共查询到20条相似文献,搜索用时 15 毫秒
1.
John Lagnese 《Journal of Functional Analysis》1973,13(3):302-316
Let V?, W?, W and X be Hilbert spaces (0 < ? ? 1) with V? ? W? ? W ? X algebraically and topologically, each space being dense in the one that follows it. For each t? [0, T] let a?(t; u, v), b?(t; u, v) and b(t; u, v) be continuous sesqui-linear forms on V?, W? and W, respectively, which satisfy certain ellipticity conditions. Consider the two equations a?(t; u?, v) + b?(t; u?, v) = 〈f?, v〉 (v?V?) and (u′, v)x + b(t; u, v) = 〈f, v〉 (v?W). Estimates are obtained on the rate of convergence of u? to u, assuming a?(t; u, v) → (u, v)x and b?(t; u, v) → b(t; u, v) in an appropriate sense. These results are then applied to singular perturbation of a class of parabolic boundary value problems. 相似文献
2.
Let C be a closed convex subset of a Hilbert space H. Let f is a contraction on C. Let S be a nonexpansive mapping of C into itself and A be an α-inverse-strongly monotone mapping of C into H. Assuming that F(S)∩VI(C,A)≠φ, and x 0=x∈C, in this paper we introduce the iterative process x n+1=α n f(x n )+β n x n +γ n (μ Sx n +(1?μ)(P C (I?λ n A)y n )), where y n =P C (I?λ n A)x n . We prove that {x n } and {y n } converge strongly to the same point z∈F(S)∩VI(C,A). As its application, we give a strong convergence theorem for nonexpansive mapping and strictly pseudo-contractive mapping in a Hilbert space. 相似文献
3.
Cecilia H. Brook William H. Graves 《Journal of Mathematical Analysis and Applications》1980,73(1):219-237
Let X be a completely regular Hausdorff space and E be a locally convex Hausdorff space. Then Cb(X) ? E is dense in (Cb(X, E), β0), (Cb(X), β) ??E = (Cb(X) ? E, β) and (Cb(X), β1) ??E = (Cb(X) ? E, β1). For a separable space E, (Cb(X, E), β0) is separable if and only if X is separably submetrizable. As a corollary, for a locally compact paracompact space X, if (Cb(X, E), β0) is separable, then X is metrizable. 相似文献
4.
B.P. Duggal 《Linear algebra and its applications》2008,428(4):1109-1116
A Hilbert space operator A∈B(H) is p-hyponormal, A∈(p-H), if |A∗|2p?|A|2p; an invertible operator A∈B(H) is log-hyponormal, A∈(?-H), if log(TT∗)?log(T∗T). Let dAB=δAB or ?AB, where δAB∈B(B(H)) is the generalised derivation δAB(X)=AX-XB and ?AB∈B(B(H)) is the elementary operator ?AB(X)=AXB-X. It is proved that if A,B∗∈(?-H)∪(p-H), then, for all complex λ, , the ascent of (dAB-λ)?1, and dAB satisfies the range-kernel orthogonality inequality ‖X‖?‖X-(dAB-λ)Y‖ for all X∈(dAB-λ)-1(0) and Y∈B(H). Furthermore, isolated points of σ(dAB) are simple poles of the resolvent of dAB. A version of the elementary operator E(X)=A1XA2-B1XB2 and perturbations of dAB by quasi-nilpotent operators are considered, and Weyl’s theorem is proved for dAB. 相似文献
5.
We construct stable invariant manifolds for semiflows generated by the nonlinear impulsive differential equation with parameters x'= A(t)x + f(t, x, λ), t≠τi and x(τ+i) = Bix(τi) + gi(x(τi), λ), i ∈ N in Banach spaces, assuming that the linear impulsive differential equation x'= A(t)x, t≠τi and x(τ+i) = Bix(τi), i ∈ N admits a nonuniform (μ, ν)-dichotomy. It is shown that the stable invariant manifolds are Lipschitz continuous in the parameter λ and the initial values provided that the nonlinear perturbations f, g are sufficiently small Lipschitz perturbations. 相似文献
6.
