This is the first of two volumes dedicated to the centennial of the distinguished mathematician Selim Grigorievich Krein. The companion volume is Contemporary Mathematics, Volume 734.Krein was a ...major contributor to functional analysis, operator theory, partial differential equations, fluid dynamics, and other areas, and the author of several influential monographs in these areas. He was a prolific teacher, graduating 83 Ph.D. students. Krein also created and ran, for many years, the annual Voronezh Winter Mathematical Schools, which significantly influenced mathematical life in the former Soviet Union.The articles contained in this volume are written by prominent mathematicians, former students and colleagues of Selim Krein, as well as lecturers and participants of Voronezh Winter Schools. They are devoted to a variety of contemporary problems in functional analysis, operator theory, several complex variables, topological dynamics, and algebraic, convex, and integral geometry.
This volume contains the proceedings of the 10th International Congress on Finite Fields and their Applications (Fq 10), held July 11-15, 2011, in Ghent, Belgium. Research on finite fields and their ...practical applications continues to flourish. This volume's topics, which include finite geometry, finite semifields, bent functions, polynomial theory, designs, and function fields, show the variety of research in this area and prove the tremendous importance of finite field theory.
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a ...major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
If X is a manifold then the \mathbb R-algebra C^\infty (X) of smooth functions c:X\rightarrow \mathbb R is a C^\infty -ring. That is, for each smooth function f:\mathbb R^n\rightarrow \mathbb R there ...is an n-fold operation \Phi _f:C^\infty (X)^n\rightarrow C^\infty (X) acting by \Phi _f:(c_1,\ldots ,c_n)\mapsto f(c_1,\ldots ,c_n), and these operations \Phi _f satisfy many natural identities. Thus, C^\infty (X) actually has a far richer structure than the obvious \mathbb R-algebra structure. The author explains the foundations of a version of algebraic geometry in which rings or algebras are replaced by C^\infty -rings. As schemes are the basic objects in algebraic geometry, the new basic objects are C^\infty -schemes, a category of geometric objects which generalize manifolds and whose morphisms generalize smooth maps. The author also studies quasicoherent sheaves on C^\infty -schemes, and C^\infty -stacks, in particular Deligne-Mumford C^\infty-stacks, a 2-category of geometric objects generalizing orbifolds. Many of these ideas are not new: C^\infty-rings and C^\infty -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".
In this paper, we classified the paracontact metric κ,μ-manifold satisfying the Miao-Tam critical equation with κ>−1. We proved that it is locally isometric to the product of a flat n+1-dimensional ...manifold and an n-dimensional manifold of negative constant curvature −4.
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