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41.
Let S be a semigroup of words over an alphabet ∑ . Suppose tliar every two words u and e over ∑ are equal in S if (1) the sets of subwords of length k of the words a and b coincide and are non-empty. (2) the prefix (suffix) of u of length k1 is equal to the prefix (suffix) of e. Then S is called k-testable. A semigroup is locally testable if it is k-testable for some k > 0. We present a finite basis of identities of the variety of A'-testable semigroups. The structure of k-testable semigroup is studied. Necessarv and sufficient conditions for local testability will be given. A solution to one problem from the survey of Shevrin and Sukhanov (1985) will be presented. 相似文献
42.
Let 𝔽 be a field of characteristic two. Let S n (𝔽) denote the vector space of all n?×?n symmetric matrices over 𝔽. We characterize i. subspaces of S n (𝔽) all whose elements have rank at most two where n???3, ii. linear maps from S m (𝔽) to S n (𝔽) that sends matrices of rank at most two into matrices of rank at most two where m, n???3 and |𝔽|?≠?2. 相似文献
43.
Honglin Wu 《Linear and Multilinear Algebra》2013,61(6):609-623
For a symmetric 0–1 matrix A, we give the number of ones in A 2 when rank(A) = 1, 2, and give the maximal number of ones in A 2 when rank(A) = k (3 ≤ k ≤ n). The sufficient and necessary condition under which the maximal number is achieved is also obtained. For generic 0–1 matrices, we only study the cases of rank 1 and rank 2. 相似文献
44.
Guochun Wen 《分析论及其应用》2005,21(2):118-131
The present paper deals with the mixed boundary value problem for elliptic equations with degenerate rank 0. We first give the formulation of the problem and estimates of solutions of the problem, and then prove the existence of solutions of the above problem for elliptic equations by the above estimates and the method of parameter extension. We use the complex method, namely first discuss the corresponding problem for degenerate elliptic complex equations of first order, afterwards discuss the above problem for degenerate elliptic equations of second order. 相似文献
45.
46.
Chi-Kwong Li 《Journal of Mathematical Analysis and Applications》2008,348(2):843-855
For a positive integer k, the rank-k numerical range Λk(A) of an operator A acting on a Hilbert space H of dimension at least k is the set of scalars λ such that PAP=λP for some rank k orthogonal projection P. In this paper, a close connection between low rank perturbation of an operator A and Λk(A) is established. In particular, for 1?r<k it is shown that Λk(A)⊆Λk−r(A+F) for any operator F with rank(F)?r. In quantum computing, this result implies that a quantum channel with a k-dimensional error correcting code under a perturbation of rank at most r will still have a (k−r)-dimensional error correcting code. Moreover, it is shown that if A is normal or if the dimension of A is finite, then Λk(A) can be obtained as the intersection of Λk−r(A+F) for a collection of rank r operators F. Examples are given to show that the result fails if A is a general operator. The closure and the interior of the convex set Λk(A) are completely determined. Analogous results are obtained for Λ∞(A) defined as the set of scalars λ such that PAP=λP for an infinite rank orthogonal projection P. It is shown that Λ∞(A) is the intersection of all Λk(A) for k=1,2,…. If A−μI is not compact for all μ∈C, then the closure and the interior of Λ∞(A) coincide with those of the essential numerical range of A. The situation for the special case when A−μI is compact for some μ∈C is also studied. 相似文献
47.
O. Yu. Dashkova 《Siberian Mathematical Journal》2008,49(6):1023-1033
Under study are the solvable nonabelian linear groups of infinite central dimension and sectional p-rank, p ≥ 0, in which all proper nonabelian subgroups of infinite sectional p-rank have finite central dimension. We describe the structure of the groups of this class. 相似文献
48.
Finite groups of Lie type form the greater part of known finite simple groups. An important class of subgroups of finite groups
of Lie type are so-called reductive subgroups of maximal rank. These arise naturally as Levi factors of parabolic groups and
as centralizers of semisimple elements, and also as subgroups with maximal tori. Moreover, reductive groups of maximal rank
play an important part in inductive studies of subgroup structure of finite groups of Lie type. Yet a number of vital questions
dealing in the internal structure of such subgroups are still not settled. In particular, we know which quasisimple groups
may appear as central multipliers in the semisimple part of any reductive group of maximal rank, but we do not know how normalizers
of those quasisimple groups are structured. The present paper is devoted to tackling this problem.
Supported by RFBR (grant No. 05-01-00797) and by SB RAS (Young Researchers Support grant No. 29 and Integration project No.
2006.1.2).
__________
Translated from Algebra i Logika, Vol. 47, No. 1, pp. 3–30, January–February, 2008. 相似文献
49.
M. Van Barel E. Van Camp N. Mastronardi 《Numerical Linear Algebra with Applications》2005,12(10):981-1000
Very recently, an algorithm, which reduces any symmetric matrix into a semiseparable one of semi‐ separability rank 1 by similar orthogonality transformations, has been proposed by Vandebril, Van Barel and Mastronardi. Partial execution of this algorithm computes a semiseparable matrix whose eigenvalues are the Ritz‐values obtained by the Lanczos' process applied to the original matrix. Also a kind of nested subspace iteration is performed at each step. In this paper, we generalize the above results and propose an algorithm to reduce any symmetric matrix into a similar block‐semiseparable one of semiseparability rank k, with k ∈ ?, by orthogonal similarity transformations. Also in this case partial execution of the algorithm computes a block‐semiseparable matrix whose eigenvalues are the Ritz‐values obtained by the block‐Lanczos' process with k starting vectors, applied to the original matrix. Subspace iteration is performed at each step as well. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
50.
We computed the test rank of a free solvable Lie algebra of finite rank. 相似文献