共查询到20条相似文献,搜索用时 31 毫秒
1.
Michel Las Vergnas 《Discrete Mathematics》1978,23(3):241-255
We prove the following theorem: Let G be a graph with vertex-set V and ?, g be two integer-valued functions defined on V such that for all x ∈ V. Then G contains a factor F such that for all x ∈ V if and only if for every subset X of V, is at least equal to the number of connected components C of G[V ? X] such that either C = {x} and g(x) = 1, or |C| is odd ?3 and for all x ∈ C. Applications are given to certain combinatorial geometries associated with factors of graphs. 相似文献
2.
3.
《Topology and its Applications》1986,22(2):109-122
We write 2x for the hyperspace of all non-empty compact sets in a complete metric linear space X topologized by the Hausdorff metric. Using the notation (X) = {A ϵ 2X: A is finite}, lf2 = {x} = (xi) ϵ l2: xi = 0 for almost all i}, and lσ2 = {x = (x i) ϵ l2:σ∞i=1 (ixi)2 < ∞}, we have the following theorem:A family ⊂(X) is homeomorphic to lf2 if is σ-fd-compact, the closure of in 2x is not locally compact and if whenever A, B ∈ , λ ∈ [0, 1] and C ⊂ λA + (1 - λ)B with card C⩽ max{card A, card B} then C ϵ .Moreover, for any Gδ-AR-set of with ⊃ we have (, )≅(l2, lƒ2).Similar conditions for hyperspaces to be homeomorphic to lσ2 are also established. 相似文献
4.
Klaus D. Schmidt 《Journal of multivariate analysis》1980,10(1):123-134
For certain types of stochastic processes {Xn | n ∈ }, which are integrable and adapted to a nondecreasing sequence of σ-algebras n on a probability space (Ω, , P), several authors have studied the following problems: IfSdenotes the class of all stopping times for the stochastic basis {n | n ∈ }, when isfinite, and when is there a stopping time for which this supremum is attained? In the present paper we set the problem in a measure theoretic framework. This approach turns out to be fruitful since it reveals the root of the problem: It avoids the use of such notions as probability, null set, integral, and even σ-additivity. It thus allows a considerable generalization of known results, simplifies proofs, and opens the door to further research. 相似文献
5.
For finite graphs F and G, let NF(G) denote the number of occurrences of F in G, i.e., the number of subgraphs of G which are isomorphic to F. If and are families of graphs, it is natural to ask then whether or not the quantities NF(G), F∈, are linearly independent when G is restricted to . For example, if = {K1, K2} (where Kn denotes the complete graph on n vertices) and is the family of all (finite) trees, then of course NK1(T) ? NK2(T) = 1 for all T∈. Slightly less trivially, if = {Sn: n = 1, 2, 3,…} (where Sn denotes the star on n edges) and again is the family of all trees, then Σn=1∞(?1)n+1NSn(T)=1 for all T∈. It is proved that such a linear dependence can never occur if is finite, no F∈ has an isolated point, and contains all trees. This result has important applications in recent work of L. Lovász and one of the authors (Graham and Lovász, to appear). 相似文献
6.
Chungming An 《Journal of Number Theory》1974,6(1):1-6
A Dirichlet series associated with a positive definite form of degree δ in n variables is defined by where ? ∈ , α ∈ n, 〈x, y〉 = x1y1 + ? + xnyn, e(a) = exp (2πia) for a ∈ , and s = σ + ti is a complex number. The author proves that: (1) DF(s, ?, α) has analytic continuation into the whole s-plane, (2) DF(s, ?, α), ? ≠ 0, is a meromorphic function with at most a simple pole at . The residue at is given explicitly. (3) ? = 0, α ? n, DF(s, 0, α) is analytic for . 相似文献
7.
Let F be a Sperner family of subsets of {1,…,m}. Bollobás showed that if , and if the parameters of F are p0,…,pm then Here we generalize this result and prove some analogues of it. A corollary of Bollobás' result is that . Purdy proved that if then , which implies Bollobás' corollary. We also show that Purdy's result may be deduced from Bollobás' by a short argument. Finally, we give a canonical form for Sperner families which are also pairwise intersecting. 相似文献
8.
Let X be a finite set of n-melements and suppose t ? 0 is an integer. In 1975, P. Erdös asked for the determination of the maximum number of sets in a family = {F1,…, Fm}, Fi ? X, such that ∥Fi ∩ Fj∥ ≠ t for 1 ? i ≠ j ? m. This problem is solved for n ? n0(t). Let us mention that the case t = 0 is trivial, the answer being 2n ? 1. For t = 1 the problem was solved in [3]. For the proof a result of independent interest (Theorem 1.5) is used, which exhibits connections between linear algebra and extremal set theory. 相似文献
9.
Kai Wang 《Journal of Number Theory》1984,18(3):306-312
For a positive integer m, let and let n = |A|. For an integer x, let R(x) be the least positive residue of x modulo m and if (x, m) = 1, let x′ be the inverse of x modulo m. If m is odd, then |R(ab′)|a,b∈A = ?21?n(∏χ(Σa = 1m ? 1aχ(a))), where χ runs over all the odd Dirichlet characters modulo m. 相似文献
10.
