共查询到20条相似文献,搜索用时 31 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.
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
3.
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
4.
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
5.
The Dirichlet problem for the region of the plane inside closed smooth curve C for second-order elliptic equations is considered. It is shown that under certain circumstances the solution u can be written uniquely in the form u(P) = ∝cF(P, Q) g(Q) dsQ, where F(P, Q) is the fundamental solution of the elliptic equation, and g?L2 if the boundary value function f is absolutely continuous with square integrable derivative (f?W); and u(P) = p(F(P, ·)) where p is a unique bounded linear functional on W if f?L2. These representations are valid in the exterior of C also. As special cases with slight modifications, the exterior Dirichlet problems for the Helmholtz and Laplace equations are mentioned.It is shown also that if kernel F(P′, Q), with P′ and Q on C, has a complete set of eigenfunctions {ψk(P′)} then u(P) can be expanded in a series of their extensions {ψk(P)}, where ψk(P) = λk ∝cF(P, Q) ψk(Q) dsQ. 相似文献
6.
R.E White 《Journal of Mathematical Analysis and Applications》1979,68(1):157-170
We consider weak solutions to the nonlinear boundary value problem (r, (x, u(x)) u′(x))′ = (Fu)′(x) with r(0, u(0)) u′(0) = ku(0), r(L, u(L)) u′(L) = hu(L) and k, h are suitable elements of [0, ∞]. In addition to studying some new boundary conditions, we also relax the constraints on r(x, u) and (Fu)(x). r(x, u) > 0 may have a countable set of jump discontinuities in u and r(x, u)?1?Lq((0, L) × (0, p)). F is an operator from a suitable set of functions to a subset of Lp(0, L) which have nonnegative values. F includes, among others, examples of the form (Fu)(x) = (1 ? H(x ? x0)) u(x0), (Fu)(x) = ∫xLf(y, u(y)) dy where f(y, u) may have a countable set of jump discontinuities in u or F may be chosen so that (Fu)′(x) = ? g(x, u(x)) u′(x) ? q(x) u(x) ? f(x, u(x)) where q is a distributional derivative of an L2(0, L) function. 相似文献
7.
Let R be a noncommutative prime ring of characteristic different from 2, U the Utumi quotient ring of R, C the extended centroid of R, and L a noncentral Lie ideal of R. If F and G are generalized derivations of R and k ≥1 a fixed integer such that [F(x), x] k x ? x[G(x), x] k = 0 for any x ∈ L, then one of the following holds:
- either there exists an a ∈ U and an α ∈ C such that F(x) = xa and G(x) = (a + α)x for all x ∈ R
- or R satisfies the standard identity s 4(x 1, …, x 4) and one of the following conclusions occurs
- there exist a, b, c, q ∈ U, such that a ?b + c ?q ∈ C and F(x) = ax + xb, G(x) = cx + xq for all x ∈ R
- there exist a, b, c ∈ U and a derivation d of U such that F(x) = ax+d(x) andG(x) = bx+xc?d(x) for all x ∈ R, with a + b ? c ∈ C.
8.
F.K. Hwang 《Discrete Mathematics》1980,32(2):163-165
Let Tn denote a binary tree with n terminal nodes V={υ1,…,υn} and let li denote the path length from the root to υi. Consider a set of nonnegative numbers W={w1,…,wn} and for a permutation π of {1,…,n} to {1,…,n}, associate the weight wi to the node υπ(i). The cost of Tn is defined as C(Tn∣W)=Minπ∑ni=1wilπ(i).A Huffman tree Hn is a binary tree which minimizes C(Tn∣W) over all possible Tn. In this note, we give an explicit expression for C(Hn∣W) when W assumes the form: wi=k for i=1,…,n?m; wi=x for i=n?m+1,…,n. This simplifies and generalizes earlier results in the literature. 相似文献
9.
Daniel A. Klain 《Advances in Mathematics》2010,224(2):601-4601
For n?2 a construction is given for convex bodies K and L in Rn such that the orthogonal projection Lu onto the subspace u⊥ contains a translate of Ku for every direction u, while the volumes of K and L satisfy Vn(K)>Vn(L).A more general construction is then given for n-dimensional convex bodies K and L such that each orthogonal projection Lξ onto a k-dimensional subspace ξ contains a translate of Kξ, while the mth intrinsic volumes of K and L satisfy Vm(K)>Vm(L) for all m>k.For each k=1,…,n, we then define the collection Cn,k to be the closure (under the Hausdorff topology) of all Blaschke combinations of suitably defined cylinder sets (prisms).It is subsequently shown that, if L∈Cn,k, and if the orthogonal projection Lξ contains a translate of Kξ for every k-dimensional subspace ξ of Rn, then Vn(K)?Vn(L).The families Cn,k, called k-cylinder bodies of Rn, form a strictly increasing chain
Cn,1⊂Cn,2⊂?⊂Cn,n−1⊂Cn,n, 相似文献
10.
Y. Stein 《Israel Journal of Mathematics》1995,89(1-3):301-319
LetP=x n +P n?1(y)x n?1+…+P 0(y),Q=x m +Q m?2(y)x m?2+…+Q 0(y) belong toK[x, y], whereK is a field of characteristic zero. The main result of this paper is the following: Assume thatP x Q y ?P y Q x =1. Then:*
- K[Q m?2(y), …,Q 0(y)]=K[y],
- K[P, Q]=K[x, y] ifQ=x m +Q k (y)x k +Q r (y)x r
11.
