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941.
We base ourselves on the construction of the two-dimensional random interlacements (Comets et al., 2016) to define the one-dimensional version of the process. For this, we consider simple random walks conditioned on never hitting the origin. We compare this process to the conditional random walk on the ring graph. Our results are the convergence of the vacant set on the ring graph to the vacant set of one-dimensional random interlacements, a central limit theorem for the interlacements’ local time and the convergence in law of the local times of the conditional walk on the ring graph to the interlacements’ local times. 相似文献
942.
《Journal of Graph Theory》2018,87(2):176-187
For graphs G and H, let denote the property that for every proper edge‐coloring of G (with an arbitrary number of colors) there is a rainbow copy of H in G, that is, a copy of H with no two edges of the same color. The authors (2014) proved that, for every graph H, the threshold function of this property for the binomial random graph is asymptotically at most , where denotes the so‐called maximum 2‐density of H. Nenadov et al. (2014) proved that if H is a cycle with at least seven vertices or a complete graph with at least 19 vertices, then . We show that there exists a fairly rich, infinite family of graphs F containing a triangle such that if for suitable constants and , where , then almost surely. In particular, for any such graph F. 相似文献
943.
944.
Nguyen Huy Tuan Nguyen Hoang Tuan Dumitru Baleanu Tran Ngoc Thach 《Mathematical Methods in the Applied Sciences》2020,43(3):1292-1312
In the present paper, we study the initial inverse problem (backward problem) for a two-dimensional fractional differential equation with Riemann-Liouville derivative. Our model is considered in the random noise of the given data. We show that our problem is not well-posed in the sense of Hadamard. A truncated method is used to construct an approximate function for the solution (called the regularized solution). Furthermore, the error estimate of the regularized solution in L2 and Hτ norms is considered and illustrated by numerical example. 相似文献
945.
建立并求解了弹性介质中圆柱壳的径向位移控制方程,考虑边界条件及相容条件,得到了应力波传播及反射过程中圆柱壳的动力屈曲分叉条件.通过计算得到了不同时间段屈曲临界载荷与应力波波阵面到达圆柱壳的位置、弹性介质的刚度、壳体未嵌入弹性介质部分的长度与总长之比的关系.数值计算结果表明,弹性介质中的圆柱壳发生轴对称屈曲和非轴对称屈曲趋势一致;嵌入弹性介质部分越深、弹性介质刚度越大圆柱壳越难屈曲;屈曲临界载荷随着弹性介质刚度的增大经历了增长缓慢、增长迅速以及增长较慢3个阶段;应力波反射前波阵面通过分界面后,屈曲仅发生在应力波传播区域,反射波波阵面通过分界面前,临界载荷较小时屈曲先发生在反射端部,随着轴向阶数增大,屈曲覆盖整个圆柱壳区域,反射波波阵面通过分界面后,壳体发生的屈曲始终覆盖整个圆柱壳区域. 相似文献
946.
947.
We study a family of directed random graphs whose arcs are sampled independently of each other, and are present in the graph with a probability that depends on the attributes of the vertices involved. In particular, this family of models includes as special cases the directed versions of the Erd?s‐Rényi model, graphs with given expected degrees, the generalized random graph, and the Poissonian random graph. We establish a phase transition for the existence of a giant strongly connected component and provide some other basic properties, including the limiting joint distribution of the degrees and the mean number of arcs. In particular, we show that by choosing the joint distribution of the vertex attributes according to a multivariate regularly varying distribution, one can obtain scale‐free graphs with arbitrary in‐degree/out‐degree dependence. 相似文献
948.
We study a generalization of the Turán problem in random graphs. Given graphs T and H, let ex(G(n,p),T,H) be the largest number of copies of T in an H‐free subgraph of G(n,p). We study the threshold phenomena arising in the evolution of the typical value of this random variable, for every H and every 2‐balanced T. Our results in the case when m2(H) > m2(T) are a natural generalization of the Erd?s‐Stone theorem for G(n,p), proved several years ago by Conlon‐Gowers and Schacht; the case T = Km was previously resolved by Alon, Kostochka, and Shikhelman. The case when m2(H) ≤ m2(T) exhibits a more complex behavior. Here, the location(s) of the (possibly multiple) threshold(s) are determined by densities of various coverings of H with copies of T and the typical value(s) of ex(G(n,p),T,H) are given by solutions to deterministic hypergraph Turán‐type problems that we are unable to solve in full generality. 相似文献
949.
Let be a supercritical branching process in an independent and identically distributed random environment. We prove Cramér moderate deviations and Berry-Esseen bounds for log( ) uniformly in ,which extend the corresponding results by I. Grama, Q. Liu, and M. Miqueu [Stochastic Process. Appl., 2017, 127: 1255–1281] established for . The extension is interesting in theory, and is motivated by applications. A new method is developed for the proofs; some conditions of Grama et al. are relaxed in our present setting. An example of application is given in constructing confidence intervals to estimate the criticality parameter in terms of log( ) and n. 相似文献
950.