegen und Studenten begleitet worden. Ihnen sei an dieser Stelle gedankt. Mein Dank gilt insbesondere Herrn Professor Dr.-Ing. H. Schoof, Frau Professor Dr.rer.nat. Dr.rer.pol. W. Rödding, Herrn Professor Dr.rer. nat. V. Kreibich, alle Universität Dortmund, Herrn Professor Dr.rer. nat. G. Frank, Universität Hagen sowie meinen Kollegen am Fachgebiet Stadt- und Regionalplanung der Abteilung Raumplanung, Herrn Dr.-Ing. M. Hauschild, Herrn Dr.rer.pol. R. Hoberg, Herrn Dipl.-Ing. c. Reetz und Herrn Lic.rer.reg. Dipl.-Kfm. D. Schiebold. Dortmund, im September 1977 Lüder Bach I N H A L S T U B E R S I C H T Seite Einleitung Teil I: Standortbestimmung für zentrale Einrichtungen im Rah­ men sektoraler räumlicher Entwicklungsplanungen Systeme zentraler Einrichtungen als Gegenstand raum­ 1.

The authors of this book analyse these instruments - green taxes, tradeable permits, covenants, joint implementation, internationally tradeable quotas - from the point of view of costeffectiveness, their ability to achieve environmental goals, and public and corporate acceptability.

This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis.

The main research theme explores how atomic agents that act locally and microscopically lead to discontinuous macroscopic changes. In turn, the book's second part is devoted to mathematical and computational methods applied to the pricing of financial contracts and the measurement of financial risks.

This book provides a unique frame work for examining acute lung syndromes that arise from hematologic disorders or is defined by a hematologic abnormality as a key feature.

Different communication protocols for MAS evolution, the robustness of tracking of a desired motion by an MAS evolving in n, and the effect of communication delays in an MAS evolving under consensus algorithms or homogeneous maps are also explored.

This book illustrates several aspects of the current research activity in operator theory, operator algebras and applications in various areas of mathematics and mathematical physics.

It provides a valuable resource to pediatricians and pediatric urologists facing urological management issues beyond their expertise in their aging patients as well as technical guidance to adult urologists who may have had little or no experience caring for patients with a congenital condition.

It helps students in preparing for national and international mathematical contests form high school level to more advanced competitions and will also be useful for their first year of mathematical studies at the university.

Many arthropods use celestial (skylight) and terrestrial (magnetic) compass cues for orientation, and some of them were shown to develop, through experience, oriented behaviours based on a variety of innate, hard-wired orientation mechanisms.

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.

To date, the theoretical development of q-calculus has rested on a non-uniform basis. Generally, the bulky Gasper-Rahman notation was used, but the published works on q-calculus looked different depending on where and by whom they were written. This confusion of tongues not only complicated the theoretical development but also contributed to q-calculus remaining a neglected mathematical field. This book overcomes these problems by introducing a new and interesting notation for q-calculus based on logarithms.For instance, q-hypergeometric functions are now visually clear and easy to trace back to their hypergeometric parents. With this new notation it is also easy to see the connection between q-hypergeometric functions and the q-gamma function, something that until now has been overlooked.The book covers many topics on q-calculus, including special functions, combinatorics, and q-difference equations. Apart from a thorough review of the historical development of q-calculus, this book also presents the domains of modern physics for which q-calculus is applicable, such as particle physics and supersymmetry, to name just a few.

This is an outgrowth of the session by the same name which took place during the eighth international, interdisciplinary conference "Nexus 2010: Relationships between Architecture and Mathematics, held in Porto, Portugal, in June 2010.

Letter From The Editor.- Letter From The Editor.- Architecture, Mathematics and Perspective.- Giotto and Renaissance Perspective.- Perspective, a Visionary Process: The Main Generative Road for Crossing Dimensions.- Perspective in a box.- Juan Bautista Villalpando and the Nature and Science of Architectural Drawing.- Perspective versus Stereotomy: From Quattrocento Polyhedral Rings to Sixteenth-Century Spanish Torus Vaults.- The Sunlight Effect of the Kukulc¿Pyramid or The History of a Line.- Some Adaptations of Relativity in the 1920s and the Birth of Abstract Architecture.- Book Reviews.- The Mirror, the Window, and the Telescope: How Renaissance Linear Perspective Changed Our Vision of the Universe.- The Geometry of an Art. The History of Perspective from Alberti to Monge.- Forma y Representaci¿n. Un An¿sis Geom¿ico.

Letter from the Editor.- Letter from the Editor.- Recalling Eero Saarinen 1910-2010.- How the Gateway Arch Got its Shape.- Saarinen's Shell Game: Tensions, Structures, and Sounds at MIT.- The Next Largest Thing: The Spatial Dimensions of Liturgy in Eliel and Eero Saarinen's Christ Church Lutheran, Minneapolis.- Morphocontinuity in the work of Eero Saarinen.- Eero Saarinen, Eduardo Catalano and the Influence of Matthew Nowicki: A Challenge to Form and Function.- Eero Saarinen's North Christian Church in Columbus, Indiana.- Other Research.- On the Modular Design of Mughal Riverfront Funerary Gardens.- Discontinuous Double-shell Domes through Islamic eras in the Middle East and Central Asia: History, Morphology, Typologies, Geometry, and Construction.- At the Other End of the Sun's Path: A New Interpretation of Machu Picchu.- The Body, the Temple and the Newtonian Man Conundrum.- Book Review.- The Symbol at Your Door: Number and Geometry in Religious Architecture of the Greek and Latin Middle Ages.- Conference Report.- Architecture and Mathematics. A seminar to celebrate Professor emeritus Staale Sinding-Larsen's 80th birthday.- Erratum.- Erratum to: The Sunlight Effect of the Kukulcán Pyramid or The History of a Line.