Robert Chen 《Journal of multivariate analysis》1978,8(2):328-333
Let {Xn}n≥1 be a sequence of independent and identically distributed random variables. For each integer n ≥ 1 and positive constants r, t, and ?, let Sn = Σj=1nXj and . In this paper, we prove that (1) lim?→0+?α(r?1)E{N∞(r, t, ?)} = K(r, t) if E(X1) = 0, Var(X1) = 1, and E(| X1 |t) < ∞, where 2 ≤ t < 2r ≤ 2t, , and ; (2) if 2 < t < 4, E(X1) = 0, Var(X1) > 0, and E(|X1|t) < ∞, where G(t, ?) = E{N∞(t, t, ?)} = Σn=1∞nt?2P{| Sn | > ?n} → ∞ as ? → 0+ and , i.e., H(t, ?) goes to infinity much faster than G(t, ?) as ? → 0+ if 2 < t < 4, E(X1) = 0, Var(X1) > 0, and E(| X1 |t) < ∞. Our results provide us with a much better and deeper understanding of the tail probability of a distribution. 相似文献
11.
A space X is said to satisfy condition (C) if for every Y?X with |Y|=ω1, any family of open subsets of Y with ||=ω1 has a countable network. It is easy to see that if X satisfies condition (C), then its Pixley-Roy hyperspace [X] is CCC. We show that under MAω1 condition (C) is also necessary for [X] to be CCC, but under CH it is not. 相似文献
12.
Following a conjecture of P. Erdös, we show that if is a family of k-subsets of and n-set no two of which intersect in exactly l elements then for k ? 2l + 2 and n sufficiently large || ? (k ? l ? 1n ? l ? 1) with equality holding if and only if consists of all the k-sets containing a fixed (l + 1)-set. In general we show || ? dknmax;{;l,k ? l ? 1};, where dk is a constant depending only on k. These results are special cases of more general theorems (Theorem 2.1–2.3). 相似文献
13.
Cai Mao-cheng 《Discrete Mathematics》1984,48(1):121-123
Let S be a set of n elements, and k a fixed positive integer . Katona's problem is to determine the smallest integer m for which there exists a family = {A1, …, Am} of subsets of S with the following property: |i| ? k (i = 1, …, m), and for any ordered pair xi, xi ∈ S (i ≠ j) there is A1 ∈ such that xi ∈ A1, xj ? A1. It is given in this note that . 相似文献
14.
Let (F,G) be a pair of matrices defined over an arbitrary field, Fn × n, Gn × m. Consider the natural action of GLn x GLm on this pair given by (F,G) ? (gFg-1,gGh-1), where (g,h) ∈ GLn × GLm. This action is of interest in system theory as well as the representation theory of quivers. In this paper we study the stabilizer subgroup of this action stab(F,G), i.e. . 相似文献
15.
Peter Frankl 《Journal of Combinatorial Theory, Series A》1978,24(2):146-161
Let X = [1, n] be a finite set of cardinality n and let be a family of k-subsets of X. Suppose that any two members of intersect in at least t elements and for some given positive constant c, every element of X is contained in less than c || members of . How large || can be and which are the extremal families were problems posed by Erdös, Rothschild, and Szemerédi. In this paper we answer some of these questions for n > n0(k, c). One of the results is the following: let . Then whenever is an extremal family we can find a 7-3 Steiner system such that consists exactly of those k-subsets of X which contain some member of . 相似文献
16.
A compactificaton αX of a completely regular space X is “determined” by a subset F of C1(X) if αX is the smallest compactificaton of X to which each element of F extends, and is “generated” by F if the evaluation map , is an embedding and . Evidently, if F either determines or generates αX, then every elements of F has an extension to αX; whenever F satisfies this latter condition, the set of all such extensions is denoted Fα.A major results of our previous paper is that F determines αX if and only if Fα separates points of αX ? X. A major result of the present paper is that F generates αX if and only if Fα separates points of αX. 相似文献
17.
Joel M Cohen 《Journal of Functional Analysis》1982,48(3):301-309
Let G be a group and g1,…, gt a set of generators. There are approximately (2t ? 1)n reduced words in g1,…, gt, of length ?n. Let be the number of those which represent 1G. We show that exists. Clearly 1 ? γ ? 2t ? 1. is the cogrowth. 0 ? η ? 1. In fact . The entropic dimension of G is shown to be 1 ? η. It is then proved that d(G) = 1 if and only if G is free on g1,…, gt and d(G) = 0 if and only if G is amenable. 相似文献
18.
In this note we demonstrate the existence of E0L forms F and G which are n-similar, i.e. n(F) = n(G) but n+1(F)≠n+1(G) for n ∈ {2, 3}. This partially solves an open problem from [3]. 相似文献
19.
Let (Xn)n? be a sequence of real, independent, not necessarily identically distributed random variables (r.v.) with distribution functions FXn, and Sn = Σi=1nXi. The authors present limit theorems together with convergence rates for the normalized sums ?(n)Sn, where ?: → +, ?(n) → 0, n → ∞, towards appropriate limiting r.v. X, the convergence being taken in the weak (star) sense. Thus higher order estimates are given for the expression ∝f(x) d[F?(n)Sn(x) ? FX(x)] which depend upon the normalizing function ?, decomposability properties of X and smoothness properties of the function f under consideration. The general theorems of this unified approach subsume O- and o-higher order error estimates based upon assumptions on associated moments. These results are also extended to multi-dimensional random vectors. 相似文献
20.
Ivan Singer 《Journal of Mathematical Analysis and Applications》1984,104(2):351-389
For the optimization problem (P) α = inf h(G), where G ≠ Ø is a subset of a locally convex space , we introduce and study two general concepts of dual problems, encompassing the classical surrogate dual problem. The first one involves only a family of surrogate constraints sets ΔG, Φ ? F (Φ ∈ W), where W ? RX, X being a locally convex space. The second one uses a perturbation functional and a family of sets , where W ? RX. We give duality theorems, introduce Lagrangians, and show some relations between these problems and the dual problems to (P) defined with the aid of a perturbation and a concept of conjugation of functionals. 相似文献