共查询到20条相似文献,搜索用时 31 毫秒
1.
Roberto Beneduci 《Linear algebra and its applications》2010,433(6):1224-1239
Our starting point is the proof of the following property of a particular class of matrices. Let T={Ti,j} be a n×m non-negative matrix such that ∑jTi,j=1 for each i. Suppose that for every pair of indices (i,j), there exists an index l such that Ti,l≠Tj,l. Then, there exists a real vector k=(k1,k2,…,km)T,ki≠kj,i≠j;0<ki?1, such that, if i≠j.Then, we apply that property of matrices to probability theory. Let us consider an infinite sequence of linear functionals , corresponding to an infinite sequence of probability measures {μ(·)(i)}i∈N, on the Borel σ-algebra such that, . The property of matrices described above allows us to construct a real bounded one-to-one piecewise continuous and continuous from the left function f such that
2.
Singular values, norms, and commutators 总被引:1,自引:0,他引:1
Omar Hirzallah 《Linear algebra and its applications》2010,432(5):1322-1336
Let and Xi, i=1,…,n, be bounded linear operators on a separable Hilbert space such that Xi is compact for i=1,…,n. It is shown that the singular values of are dominated by those of , where ‖·‖ is the usual operator norm. Among other applications of this inequality, we prove that if A and B are self-adjoint operators such that a1?A?a2 and b1?B?b2 for some real numbers and b2, and if X is compact, then the singular values of the generalized commutator AX-XB are dominated by those of max(b2-a1,a2-b1)(X⊕X). This inequality proves a recent conjecture concerning the singular values of commutators. Several inequalities for norms of commutators are also given. 相似文献
3.
Songqiao Wen 《Journal of multivariate analysis》2007,98(4):743-756
Let X1,X2,…,Xn be independent exponential random variables such that Xi has failure rate λ for i=1,…,p and Xj has failure rate λ* for j=p+1,…,n, where p≥1 and q=n-p≥1. Denote by Di:n(p,q)=Xi:n-Xi-1:n the ith spacing of the order statistics , where X0:n≡0. It is shown that Di:n(p,q)?lrDi+1:n(p,q) for i=1,…,n-1, and that if λ?λ* then , and for i=1,…,n, where ?lr denotes the likelihood ratio order. The main results are used to establish the dispersive orderings between spacings. 相似文献
4.
Let K1,…,Kn be (infinite) non-negative matrices that define operators on a Banach sequence space. Given a function f:[0,∞)×…×[0,∞)→[0,∞) of n variables, we define a non-negative matrix and consider the inequality
5.
Very few Banach spaces E are known for which the lattice of closed ideals in the Banach algebra of all (bounded, linear) operators on E is fully understood. Indeed, up to now the only such Banach spaces are, up to isomorphism, Hilbert spaces and the sequence spaces c0 and ?p for 1?p<∞. We add a new member to this family by showing that there are exactly four closed ideals in for the Banach space E?(⊕?2n)c0, that is, E is the c0-direct sum of the finite-dimensional Hilbert spaces ?21,?22,…,?2n,… . 相似文献
6.
Let A1,A2 be standard operator algebras on complex Banach spaces X1,X2, respectively. For k?2, let (i1,…,im) be a sequence with terms chosen from {1,…,k}, and define the generalized Jordan product
7.
Bo Hou 《Linear algebra and its applications》2011,435(8):1987-1996
Let F denote a field and let V denote a vector space over F with finite positive dimension. We consider an ordered pair of F-linear transformations A:V→V and A∗:V→V that satisfy the following conditions: (i) each of A,A∗ is diagonalizable on V; (ii) there exists an ordering of the eigenspaces of A such that A∗Vi⊆V0+V1+?+Vi+1 for 0?i?d, where V-1:=0 and Vd+1:=0; (iii) there exists an ordering of the eigenspaces of A∗ such that for 0?i?δ, where and . We call such a pair a Hessenberg pair on V. It is known that if the Hessenberg pair A,A∗ on V is irreducible then d=δ and for 0?i?d the dimensions of Vi and coincide. We say a Hessenberg pair A,A∗ on V is sharp whenever it is irreducible and .In this paper, we give the definitions of a Hessenberg system and a sharp Hessenberg system. We discuss the connection between a Hessenberg pair and a Hessenberg system. We also define a finite sequence of scalars called the parameter array for a sharp Hessenberg system, which consists of the eigenvalue sequence, the dual eigenvalue sequence and the split sequence. We calculate the split sequence of a sharp Hessenberg system. We show that a sharp Hessenberg pair is a tridiagonal pair if and only if there exists a nonzero nondegenerate bilinear form on V that satisfies 〈Au,v〉=〈u,Av〉 and 〈A∗u,v〉=〈u,A∗v〉 for all u,v∈V. 相似文献
8.
