共查询到10条相似文献,搜索用时 31 毫秒
1.
矩阵指数的偏迹不等式 总被引:1,自引:0,他引:1
In this paper it is shown that if C is an n×n complex matrix and C(k) is the k-th compound of C, 1≤k≤n, N = (n k) and if the eigenvalues of C(k) are labeled inorder of decreasing magnitude |λ1(C(k))|≥λ2(C(k))|≥…≥λN(C(k))|define the partial trace tri(k)(C) by (?) Then for two n×n Hermrtian matrices A, B,with equality holds if A, B are commutative or k = n. 相似文献
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关于集值系统x∈F(x,y),y∈G(x,y)解的存在性 总被引:2,自引:0,他引:2
Let (E, ‖·‖) be a uniformly convex Banach space, X a nonempty compact and convex subset of E. Let F be a closed mapping of X×X into 2X, G a mapping of X×X into C(X). It is shown that if for any f∈C(X), x∈X, F(x,f(x)) is a closed and convex subset of X, and G(x,f(x)) is a continuous function and for any x,y1,y2∈X,H(x,G(x,y1),G(x,y2))≤‖y1-y2‖ then there exist X0,y0∈X such that X0∈F(x0,y0) and y0∈G(x0, y0). 相似文献
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We introduce three classes of cohn rings C1,C2 and C3). Let R and S are rings,φ : R→S is a ring homomorphism. We prove that R∈Ci if and only if R/J(R) ∈ Ci. In We also discuss the relation between the 相似文献
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Theorem. A mapping x** of X* into sealar field Φ is a linear functional if and only if there exists a μ∈ba(S) such that X**(X*)=∫sx*(s)μ(ds),x*∈X* Theorem. F∈ba(S.Σ)* if and only if there exists a λ∈ba (T) (T is the closed unit sphere of the space B(S,Σ))such that F(μ)=∫(∫st(s)μ(ds))λ(dt),μ∈ba(S,Σ). 相似文献
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Let f(x) be a periodic function of period 2π,|f(x)|and |f(x)|p integrable on [0,2π].It is said to be f∈HX1,if (∫02π|f(x+h)-f(x)|pdx)1/p≤|h|.It is said to be f∈HX2,if (∫02π|f(x+h)+f(x-h)-2f(x)|pdx)1/p≤2|h|. 相似文献
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Given the space C[-1,1]k consisting of k-times continuonsly differentiable real-valued function. Further, we provide C[-1,1]k with the norm ‖f‖k which for a given f∈C[-1,1]k is defined by. 相似文献
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关于组合合成阵 总被引:2,自引:0,他引:2
We define the rth combinatorial compound Cr*(A) of a matrix A, which can be viewed as the characteristic function of the subset of the rxr submatrices of A which are combinatorially nonsingular. We prove that for 1≤rr*(A)is. We determine the minimum number of 2×2 and 3×3 combinatorially nonsingular submatrices over all n×n fully indecomposable matrices and make a jecture for general r. 相似文献
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Let M be an open Riemann surface and G : M → Pn(C) be a holomorphic map. Consider the conformal metric on M which is given by ds2 = k e Gk2m|ω|2, where eG is a reduced representation of G, ω is a holomorphic 1-form on M and m is a positive integer. Assume that ds2 is complete and G is k-nondegenerate(0 ≤ k ≤ n). If there are q hyperplanes H1, H2, · · · , Hq Pn(C) located in general position such that G is ramified over Hj with multiplicity at least γj (> k) for each j ∈ {1, 2, · · · , q}, and it holds that Xj=1 1 -k/γj> (2n - k + 1) (mk/2+ 1),then M is flat, or equivalently, G is a constant map. Moreover, one further give a curvature estimate on M without assuming the completeness of the surface. 相似文献
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Let F be a graph. A hypergraph H is Berge-F if there is a bijection f : E(F) → E(H) such that e ? f(e) for every e ∈ E(F). A hypergraph is Berge-F-free if it does not contain a subhypergraph isomorphic to a Berge-F hypergraph. The authors denote the maximum number of hyperedges in an n-vertex r-uniform Berge-F-free hypergraph by exr(n, Berge-F).A (k, p)-fan, denoted by Fk,p, is a graph on k(p ? 1) + 1 vertices consisting of k cliques with p vertices that intersect in exactly one common vertex. In this paper they determine the bounds of exr(n, Berge-F) when F is a (k, p)-fan for k ≥ 2, p ≥ 3 and r ≥ 3. 相似文献