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This paper is devoted to a problem of finding the smallest positive integer s(m,n,k) such that (m+1) generic skew-symmetric (k+1)-forms in (n+1) variables as linear combinations of the same s(m,n,k) decomposable skew-symmetric (k+1)-forms. 相似文献
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For any n-by-n matrix A , we consider the maximum number k=k(A) for which there is a k-by-k compression of A with all its diagonal entries in the boundary ∂W(A) of the numerical range W(A) of A. If A is a normal or a quadratic matrix, then the exact value of k(A) can be computed. For a matrix A of the form B⊕C, we show that k(A)=2 if and only if the numerical range of one summand, say, B is contained in the interior of the numerical range of the other summand C and k(C)=2. For an irreducible matrix A , we can determine exactly when the value of k(A) equals the size of A . These are then applied to determine k(A) for a reducible matrix A of size 4 in terms of the shape of W(A). 相似文献
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M. Gürdal 《Expositiones Mathematicae》2009,27(2):153-160
In the present paper we consider the Volterra integration operator V on the Wiener algebra W(D) of analytic functions on the unit disc D of the complex plane C. A complex number λ is called an extended eigenvalue of V if there exists a nonzero operator A satisfying the equation AV=λVA. We prove that the set of all extended eigenvalues of V is precisely the set C?{0}, and describe in terms of Duhamel operators and composition operators the set of corresponding extended eigenvectors of V. The similar result for some weighted shift operator on ?p spaces is also obtained. 相似文献
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Given an arbitrarily weak notion of left-〈f〉-porosity and an arbitrarily strong notion of right-〈g〉-porosity, we construct an example of closed subset of R which is not σ -left-〈f〉-porous and is right-〈g〉-porous. We also briefly summarize the relations between three different definitions of porosity controlled by a function; we then observe that our construction gives the example for any combination of these definitions of left-porosity and right-porosity. 相似文献
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Let F be an infinite field with characteristic not equal to two. For a graph G=(V,E) with V={1,…,n}, let S(G;F) be the set of all symmetric n×n matrices A=[ai,j] over F with ai,j≠0, i≠j if and only if ij∈E. We show that if G is the complement of a partial k -tree and m?k+2, then for all nonsingular symmetric m×m matrices K over F, there exists an m×n matrix U such that UTKU∈S(G;F). As a corollary we obtain that, if k+2?m?n and G is the complement of a partial k-tree, then for any two nonnegative integers p and q with p+q=m, there exists a matrix in S(G;R) with p positive and q negative eigenvalues. 相似文献
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Let G denote a locally compact Hausdorff group and M(G) be the space of all bounded complex-valued regular Borel measures on G . In this paper, we define two strict topologies on M(G) and study various properties of these topologies such as metrizability, barrelledness and completeness. We also determine the dual space of M(G) and consider various continuity properties for the convolution product on M(G) under these topologies. 相似文献
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Let K be a closed convex subset of a q-uniformly smooth separable Banach space, T:K→K a strictly pseudocontractive mapping, and f:K→K an L-Lispschitzian strongly pseudocontractive mapping. For any t∈(0,1), let xt be the unique fixed point of tf+(1-t)T. We prove that if T has a fixed point, then {xt} converges to a fixed point of T as t approaches to 0. 相似文献
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An ACI-matrix over a field F is a matrix whose entries are polynomials with coefficients on F, the degree of these polynomials is at most one in a number of indeterminates, and where no indeterminate appears in two different columns. In 2011 Huang and Zhan characterized the m×n ACI-matrices such that all its completions have rank equal to min{m,n} whenever |F|?max{m,n+1}. We will give a characterization for arbitrary fields by introducing two classes of ACI-matrices: the maximal and the minimal full rank ACI-matrices. 相似文献
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Let F be an algebraically closed field. Let V be a vector space equipped with a non-degenerate symmetric or symplectic bilinear form B over F. Suppose the characteristic of F is sufficiently large , i.e. either zero or greater than the dimension of V. Let I(V,B) denote the group of isometries. Using the Jacobson–Morozov lemma we give a new and simple proof of the fact that two elements in I(V,B) are conjugate if and only if they have the same elementary divisors. 相似文献
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Bárat and the present author conjectured that, for each tree T , there exists a natural number kT such that the following holds: If G is a kT-edge-connected graph such that |E(T)| divides |E(G)|, then G has a T-decomposition, that is, a decomposition of the edge set into trees each of which is isomorphic to T . The conjecture has been verified for infinitely many paths and for each star. In this paper we verify the conjecture for an infinite family of trees that are neither paths nor stars, namely all the bistars S(k,k+1). 相似文献
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In this paper we examine the resolvability of infinite designs. We show that in stark contrast to the finite case, resolvability for infinite designs is fairly commonplace. We prove that every t -(v,k,Λ) design with t finite, v infinite and k,λ<v is resolvable and, in fact, has α orthogonal resolutions for each α<v. We also show that, while a t -(v,k,Λ) design with t and λ finite, v infinite and k=v may or may not have a resolution, any resolution of such a design must have v parallel classes containing v blocks and at most λ−1 parallel classes containing fewer than v blocks. Further, a resolution into parallel classes of any specified sizes obeying these conditions is realisable in some design. When k<v and λ=v and when k=v and λ is infinite, we give various examples of resolvable and non-resolvable t -(v,k,Λ) designs. 相似文献