Mordecai J. Golin 《Discrete Mathematics》2010,310(4):792-803
Let T(G) be the number of spanning trees in graph G. In this note, we explore the asymptotics of T(G) when G is a circulant graph with given jumps.The circulant graph is the 2k-regular graph with n vertices labeled 0,1,2,…,n−1, where node i has the 2k neighbors i±s1,i±s2,…,i±sk where all the operations are . We give a closed formula for the asymptotic limit as a function of s1,s2,…,sk. We then extend this by permitting some of the jumps to be linear functions of n, i.e., letting si, di and ei be arbitrary integers, and examining
9.
Peter Borg 《Discrete Mathematics》2009,309(14):4750-4753
Families A1,…,Ak of sets are said to be cross-intersecting if for any Ai∈Ai and Aj∈Aj, i≠j. A nice result of Hilton that generalises the Erd?s-Ko-Rado (EKR) Theorem says that if r≤n/2 and A1,…,Ak are cross-intersecting sub-families of , then
10.
Let H be a Hilbert space and C be a nonempty closed convex subset of H, {Ti}i∈N be a family of nonexpansive mappings from C into H, Gi:C×C→R be a finite family of equilibrium functions (i∈{1,2,…,K}), A be a strongly positive bounded linear operator with a coefficient and -Lipschitzian, relaxed (μ,ν)-cocoercive map of C into H. Moreover, let , {αn} satisfy appropriate conditions and ; we introduce an explicit scheme which defines a suitable sequence as follows:
11.
For a simple graph G, the energy E(G) is defined as the sum of the absolute values of all the eigenvalues of its adjacency matrix A(G). Let n,m, respectively, be the number of vertices and edges of G. One well-known inequality is that , where λ1 is the spectral radius. If G is k-regular, we have . Denote . Balakrishnan [R. Balakrishnan, The energy of a graph, Linear Algebra Appl. 387 (2004) 287-295] proved that for each ?>0, there exist infinitely many n for each of which there exists a k-regular graph G of order n with k<n-1 and , and proposed an open problem that, given a positive integer n?3, and ?>0, does there exist a k-regular graph G of order n such that . In this paper, we show that for each ?>0, there exist infinitely many such n that . Moreover, we construct another class of simpler graphs which also supports the first assertion that . 相似文献
12.
Lance L. Littlejohn José L. López 《Journal of Mathematical Analysis and Applications》2010,369(2):658-670
Given a basis of solutions to k ordinary linear differential equations ?j[y]=0(j=1,2,…,k), we show how Green's functions can be used to construct a basis of solutions to the homogeneous differential equation ?[y]=0, where ? is the composite product ?=?1?2…?k. The construction of these solutions is elementary and classical. In particular, we consider the special case when . Remarkably, in this case, if {y1,y2,…,yn} is a basis of ?1[y]=0, then our method produces a basis of for any k∈N. We illustrate our results with several classical differential equations and their special function solutions. 相似文献
13.
Luigi Santocanale 《Annals of Pure and Applied Logic》2010,162(1):55-82
This paper exhibits a general and uniform method to prove axiomatic completeness for certain modal fixpoint logics. Given a set Γ of modal formulas of the form γ(x,p1,…,pn), where x occurs only positively in γ, we obtain the flat modal fixpoint language L?(Γ) by adding to the language of polymodal logic a connective ?γ for each γ∈Γ. The term ?γ(φ1,…,φn) is meant to be interpreted as the least fixed point of the functional interpretation of the term γ(x,φ1,…,φn). We consider the following problem: given Γ, construct an axiom system which is sound and complete with respect to the concrete interpretation of the language L?(Γ) on Kripke structures. We prove two results that solve this problem.First, let be the logic obtained from the basic polymodal by adding a Kozen-Park style fixpoint axiom and a least fixpoint rule, for each fixpoint connective ?γ. Provided that each indexing formula γ satisfies a certain syntactic criterion, we prove this axiom system to be complete.Second, addressing the general case, we prove the soundness and completeness of an extension of . This extension is obtained via an effective procedure that, given an indexing formula γ as input, returns a finite set of axioms and derivation rules for ?γ, of size bounded by the length of γ. Thus the axiom system is finite whenever Γ is finite. 相似文献
14.
For n∈N and D⊆N, the distance graph has vertex set {0,1,…,n−1} and edge set {ij∣0≤i,j≤n−1,|j−i|∈D}. Note that the important and very well-studied circulant graphs coincide with the regular distance graphs.A fundamental result concerning circulant graphs is that for these graphs, a simple greatest common divisor condition, their connectivity, and the existence of a Hamiltonian cycle are all equivalent. Our main result suitably extends this equivalence to distance graphs. We prove that for a finite set D of order at least 2, there is a constant cD such that the greatest common divisor of the integers in D is 1 if and only if for every n, has a component of order at least n−cD if and only if for every n≥cD+3, has a cycle of order at least n−cD. Furthermore, we discuss some consequences and variants of this result. 相似文献
15.
