Moderate and Small Deviations for the Ranges of One-Dimensional Random Walks

We establish moderate and small deviations for the ranges of integer valued random walks. Our theorems apply to the limsup and the liminf laws of the iterated logarithm. We establish moderate and small deviations for the ranges of integer valued random walks. Our theorems apply to the limsup and the liminf laws of the iterated logarithm.     

Physics with large extra dimensions

The recent understanding of string theory opens the possibility that the string scale can be as low as a few TeV. The apparent weakness of gravitational interactions can then be accounted by the existence of large internal dimensions, in the sub-millimeter region. Furthermore, our world must be confined to live on a brane transverse to these large dimensions, with which it interacts only gravitationally. In my lecture, I describe briefly this scenario which gives a new theoretical framework for solving the gauge hierarchy problem and the unification of all interactions. I also discuss a minimal embedding of the standard model, gauge coupling unification and proton stability. On leave from: Centre de Physique Théorique, Ecole Polytechnique, 91128 Palaiseau, Cedex, France.     

Separation and determination of m-phenoxybenzaldehyde reaction products by capillary gas chromatography

A capillary GC method employing an internal standard has been developed and successfully used for quantitative determination both of the raw materials used for the manufacture of m-phenoxybenzaldehyde and for the components of the reaction mixtures obtained at various stages of the development of the process. A complete analysis can be performed in a single temperature programmed run.     

微观世界探索

论文系统地阐述了从原子、原子核到基本粒子内部结构研究的历史及现状，讨论了微观物理理论和实验研究的前景和展望．论文还阐述了微观物理与宏观物理(宇宙论和天体物理等)的结合与交叉，以无可争辨的实验事实阐明了微观世界和宏观世界的无限性．     

微观世界探索(续)

论文系统地阐述了从原子、原子核到基本粒子内部结构研究的历史及现状，讨论了微观物理理论和实验研究的前景和展望．论文还阐述了微观物理与宏观物理(宇宙论和天体物理等)的结合与交叉，以无可争辨的实验事实阐明了微观世界和宏观世界的无限性．     

更新时间概率模型及其无偏估计定理的论证

本文提出应用小参数法 ,探讨 Markov链中相邻两次更新时刻内稀疏事件的概率估计问题 .建立了三种最重要的具有更新时间的概率模型 .通过小参数的引入和对概率式的幂展开 ,进而推证出幂渐近展开系数的模型估算法 .论证了无偏估计的重要定理 ,给出了概率估计式和无偏估计精度 .亦将许多算法扩展到Markov链的任意状态空间     

逻辑函数在布尔减-异或、布尔除-符合代数系统中的规范展开式

证明了布尔减、异或运算以及布尔除、符合运算的完备性,并从与-异或及或-符合代数系统中的RM、CRM展开式出发,分别推导了任意逻辑函数在布尔减-异或及布尔除-符合代数系统中的规范展开式.举例说明了与-或-非代数系统中规范展开式与布尔减-异或、布尔除-符合代数系统中的规范展开式之间的转换.     

Second Order Representations of the Least Absolute Deviation Regression Estimator

We consider exact weak and strong Bahadur-Kiefer representations of the least absolute deviation estimator for the linear regression model. The precise behavior of these representations is obtained under minimal conditions.     

Logarithmic asymptotics of solutions of the large deviation problem for the boltzmann equation with small transfer of momentum

For the Boltzmann equation with small transfer of momentum, we derive a system of nonlinear integral-differential equations describing the logarithmic asymptotics of the solution to the Cauchy problem in the domain at the distanceO(1) from the support of the initial condition.Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 73–94, July, 1998.This research was partially supported by INTAS-RFBR under grant No. 95-91 in the case of the first author, and by INTAS under grant No. 96-0698 in the case of the second author.     

Large deviation principle for enhanced Gaussian processes

We study large deviation principles for Gaussian processes lifted to the free nilpotent group of step N. We apply this to a large class of Gaussian processes lifted to geometric rough paths. A large deviation principle for enhanced (fractional) Brownian motion, in Hölder- or modulus topology, appears as special case.