P.D. Johnson Jr. 《Discrete Mathematics》2009,309(14):4746-4749
Let χf denote the fractional chromatic number and ρ the Hall ratio, and let the lexicographic product of G and H be denoted GlexH. Main results: (i) ρ(GlexH)≤χf(G)ρ(H); (ii) if ρ(G)=χf(G) then ρ(GlexH)=ρ(G)ρ(H) for all H; (iii) χf−ρ is unbounded. In addition, the question of how big χf/ρ can be is discussed. 相似文献
7.
We consider equations (E) −Δu+g(u)=μ in smooth bounded domains Ω⊂RN, where g is a continuous nondecreasing function and μ is a finite measure in Ω. Given a bounded sequence of measures (μk), assume that for each k?1 there exists a solution uk of (E) with datum μk and zero boundary data. We show that if uk→u# in L1(Ω), then u# is a solution of (E) relative to some finite measure μ#. We call μ# the reduced limit of (μk). This reduced limit has the remarkable property that it does not depend on the boundary data, but only on (μk) and on g. For power nonlinearities g(t)=|t|q−1t, ∀t∈R, we show that if (μk) is nonnegative and bounded in W−2,q(Ω), then μ and μ# are absolutely continuous with respect to each other; we then produce an example where μ#≠μ. 相似文献
8.
We consider which ordinals, with the order topology, can be Stone-?ech remainders of which spaces of the form ψ(κ,M), where ω?κ is a cardinal number and M⊂ω[κ] is a maximal almost disjoint family of countable subsets of κ (MADF). The cardinality of the continuum, denoted c, and its successor cardinal, c+, play important roles. We show that if κ>c+, then no ψ(κ,M) has any ordinal as a Stone-?ech remainder. If κ?c then for every ordinal δ<κ+ there exists Mδ⊂ω[κ], a MADF, such that βψ(κ,Mδ)?ψ(κ,Mδ) is homeomorphic to δ+1. For κ=c+, βψ(κ,Mδ)?ψ(κ,Mδ) is homeomorphic to δ+1 if and only if c+?δ<c+⋅ω. 相似文献
9.
Sun Haina Bu Yuehua 《高校应用数学学报(英文版)》2006,21(4):487-492
The relations among the dominating number, independence number and covering number of hypergraphs are investigated. Main results are as follows:Dv(H)≤min{α≤(H), p(H), p(H), T(H)}; De(H)≤min{v(H), T(H), p(H)}; DT(H) ≤αT(H); S(H)≤ Dv (H) + α(H)≤n; 2≤ Dv (H) + T(H) ≤n; 2 〈 Dv (H) + v(H)≤n/2 + [n/r]; Dv (H) + p(H) 〈_n;2≤De(H) + Dv(H)≤n/2 + [n/r];α(H) + De(H)≤n;2 ≤ De(H) + v(H)≤2[n/r]; 2 De(H) + p(H)≤n-r + 2. 相似文献
10.
A.R. Ashrafi M. SaheliM. Ghorbani 《Journal of Computational and Applied Mathematics》2011,235(16):4561-4566
Let G be a molecular graph. The eccentric connectivity index ξc(G) is defined as ξc(G)=∑u∈V(G)degG(u)εG(u), where degG(u) denotes the degree of vertex u and εG(u) is the largest distance between u and any other vertex v of G. In this paper exact formulas for the eccentric connectivity index of TUC4C8(S) nanotube and TC4C8(S) nanotorus are given. 相似文献
11.
