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Author: Markus Banagl Publisher: Springer ISBN: 3642125891 Category : Mathematics Languages : en Pages : 237
Book Description
Intersection cohomology assigns groups which satisfy a generalized form of Poincaré duality over the rationals to a stratified singular space. This monograph introduces a method that assigns to certain classes of stratified spaces cell complexes, called intersection spaces, whose ordinary rational homology satisfies generalized Poincaré duality. The cornerstone of the method is a process of spatial homology truncation, whose functoriality properties are analyzed in detail. The material on truncation is autonomous and may be of independent interest tohomotopy theorists. The cohomology of intersection spaces is not isomorphic to intersection cohomology and possesses algebraic features such as perversity-internal cup-products and cohomology operations that are not generally available for intersection cohomology. A mirror-symmetric interpretation, as well as applications to string theory concerning massless D-branes arising in type IIB theory during a Calabi-Yau conifold transition, are discussed.
Author: Markus Banagl Publisher: Springer ISBN: 3642125891 Category : Mathematics Languages : en Pages : 237
Book Description
Intersection cohomology assigns groups which satisfy a generalized form of Poincaré duality over the rationals to a stratified singular space. This monograph introduces a method that assigns to certain classes of stratified spaces cell complexes, called intersection spaces, whose ordinary rational homology satisfies generalized Poincaré duality. The cornerstone of the method is a process of spatial homology truncation, whose functoriality properties are analyzed in detail. The material on truncation is autonomous and may be of independent interest tohomotopy theorists. The cohomology of intersection spaces is not isomorphic to intersection cohomology and possesses algebraic features such as perversity-internal cup-products and cohomology operations that are not generally available for intersection cohomology. A mirror-symmetric interpretation, as well as applications to string theory concerning massless D-branes arising in type IIB theory during a Calabi-Yau conifold transition, are discussed.
Author: John Michael Rassias Publisher: World Scientific ISBN: 9814506052 Category : Mathematics Languages : en Pages : 340
Book Description
This book consists of papers written by outstanding mathematicians. It deals with both theoretical and applied aspects of the mathematical contributions of BANACH, ULAM, and OSTROWSKI, which broaden the horizons of Functional Analysis, Approximation Theory, and Numerical Analysis in accordance with contemporary mathematical standards.
Author: Jussi Behrndt Publisher: Springer Science & Business Media ISBN: 3764389117 Category : Mathematics Languages : en Pages : 261
Book Description
Contains a collection of research papers originating from the 6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, which was held at the TU Berlin, Germany, December 14 to 17. This work discusses topics such as linear relations, singular perturbations, de Branges spaces, nonnegative matrices, and abstract kinetic equations.
Author: Nick Wilson Publisher: Routledge ISBN: 1317432177 Category : Philosophy Languages : en Pages : 222
Book Description
The Space that Separates: A Realist Theory of Art radically challenges our assumptions about what art is, what art does, who is doing it, and why it matters. Rejecting the modernist and market-driven misconception that art is only what artists do, Wilson instead presents a realist case for living artfully. Art is defined as the skilled practice of giving shareable form to our experiences of being-in-relation with the real; that is to say, the causally generative domain of the world that extends beyond our direct observation, comprising relations, structures, mechanisms, possibilities, powers, processes, systems, forces, values, ways of being. In communicating such aesthetic experience we behold life’s betweenness – "the space that separates", so coming to know ourselves as connected. Providing the first dedicated and comprehensive account of art and aesthetics from a critical realist perspective – Aesthetic Critical Realism (ACR), Wilson argues for a profound paradigm shift in how we understand and care for culture in terms of our system(s) of value recognition. Fortunately, we have just the right tool to help us achieve this transformation – and it’s called art. Offering novel explanatory accounts of art, aesthetic experience, value, play, culture, creativity, artistic truth and beauty, this book will appeal to a wide audience of students and scholars of art, aesthetics, human development, philosophy and critical realism, as well as cultural practitioners and policy-makers.
