共查询到20条相似文献,搜索用时 15 毫秒
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姚裕丰 《数学年刊A辑(中文版)》2012,33(4):483-496
设L=H(2r;1)或K(2r+1;1)是定义在特征p>2的代数封闭域F上的限制Hamiltonian型或Contact型李代数.在对广义Jacobson-Witt代数及特殊代数不可约表示的研究基础上,通过定义L的如下阶化:L=L[q],I,其中I是{1,2,…,r}的子集,得到当p-特征函数χ是正则半单时,所有不可约Uχ(L)-模都是从不可约Uχ(L[O].I)-模诱导的. 相似文献
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Gr-Morita对偶与Morita对偶 总被引:1,自引:0,他引:1
设G为有单位元e的群R=(?)Rx和A=(?)Ax都是有单位元的G型强分次环,U=(?)Uz是分次(R,A)一双模.本文主要证明了RUA导出一个Gr—Morita对偶当且仅当ReU(eAc)导出一个Morita对偶. 相似文献
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A relation is described between Arnold's strange duality anda polar duality between the Newton polytopes which is mostlydue to M. Kobayashi. It is shown that this relation continuesto hold for the extension of Arnold's strange duality foundby C. T. C. Wall and the author. By a method of EhlersVarchenko,the characteristic polynomial of the monodromy of a hypersurfacesingularity can be computed from the Newton diagram. This methodis generalized to the isolated complete intersection singularitiesembraced in the extended duality. This is used to explain theduality of characteristic polynomials of the monodromy discoveredby K. Saito for Arnold's original strange duality and extendedby the author to the other cases. 相似文献
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Convergence and Duality 总被引:2,自引:0,他引:2
Roman Frič 《Applied Categorical Structures》2002,10(3):257-266
We describe dualities related to the foundations of probability theory in which sequential convergence and sequential continuity play an important role. 相似文献
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Elmor L. Peterson 《Annals of Operations Research》2001,105(1-4):109-153
Every formulation of mathematical programming duality (known to the author) for continuous finite-dimensional optimization can easily be viewed as a special case of at least one of the following three formulations: the geometric programming formulation (of the generalized geometric programming type), the parametric programming formulation (of the generalized Rockafellar-perturbation type), and the ordinary Lagrangian formulation (of the generalized Falk type). The relative strengths and weaknesses of these three duality formulations are described herein, as are the fundamental relations between them. As a theoretical application, the basic duality between Fenchel's hypothesis and the existence of recession directions in convex programming is established and then expressed within each of these three duality formulations 相似文献
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三角形Toeplize矩阵的三角本原指数 总被引:1,自引:0,他引:1
讨论了三角形 Toeplize矩阵与一元多项式的关系以及非负三角形 Toeplize矩阵的三角本原指数 ,证明了 n阶非负上三角 Toeplize矩阵的三角本原指数集 Sn={1 ,2 ,… ,k-1 ,k,k1,k2 ,… ,ks,n-1 },其中 k是满足 k >4n -3 -12 和 n -1k +1 =n -1k 的最小整数 . 相似文献
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Lyle Noakes 《Advances in Computational Mathematics》2006,25(1-3):195-209
Riemannian cubics are curves used for interpolation in Riemannian manifolds. Applications in trajectory planning for rigid bodiy motion emphasise
the group SO(3) of rotations of Euclidean 3-space. It is known that a Riemannian cubic in a Lie group G with bi-invariant Riemannian metric defines a Lie quadratic V in the Lie algebra, and satisfies a linking equation. Results of the present paper include explicit solutions of the linking equation by quadrature in terms of the Lie quadratic,
when G is SO(3) or SO(1,2). In some cases we are able to give examples where the Lie quadratic is also given in closed form. A basic
tool for constructing solutions is a new duality theorem. Duality is also used to study asymptotics of differential equations
of the form
, where β0,β1 are skew-symmetric 3×3 matrices, and x :ℝ→ SO(3). This is done by showing that the dual of β0+tβ1 is a null Lie quadratic. Then results on asymptotics of x follow from known properties of null Lie quadratics.