《Stochastic Processes and their Applications》1987,24(2):279-286
For every positive integer n, let Sn be the n-th partial sum of a sequence of independent and identically distributed random variables, each assuming the values +1 and −1 with respective probabilities p (0<p<1)) and q (= 1 −p) and having mean μ = p − q. For a fixed positive real number λ, let N+[N1] be the total number of values of n for which Sn > (μ + λ)n [Sn⩾(μ + λ)n] and let L+[L1] be the supremum of the values of n for which Sn > (μ + λ)n [Sn⩾(μ + λ)n], where sup Oslash; = 0. Explicit expressions for the exact distributions of N+, N1, L+ and L1 are given when μ + λ = ±k/(k + 2) for any nonnegative integer k. 相似文献
12.
A monadic formula ψ(Y) is a selector for a monadic formula φ(Y) in a structure M if ψ defines in M a unique subset P of the domain and this P also satisfies φ in M. If C is a class of structures and φ is a selector for ψ in every M∈C, we say that φ is a selector for φ over C.For a monadic formula φ(X,Y) and ordinals α≤ω1 and δ<ωω, we decide whether there exists a monadic formula ψ(X,Y) such that for every P⊆αof order-type smaller thanδ, ψ(P,Y) selects φ(P,Y) in (α,<). If so, we construct such a ψ.We introduce a criterion for a class C of ordinals to have the property that every monadic formula φ has a selector over it. We deduce the existence of S⊆ωω such that in the structure (ωω,<,S) every formula has a selector.Given a monadic sentence π and a monadic formula φ(Y), we decide whether φ has a selector over the class of countable ordinals satisfying π, and if so, construct one for it. 相似文献
13.
Jiuying Dong 《Journal of Applied Mathematics and Computing》2010,34(1-2):485-493
The theory of vertex-disjoint cycles and 2-factor of graphs has important applications in computer science and network communication. For a graph G, let σ 2(G):=min?{d(u)+d(v)|uv ? E(G),u≠v}. In the paper, the main results of this paper are as follows:
- Let k≥2 be an integer and G be a graph of order n≥3k, if σ 2(G)≥n+2k?2, then for any set of k distinct vertices v 1,…,v k , G has k vertex-disjoint cycles C 1,C 2,…,C k of length at most four such that v i ∈V(C i ) for all 1≤i≤k.
- Let k≥1 be an integer and G be a graph of order n≥3k, if σ 2(G)≥n+2k?2, then for any set of k distinct vertices v 1,…,v k , G has k vertex-disjoint cycles C 1,C 2,…,C k such that:
- v i ∈V(C i ) for all 1≤i≤k.
- V(C 1)∪???∪V(C k )=V(G), and
- |C i |≤4, 1≤i≤k?1.
14.
Wen Zhang 《Linear algebra and its applications》2011,435(6):1326-1335
Let A and B be (not necessarily unital or closed) standard operator algebras on complex Banach spaces X and Y, respectively. For a bounded linear operator A on X, the peripheral spectrum σπ(A) of A is the set σπ(A)={z∈σ(A):|z|=maxω∈σ(A)|ω|}, where σ(A) denotes the spectrum of A. Assume that Φ:A→B is a map the range of which contains all operators of rank at most two. It is shown that the map Φ satisfies the condition that σπ(BAB)=σπ(Φ(B)Φ(A)Φ(B)) for all A,B∈A if and only if there exists a scalar λ∈C with λ3=1 and either there exists an invertible operator T∈B(X,Y) such that Φ(A)=λTAT-1 for every A∈A; or there exists an invertible operator T∈B(X∗,Y) such that Φ(A)=λTA∗T-1 for every A∈A. If X=H and Y=K are complex Hilbert spaces, the maps preserving the peripheral spectrum of the Jordan skew semi-triple product BA∗B are also characterized. Such maps are of the form A?UAU∗ or A?UAtU∗, where U∈B(H,K) is a unitary operator, At denotes the transpose of A in an arbitrary but fixed orthonormal basis of H. 相似文献
15.