Vyacheslav V. Chistyakov Yuliya V. Tretyachenko 《Journal of Mathematical Analysis and Applications》2010,369(1):82-93
Given a=(a1,…,an), b=(b1,…,bn)∈Rn with a<b componentwise and a map f from the rectangle into a metric semigroup M=(M,d,+), denote by the Hildebrandt-Leonov total variation of f on , which has been recently studied in [V.V. Chistyakov, Yu.V. Tretyachenko, Maps of several variables of finite total variation. I, J. Math. Anal. Appl. (2010), submitted for publication]. The following Helly-type pointwise selection principle is proved: If a sequence{fj}j∈Nof maps frominto M is such that the closure in M of the set{fj(x)}j∈Nis compact for eachandis finite, then there exists a subsequence of{fj}j∈N, which converges pointwise onto a map f such that. A variant of this result is established concerning the weak pointwise convergence when values of maps lie in a reflexive Banach space (M,‖⋅‖) with separable dual M∗. 相似文献
16.
Catherine Greenhill 《Journal of Combinatorial Theory, Series A》2006,113(2):291-324
Let s=(s1,…,sm) and t=(t1,…,tn) be vectors of non-negative integer-valued functions with equal sum . Let N(s,t) be the number of m×n matrices with entries from {0,1} such that the ith row has row sum si and the jth column has column sum tj. Equivalently, N(s,t) is the number of labelled bipartite graphs with degrees of the vertices in one side of the bipartition given by s and the degrees of the vertices in the other side given by t. We give an asymptotic formula for N(s,t) which holds when S→∞ with 1?st=o(S2/3), where and . This extends a result of McKay and Wang [Linear Algebra Appl. 373 (2003) 273-288] for the semiregular case (when si=s for 1?i?m and tj=t for 1?j?n). The previously strongest result for the non-semiregular case required 1?max{s,t}=o(S1/4), due to McKay [Enumeration and Design, Academic Press, Canada, 1984, pp. 225-238]. 相似文献
17.
Xiaosong Liu 《Journal of Mathematical Analysis and Applications》2006,324(1):604-614
Suppose f is a spirallike function of type β (or starlike function of order α) on the unit disk D in C. Let , where 1?p1?2 (or 0<p1?2), pj?1, j=2,…,n, are real numbers. In this paper, we prove that
18.
Jan O. Kleppe 《Journal of Pure and Applied Algebra》2011,215(7):1711-1725
A scheme X⊂Pn of codimension c is called standard determinantal if its homogeneous saturated ideal can be generated by the t×t minors of a homogeneous t×(t+c−1) matrix (fij). Given integers a0≤a1≤?≤at+c−2 and b1≤?≤bt, we denote by the stratum of standard determinantal schemes where fij are homogeneous polynomials of degrees aj−bi and is the Hilbert scheme (if n−c>0, resp. the postulation Hilbert scheme if n−c=0).Focusing mainly on zero and one dimensional determinantal schemes we determine the codimension of in and we show that is generically smooth along under certain conditions. For zero dimensional schemes (only) we find a counterexample to the conjectured value of appearing in Kleppe and Miró-Roig (2005) [25]. 相似文献
19.
Weidong Gao 《Journal of Pure and Applied Algebra》2010,214(6):898-909
Let G be a non-cyclic finite solvable group of order n, and let S=(g1,…,gk) be a sequence of k elements (repetition allowed) in G. In this paper we prove that if , then there exist some distinct indices i1,i2,…,in such that the product gi1gi2?gin=1. This result substantially improves the Erd?s-Ginzburg-Ziv theorem and other existing results. 相似文献
20.
Sukumar Das Adhikari 《Journal of Combinatorial Theory, Series A》2008,115(1):178-184
Let G be a finite abelian group of order n and let A⊆Z be non-empty. Generalizing a well-known constant, we define the Davenport constant of G with weight A, denoted by DA(G), to be the least natural number k such that for any sequence (x1,…,xk) with xi∈G, there exists a non-empty subsequence (xj1,…,xjl) and a1,…,al∈A such that . Similarly, for any such set A, EA(G) is defined to be the least t∈N such that for all sequences (x1,…,xt) with xi∈G, there exist indices j1,…,jn∈N,1?j1<?<jn?t, and ?1,…,?n∈A with . In the present paper, we establish a relation between the constants DA(G) and EA(G) under certain conditions. Our definitions are compatible with the previous generalizations for the particular group G=Z/nZ and the relation we establish had been conjectured in that particular case. 相似文献