独立同分布随机环境中两性Galton-Watson分支过程灭绝概率的渐近行为

本文研究了独立同分布随机环境中的两性Galton-Watson分支过程,在上临界情形下,当k充分大时,qk≤ck<'-α>.     

Asymptotic Behaviors for Critical Branching Processes with Immigration

In this paper, we investigate the asymptotic behaviors of the critical branching process with immigration {Z_n, n ≥ 0}. First we get some estimation for the probability generating function of Zn. Based on it, we get a large deviation for Z_(n+1)/Z_n. Lower and upper deviations for Zn are also studied. As a by-product, an upper deviation for max_(1≤i≤n) Z_i is obtained.     

A fast calculation of excitation autoionization cross-sections of Na-like ions

In this work, based on the calculation in detail, two new fitting formulae of total excitation and excitation autoionization cross-sections for Na-like ions (18?Z?39) are given. For discussing the variation of the total excitation autoionization cross-section, a systematic study of the dependence of the overall branching ratio on incident electron energy and nuclear charge is also carried out.     

Dual bimodal polyethylene prepared by intercalated silicate with nickel diimine complex

The ethylene polymerization was catalyzed by the intercalated montmorillonite with the nickel complex, [ArN?C(Me)? C(Me)?NAr]NiBr₂ (Ar = 2,6‐C₆H₃ (i‐Pr)₂). Polymer with low melting point and high molecular weight was produced at the early stage of polymerization followed by formation of polymer with high melting point and low molecular weight. It is proposed that the gallery of silicate lowers the propagation rate of polymerization and frequency of “chain walking” process of nickel complex anchored inside the gallery, which produces polymer with low molecular weight and low branching, whereas the nickel complex immobilized on the surface of silicate generates polymer with high molecular weight and high branching. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5506–5511, 2005     

Molecular weight distribution in free radical polymerization with long-chain branching

A new theory to predict the molecular weight distribution in free radical polymerization that includes chain transfer to polymer is proposed. This theory is based on the branching density distribution of the primary polymer molecules. The branching density distribution provides the information on how each chain is connected to other chains, and therefore, a full molecular weight distribution can be calculated by application of the Monte Carlo simulation. The present theory accounts for the history of the generated branched structure and can be applied to various reaction systems that involve branching and crosslinking regardless of the reactor types used. The present simulation confirmed the validity of the method of moments in a batch polymerization proposed earlier. It was shown clearly why gelation never occurs by chain transfer to polymer without the assistance of other interlinking reaction such as bimolecular termination by combination. © 1993 John Wiley & Sons, Inc.     

No directed fractal percolation in zero area

We consider the fractal percolation process on the unit square with fixed decimation parameterN and level-dependent retention parameters {p _k}; that is, for allk ⩾ 1, at thek th stage every retained square of side lengthN ¹⁻ k is partitioned intoN ² congruent subsquares, and each of these is retained with probabilityp _k. independent of all others. We show that if Π_k p _k =0 (i.e., if the area of the limiting set vanishes a.s.), then a.s. the limiting set contains no directed crossings of the unit square (a directed crossing is a path that crosses the unit square from left to right, and moves only up, down, and to the right).     

Cs-He光学碰撞中的非绝热跃迁

激光激发Cs He碰撞复合物,测量了Cs(62P)精细结构布居数分支比,由此证实了发生在光学碰撞中的非绝热跃迁.激光频率从Cs(6P3/2)红翼30cm-1调至蓝翼30cm-1,在6P3/2的近翼,分支比与矢谐量有很大的关系.同时测量了Cs(6PJ)态的精细结构转移截面,截面值σ21=9.8×10-19cm2.     

On the height of random m-ary search trees

A random m-ary seach tree is constructed from a random permutation of 1,…, n. A law of large numbers is obtained for the height H_n of these trees by applying the theory of branching random walks. in particular, it is shown that H_n/log n→γ in probability as n→∞ where γ = γ(m) is a constant depending upon m only. Interestingly, as m→∞, γ(m) is asymptotic to 1/log m, the coefficient of log n in the asymptotic expression for the height of the complete m-ary search tree. This proves that for large m, random m-ary search trees behave virtually like complete m-ary trees.     

An O(K·n4) algorithm for finding the k best cuts in a network

An algorithm for finding the K best cuts in a network is presented. Using a branch technique introduced by Lawler [4] we reduce the problem to K computations of 2nd best cuts. The latter problem can be solved by an O(n⁴) algorithm yielding an overall complexity of O(K·n⁴) for the presented algorithm.