Let us denote by R(k, ? λ)[R(k, ? λ)] the maximal number such that there exist different permutations of the set {1,…, k} such that any two of them have at least λ (at most λ, respectively) common positions. We prove the inequalities R(k, ? λ) ? kR(k ? 1, ? λ ? 1), R(k, ? λ) ? R(k, ? λ ? 1) ? k!, R(k, ? λ) ? kR(k ? 1, ? λ ? 1). We show: R(k, ? k ? 2) = 2, R(k, ? 1) = (k ? 1)!, R(pm, ? 2) = (pm ? 2)!, R(pm + 1, ? 3) = (pm ? 2)!, , R(k, ? 0) = k, R(pm, ? 1) = pm(pm ? 1), R(pm + 1, ? 2) = (pm + 1)pm(pm ? 1). The exact value of R(k, ? λ) is determined whenever k ? k0(k ? λ); we conjecture that R(k, ? λ) = (k ? λ)! for k ? k0(λ). Bounds for the general case are given and are used to determine that the minimum of |R(k, ? λ) ? R(k, ? λ)| is attained for . 相似文献
16.
Arnold W. Miller 《Topology and its Applications》2009,156(5):872-878
For X a separable metric space define p(X) to be the smallest cardinality of a subset Z of X which is not a relative γ-set in X, i.e., there exists an ω-cover of X with no γ-subcover of Z. We give a characterization of p(ω2) and p(ωω) in terms of definable free filters on ω which is related to the pseudo-intersection number p. We show that for every uncountable standard analytic space X that either p(X)=p(ω2) or p(X)=p(ωω). We show that the following statements are each relatively consistent with ZFC: (a) p=p(ωω)<p(ω2) and (b) p<p(ωω)=p(ω2) 相似文献
17.
Oscillation criteria for the class of forced functional differential inequalities x(t){Lnx(t) + f(t, x(t), x[g1(t)],…, x[gm(t)]) ? h(t)} ? 0, for n even, and x(t){Lnx(t) ? f(t, x(t), x[g1(t)],…, x[gm(t)]) ? h(t)} ? 0, for n odd, are established. 相似文献
18.
Let Wk(A) denote the k-numerical range of an n × n matrix A. It is known that Wi(A) ? Wj(A) for 1 ? j? i? n. It this paper we derive more general inclusion relations of the form ΣniλiWi(A) ? ΣniμiWi(A), where λi, μi are real coefficients. 相似文献
19.
For a set A of nonnegative integers the representation functions R2(A,n), R3(A,n) are defined as the number of solutions of the equation n=a+a′,a,a′∈A with a<a′, a?a′, respectively. Let D(0)=0 and let D(a) denote the number of ones in the binary representation of a. Let A0 be the set of all nonnegative integers a with even D(a) and A1 be the set of all nonnegative integers a with odd D(a). In this paper we show that (a) if R2(A,n)=R2(N?A,n) for all n?2N−1, then R2(A,n)=R2(N?A,n)?1 for all n?12N2−10N−2 except for A=A0 or A=A1; (b) if R3(A,n)=R3(N?A,n) for all n?2N−1, then R3(A,n)=R3(N?A,n)?1 for all n?12N2+2N. Several problems are posed in this paper. 相似文献
20.
Changqing Xu Xianli Ma Shouliang Hua 《Journal of Applied Mathematics and Computing》2009,31(1-2):45-50
Let G=(V(G),E(G)) be a simple graph. Given non-negative integers r,s, and t, an [r,s,t]-coloring of G is a mapping c from V(G)∪E(G) to the color set {0,1,…,k?1} such that |c(v i )?c(v j )|≥r for every two adjacent vertices v i ,v j , |c(e i )?c(e j )|≥s for every two adjacent edges e i ,e j , and |c(v i )?c(e j )|≥t for all pairs of incident vertices and edges, respectively. The [r,s,t]-chromatic number χ r,s,t (G) of G is defined to be the minimum k such that G admits an [r,s,t]-coloring. We determine χ r,s,t (K n,n ) in all cases. 相似文献