Sensitivity of sample values not generated by inversion

The perturbation generation rule of Suri (Ref. 1) is extended to cases where random variables are not generated by inversion. Conditions are given for the use of other methods. Infinitesimal perturbation analysis is shown to be compatible with common random number techniques in cases where finite-difference approximations are not.This work was supported by the National Science Foundation, Grants Nos. ECS-82-13680 and CDR-85-001-08.     

Strong Approximation Theorems for Sums of Random Variables when Extreme Terms are Excluded

Let {X _n ;n≥1} be a sequence of i.i.d. random variables and let X ^(r) _n = X _j if |X _j | is the r-th maximum of |X ₁|, ..., |X _n |. Let S _n = X ₁+⋯+X _n and ^(r) S _n = S _n −(X ⁽¹⁾ _n +⋯+X ^(r) _n ). Sufficient and necessary conditions for ^(r) S _n approximating to sums of independent normal random variables are obtained. Via approximation results, the convergence rates of the strong law of large numbers for ^(r) S _n are studied. Received March 22, 1999, Revised November 6, 2000, Accepted March 16, 2001     

A classification of (some) Pisot-Cyclotomic numbers

A complete classification of degree 2, 3 and degree 4 Pisot-Cyclotomic numbers is given. Some examples of higher degrees are also given. Pisot-Cyclotomic numbers have applications to quasicrystals and quasilattices.     

A MODEL FOR WHITE NOISE ANALYSIS IN P-ADIC NUMBER FIELDS

ＡＭＯＤＥＬＦＯＲＷＨＩＴＥＮＯＩＳＥＡＮＡＬＹＳＩＳＩＮＰ－ＡＤＩＣＮＵＭＢＥＲＦＩＥＬＤＳ（黄志远）￥ＡｎｄｒｅｗＫｈｒｅｎｎｉｋｏｖ（ＭｏｓｃｏｗＩｎｓｔ．ｏｆＥｌｅｃｔｒｏｎｉｃＥｎｇｉｎｅｅｒｉｎｇ，１０３４９８，Ｚｅｌｅｎｏｇｒａｄ，Ｋ－...     

Parameter Estimation for Controlled Semilinear Stochastic Systems: Identifiability and Consistency

We consider a controlled stochastic semilinear evolution equation with the drift depending on the unknown parameter. We show that the maximum likelihood estimator is strongly consistent for a class of bounded predictable controls.     

Congruences Involving Bernoulli Numbers and Fermat-Euler Quotients

Let B_m be the mth Bernoulli number in the even suffix notation and let q(a, n)=(a^?(n)−1)/n be the Fermat-Euler quotient, where a, n?2 are relatively prime positive integers and ? is the Euler totient function. The main purpose of this paper is to devise a certain congruence involving the Bernoulli number and Fermat-Euler quotient, which leads to several important arithmetic properties of Bernoulli numbers.     

水中爆炸加载金属板变形的实验研究

本文给出了研究抛体大变形的光学实验测试方法,用该方法测定了水中爆炸作用下的金属板的变形过程,得到了金属板上任意点随时间变化的位移曲线和速度曲线以及金属板变形过程的真实位移场。该方法比常用的测量抛体运动速度的电测探针法前进了一步。     

Circular flows of nearly Eulerian graphs and vertex‐splitting

The odd edge connectivity of a graph G, denoted by λ_o(G), is the size of a smallest odd edge cut of the graph. Let S be any given surface and ? be a positive real number. We proved that there is a function f_S(?) (depends on the surface S and lim_?→0 f_S(?)=∞) such that any graph G embedded in S with the odd‐edge connectivity at least f_S(?) admits a nowhere‐zero circular (2+?)‐flow. Another major result of the work is a new vertex splitting lemma which maintains the old edge connectivity and graph embedding. © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 147–161, 2002     

Comparison of fuzzy numbers using a fuzzy distance measure

A new approach for ranking fuzzy numbers based on a distance measure is introduced. A new class of distance measures for interval numbers that takes into account all the points in both intervals is developed first, and then it is used to formulate the distance measure for fuzzy numbers. The approach is illustrated by numerical examples, showing that it overcomes several shortcomings such as the indiscriminative and counterintuitive behavior of several existing fuzzy ranking approaches.