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A standard matrix representation of a matroid M represents M relative to a fixed basis B, where contracting elements of B and deleting elements of E(M)–B correspond to removing rows and columns of the matrix, while retaining standard form. If M is 3-connected and N is a 3-connected minor of M, it is often desirable to perform such a removal while maintaining both 3-connectivity and the presence of an N-minor. We prove that, subject to a mild essential restriction, when M has no 4-element fans with a specific labelling relative to B, there are at least two distinct elements, s 1 and s 2, such that for each i ∈ {1, 2}, si(M/s i ) is 3-connected and has an N-minor when s i ∈ B, and co(M\s i ) is 3-connected and has an N-minor when s i ∈ E(M)–B. We also show that if M has precisely two such elements and P is the set of elements that, when removed in the appropriate way, retain the N-minor, then (P, E(M)–P) is a sequential 3-separation. 相似文献
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Guilherme Carmona 《International Journal of Game Theory》2006,34(1):131-151
We study the properties of finitely complex, symmetric, globally stable, and semi-perfect equilibria. We show that: (1) If a strategy satisfies these properties then players play a Nash equilibrium of the stage game in every period; (2) The set of finitely complex, symmetric, globally stable, semi-perfect equilibrium payoffs in the repeated game equals the set of Nash equilibria payoffs in the stage game; and (3) A strategy vector satisfies these properties in a Pareto optimal way if and only if players play some Pareto optimal Nash equilibrium of the stage game in every stage. Our second main result is a strong anti-Folk Theorem, since, in contrast to what is described by the Folk Theorem, the set of equilibrium payoffs does not expand when the game is repeated.This paper is a revised version of Chapter 3 of my Ph.D. thesis, which has circulated under the title “An Interpretation of Nash Equilibrium Based on the Notion of Social Institutions”. 相似文献
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A graph H is strongly immersed in G if H is obtained from G by a sequence of vertex splittings (i.e., lifting some pairs of incident edges and removing the vertex) and edge removals. Equivalently, vertices of H are mapped to distinct vertices of G (branch vertices) and edges of H are mapped to pairwise edge‐disjoint paths in G, each of them joining the branch vertices corresponding to the ends of the edge and not containing any other branch vertices. We describe the structure of graphs avoiding a fixed graph as a strong immersion. The theorem roughly states that a graph which excludes a fixed graph as a strong immersion has a tree‐like decomposition into pieces glued together on small edge cuts such that each piece of the decomposition has a path‐like linear decomposition isolating the high degree vertices. 相似文献
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Zhiyi Chi 《Journal of Theoretical Probability》2018,31(3):1235-1272
This paper takes the so-called probabilistic approach to the strong renewal theorem (SRT) for multivariate distributions in the domain of attraction of a stable law. A version of the SRT is obtained that allows any kind of lattice–nonlattice composition of a distribution. A general bound is derived to control the so-called small-n contribution, which arises from random walk paths that have a relatively small number of steps but make large cumulative moves. The asymptotic negligibility of the small-n contribution is essential to the SRT. Applications of the SRT are given, including some that provide a unified treatment to known results but with substantially weaker assumptions. 相似文献
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Wen Sheng WANG 《数学学报(英文版)》2005,21(6):1269-1276
By combining the Csorgo-Révész quantile transform methods and the Skorohod-Strassen martingale embedding theorem, we prove a strong approximation theorem for quasi-associated random variables with mean zero and finite (2 + δ)th moment under polynomial decay rate. As a consequence, the decay rate for a strong approximation theorem of associated sequences of Yu (1996) is weakened. 相似文献
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强完美图定理及相关的问题 总被引:1,自引:0,他引:1
介绍强完美图定理(The Strong Perfect Graph Theorem,SPGT)的历史和获证经过,同时简述SPGT被克服后生发的一些新问题,以期对图理论的一般研究起到鼓励和促进作用.因具体的证明浩大聱曲,在技术的部分仅注重框架而不涉及细节. 相似文献
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In this paper we study sequence spaces that arise from the conceptof strong weighted mean summability. Let q = (qn) be a sequenceof positive terms and set Qn = nk=1qk. Then the weighted meanmatrix Mq = (ank) is defined by if kn, ank=0 if k>n. It is well known that Mq defines a regular summability methodif and only if Qn. Passing to strong summability, we let 0<p<.Then
,
are the spaces of all sequences that are strongly Mq-summablewith index p to 0, strongly Mq-summable with index p and stronglyMq-bounded with index p, respectively. The most important specialcase is obtained by taking Mq = C1, the Cesàro matrix,which leads to the familiar sequence spaces w0(p), w(p) and w(p), respectively, see [4, 21]. We remark that strong summabilitywas first studied by Hardy and Littlewood [8] in 1913 when theyapplied strong Cesàro summability of index 1 and 2 toFourier series; orthogonal series have remained the main areaof application for strong summability. See [32, 6] for furtherreferences. When we abstract from the needs of summability theory certainfeatures of the above sequence spaces become irrelevant; forinstance, the qk simply constitute a diagonal transform. Hence,from a sequence space theoretic point of view we are led tostudy the spaces 相似文献
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In this paper, the idea of random selection in the theorem on gambling system is extended to Markov chains, by using the notion likelihood ratio and an analytic technique. A strong limit theorem on the relative frequency of ordered couple under random selection is established.AMS Subject Classification (2001)
primary 60F15 Secondary 60J10 相似文献
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Peter Schatte 《Mathematische Nachrichten》1988,137(1):249-256
Let Sn be the sum of n i.i.d.r.v. and let 1(-∞,x)(·) be the indicator function of the interval (-∞, x). Then the sequence 1(-∞, x)(Sn/√n) does not converge for any x. Likewise the arithmetic means of this sequence converge only with probability zero. But the logarithmic means converge with probability one to the standard normal distribution Ø(x). Then for any bounded and a.e. continuous function a(y) the logarithmic means of a(Sn/√n) converge a.s. to a = ∫a(y)dØ(y). The arithmetic means of a(Snk/√n) converge to the same limit a for all subsequences nk = [ck], c > 1. 相似文献
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A STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES 总被引:1,自引:0,他引:1
This paper presents a geometric characterization of convex sets in locally convex spaces on which a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem of w Asplund spaces a localized setting. 相似文献
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Arup Bose 《Journal of Theoretical Probability》1998,11(4):921-933
We prove a weighted Glivenko-Cantelli theorem and apply it to study the rate of convergence in the strong law for L-statistics. 相似文献
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The constant stepsize analog of Gelfand–Mitter type discrete-time stochastic recursive algorithms is shown to track an associated stochastic differential equation in the strong sense, i.e., with respect to an appropriate divergence measure. 相似文献
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本文利用似然比作为一般连续型随机变量相对独立随机变量偏差的一种随机性度量 ,用矩变换构造几乎处处收敛的上鞅 ,结合分析方法 ,得到了一种乘积形式的强极限定理 . 相似文献
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本文的目的是要给出一个关于可列非齐次马尔可夫链M元状态序组出现频率的新形式的强极限定理,所得结论对任意可列非齐次马尔可夫链普遍成立. 相似文献