共查询到20条相似文献,搜索用时 78 毫秒
1.
Suppose T is a bounded self-adjoint operator on the Hilbert space L2(X,μ) and let
2.
Given a graph G, for an integer c∈{2,…,|V(G)|}, define λc(G)=min{|X|:X⊆E(G),ω(G−X)≥c}. For a graph G and for an integer c=1,2,…,|V(G)|−1, define,
3.
We prove the following: Let A and B be separable C*-algebras. Suppose that B is a type I C*-algebra such that
- (i)
- B has only infinite dimensional irreducible *-representations, and
- (ii)
- B has finite decomposition rank.
0→B→C→A→0 相似文献
4.
Given a graph G and integers p,q,d1 and d2, with p>q, d2>d1?1, an L(d1,d2;p,q)-labeling of G is a function f:V(G)→{0,1,2,…,n} such that |f(u)−f(v)|?p if dG(u,v)?d1 and |f(u)−f(v)|?q if dG(u,v)?d2. A k-L(d1,d2;p,q)-labeling is an L(d1,d2;p,q)-labeling f such that maxv∈V(G)f(v)?k. The L(d1,d2;p,q)-labeling number ofG, denoted by , is the smallest number k such that G has a k-L(d1,d2;p,q)-labeling. In this paper, we give upper bounds and lower bounds of the L(d1,d2;p,q)-labeling number for general graphs and some special graphs. We also discuss the L(d1,d2;p,q)-labeling number of G, when G is a path, a power of a path, or Cartesian product of two paths. 相似文献
5.
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},
6.
Wolfgang Arendt 《Journal of Functional Analysis》2006,238(1):340-352
Let A be the generator of a cosine function on a Banach space X. In many cases, for example if X is a UMD-space, A+B generates a cosine function for each B∈L(D((ω−A)1/2),X). If A is unbounded and , then we show that there exists a rank-1 operator B∈L(D(γ(ω−A)),X) such that A+B does not generate a cosine function. The proof depends on a modification of a Baire argument due to Desch and Schappacher. It also allows us to prove the following. If A+B generates a distribution semigroup for each operator B∈L(D(A),X) of rank-1, then A generates a holomorphic C0-semigroup. If A+B generates a C0-semigroup for each operator B∈L(D(γ(ω−A)),X) of rank-1 where 0<γ<1, then the semigroup T generated by A is differentiable and ‖T′(t)‖=O(t−α) as t↓0 for any α>1/γ. This is an approximate converse of a perturbation theorem for this class of semigroups. 相似文献
7.
For any partition λ let ω(λ) denote the four parameter weight
ω(λ)=a∑i≥1⌈λ2i−1/2⌉b∑i≥1⌊λ2i−1/2⌋c∑i≥1⌈λ2i/2⌉d∑i≥1⌊λ2i/2⌋, 相似文献
8.
Maria Monks 《Discrete Mathematics》2009,309(16):5196-1883
All continuous endomorphisms f∞ of the shift dynamical system S on the 2-adic integers Z2 are induced by some , where n is a positive integer, Bn is the set of n-blocks over {0, 1}, and f∞(x)=y0y1y2… where for all i∈N, yi=f(xixi+1…xi+n−1). Define D:Z2→Z2 to be the endomorphism of S induced by the map {(00,0),(01,1),(10,1),(11,0)} and V:Z2→Z2 by V(x)=−1−x. We prove that D, V°D, S, and V°S are conjugate to S and are the only continuous endomorphisms of S whose parity vector function is solenoidal. We investigate the properties of D as a dynamical system, and use D to construct a conjugacy from the 3x+1 function T:Z2→Z2 to a parity-neutral dynamical system. We also construct a conjugacy R from D to T. We apply these results to establish that, in order to prove the 3x+1 conjecture, it suffices to show that for any m∈Z+, there exists some n∈N such that R−1(m) has binary representation of the form or . 相似文献
9.
Xianling Fan 《Journal of Mathematical Analysis and Applications》2008,339(2):1395-1412
We study boundary trace embedding theorems for variable exponent Sobolev space W1,p(⋅)(Ω). Let Ω be an open (bounded or unbounded) domain in RN satisfying strong local Lipschitz condition. Under the hypotheses that p∈L∞(Ω), 1?infp(x)?supp(x)<N, |∇p|∈Lγ(⋅)(Ω), where γ∈L∞(Ω) and infγ(x)>N, we prove that there is a continuous boundary trace embedding W1,p(⋅)(Ω)→Lq(⋅)(∂Ω) provided q(⋅), a measurable function on ∂Ω, satisfies condition for x∈∂Ω. 相似文献
10.