Author: Victoria Rimell Publisher: Cambridge University Press ISBN: 1316368602 Category : Literary Collections Languages : en Pages : 371
Book Description
This ambitious book investigates a major yet underexplored nexus of themes in Roman cultural history: the evolving tropes of enclosure, retreat and compressed space within an expanding, potentially borderless empire. In Roman writers' exploration of real and symbolic enclosures - caves, corners, villas, bathhouses, the 'prison' of the human body itself - we see the aesthetic, philosophical and political intersecting in fascinating ways, as the machine of empire is recast in tighter and tighter shapes. Victoria Rimell brings ideas and methods from literary theory, cultural studies and philosophy to bear on an extraordinary range of ancient texts rarely studied in juxtaposition, from Horace's Odes, Virgil's Aeneid and Ovid's Ibis, to Seneca's Letters, Statius' Achilleid and Tacitus' Annals. A series of epilogues puts these texts in conceptual dialogue with our own contemporary art world, and emphasizes the role Rome's imagination has played in the history of Western thinking about space, security and dwelling.
Author: Asao Arai Publisher: World Scientific ISBN: 9811288453 Category : Mathematics Languages : en Pages : 1115
Book Description
This book provides a comprehensive introduction to Fock space theory and its applications to mathematical quantum field theory. The first half of the book, Part I, is devoted to detailed descriptions of analysis on abstract Fock spaces (full Fock space, boson Fock space, fermion Fock space and boson-fermion Fock space). It includes the mathematics of second quantization, representation theory of canonical commutation and anti-commutation relations, Bogoliubov transformations, infinite-dimensional Dirac operators and supersymmetric quantum field in an abstract form. The second half of the book, Part II, covers applications of the mathematical theories in Part I to quantum field theory. Four kinds of free quantum fields are constructed and detailed analyses are made. A simple interacting quantum field model, called the van Hove-Miyatake model, is fully analyzed in an abstract form. Moreover, a list of interacting quantum field models is presented and an introductory description to each model is given. In this second edition, a new chapter (Chapter 15) is added to describe a mathematical theory of spontaneous symmetry breaking which is an important subject in modern quantum physics.This book is a good introductory text for graduate students in mathematics or physics who are interested in the mathematical aspects of quantum field theory. It is also well-suited for self-study, providing readers a firm foundation of knowledge and mathematical techniques for more advanced books and current research articles in the field of mathematical analysis on quantum fields. Numerous problems are added to aid readers in developing a deeper understanding of the field.
Author: J. Frölich Publisher: Springer Science & Business Media ISBN: 1461534720 Category : Science Languages : en Pages : 528
Book Description
Soon after the discovery of quantum mechanics, group theoretical methods were used extensively in order to exploit rotational symmetry and classify atomic spectra. And until recently it was thought that symmetries in quantum mechanics should be groups. But it is not so. There are more general algebras, equipped with suitable structure, which admit a perfectly conventional interpretation as a symmetry of a quantum mechanical system. In any case, a "trivial representation" of the algebra is defined, and a tensor product of representations. But in contrast with groups, this tensor product needs to be neither commutative nor associative. Quantum groups are special cases, in which associativity is preserved. The exploitation of such "Quantum Symmetries" was a central theme at the Ad vanced Study Institute. Introductory lectures were presented to familiarize the participants with the al gebras which can appear as symmetries and with their properties. Some models of local field theories were discussed in detail which have some such symmetries, in par ticular conformal field theories and their perturbations. Lattice models provide many examples of quantum theories with quantum symmetries. They were also covered at the school. Finally, the symmetries which are the cause of the solubility of inte grable models are also quantum symmetries of this kind. Some such models and their nonlocal conserved currents were discussed.
Author: Laura Berchielli Publisher: Springer Nature ISBN: 3030576205 Category : Science Languages : en Pages : 223
Book Description
This book explores the notions of space and extension of major early modern empiricist philosophers, especially Locke, Berkeley, Hume, and Condillac. While space is a central and challenging issue for early modern empiricists, literature on this topic is sparse. This collection shows the diversity and problematic unity of empiricist views of space. Despite their common attention to the content of sensorial experience and to the analytical method, empiricist theories of space vary widely both in the way of approaching the issue and in the result of their investigation. However, by recasting the questions and examining the conceptual shifts, we see the emergence of a programmatic core, common to what the authors discuss. The introductory chapter describes this variety and its common core. The other contributions provide more specific perspectives on the issue of space within the philosophical literature. This book offers a unique overview of the early modern understanding of these issues, of interest to historians of early modern philosophy, historians and philosophers of science, historians of ideas, and all readers who want to expand their knowledge of the empiricist tradition.
Author: Markus Banagl
Author: Markus Banagl
Author: John Michael Rassias
Author: Jussi Behrndt
Author: Lev D. Beklemishev
Author: Nick Wilson
Author: Victoria Rimell
Author: Asao Arai
Author: Emmanuel Fricain
Author: J. Frölich
Author: Laura Berchielli