A general Hsu-Robbins-Erdős Type estimate of tail probabilities of sums of independent identically distributed random variables

Periodica Mathematica Hungarica - Let X 1,X 2,... be a sequence of independent and identically distributed random variables, and put % MATHTYPE!MTEF!2!1!+-%...     

Theory of optical couplers

The propagation of solitons through optical couplers is studied here in this paper. Both the twin-core couplers as well as the multiple-core couplers are considered here in this paper. The parameter dynamics of the solitons that are governed by the coupled generalized nonlinear Schrodinger's equation, due to non-Kerr law nonlinearity, has been obtained for such couplers.     

A strong law of large numbers for generalized random sets from the viewpoint of empirical processes

In this article we prove a strong law of large numbers for Borel measurable nonseparably valued random elements in the case of generalized random sets.

     

Rigorous Generalization of Young's Law for Heterogeneous and Rough Substrates

We consider a SOS type model of interfaces on a substrate which is both heterogeneous and rough. We first show that, for appropriate values of the parameters, the differential wall tension that governs wetting on such a substrate satisfies a generalized law which combines both Cassie and Wenzel laws. Then in the case of an homogeneous substrate, we show that this differential wall tension satisfies either the Wenzel's law or the Cassie's law, according to the values of the parameters.     

转动系统的相对论性分析力学理论

本文讨论了转动相对论力学理论，主要是建立转动系统的相对论性分析力学理论·构造转动系统的相对论性广义动能函数Ｔｒ＝∑ｎｉ＝１Ｉ０ｉΓｉ２（１－１－θ·２ｉ／Γｉ２）和广义加速度能量函数Ｓｒ＝１２∑ｎｉ＝１Ｉｉ（θ·ｉ·θ¨ｉ）２Γｉ２－θ·２ｉ＋θ¨２ｉ，给出其Ｈａｍｉｌｔｏｎ原理和三种不同形式的Ｄ′Ａｌｅｍｂｅｒｔ原理；对于完整约束系统，建立了转动系统的相对论性Ｌａｇｒａｎｇｅ方程、Ｎｉｅｌｓｅｎ方程、Ａｐｐｅｌ方程和Ｈａｍｉｌｔｏｎ正则方程；对于非完整约束系统，建立了转动系统的相对论性Ｒｏｕｔｈ方程、Чаплыгин方程、Ｎｉｅｌｓｅｎ方程和Ａｐｐｅｌ方程；并给出转动系统的相对论性Ｎｏｅｔｈｅｒ守恒律     

Two long-standing problems in Tsallis’ statistics

On the basis of Tsallis’ entropy and the joint probability factorization condition, two controversial problems existing in Tsallis’ statistics are investigated, where one is whether energy is extensive or not and the other is whether it is necessary to introduce the so-called generalized zeroth law of thermodynamics or not. The results obtained show clearly that like entropy, energy is also nonextensive in Tsallis’ statistics, and that the zeroth law of thermodynamics has been implicitly used in Tsallis’ statistics since 1988. Moreover, it is expounded that the standard energy additivity rule adopted by a great number of researchers is not suitable in Tsallis’ statistics, because its corollary is in contradiction with the zeroth law of thermodynamics.     

随机删失场合半参数回归模型参数估计的重对数律‘

本文探讨了随机删失场合半参数回归模型的参数估计问题.考虑半参数回归模型Y =X}}3 + g(T)十。，其中(X,T)’为取值于Kp X [0,1〕上的随机向量，月为1'维未知参数向量，8为定义于【0.1]上的未知函数，。为随机误差，Ee = 0 . Eez = az }。未知，且(X ,T)与。独立，).被一个与之独立的随机变量V所截.此时仅能观察到:Z=min(Y,V),o=1(Y簇V)，参数I3,az的估计量禽及公 z可综合非参数的权函数估计法与参数的最小二乘估计方法得到.本文对核函数的情形得到了念及ar z的精确收敛速度即重对数律.     

Martingale property of empirical processes

It is shown that for a large collection of independent martingales, the martingale property is preserved on the empirical processes. Under the assumptions of independence and identical finite-dimensional distributions, it is proved that a large collection of stochastic processes are martingales essentially if and only if the empirical processes are also martingales. These two results have implications on the testability of the martingale property in scientific modeling. Extensions to submartingales and supermartingales are given.

     

Conservation Laws of K(m, n) and mK(m, n) Equations

Based on the rank analysis method, algorithmization idea, and symbolic computation, in this paper we have presented a method to construct the conservation laws for nonlinear evolution equations. The polynomial conservation laws for K (n 2, n) equations and mnK(m, n) equations are found by using of this approach and some new results have been obtained.