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A. A. Bondarenko 《Mathematical Notes》2009,85(5-6):638-646
Let f(X) and g(Y) be nondegenerate quadratic forms of dimensions m and n, respectively, over K, char K ≠ 2. The problem of birational composition of f(X) and g(Y) is considered: When is the product f(X) · g(Y) birationally equivalent over K to a quadratic form h(Z) over K of dimension m + n? The solution of the birational composition problem for anisotropic quadratic forms over K in the case of m = n = 2 is given. The main result of the paper is the complete solution of the birational composition problem for forms f(X) and g(Y) over a local field P, char P ≠ 2. 相似文献
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We prove that any Lie algebra g over a field K of characteristic zero admitting a unique up to a constant quadratic structure is necessarily a simple Lie algebra. If the field K is algebraically closed, such condition is also sufficient. Further, a real Lie algebra g admits a unique quadratic structure if and only if its complexification gC is a simple Lie algebra over C 相似文献
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The paper is devoted to recovering the coefficients of a pair of Hermitian quadratic forms c(x, x) and (x, x) in a special
basis, in which the matrix of the form c(x, x) is tridiagonal and the matrix of the form m(x, x) is diagonal. The form c(x,
x) is positive definite, and the form m(x, x) is nondegenerate, but is not positive difinite in contrast with a well-known
case. The data of the inverse problem include the spectrum λ1...,λn of the bundle IIλ and the set of numbers ρ1...,ρn connected with the main normalized elements of the bundle. A procedure for solving the inverse problem is described. The
characteristic conditions for λ1...,λn; are found that provide its solution. Bibliography: 5 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 186, pp. 33–36, 1990.
Translated by T. N. Surkova. 相似文献
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This note presents an algorithm which composes two reduced properly primitive binary quadratic forms of the same nonquadratic determinant D in O(M(log∥D∥)log log∥D∥) elementary operations. 相似文献
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Hiromu Tanaka 《代数通讯》2019,47(2):482-489
In this note, we prove that there exist infinite dimensional excellent rings. 相似文献
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《Stochastic Processes and their Applications》2020,130(12):7131-7169
The goal of this article is to investigate infinite dimensional affine diffusion processes on the canonical state space. This includes a derivation of the corresponding system of Riccati differential equations and an existence proof for such processes, which has been missing in the literature so far. For the existence proof, we will regard affine processes as solutions to infinite dimensional stochastic differential equations with values in Hilbert spaces. This requires a suitable version of the Yamada–Watanabe theorem, which we will provide in this paper. Several examples of infinite dimensional affine processes accompany our results. 相似文献
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Svetozar Kurepa 《Aequationes Mathematicae》1987,34(2-3):125-138
The present paper is related to the Jordan—von Neumann characterization of inner product spaces, to the Halperin problem concerning quadratic forms, to some results of the present author on quadratic and sesquilinear forms and to recently obtained results of C. T. Ng and of J. Vukman.Dedicated to Professor Otto Haupt with best wishes on his 100th birthday. 相似文献
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In this article, we construct some infinite analogues of the Fisher flocks. We also consider maximal partial flocks which may be constructed in several ways. In particular, we show that any derivation of a flock inPG(3,K), forK a full field, produces either a flock or a maximal partial flock. We provide constructions which produce maximal partial flocks or maximal partial spreads.In memoriam, Giuseppe TalliniThis article was written while the authors were visiting the Ricco Institute during June of 1994 and was partially supported by Glasgow-Caledonian University. Also, the authors are indebted to Christian Boltanski,D — S, in the writing of this article.The authors also are indebted to the referee for helpful suggestions with regard to this article. 相似文献
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We investigate the non-diagonal normal forms of a quadratic form on , in particular for n = 3. For this case it is shown that the set of normal forms is the closure of a 5-dimensional submanifold in the 6-dimensional
Grassmannian of 2-dimensional subspaces of .
Received: 27 June 2008 相似文献
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Infinite dimensional duality and applications 总被引:2,自引:0,他引:2
Patrizia Daniele Sofia Giuffrè Giovanna Idone Antonino Maugeri 《Mathematische Annalen》2007,339(1):221-239
The usual duality theory cannot be applied to infinite dimensional problems because the underlying constraint set mostly has
an empty interior and the constraints are possibly nonlinear. In this paper we present an infinite dimensional nonlinear duality
theory obtained by using new separation theorems based on the notion of quasi-relative interior, which, in all the concrete
problems considered, is nonempty. We apply this theory to solve the until now unsolved problem of finding, in the infinite
dimensional case, the Lagrange multipliers associated to optimization problems or to variational inequalities. As an example,
we find the Lagrange multiplier associated to a general elastic–plastic torsion problem. 相似文献
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