Download or read book C infinity Differentiable Spaces written by Juan A. Navarro González and published by Springer. This book was released on 2003-12-09 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume develops the foundations of differential geometry so as to include finite-dimensional spaces with singularities and nilpotent functions, at the same level as is standard in the elementary theory of schemes and analytic spaces. The theory of differentiable spaces is developed to the point of providing a handy tool including arbitrary base changes (hence fibred products, intersections and fibres of morphisms), infinitesimal neighbourhoods, sheaves of relative differentials, quotients by actions of compact Lie groups and a theory of sheaves of Fréchet modules paralleling the useful theory of quasi-coherent sheaves on schemes. These notes fit naturally in the theory of C^\infinity-rings and C^\infinity-schemes, as well as in the framework of Spallek’s C^\infinity-standard differentiable spaces, and they require a certain familiarity with commutative algebra, sheaf theory, rings of differentiable functions and Fréchet spaces.
Download or read book C infinity Differentiable Spaces written by Juan A. Navarro González and published by Springer Science & Business Media. This book was released on 2003-10-29 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume develops the foundations of differential geometry so as to include finite-dimensional spaces with singularities and nilpotent functions, at the same level as is standard in the elementary theory of schemes and analytic spaces. The theory of differentiable spaces is developed to the point of providing a handy tool including arbitrary base changes (hence fibred products, intersections and fibres of morphisms), infinitesimal neighbourhoods, sheaves of relative differentials, quotients by actions of compact Lie groups and a theory of sheaves of Fréchet modules paralleling the useful theory of quasi-coherent sheaves on schemes. These notes fit naturally in the theory of C^\infinity-rings and C^\infinity-schemes, as well as in the framework of Spallek’s C^\infinity-standard differentiable spaces, and they require a certain familiarity with commutative algebra, sheaf theory, rings of differentiable functions and Fréchet spaces.
Download or read book C Degrees Infinity Differentiable Spaces written by Juan a Navarro Gonzalez and published by . This book was released on 2014-01-15 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Geometry over C Rings written by Dominic Joyce and published by American Mathematical Soc.. This book was released on 2019-09-05 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: If X is a manifold then the R-algebra C∞(X) of smooth functions c:X→R is a C∞-ring. That is, for each smooth function f:Rn→R there is an n-fold operation Φf:C∞(X)n→C∞(X) acting by Φf:(c1,…,cn)↦f(c1,…,cn), and these operations Φf satisfy many natural identities. Thus, C∞(X) actually has a far richer structure than the obvious R-algebra structure. The author explains the foundations of a version of algebraic geometry in which rings or algebras are replaced by C∞-rings. As schemes are the basic objects in algebraic geometry, the new basic objects are C∞-schemes, a category of geometric objects which generalize manifolds and whose morphisms generalize smooth maps. The author also studies quasicoherent sheaves on C∞-schemes, and C∞-stacks, in particular Deligne-Mumford C∞-stacks, a 2-category of geometric objects generalizing orbifolds. Many of these ideas are not new: C∞-rings and C∞ -schemes have long been part of synthetic differential geometry. But the author develops them in new directions. In earlier publications, the author used these tools to define d-manifolds and d-orbifolds, “derived” versions of manifolds and orbifolds related to Spivak's “derived manifolds”.
Download or read book Stochastic Partial Differential Equations with L vy Noise written by S. Peszat and published by Cambridge University Press. This book was released on 2007-10-11 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive monograph by two leading international experts; includes applications to statistical and fluid mechanics and to finance.
