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61.
Xinwen Zhu 《Advances in Mathematics》2009,221(2):570-600
Let G be a simple algebraic group defined over C and T be a maximal torus of G. For a dominant coweight λ of G, the T-fixed point subscheme of the Schubert variety in the affine Grassmannian GrG is a finite scheme. We prove that for all such λ if G is of type A or D and for many of them if G is of type E, there is a natural isomorphism between the dual of the level one affine Demazure module corresponding to λ and the ring of functions (twisted by certain line bundle on GrG) of . We use this fact to give a geometrical proof of the Frenkel-Kac-Segal isomorphism between basic representations of affine algebras of A,D,E type and lattice vertex algebras. 相似文献
62.
Let and be the algebras of all bounded linear operators on infinite dimensional complex Banach spaces X and Y, respectively. We characterize additive maps from onto preserving different quantities such as the nullity, the defect, the ascent, and the descent of operators. 相似文献
63.
64.
The isomorphism of polynomials(IP),one of the hard problems in multivariate public key cryptography induces an equivalence relation on a set of systems of polynomials.Then the enumeration problem of IP consists of counting the numbers of different classes and counting the cardinality of each class that is highly related to the scale of key space for a multivariate public key cryptosystem.In this paper we show the enumeration of the equivalence classes containing ∑n-1 i=0 aiX2qi when char(Fq) = 2,which implies that these polynomials are all weak IP instances.Moreover,we study the cardinality of an equivalence class containing the binomial aX 2q i + bX 2qj(i=j) over Fqn without the restriction that char(Fq) = 2,which gives us a deeper understanding of finite geometry as a tool to investigate the enumeration problem of IP. 相似文献
65.
66.
67.
E. S. Lyapin 《Mathematical Notes》1999,66(1):89-93
To any ordered set with a universally maximal element, a semigroup of its transformations with some natural properties that
defines the ordered set up to an isomorphism is assigned. The system of such transformation semigroups is proved to be the
minimal element in the set of all defining systems of transformation semigroups with respect to the following ordering: one
system precedes another if for each ordered set from the class in question, the semigroup of its transformation belonging
to the first system is contained in the semigroup of its transformation from the second system.
Translated fromMatematicheskie Zametki, Vol. 66, No. 1, pp. 112–119, July, 1999. 相似文献
68.
Julio C. García 《Mathematical Notes》1999,65(2):159-167
The paper suggests a constructive characterization of unbounded completely positive maps introduced earlier by Chebotarev
for the theory of quantum dynamical semigroups. We prove that such cones are generated by a positive self-adjoint “reference”
operator ΛεB(H) as follows: for any completely positive unbounded map Ф(·)εCPn*(F) these exists a completely positive normal bounded mapR(·)εCPn(H) such that ϕ(·)=ΛR(·)Λ. The class contains mappings that are unclosable sesquilinear forms.
Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 194–205, February, 1999. 相似文献
69.
三支概念分析理论目前已经发展成为数据分析与知识发现的有效工具。主要通过形式背景特征的研究, 讨论三支概念格与概念格的同构关系, 进一步研究了三支概念格的构造方法。首先给出了对偶属性、属性对偶背景的定义, 并证明了在对偶背景下三支概念格与概念格是同构的。其次, 推广了对偶属性、属性诱导的对偶背景, 给出对偶可交属性及属性对偶可交背景的定义, 同时, 证明了在对偶可交背景下,三支概念格与概念格是同构的。最后基于上述理论, 给出了判定属性对偶背景与属性对偶可交背景的2种算法以及三支概念格的构造方法。 相似文献
70.
We study a noisy graph isomorphism problem, where the goal is to perfectly recover the vertex correspondence between two edge‐correlated graphs, with an initial seed set of correctly matched vertex pairs revealed as side information. We show that it is possible to achieve the information‐theoretic limit of graph sparsity in time polynomial in the number of vertices n. Moreover, we show the number of seeds needed for perfect recovery in polynomial‐time can be as low as in the sparse graph regime (with the average degree smaller than ) and in the dense graph regime, for a small positive constant . Unlike previous work on graph matching, which used small neighborhoods or small subgraphs with a logarithmic number of vertices in order to match vertices, our algorithms match vertices if their large neighborhoods have a significant overlap in the number of seeds. 相似文献