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1.
Let D={{0},K,L,M,X} be a strongly double triangle subspace lattice on a non-zero complex reflexive Banach space X, which means that at least one of three sums K + L, L + M and M + K is closed. It is proved that a non-zero element S of AlgD is single in the sense that for any A,B∈AlgD, either AS = 0 or SB = 0 whenever ASB = 0, if and only if S is of rank two. We also show that every algebraic isomorphism between two strongly double triangle subspace lattice algebras is quasi-spatial. 相似文献
2.
Hortensia Galeana-Sánchez 《Discrete Mathematics》2006,306(16):1969-1974
Let D be a digraph, V(D) and A(D) will denote the sets of vertices and arcs of D, respectively.A kernel N of D is an independent set of vertices such that for every w∈V(D)-N there exists an arc from w to N. A digraph is called quasi-transitive when (u,v)∈A(D) and (v,w)∈A(D) implies (u,w)∈A(D) or (w,u)∈A(D). This concept was introduced by Ghouilá-Houri [Caractérisation des graphes non orientés dont on peut orienter les arrêtes de maniere à obtenir le graphe d’ un relation d’ordre, C.R. Acad. Sci. Paris 254 (1962) 1370-1371] and has been studied by several authors. In this paper the following result is proved: Let D be a digraph. Suppose D=D1∪D2 where Di is a quasi-transitive digraph which contains no asymmetrical infinite outward path (in Di) for i∈{1,2}; and that every directed cycle of length 3 contained in D has at least two symmetrical arcs, then D has a kernel. All the conditions for the theorem are tight. 相似文献
3.
Jianping Li Haiyan Wang Binchao Huang Junran Lichen 《Journal of Global Optimization》2013,57(3):783-801
Given n terminals in the Euclidean plane and a positive constant l, find a Steiner tree T interconnecting all terminals with the minimum total cost of Steiner points and a specific material used to construct all edges in T such that the Euclidean length of each edge in T is no more than l. In this paper, according to the cost b of each Steiner point and the different costs of some specific materials with the different lengths, we study two variants of the Steiner tree problem in the Euclidean plane as follows: (1) If a specific material to construct all edges in such a Steiner tree has its infinite length and the cost of per unit length of such a specific material used is c 1, the objective is to minimize the total cost of the Steiner points and such a specific material used to construct all edges in T, i.e., ${{\rm min} \{b \cdot k_1+ c_1 \cdot \sum_{e \in T} w(e)\}}$ , where T is a Steiner tree constructed, k 1 is the number of Steiner points and w(e) is the length of part cut from such a specific material to construct edge e in T, and we call this version as the minimum-cost Steiner points and edges problem (MCSPE, for short). (2) If a specific material to construct all edges in such a Steiner tree has its finite length L (l ≤ L) and the cost of per piece of such a specific material used is c 2, the objective is to minimize the total cost of the Steiner points and the pieces of such a specific material used to construct all edges in T, i.e., ${{\rm min} \{b \cdot k_2+ c_2 \cdot k_3\}}$ , where T is a Steiner tree constructed, k 2 is the number of Steiner points in T and k 3 is the number of pieces of such a specific material used, and we call this version as the minimum-cost Steiner points and pieces of specific material problem (MCSPPSM, for short). These two variants of the Steiner tree problem are NP-hard with some applications in VLSI design, WDM optical networks and wireless communications. In this paper, we first design an approximation algorithm with performance ratio 3 for the MCSPE problem, and then present two approximation algorithms with performance ratios 4 and 3.236 for the MCSPPSM problem, respectively. 相似文献
4.
Heng-you Lan Yi-shun CuiYu Fu 《Communications in Nonlinear Science & Numerical Simulation》2012,17(4):1844-1851
In this paper, we consider and study a class of general nonlinear operator inclusion couples involving (A, η, m)-resolvent operators and relaxed cocoercive type operators in Hilbert spaces. We also construct a new perturbed iterative algorithm framework with errors and investigate variational graph convergence analysis for this algorithm framework in the context of solving the nonlinear operator inclusion couple along with some results on the resolvent operator corresponding to (A, η, m)-maximal monotonicity. The obtained results improve and generalize some well known results in recent literatures. 相似文献
5.
For real A, B such that −1 ? B < A ? 1, we denote by R(A,B) the class of functions, such that f′ ? (1 + Az)/(1 + Bz). Sharp distortion results for functions from RA,B are obtained. 相似文献
6.
Reza AhangarEbrahim Salehi 《Journal of Mathematical Analysis and Applications》2002,268(2):400-405
We would like to investigate on the solution to the automatic control problem given by the differential equation y′(t) = f(t, y(t), w(t)) for a given initial function x in the initial domain D(x, ω, Y) for almost all t in the interval I, with controls given by w(t) = g(t, y(t), T(y)(t)), where T is a nonanticipating and Lipschitzian operator. The result will be generalized for a dynamical system y′(t) = f(t, y(t), T(y), u(t)). 相似文献
7.