To Charles Micchelli, with warm greetings and deep respect, on his 60th birthday
Mathematics subject classifications (2000) 53A17, 53B20, 65D18, 68U05, 70E60. 相似文献
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M. B. Zvyagina 《Journal of Mathematical Sciences》2004,120(4):1591-1602
Let
be an associative ring with identity, and let
be the category of left unitary
-modules. A complete characterization of continuous additive co- and contravariant functors
is given. Such functors are either representable, or equivalent to a tensor product, or trivial ones. The class of categories that are dual to
and, therefore, are equivalent to the category of compact right
-modules is constructed by purely algebraic means. A canonical category is singled out in this class. A purely algebraic structure that is equivalent to the topology-algebraic structure of compact right
-modules is constructed. Algebraic analogs of connection and complete disconnection are given. Bibliography: 6 titles. 相似文献
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We describe a space of functions contained inxxLx
(D)C(D G) but not necessarily inU. We give a representation of these functions as bounded multiplication operators on the Bergman spacexxLx
a
2
and identify the subspace consisting of functions which induce compact multiplication operators. We also describe a newC
*-subalgebra ofxxLx
(D) which we conjecture to be a proper super-set ofU.Most of this research was done while the second author was visiting Cleveland State University. He would like to thank the Mathematics Department for its hospitality. He would also like to thank the NNSFC for partial support. 相似文献
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The paper studies the dual algebras of localization Roe algebrasover proper metric spaces and develops a localization versionof Paschke duality for K-homology. It is shown that the localizationK-homology groups are isomorphic to Kasparov's K-homology groupsfor the Rips complex of proper metric spaces with bounded geometry.It follows that the obstruction groups to the coarse BaumConnesconjecture can also be derived from the dual localization algebras. 相似文献
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R. I. Boţ S. M. Grad PhD Student G. Wanka 《Journal of Optimization Theory and Applications》2006,129(1):33-54
We present a new duality theory to treat convex optimization problems and we prove that the geometric duality used by Scott
and Jefferson in different papers during the last quarter of century is a special case of it. Moreover, weaker sufficient
conditions to achieve strong duality are considered and optimality conditions are derived. Next, we apply our approach to
some problems considered by Scott and Jefferson, determining their duals. We give weaker sufficient conditions to achieve
strong duality and the corresponding optimality conditions. Finally, posynomial geometric programming is viewed also as a
particular case of the duality approach that we present.
Communicated by V. F. Demyanov
The first author was supported in part by Gottlieb Daimler and Karl Benz Stiftung 02-48/99.
The second author was supported in part by Karl und Ruth Mayer Stiftung. 相似文献
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Pham Huu Tiep 《Mathematische Nachrichten》1997,184(1):313-327
The notion of globally irreducible representations of finite groups was introduced by B.H. Gross, in order to explain new series of Euclidean lattices discovered recently by N. Elkies and T. Shioda using Mordell–Weil lattices of elliptic curves. It has been observed by R. Gow and Gross that irreducible Weil representations of certain finite classical groups lead to globally irreducible representations. In this paper we classify all globally irreducible representations coming from Weil representations of finite classical groups. 相似文献
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We extend the Lagrangian duality theory for convex optimization problems to incorporate approximate solutions. In particular,
we generalize well-known relationships between minimizers of a convex optimization problem, maximizers of its Lagrangian dual,
saddle points of the Lagrangian, Kuhn–Tucker vectors, and Kuhn–Tucker conditions to incorporate approximate versions. As an
application, we show how the theory can be used for convex quadratic programming and then apply the results to support vector
machines from learning theory. 相似文献
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We introduce a duality on complex flag manifolds that extendsthe usual point-hyperplane duality of complex projective spaces. Thishas consequences for the structure of the linear cycle spaces of flagdomains, especially when those flag domains are not measurable. 相似文献