Download or read book Partial Differential Equations written by András Vasy and published by American Mathematical Society. This book was released on 2022-07-15 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on partial differential equations is intended for readers who want to understand the theoretical underpinnings of modern PDEs in settings that are important for the applications without using extensive analytic tools required by most advanced texts. The assumed mathematical background is at the level of multivariable calculus and basic metric space material, but the latter is recalled as relevant as the text progresses. The key goal of this book is to be mathematically complete without overwhelming the reader, and to develop PDE theory in a manner that reflects how researchers would think about the material. A concrete example is that distribution theory and the concept of weak solutions are introduced early because while these ideas take some time for the students to get used to, they are fundamentally easy and, on the other hand, play a central role in the field. Then, Hilbert spaces that are quite important in the later development are introduced via completions which give essentially all the features one wants without the overhead of measure theory. There is additional material provided for readers who would like to learn more than the core material, and there are numerous exercises to help solidify one's understanding. The text should be suitable for advanced undergraduates or for beginning graduate students including those in engineering or the sciences.
Download or read book High Accuracy Algorithm For The Differential Equations Governing Anomalous Diffusion Algorithm And Models For Anomalous Diffusion written by Weihua Deng and published by World Scientific. This book was released on 2019-01-22 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to extend the application field of 'anomalous diffusion', and describe the newly built models and the simulation techniques to the models.The book first introduces 'anomalous diffusion' from the statistical physics point of view, then discusses the models characterizing anomalous diffusion and its applications, including the Fokker-Planck equation, the Feymann-Kac equations describing the functional distribution of the anomalous trajectories of the particles, and also the microscopic model — Langevin type equation. The second main part focuses on providing the high accuracy schemes for these kinds of models, and the corresponding convergence and stability analysis.
Download or read book Fundamentals of the Theory of Structured Dependence between Stochastic Processes written by Tomasz R. Bielecki and published by Cambridge University Press. This book was released on 2020-08-27 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive presentation of the technical aspects and applications of the theory of structured dependence between random processes.
Download or read book Smooth Manifolds and Observables written by Jet Nestruev and published by Springer Nature. This book was released on 2020-09-10 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to fiber spaces and differential operators on smooth manifolds. Over the last 20 years, the authors developed an algebraic approach to the subject and they explain in this book why differential calculus on manifolds can be considered as an aspect of commutative algebra. This new approach is based on the fundamental notion of observable which is used by physicists and will further the understanding of the mathematics underlying quantum field theory.
Download or read book Probability on Compact Lie Groups written by David Applebaum and published by Springer. This book was released on 2014-06-26 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability theory on compact Lie groups deals with the interaction between “chance” and “symmetry,” a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topics presented are: the study of measures via the non-commutative Fourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures and the statistical problem of deconvolution. The emphasis on compact (rather than general) Lie groups helps readers to get acquainted with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance of these groups for applications. The book is primarily aimed at researchers working in probability, stochastic analysis and harmonic analysis on groups. It will also be of interest to mathematicians working in Lie theory and physicists, statisticians and engineers who are working on related applications. A background in first year graduate level measure theoretic probability and functional analysis is essential; a background in Lie groups and representation theory is certainly helpful but the first two chapters also offer orientation in these subjects.
Download or read book Selected Topics in Almost Periodicity written by Marko Kostić and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-11-22 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers uniformly recurrent solutions and c-almost periodic solutions of abstract Volterra integro-differential equations as well as various generalizations of almost periodic functions in Lebesgue spaces with variable coefficients. Treats multi-dimensional almost periodic type functions and their generalizations in adequate detail.
Download or read book Photons In Fock Space And Beyond In 3 Volumes written by Reinhard Honegger and published by World Scientific. This book was released on 2015-04-22 with total page 2353 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three-volume major reference “Photons in Fock Space and Beyond” undertakes a new mathematical and conceptual foundation of the theory of light emphasizing mesoscopic radiation systems. The quantum optical notions are generalized beyond Fock representations where the richness of an infinite dimensional quantum field system, with its mathematical difficulties and theoretical possibilities, is fully taken into account. It aims at a microscopic formulation of a mesoscopic model class which covers in principle all stages of the generation and propagation of light within a unified and well-defined conceptual frame.The dynamics of the interacting systems is founded — according to original works of the authors — on convergent perturbation series and describes the developments of the quantized microscopic as well as the classical collective degrees of freedom at the same time. The achieved theoretical unification fits especially to laser and microwave applications inheriting objective information over quantum noise.A special advancement is the incorporation of arbitrary multiply connected cavities where ideal conductor boundary conditions are imposed. From there arises a new category of classical and quantized field parts, apparently not treated in Quantum Electrodynamics before. In combination with gauge theory, the additional “cohomological fields” explain topological quantum effects in superconductivity. Further applications are to be expected for optoelectronic and optomechanical systems.
