掺偶氮苯聚合物的光致折射率改变特性

采用表面反射方法研究块状掺偶氮苯聚合物的光致折射率改变特性及其与光强的依赖关系；实验中，使用514nm的圆偏振Ar^ 激光作为抽运光，632．8nm的He-Ne激光(s偏振)作为探测光。通过改变探测光入射角，测量样品在固定光强(0．570W／cm^2)的前向抽运光激励下表面反射率的改变量．研究样品的折射率改变特性．发现样品的光致折射率改变约为0．0035；研究了这种效应对抽运光强度的依赖关系．发现光致折射率改变随抽运光强度增大而增大．当抽运光强为0．800W／cm^2时，折射率改变量可达10^-2量级。     

Singularity of self-similar measures with respect to Hausdorff measures

Besicovitch (1934) and Eggleston (1949) analyzed subsets of points of the unit interval with given frequencies in the figures of their base- expansions. We extend this analysis to self-similar sets, by replacing the frequencies of figures with the frequencies of the generating similitudes. We focus on the interplay among such sets, self-similar measures, and Hausdorff measures. We give a fine-tuned classification of the Hausdorff measures according to the singularity of the self-similar measures with respect to those measures. We show that the self-similar measures are concentrated on sets whose frequencies of similitudes obey the Law of the Iterated Logarithm.

     

The law of the iterated logarithm for non-instantaneous filters of strongly dependent Gaussian sequences

It is shown in the present paper that the upper-half law of the iterated logarithm with the usual norming rate still holds for certain class of non-instantaneous filters of strongly dependent Gaussian sequences.     

The low of the iterated logarithm for empirical processes under absolute regularity

The compact law of the iterated logarithm for empirical processes whose underlying sequence satisfies a -mixing condition is considered. In particular, we show a compact law of the iterated logarithm for VC subgraph classes of functions, for classes of functions which satisfy the bracketing condition in Doukhanet al. ⁽⁶⁾ and for some classes of smooth functions.Research partially supported by NSF Grant DMS-93-02583.     

Some asymptotic results related to the law of iterated logarithm for Brownian motion

For 0<<1, let . The questions addressed in this paper are motivated by a result due to Strassen: almost surely, lim sup _t U ((t))=1–exp{–4(^–1)–1}. We show that Strassen's result is closely related to a large deviations principle for the family of random variablesU (t), t>0. Also, when =1,U (t)0 almost surely and we obtain some bounds on the rate of convergence. Finally, we prove an analogous limit theorem for discounted averages of the form as 0, whereD is a suitable discount function. These results also hold for symmetric random walks.     

分析光栅分数塔尔博特效应的一组新方程

对一维开口比为1/M(这里M为大于1的正整数)的短形光栅,建立了一组新 在分数塔尔博特(Talbot)距离上计算其菲涅 法射光场分布的简单方程.在该方程中考虑了光栅结构与分数塔尔博特距离的联系,显然比迭代方程和基于距离的方程更方便地描述分数塔尔博特效应.给出了一种研究光栅分数塔尔博特铲应的新途径.     

Stability diagram of higher modes of the Fabry-Perot resonator

We have numerically calculated the stability diagram of the higher modes of the Fabry-Perot resonator by direct diagonalization of the Fox-Li equation. The diagram has an exotic behavior in the small Fresnel number region and its higher modes in our numerical experiments.     

Scale-Distortion Inequalities for Mantissas of Finite Data Sets

In scientific computations using floating point arithmetic, rescaling a data set multiplicatively (e.g., corresponding to a conversion from dollars to euros) changes the distribution of the mantissas, or fraction parts, of the data. A scale-distortion factor for probability distributions is defined, based on the Kantorovich distance between distributions. Sharp lower bounds are found for the scale-distortion of n-point data sets, and the unique data set of size n with the least scale-distortion is identified for each positive integer n. A sequence of real numbers is shown to follow Benford’s Law (base b) if and only if the scale-distortion (base b) of the first n data points tends zero as n goes to infinity. These results complement the known fact that Benford’s Law is the unique scale-invariant probability distribution on mantissas. The first author was partly supported by a Humboldt research fellowship. The second author was supported in part by the National Security Agency and as a Research Scholar in Residence at California Polytechnic State University.     

The law of the iterated logarithm for positively dependent random variables

The Levy's type maximal inequality is a key to establish the law of the iterated logarithm for associated random variables. Unfortunately, this type inequality cannot be obtained for a generalization of association, i.e., linear positive quadrant dependence, because of their special dependence structure. The purpose of this paper is to provide a different approach to obtain a law of the iterated logarithm for a sequence of linear positive quadrant dependent random variables.     

An indirect algorithm of Fresnel diffraction

An indirect algorithm for Fresnel diffraction calculation at any distance is presented in this paper. Using this indirect algorithm, the Fresnel diffraction on a near plane can be realized in two steps, the first is to acquire the diffractive field on a far field and the second is to obtain the diffractive field on a near plane using an inverse Fresnel integral. Compared with conventional algorithms, this algorithm is valid at any range of distance. The sampling theorem, as the basis of this indirect algorithm, is discussed in detail. Theoretical calculations show good agreements with experimental results.