R. Balakrishnan 《Discrete Mathematics》2008,308(12):2607-2610
In a search for triangle-free graphs with arbitrarily large chromatic numbers, Mycielski developed a graph transformation that transforms a graph G into a new graph μ(G), which is called the Mycielskian of G. This paper investigates the vertex-connectivity κ(μ(G)) and edge-connectivity κ′(μ(G)) of μ(G) . We show that κ(μ(G))=min{δ(μ(G)),2κ(G)+1} and κ′(μ(G))=δ(μ(G)). 相似文献
12.
Alan Dow 《Topology and its Applications》2010,157(8):1379-1857
We consider generalizations of a well-known class of spaces, called by S. Mrówka, N∪R, where R is an infinite maximal almost disjoint family (MADF) of countable subsets of the natural numbers N. We denote these generalizations by ψ=ψ(κ,R) for κ?ω. Mrówka proved the interesting theorem that there exists an R such that |βψ(ω,R)?ψ(ω,R)|=1. In other words there is a unique free z-ultrafilter p0 on the space ψ. We extend this result of Mrówka to uncountable cardinals. We show that for κ?c, Mrówka's MADF R can be used to produce a MADF M⊂ω[κ] such that |βψ(κ,M)?ψ(κ,M)|=1. For κ>c, and every M⊂ω[κ], it is always the case that |βψ(κ,M)?ψ(κ,M)|≠1, yet there exists a special free z-ultrafilter p on ψ(κ,M) retaining some of the properties of p0. In particular both p and p0 have a clopen local base in βψ (although βψ(κ,M) need not be zero-dimensional). A result for κ>c, that does not apply to p0, is that for certain κ>c, p is a P-point in βψ. 相似文献
13.
W.Y. Chan 《Journal of Computational and Applied Mathematics》2011,235(13):3831-3840
For the problem given by uτ=(ξrumuξ)ξ/ξr+f(u) for 0<ξ<a, 0<τ<Λ≤∞, u(ξ,0)=u0(ξ) for 0≤ξ≤a, and u(0,τ)=0=u(a,τ) for 0<τ<Λ, where a and m are positive constants, r is a constant less than 1, f(u) is a positive function such that limu→c−f(u)=∞ for some positive constant c, and u0(ξ) is a given function satisfying u0(0)=0=u0(a), this paper studies quenching of the solution u. 相似文献
14.
Let G be a graph. If u,v∈V(G), a u-vshortest path of G is a path linking u and v with minimum number of edges. The closed interval I[u,v] consists of all vertices lying in some u-v shortest path of G. For S⊆V(G), the set I[S] is the union of all sets I[u,v] for u,v∈S. We say that S is a convex set if I[S]=S. The convex hull of S, denoted Ih[S], is the smallest convex set containing S. A set S is a hull set of G if Ih[S]=V(G). The cardinality of a minimum hull set of G is the hull number of G, denoted by hn(G). In this work we prove that deciding whether hn(G)≤k is NP-complete.We also present polynomial-time algorithms for computing hn(G) when G is a unit interval graph, a cograph or a split graph. 相似文献
15.
Hui-Hsiung Kuo 《Journal of Functional Analysis》1976,21(1):63-75
Some parallel results of Gross' paper (Potential theory on Hilbert space, J. Functional Analysis1 (1967), 123–181) are obtained for Uhlenbeck-Ornstein process U(t) in an abstract Wiener space (H, B, i). Generalized number operator is defined by f(x) = ?lim∈←0{E[f((τ∈ξ))] ? f(x)}/E[τ∈ξ, where τx? is the first exit time of U(t) starting at x from the ball of radius ? with center x. It is shown that f(x) = ?trace D2f(x)+〈Df(x),x〉 for a large class of functions f. Let rt(x, dy) be the transition probabilities of U(t). The λ-potential Gλf, λ > 0, and normalized potential Rf of f are defined by Gλf(X) = ∫0∞e?λtrtf(x) dt and Rf(x) = ∫0∞ [rtf(x) ? rtf(0)] dt. It is shown that if f is a bounded Lip-1 function then trace D2Gλf(x) ? 〈DGλf(x), x〉 = ?f(x) + λGλf(x) and trace D2Rf(x) ? 〈DRf(x), x〉 = ?f(x) + ∫Bf(y)p1(dy), where p1 is the Wiener measure in B with parameter 1. Some approximation theorems are also proved. 相似文献
16.
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
17.
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
18.
《Discrete Mathematics》2002,231(1-3):319-324
A graph G is called n-factor-critical if the removal of every set of n vertices results in a~graph with a~1-factor. We prove the following theorem: Let G be a~graph and let x be a~locally n-connected vertex. Let {u,v} be a~pair of vertices in V(G)−{x} such that uv∉E(G), x∈NG(u)∩NG(v), and NG(x)⊂NG(u)∪NG(v)∪{u,v}. Then G is n-factor-critical if and only if G+uv is n-factor-critical. 相似文献
19.
In this paper we introduce a generalized vector-valued paranormed sequence space Np(Ek,Δm,f,s) using modulus function f, where p=(pk) is a bounded sequence of positive real numbers such that infkpk>0,(Ek,qk) is a sequence of seminormed spaces with Ek+1⊆Ek for each k ∈ N and s?0. We have also studied sequence space Np(Ek,Δm,fr,s), where fr=f°f°f°,…,f (r-times composition of f with itself) and r∈N={1,2,3,…}. Results regarding completeness, K-space, normality, inclusion relations etc. are derived. Further, a study of multiplier of the set Np(Ek,f,s) is also made by choosing (Ek,‖·‖k) as sequence of normed algebras. 相似文献
20.
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