Download or read book Distribution Theory Applied to Differential Equations written by Adina Chirilă and published by Springer Nature. This book was released on 2021-02-08 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents important contributions to modern theories concerning the distribution theory applied to convex analysis (convex functions, functions of lower semicontinuity, the subdifferential of a convex function). The authors prove several basic results in distribution theory and present ordinary differential equations and partial differential equations by providing generalized solutions. In addition, the book deals with Sobolev spaces, which presents aspects related to variation problems, such as the Stokes system, the elasticity system and the plate equation. The authors also include approximate formulations of variation problems, such as the Galerkin method or the finite element method. The book is accessible to all scientists, and it is especially useful for those who use mathematics to solve engineering and physics problems. The authors have avoided concepts and results contained in other books in order to keep the book comprehensive. Furthermore, they do not present concrete simplified models and pay maximal attention to scientific rigor.
Download or read book C infinity Differentiable Spaces written by Juan A. Navarro González and published by Springer. This book was released on 2003-10-29 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume develops the foundations of differential geometry so as to include finite-dimensional spaces with singularities and nilpotent functions, at the same level as is standard in the elementary theory of schemes and analytic spaces. The theory of differentiable spaces is developed to the point of providing a handy tool including arbitrary base changes (hence fibred products, intersections and fibres of morphisms), infinitesimal neighbourhoods, sheaves of relative differentials, quotients by actions of compact Lie groups and a theory of sheaves of Fréchet modules paralleling the useful theory of quasi-coherent sheaves on schemes. These notes fit naturally in the theory of C^\infinity-rings and C^\infinity-schemes, as well as in the framework of Spallek’s C^\infinity-standard differentiable spaces, and they require a certain familiarity with commutative algebra, sheaf theory, rings of differentiable functions and Fréchet spaces.
Download or read book Topological Vector Spaces and Distributions written by John Horvath and published by Courier Corporation. This book was released on 2013-10-03 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Precise exposition provides an excellent summary of the modern theory of locally convex spaces and develops the theory of distributions in terms of convolutions, tensor products, and Fourier transforms. 1966 edition.
Download or read book Spaces of Fundamental and Generalized Functions written by I. M. Gel'Fand and published by Academic Press. This book was released on 2013-09-03 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spaces of Fundamental and Generalized Functions, Volume 2, analyzes the general theory of linear topological spaces. The basis of the theory of generalized functions is the theory of the so-called countably normed spaces (with compatible norms), their unions (inductive limits), and also of the spaces conjugate to the countably normed ones or their unions. This set of spaces is sufficiently broad on the one hand, and sufficiently convenient for the analyst on the other. The book opens with a chapter that discusses the theory of these spaces. This is followed by separate chapters on fundamental and generalized functions, Fourier transformations of fundamental and generalized functions, and spaces of type S.
Download or read book Measure Theory and Fine Properties of Functions Revised Edition written by Lawrence Craig Evans and published by CRC Press. This book was released on 2015-04-17 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. The book covers theorems and differentiation in Rn , Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions and functions of bounded variation. This second edition includes countless improvements in notation, format, and clarity of exposition. Also new are several sections describing the p- theorem, weak compactness criteria in L1, and Young measure methods for weak convergence. In addition, the bibliography has been updated.
