一致椭圆扩散过程的正则点判据

本文研究了一致椭圆扩散过程的点的正则性判别准则 ,得到了x是B的正则点的充要条件。此结果可视为布朗运动中的Wiener判别法的推广。     

Vesta-2M流密码的密码分析

分析了俄国商用密码Vesta-2M流密码的安全性。流密码Vesta-2M的密钥流发生器的初始密钥规模为O(2^536)。本文指出文献[1]中攻击方法的错误，并提出一种已知明文攻击方法，所需明文量很小(约几百比特)，计算复杂度的上界为O(2^372)。     

Factorable polynomial matrices

It is shown that any regular polynomial matrix over the field of complex numbers that has at most one elementary divisor of degree 3 and whose remaining elementary divisors are of degree no greater than 2 can be factored into linear regular factors. Translated fromMatematicheskie Zametki, Vol. 68, No. 4, pp. 593–607, October, 2000.     

On convergence of the Gauss-Newton method for convex composite optimization

The local quadratic convergence of the Gauss-Newton method for convex composite optimization f=h∘F is established for any convex function h with the minima set C, extending Burke and Ferris’ results in the case when C is a set of weak sharp minima for h. Received: July 24, 1998 / Accepted: November 29, 2000?Published online September 3, 2001     

阿贝尔群的完整子半群的若干结果

本文证明了无扭阿贝尔群Ｇ是唯一线性序的，当且仅当Ｇ的每一个完整子半群只含唯一的极小完整子半群。若群Ｇ的每一个完整子半群只含有限多个极小完整子半群，则Ｇ中所有完整子半群组成的集Ｔ（Ｇ）满足ＤＣＣ。     

l-群的极小素子群

本文研究l-群的极小素子群,主要证明如下结果:设G是一个l-群.（1）N∈Γ_m（G）,则N=a^⊥当且仅当{P_N^C}是一个归纳集;（2）g∈G⁺,如果g是特殊的,且g的唯一值是原子,则g^⊥∈Γ_m（G）;（3）G∈B_w,Γ₁（C）是原子的当且仅当Γ_m(G）?Γ₁（G）。     

正则半开集和半同胚空间类

设A■X,v为X上的拓扑,用A_v~0、A_v~-、(A_v)_0、(A_v)_-、A’_v分别记A在(X,v)中的内部、闭包、半内部、半闭包和补集。用η_v、ζ_v、ζ_v分别记(X,v)中的半开集族、无处稠密集族和稠密集族。当v=u时,略去上述记号中的足码v。令[u]={v|v为X上的拓扑且     

An age-dependent model of cavity radiation and its detection II. Anti-bunched and thermal characteristics

The model of cavity radiation introduced earlier is analysed further by considering special types of age-specific population growth interpretable in terms of evolution through phases. The model is shown to be versatile enough to admit anti-bunched photon statistics provided the process of spontaneous emission is appropriately modelled. A four-phase model is analysed and the resulting radiation is shown to correspond to the one obtained by the superposition of two independent thermal streams each with a Lorentzian spectrum.     

Hitting time of a moving boundary for a diffusion

We obtain asymptotic estimates for the quantity r = log P[T_f[rang]t] as t → ∞ where T_f = inf\s{s : |X(s)|[rang]f(s)\s} and X is a real diffusion in natural scale with generator a(x) d²(·)/dx² and the ‘boundary’ f(s) is an increasing function. We impose regular variation on a and f and the result is expressed as r = ∫^t₀ λ₁ (f(s) ds(1 + o(1)) where λ₁(f) is the smallest eigenvalue for the process killed at ±f.     

Maxima of branching random walks vs. independent random walks

In recent years several authors have obtained limit theorems for the location of the right most particle in a supercritical branching random walk. In this paper we will consider analogous problems for an exponentially growing number of independent random walks. A comparison of our results with the known results of branching random walk then identifies the limit behaviors which are due to the number of particles and those which are determined by the branching structure.