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21.
Frédéric Bernard 《Journal of Mathematical Analysis and Applications》2005,303(1):1-14
This paper studies the prox-regularity concept for functions in the general context of Hilbert space. In particular, a subdifferential characterization is established as well as several other properties. It is also shown that the Moreau envelopes of such functions are continuously differentiable. 相似文献
22.
A subset S of vertices of a graph G is a secure set if |N [X] ∩ S| ≥ |N [X] ? S| holds for any subset X of S, where N [X] denotes the closed neighborhood of X. The minimum cardinality s(G) of a secure set in G is called the security number of G. We investigate the security number of lexicographic product graphs by defining a new concept of tightly-securable graphs. In particular we derive several exact results for different families of graphs which yield some general results. 相似文献
23.
We give an alternative proof of a theorem of Stein and Weiss: The distribution function of the Hilbert transform of a characteristic function of a set E only depends on the Lebesgue measure |E| of such a set. We exploit a rational change of variable of the type used by George Boole in his paper “On the comparison of transcendents, with certain applications to the theory of definite integrals” together with the observation that if two functions f and g have the same Lp norm in a range of exponents p1<p<p2 then their distribution functions coincide. 相似文献
24.
Jianhua Hu 《Linear algebra and its applications》2010,433(4):796-809
Let Y be an n×p multivariate normal random matrix with general covariance ΣY and W be a symmetric matrix. In the present article, the property that a matrix quadratic form Y′WY is distributed as a difference of two independent (noncentral) Wishart random matrices is called the (noncentral) generalized Laplacianness (GL). Then a set of algebraic results are obtained which will give the necessary and sufficient conditions for the (noncentral) GL of a matrix quadratic form. Further, two extensions of Cochran’s theorem concerning the (noncentral) GL and independence of a family of matrix quadratic forms are developed. 相似文献
25.
In 1967 Komlós proved that for any sequence n{fn} in L1(μ), with ‖fn‖?M<∞ (where μ is a probability measure), there exists a subsequence n{gn} of n{fn} and a function g∈L1(μ) such that for any further subsequence n{hn} of n{gn},
26.
We use the Hilbert?s Nullstellensatz (Hilbert?s Zero Point Theorem) to give a direct proof of the formula for the determinants of the products of tensors. By using this determinant formula and using tensor product to represent the transformations of the slices of tensors, we prove some basic properties of the determinants of tensors which are the generalizations of the corresponding properties of the determinants for matrices. We also study the determinants of tensors after two types of transposes. We use the permutational similarity of tensors to discuss the relation between weakly reducible tensors and the triangular block tensors, and give a canonical form of the weakly reducible tensors. 相似文献
27.
Herbert A. Robinson 《Linear and Multilinear Algebra》2013,61(4):233-241
Let V:1,…,Vm be inner product spaces, and let L be a linear transformation on V1 ?…?Vm which satisfies (Lz,z)=0 for every decomposable tensor z. It is known that if the field is the complex numbers, then (Lz,z)=0 for every z. This paper contains a short proof of this result, an extension of it to arbitrary symmetry classes of tensors, and an analysis of its failure when the field is the real numbers. 相似文献
28.
M.H. Lim 《Linear and Multilinear Algebra》2013,61(3):231-234
In this note we give a simple proof and an extension of a dimension inequality of Howard concerning the range of a multilinear function with vector space range by using some results on algebraic varieties. 相似文献
29.
M. H. Lim 《Linear and Multilinear Algebra》2013,61(4):333-354
Let G be a subgroup of the symmetric group Sm and V be an n-dimensional unitary space where nm. Let V(G) be the symmetry class of tensors over V associated with G and the identity character. Let D(G) be the set of all decomposable elements of V(G) and O(G) be its subset consisting of all nonzero decomposable tensors x 1 ?…? xm such that {x 1,…,xm } is an orthogonal set. In this paper we study the structure of linear mappings on V(G) that preserve one of the following subsets: (i)O(G), (ii) D(G)\(O(G)?{0}). 相似文献
30.
In this paper, we study lower bounds on the size of a maximum independent set and a maximum matching in a hypergraph of rank three. The rank in a hypergraph is the size of a maximum edge in the hypergraph. A hypergraph is simple if no two edges contain exactly the same vertices. Let H be a hypergraph and let and be the size of a maximum independent set and a maximum matching, respectively, in H, where a set of vertices in H is independent (also called strongly independent in the literature) if no two vertices in the set belong to a common edge. Let H be a hypergraph of rank at most three and maximum degree at most three. We show that with equality if and only if H is the Fano plane. In fact, we show that if H is connected and different from the Fano plane, then and we characterize the hypergraphs achieving equality in this bound. Using this result, we show that that if H is a simple connected 3‐uniform hypergraph of order at least 8 and with maximum degree at most three, then and there is a connected 3‐uniform hypergraph H of order 19 achieving this lower bound. Finally, we show that if H is a connected hypergraph of rank at most three that is not a complete hypergraph on vertices, where denotes the maximum degree in H, then 69-4ffe-a470-a0a6a001f211/jgt21640-math-0008.png"> and this bound is asymptotically best possible. 69; 2012 Wiley Periodicals, Inc. J. Graph Theory 相似文献