Gerard J. Chang Jer-Jeong Chen David Kuo Sheng-Chyang Liaw 《Discrete Applied Mathematics》2007,155(8):1007-1013
For positive integers j?k, an L(j,k)-labeling of a digraph D is a function f from V(D) into the set of nonnegative integers such that |f(x)-f(y)|?j if x is adjacent to y in D and |f(x)-f(y)|?k if x is of distance two to y in D. Elements of the image of f are called labels. The L(j,k)-labeling problem is to determine the -number of a digraph D, which is the minimum of the maximum label used in an L(j,k)-labeling of D. This paper studies -numbers of digraphs. In particular, we determine -numbers of digraphs whose longest dipath is of length at most 2, and -numbers of ditrees having dipaths of length 4. We also give bounds for -numbers of bipartite digraphs whose longest dipath is of length 3. Finally, we present a linear-time algorithm for determining -numbers of ditrees whose longest dipath is of length 3. 相似文献
11.
We consider L1-solutions of the following refinement type equations
12.
Chi-Wai Leung 《Journal of Functional Analysis》2006,238(2):636-648
Let Ω be a measurable subset of a compact group G of positive Haar measure. Let be a non-negative function defined on the dual space and let L2(μ) be the corresponding Hilbert space which consists of elements (ξπ)π∈suppμ satisfying , where ξπ is a linear operator on the representation space of π, and is equipped with the inner product: . We show that the Fourier transform gives an isometric isomorphism from L2(Ω) onto L2(μ) if and only if the restrictions to Ω of all matrix coordinate functions , π∈suppμ, constitute an orthonormal basis for L2(Ω). Finally compact connected Lie groups case is studied. 相似文献
13.
An independent set of a graph G is a set of pairwise non-adjacent vertices. Let α(G) denote the cardinality of a maximum independent set and fs(G) for 0≤s≤α(G) denote the number of independent sets of s vertices. The independence polynomial defined first by Gutman and Harary has been the focus of considerable research recently. Wingard bounded the coefficients fs(T) for trees T with n vertices: for s≥2. We generalize this result to bounds for a very large class of graphs, maximal k-degenerate graphs, a class which includes all k-trees. Additionally, we characterize all instances where our bounds are achieved, and determine exactly the independence polynomials of several classes of k-tree related graphs. Our main theorems generalize several related results known before. 相似文献
14.
Consider Robin problem involving the p(x)-Laplacian on a smooth bounded domain Ω as follows Applying the sub-supersolution method and the variational method, under appropriate assumptions on f, we prove that there exists λ*>0 such that the problem has at least two positive solutions if λ(0,λ*), has at least one positive solution if λ=λ*<+∞ and has no positive solution if λ>λ*. To prove the results, we prove a norm on W1,p(x)(Ω) without the part of ||Lp(x)(Ω) which is equivalent to usual one and establish a special strong comparison principle for Robin problem. 相似文献
15.
We prove that an analytic function f on the unit ball B with Hadamard gaps, that is, (the homogeneous polynomial expansion of f) satisfying nk+1/nk?λ>1 for all k∈N, belongs to the space if and only if . Moreover, we show that the following asymptotic relation holds . Also we prove that limr→1(1-r2)α‖Rfr‖p=0 if and only if . These results confirm two conjectures from the following recent paper [S. Stevi?, On Bloch-type functions with Hadamard gaps, Abstr. Appl. Anal. 2007 (2007) 8 pages (Article ID 39176)]. 相似文献
16.
An L(2,1)-labeling of a graph G is a function f from the vertex set of G to the set of nonnegative integers such that |f(x)−f(y)|≥2 if d(x,y)=1, and |f(x)−f(y)|≥1 if d(x,y)=2, where d(x,y) denotes the distance between the pair of vertices x,y. The lambda number of G, denoted λ(G), is the minimum range of labels used over all L(2,1)-labelings of G. An L(2,1)-labeling of G which achieves the range λ(G) is referred to as a λ-labeling. A hole of an L(2,1)-labeling is an unused integer within the range of integers used. The hole index of G, denoted ρ(G), is the minimum number of holes taken over all its λ-labelings. An island of a given λ-labeling of G with ρ(G) holes is a maximal set of consecutive integers used by the labeling. Georges and Mauro [J.P. Georges, D.W. Mauro, On the structure of graphs with non-surjective L(2,1)-labelings, SIAM J. Discrete Math. 19 (2005) 208-223] inquired about the existence of a connected graph G with ρ(G)≥1 possessing two λ-labelings with different ordered sequences of island cardinalities. This paper provides an infinite family of such graphs together with their lambda numbers and hole indices. Key to our discussion is the determination of the path covering number of certain 2-sparse graphs, that is, graphs containing no pair of adjacent vertices of degree greater than 2. 相似文献
17.
Qiyi Fan Wentao Wang Xuejun Yi 《Journal of Computational and Applied Mathematics》2009,230(2):762-769
In this paper, we use the Leray–Schauder degree theory to establish new results on the existence and uniqueness of anti-periodic solutions for a class of nonlinear nth-order differential equations with delays of the form
x(n)(t)+f(t,x(n−1)(t))+g(t,x(t−τ(t)))=e(t).