Generalized Mercer Kernels and Reproducing Kernel Banach Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Generalized Mercer Kernels and Reproducing Kernel Banach Spaces write by Yuesheng Xu. This book was released on 2019-04-10. Generalized Mercer Kernels and Reproducing Kernel Banach Spaces available in PDF, EPUB and Kindle. This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that machine learning in RKBSs can be well-posed and of easy implementation. First the authors verify many advanced properties of the general RKBSs such as density, continuity, separability, implicit representation, imbedding, compactness, representer theorem for learning methods, oracle inequality, and universal approximation. Then, they develop a new concept of generalized Mercer kernels to construct p-norm RKBSs for 1≤p≤∞ .
Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan
Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan write by Josef Dick. This book was released on 2018-05-23. Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan available in PDF, EPUB and Kindle. This book is a tribute to Professor Ian Hugh Sloan on the occasion of his 80th birthday. It consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporary computational mathematics. These papers highlight the impact and many achievements of Professor Sloan in his distinguished academic career. The book also presents state of the art knowledge in many computational fields such as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi-level methods, finite element methods, uncertainty quantification, spherical designs and integration on the sphere, approximation and interpolation of multivariate functions, oscillatory integrals, and in general in information-based complexity and tractability, as well as in a range of other topics. The book also tells the life story of the renowned mathematician, family man, colleague and friend, who has been an inspiration to many of us. The reader may especially enjoy the story from the perspective of his family, his wife, his daughter and son, as well as grandchildren, who share their views of Ian. The clear message of the book is that Ian H. Sloan has been a role model in science and life.
Compact Quotients of Cahen-Wallach Spaces
Compact Quotients of Cahen-Wallach Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Compact Quotients of Cahen-Wallach Spaces write by Ines Kath. This book was released on 2020-02-13. Compact Quotients of Cahen-Wallach Spaces available in PDF, EPUB and Kindle. Indecomposable symmetric Lorentzian manifolds of non-constant curvature are called Cahen-Wallach spaces. Their isometry classes are described by continuous families of real parameters. The authors derive necessary and sufficient conditions for the existence of compact quotients of Cahen-Wallach spaces in terms of these parameters.
Algebraic Geometry over C∞-Rings
Algebraic Geometry over C∞-Rings - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Geometry over C∞-Rings write by Dominic Joyce. This book was released on 2019-09-05. Algebraic Geometry over C∞-Rings available in PDF, EPUB and Kindle. 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”.
On the Stability of Type I Blow Up for the Energy Super Critical Heat Equation
On the Stability of Type I Blow Up for the Energy Super Critical Heat Equation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On the Stability of Type I Blow Up for the Energy Super Critical Heat Equation write by Charles Collot. This book was released on 2019-09-05. On the Stability of Type I Blow Up for the Energy Super Critical Heat Equation available in PDF, EPUB and Kindle. The authors consider the energy super critical semilinear heat equation The authors first revisit the construction of radially symmetric self similar solutions performed through an ode approach and propose a bifurcation type argument which allows for a sharp control of the spectrum of the corresponding linearized operator in suitable weighted spaces. They then show how the sole knowledge of this spectral gap in weighted spaces implies the finite codimensional nonradial stability of these solutions for smooth well localized initial data using energy bounds. The whole scheme draws a route map for the derivation of the existence and stability of self-similar blow up in nonradial energy super critical settings.
