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11.
In this paper we develop a general theory for the Ribaucour transformation of sub-manifolds. In the process, a beautiful correspondence between Ribaucour transforms of a submanifold and Codazzi tensors that commute with its second fundamental form is revealed. 相似文献
12.
Ruy Exel 《K-Theory》1993,7(3):285-308
GivenC*-algebrasA andB and an imprimitivityA-B-bimoduleX, we construct an explicit isomorphismX
*:K
i
(A)K
i
(B), whereK
i
denotes the complexK-theory functors fori=0, 1. Our techniques do not require separability nor the existence of countable approximate identities. We thus extend to generalC*-algebras the result of Brown, Green, and Rieffel according to which, strongly Morita equivalentC*-algebras have isomorphicK-groups. The method employed includes a study of Fredholm operators on Hilbert modules.On leave from the University of São Paulo, Brazil. 相似文献
13.
14.
15.
We obtain a reduction of the vectorial Ribaucour transformation that preserves the class of submanifolds of constant sectional curvature of space forms, which we call the L-transformation. It allows to construct a family of such submanifolds starting with a given one and a vector-valued solution of a system of linear partial differential equations. We prove a decomposition theorem for the L-transformation, which is a far-reaching generalization of the classical permutability formula for the Ribaucour transformation of surfaces of constant curvature in Euclidean three space. As a consequence, we derive a Bianchi-cube theorem, which allows to produce, from k initial scalar L-transforms of a given submanifold of constant curvature, a whole k-dimensional cube all of whose remaining \(2^k-(k+1)\) vertices are submanifolds with the same constant sectional curvature given by explicit algebraic formulae. We also obtain further reductions, as well as corresponding decomposition and Bianchi-cube theorems, for the classes of n-dimensional flat Lagrangian submanifolds of \({\mathbb {C}}^n\) and n-dimensional Lagrangian submanifolds with constant curvature c of the complex projective space \({\mathbb {C}}{\mathbb {P}}^n(4c)\) or the complex hyperbolic space \({\mathbb {C}}{\mathbb {H}}^n(4c)\) of complex dimension n and constant holomorphic curvature 4c. 相似文献
16.
17.
Dividing chains have been used as conditions to isolate adequate subclasses of simple theories. In the first part of this
paper we present an introduction to the area. We give an overview on fundamental notions and present proofs of some of the
basic and well-known facts related to dividing chains in simple theories. In the second part we discuss various characterizations
of the subclass of low theories. Our main theorem generalizes and slightly extends a well-known fact about the connection
between dividing chains and Morley sequences (in our case: independent sequences). Moreover, we are able to give a proof that
is shorter than the original one. This result motivates us to introduce a special property of formulas concerning independent
dividing chains: For any dividing chain there exists an independent dividing chain of the same length. We study this property
in the context of low, short and ω -categorical simple theories, outline some examples and define subclasses of low and short theories, which imply this property.
The results give rise to further studies of the relationships between some subclasses of simple theories.
Research supported by CNPq grant 150309/2003-1.
Research supported by CNPq grant 304365/2003-3 (Modelos, Provas e Algoritmos) 相似文献
18.
Jorge L. Arocha Imre Bárány Javier Bracho Ruy Fabila Luis Montejano 《Discrete and Computational Geometry》2009,42(2):142-154
We prove several colorful generalizations of classical theorems in discrete geometry. Moreover, the colorful generalization
of Kirchberger’s theorem gives a generalization of the theorem of Tverberg on non-separated partitions. 相似文献
19.
A procedure for the use of the amino acid ratio on thin layer chromatography is described. Its use in developing countries is emphasized. The advantages of the amino acid ratio on thin layer chromatography versus paper chromatography are presented. 相似文献
20.
Given a zero-one matrix A we consider certain one-parameter groups of automorphisms of the Cuntz-Krieger algebra
, generalizing the usual gauge group, and depending on a positive continuous function H defined on the Markov space A. The main result consists of an application of Ruelles Perron-Frobenius Theorem to show that these automorphism groups admit a single KMS state.*Partially supported by CNPq. 相似文献