非负整值随机变量序列的一类强偏差定理

设是在中取值的一列随机变量，其联合分布为是S上的一个分布，该文研究对数似然比与之间的若干极限关系，得到了一类用不等式表示的强极限定理（称之为强偏差定理），其偏差界依赖于样本点．证明中结合区间刻分法，提出了将母函数的工具应用于强极限定理研究的一种途径．     

Asymptotic Properties of a Nonparametric Regression Function Estimator with Randomly Truncated Data

In this paper, we define a new kernel estimator of the regression function under a left truncation model. We establish the pointwise and uniform strong consistency over a compact set and give a rate of convergence of the estimate. The pointwise asymptotic normality of the estimate is also given. Some simulations are given to show the asymptotic behavior of the estimate in different cases. The distribution function and the covariable’s density are also estimated.     

Strong convergence of estimators as ε n -minimisers of optimisation problemsof optimisation problems

In the paper we prove strong consistency of estimators as solution of optimisation problems. The approach of the paper covers non-identifiable models, and models for dependent samples. We provide statements about consistency of M-estimators in regression models with random and with non-random design. The research was partially supported by the Deutsche Forschungsgemeinschaft (project number 436TSE113/40) and by the Grant Agency of the Czech Republic under Grant 201/03/1027.     

Luminescence related processes in semiconductor nanocrystals —The strong confinement regime

This paper summarizes systematic studies on the luminescence from CdSe nanocrystals in the situation of strong zero-dimensional confinement. We discuss the role of surface and defect states, the origin of the photo-darkening and demonstrate by calorimetric adsorption measurements that the internal quantum efficiency is in the range of some 10%. The lifetimes of the intrinsic excitations are strongly size-dependent. While the radiative recombination (≈ 1 ns) is dominant for larger nanocrystals, we observe a dramatic increase of the non-radiative rate below 4 nm as a result of the reduced volume to surface ratio. The combination of ultra-fast and size-selective excitation allows us to observe a progression of sharp LO-phonon lines signifying the zero-dimensional character of the nanocrystals and providing information on the strength of the phonon coupling and the homogeneous width of the quantum-confined ground state.     

满足强分离条件的自相似集的填充测度

对满足强分离条件的自相似集,本文给出一种估计填充测度下界的方法,称为部分估计原理。利用这种估计方法得出的某些自相似集的填充测度的下界,往往和准确的填充测度值相等     

双无限环境中马氏链的强大数定律

在随机环境中马氏链的研究领域 ,构造了一时齐的马氏双链 ,讨论了它的存在性及基本性质 ,最后利用马氏双链的性质 ,得到了双无限环境中马氏链的函数极限定律 ,并给出了该链的函数强大数定律成立的两个充分条件     

一类以鞅为驱动的随机泛函微分方程强解的存在性与唯一性

在积分型Lipschitz条件下,证明了一类以连续鞅为驱动的随机泛函微分方程解的存在性与唯一性.     

强定向图的k-强距离

对强连通有向图D的一个非空顶点子集S,D中包含S的具有最少弧数的强连通有向子图称为S的Steiner子图,S的强Steiner距离d(S)等于S的Steiner子图的弧数. 如果|S|=k, 那么d(S)称为S的k-强距离. 对整数k≥2和强有向图D的顶点v,v的k-强离心率sek(v)为D中所有包含v的k个顶点的子集的k-强距离的最大值. D中顶点的最小k-强离心率称为D的k-强半径,记为sradk(D),最大k-强离心率称为D的k-强直径,记为sdiamk(D). 本文证明了,对于满足k+1≤r,d≤n的任意整数r,d,存在顶点数为n的强竞赛图T′和T″,使得sradk(T′)=r和sdiamk(T″)=d;进而给出了强定向图的k-强直径的一个上界.     

Studying invisible axion models at high temperature

During the thermal evolution of the universe, symmetry of the vacuum state in the presence of quantum fields should have changed at various stages. A possible indication of this effect on the DFSZ invisible axion model of the Peccei-Quinn CP conserving mechanism is presented here. To start with, the background theory of this mechanism in the cosmic evolution has been fully reviewed, as well as the leading cosmological arguments setting limits on the mass and coupling of such a particle. The CP conserving lagrangian of the invisible axion model also includes instanton gauge field configurations. In our opinion, these configurations could behave non trivially while decreasing the temperature as a consequence of the vacuum symmetry modifications. The interplay between symmetry modifications and cosmic evolution may thus lead to yet unclear effects. In fact, the model considered here is really quite a baby version of the real world, so that only preliminary indications and bare consistency arguments have been done from it. Nevertheless, the underlying idea, a possible neutral Higgs fields approximate resonance condition, seems to survive even in more sophisticated models.     

离散随机序列随机和的一类强偏差定理

In this paper, the notion of limit random logarithmic likelihood ratio of stochastic se-quences,as a measure of “dissimilarity“ between their joint distributions and the product of theirmarginals,is introduced. Construct a. s. convergence supermartingale by means of truncation methodand under suitable restrict Chung-Teicher type conditions,some strong deviation theorems for arbi-trary discrete stochastic sequence are obtained.