Let B(X) be the algebra of all bounded linear operators on the Banach space X, and let N(X) be the set of nilpotent operators in B(X). Suppose ?:B(X)→B(X) is a surjective map such that A,B∈B(X) satisfy AB∈N(X) if and only if ?(A)?(B)∈N(X). If X is infinite dimensional, then there exists a map f:B(X)→C?{0} such that one of the following holds:
- (a)
- There is a bijective bounded linear or conjugate-linear operator S:X→X such that ? has the form A?S[f(A)A]S-1.
- (b)
- The space X is reflexive, and there exists a bijective bounded linear or conjugate-linear operator S : X′ → X such that ? has the form A ? S[f(A)A′]S−1.
8.
Travis J. Herbranson Richard F. Deckro James W. Chrissis Jonathan Hamill 《European Journal of Operational Research》2013
Given a network, G = [N, E] the Isolation Set Problem (ISP) finds the set of arcs, D ⊆ E, that when removed will separate a predefined set of r distinguished nodes [2]. This involves eliminating connections from a specific set of nodes to the rest of a network. In our increasingly interconnected network-centric world, this might be isolating various units from Headquarters; isolating a portion of a computer network to disrupt communications or to quarantine a virus or some other form of cyber attack; or isolating a cell or sub-group in a terrorist or “dark” network, for example. 相似文献
9.
We completely describe those positive Borel measures μ in the unit disc D such that the Bergman space Ap(w)⊂Lq(μ), 0<p,q<∞, where w belongs to a large class W of rapidly decreasing weights which includes the exponential weights , α>0, and some double exponential type weights.As an application of that result, we characterize the boundedness and the compactness of Tg:Ap(w)→Aq(w), 0<p,q<∞, w∈W, where Tg is the integration operator
10.
Miodrag ?ivkovi? 《Linear algebra and its applications》2006,414(1):310-346
Denote by An the set of square (0, 1) matrices of order n. The set An, n ? 8, is partitioned into row/column permutation equivalence classes enabling derivation of various facts by simple counting. For example, the number of regular (0, 1) matrices of order 8 is 10160459763342013440. Let Dn, Sn denote the set of absolute determinant values and Smith normal forms of matrices from An. Denote by an the smallest integer not in Dn. The sets D9 and S9 are obtained; especially, a9 = 103. The lower bounds for an, 10 ? n ? 19 (exceeding the known lower bound an ? 2fn − 1, where fn is nth Fibonacci number) are obtained. Row/permutation equivalence classes of An correspond to bipartite graphs with n black and n white vertices, and so the other applications of the classification are possible. 相似文献
11.
The matrix A = (aij) ∈ Sn is said to lie on a strict undirected graph G if aij = 0 (i ≠ j) whenever (i, j) is not in E(G). If S is skew-symmetric, the isospectral flow maintains the spectrum of A. We consider isospectral flows that maintain a matrix A(t) on a given graph G. We review known results for a graph G that is a (generalised) path, and construct isospectral flows for a (generalised) ring, and a star, and show how a flow may be constructed for a general graph. The analysis may be applied to the isospectral problem for a lumped-mass finite element model of an undamped vibrating system. In that context, it is important that the flow maintain other properties such as irreducibility or positivity, and we discuss whether they are maintained. 相似文献
12.
Zhiping XiongYingying Qin 《Applied mathematics and computation》2011,218(7):3330-3337
In this article, we consider common Re-nnd and Re-pd solutions of the matrix equations AX = C and XB = D with respect to X, where A, B, C and D are given matrices. We give necessary and sufficient conditions for the existence of common Re-nnd and Re-pd solutions to the pair of the matrix equations and derive a representation of the common Re-nnd and Re-pd solutions to these two equations when they exist. The presented examples show the advantage of the proposed approach. 相似文献
13.
A kernel N of a digraph D is an independent set of vertices of D such that for every w∈V(D)−N there exists an arc from w to N. If every induced subdigraph of D has a kernel, D is said to be a kernel perfect digraph. D is called a critical kernel imperfect digraph when D has no kernel but every proper induced subdigraph of D has a kernel. If F is a set of arcs of D, a semikernel modulo F of D is an independent set of vertices S of D such that for every z∈V(D)−S for which there exists an (S,z)-arc of D−F, there also exists an (z,S)-arc in D. In this work we show sufficient conditions for an infinite digraph to be a kernel perfect digraph, in terms of semikernel modulo F. As a consequence it is proved that symmetric infinite digraphs and bipartite infinite digraphs are kernel perfect digraphs. Also we give sufficient conditions for the following classes of infinite digraphs to be kernel perfect digraphs: transitive digraphs, quasi-transitive digraphs, right (or left)-pretransitive digraphs, the union of two right (or left)-pretransitive digraphs, the union of a right-pretransitive digraph with a left-pretransitive digraph, the union of two transitive digraphs, locally semicomplete digraphs and outward locally finite digraphs. 相似文献
14.
