Metallic radii of nonmetals

Experimental data are used to determine the atomic volumes and radii of the elements of subgroups IV–VIIA in the structures of metallic phases at high pressures. Metallic radii of nonmetals are compared with values based on Pauling and Goldschmidt calculations.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 220–222, February, 1994.     

Large Sample Properties of Mixture Models with Covariates for Competing Risks

We study the large-sample properties of a class of parametric mixture models with covariates for competing risks. The models allow general distributions for the survival times and incorporate the idea of long-term survivors. Asymptotic results are obtained under a commonly assumed independent censoring mechanism and some modest regularity conditions on the survival distributions. The existence, consistency, and asymptotic normality of maximum likelihood estimators for the parameters of the model are rigorously derived under general sufficient conditions. Specific conditions for particular models can be derived from the general conditions for ready check. In addition, a likelihood-ratio statistic is proposed to test various hypotheses of practical interest, and its asymptotic distribution is provided.     

Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices

The sum of the largest eigenvalues of a symmetric matrix is a nonsmooth convex function of the matrix elements. Max characterizations for this sum are established, giving a concise characterization of the subdifferential in terms of a dual matrix. This leads to a very useful characterization of the generalized gradient of the following convex composite function: the sum of the largest eigenvalues of a smooth symmetric matrix-valued function of a set of real parameters. The dual matrix provides the information required to either verify first-order optimality conditions at a point or to generate a descent direction for the eigenvalue sum from that point, splitting a multiple eigenvalue if necessary. Connections with the classical literature on sums of eigenvalues and eigenvalue perturbation theory are discussed. Sums of the largest eigenvalues in the absolute value sense are also addressed.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.The work of this author was supported by the National Science Foundation under grants CCR-8802408 and CCR-9101640.The work of this author was supported in part during a visit to Argonne National Laboratory by the Applied Mathematical Sciences subprogram of the Office of Energy Research of the U.S. Department of Energy under contract W-31-109-Eng-38, and in part during a visit to the Courant Institute by the U.S. Department of Energy under Contract DEFG0288ER25053.     

几类数列通项的矩阵求法

本利用矩阵给出了几类数列的通项公式的求法，把数列通项公式的求法转化为矩阵幂的计算，思路简单、计算简便，并能判别其敛散性。     

Fermi能区核－核碰撞的平衡前中子发射

利用ＢＵＵ模型模拟核－核碰撞３６Ａｒ＋１０８Ａｇ（３５Ｍｅｖ／ｕ）、１４Ｎ＋１０８Ａｇ（３５ＭｅＶ／ｕ）中的平衡前中子发射．模拟结果与唯象的运动源拟合给出的中等速度源成份相吻合．这说明中等速度源成份产生于核－核碰撞的早期，对应平衡前发射．并从级联碰撞的角度定量地研究了平衡前发射的持续时间     

Linear Ramsey numbers of sparse graphs

The Ramsey number R(G₁,G₂) of two graphs G₁ and G₂ is the least integer p so that either a graph G of order p contains a copy of G₁ or its complement G^c contains a copy of G₂. In 1973, Burr and Erd?s offered a total of $25 for settling the conjecture that there is a constant c = c(d) so that R(G,G)≤ c|V(G)| for all d‐degenerate graphs G, i.e., the Ramsey numbers grow linearly for d‐degenerate graphs. We show in this paper that the Ramsey numbers grow linearly for degenerate graphs versus some sparser graphs, arrangeable graphs, and crowns for example. This implies that the Ramsey numbers grow linearly for degenerate graphs versus graphs with bounded maximum degree, planar graphs, or graphs without containing any topological minor of a fixed clique, etc. © 2005 Wiley Periodicals, Inc. J Graph Theory     

Optimizing in the class of Fuller modified limited information maximum likelihood estimators

A general class of Fuller modified maximum likelihood estimators are considered. It is shown that this class possesses finite moments. Asymptotic bias and asymptotic mean squared error are derived using small-σ expansions. A simulation study is carried out to compare different estimators in this class with standard estimators.     

无原子布氏代数理论的计算复杂性

研究无原子布氏代数的计算复杂性 .得到了下面的新定理 :定理 1　无原子布氏代数理论Δ具有完全的量词消去法 ,也就是说每一个式子都Δ等价于一个开式子 .定理 2　无原子布氏代数的初等型Γ (x1,… ,xn)是由型内的不含量词的全体开式子所唯一决定 .定理 3　无原子布氏代数的一个长度为 n的语句的判断过程所消耗的 Turing时间和空间都是属于 2 2 cn指数级 .     

PERIODIC BOUNDARY VALUE PROBLEM FOR SECOND ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

This paper investigates the periodic boundary value problems for a class of second order functional differential equations. The monotone iterative technique and the maximum principle are applied to obtain the existence of maximal and minimal solutions.     

一类周期种群系统的适定性及最优控制

本文研究了一类非线性周期种群系统的适定性及最优控制问题 .利用压缩不动点原理讨论了该种群系统的周期解的存在唯一性 .并用变分法给出了最优控制所满足的必要条件 .