In this paper, we have found upper and lower bounds for the spectral norms of r-circulant matrices in the forms A = Cr(F0, F1, …, Fn−1), B = Cr(L0, L1, …, Ln−1), and we have obtained some bounds for the spectral norms of Kronecker and Hadamard products of A and B matrices. 相似文献
15.
In a recent paper, Neumann and Sze considered for an n × n nonnegative matrix A, the minimization and maximization of ρ(A + S), the spectral radius of (A + S), as S ranges over all the doubly stochastic matrices. They showed that both extremal values are always attained at an n × n permutation matrix. As a permutation matrix is a particular case of a normal matrix whose spectral radius is 1, we consider here, for positive matrices A such that (A + N) is a nonnegative matrix, for all normal matrices N whose spectral radius is 1, the minimization and maximization problems of ρ(A + N) as N ranges over all such matrices. We show that the extremal values always occur at an n × n real unitary matrix. We compare our results with a less recent work of Han, Neumann, and Tastsomeros in which the maximum value of ρ(A + X) over all n × n real matrices X of Frobenius norm was sought. 相似文献
16.
T. Ando 《Linear algebra and its applications》2006,417(1):3-7
We determine the maximum in the class of unitarily invariant norms ∥·∥ such that w(A) ? ∥A∥ for all n-square matrices A. Here w(A) denotes the numerical radius of A. 相似文献
17.
Ameur Seddik 《Linear algebra and its applications》2007,424(1):177-183
Let A be a standard operator algebra acting on a (real or complex) normed space E. For two n-tuples A = (A1, … , An) and B = (B1, … , Bn) of elements in A, we define the elementary operator RA,B on A by the relation for all X in A. For a single operator A∈A, we define the two particular elementary operators LA and RA on A by LA(X) = AX and RA(X) = XA, for every X in A. We denote by d(RA,B) the supremum of the norm of RA,B(X) over all unit rank one operators on E. In this note, we shall characterize: (i) the supremun d(RA,B), (ii) the relation , (iii) the relation d(LA − RB) = ∥A∥ + ∥B∥, (iv) the relation d(LARB − LBRA) = 2∥A∥ + ∥B∥. Moreover, we shall show the lower estimate d(LA − RB) ? max{supλ∈V(B)∥A − λI∥, supλ∈V(A)∥B − λI∥} (where V(X) is the algebraic numerical range of X in A). 相似文献
18.
For a digraph D, let L(D) and S(D) denote its line digraph and subdivision digraph, respectively. The motivation of this paper is to solve the digraph equation L(S(D))=S(L(D)). We show that L(S(D)) and S(L(D)) are cospectral if and only if D and L(D) have the same number of arcs. Further, we characterize the situation that L(S(D)) and S(L(D)) are isomorphic. Our approach introduces the new notion, the proper image D* of a digraph D, and a new type of connectedness for digraphs. The concept D* plays an important role in the main result of this paper. It is also useful in other aspects of the study of line digraphs. For example, L(D) is connected if and only if D* is connected; L(D) is functional (contrafunctional) if and only if D* is functional (contrafunctional). Some related results are also presented. 相似文献
19.
Dora Seleši 《Chaos, solitons, and fractals》2011,44(7):526-537
This paper deals with some models of mathematical physics, where random fluctuations are modeled by white noise or other singular Gaussian generalized processes. White noise, as the distributional derivative od Brownian motion, which is the most important case of a Lévy process, is defined in the framework of Hida distribution spaces. The Fourier transformation in the framework of singular generalized stochastic processes is introduced and its applications to solving stochastic differential equations involving Wick products and singularities such as the Dirac delta distribution are presented. Explicit solutions are obtained in form of a chaos expansion in the Kondratiev white noise space, while the coefficients of the expansion are tempered distributions. Stochastic differential equations of the form P(ω, D) ◊ u(x, ω) = A(x, ω) are considered, where A is a singular generalized stochastic process and P(ω, D) is a partial differential operator with random coefficients. We introduce the Wick-convolution operator which enables us to express the solution as u = sA ◊ I◊(−1), where s denotes the fundamental solution and I is the unit random variable. In particular, the stochastic Helmholtz equation is solved, which in physical interpretation describes waves propagating with a random speed from randomly appearing point sources. 相似文献
20.
Alexey Goncharov 《Journal of Mathematical Analysis and Applications》2009,350(1):313-326
We construct an example of a non-convex star-shaped origin-symmetric body D⊂R3 such that its section function AD,ξ(t):=area(D∩{ξ⊥+tξ}) is decreasing in t?0 for every fixed direction ξ∈S2. 相似文献