P-范分布及其抽样分布

本文构造了n维P-范分布的密度函数，使拉普拉斯分布、正态分布、均匀分布与退化分布均为一维P-范分布的特例。然后，定义了三个与P-范分布有密切关系的抽样分布，并给出了密度函数。     

普阿松分布的极限分布

本文主要阐明概率论中三个重要分布之间的关系 ,重点证明了普阿松分布的极限分布是正态分布     

普阿松分布的极限分布

本主要阐明概率论中三个重要分布之间的关系，重点证明了普阿松分布的极限分布是正态分布。     

Pareto-Geometric分布

本文提出了一种具有单调失效率的新型寿命分布, 即由Pareto分布和Geometric分布生成的两参数的Pareto-Geometric分布, 研究了该分布的各种性质和参数极大似然估计的存在唯一性, 并应用 EM 算法得到了参数的极大似然估计值和相应的渐近方差、协方差.     

幂分布

讨论了一类新的统计分布——幂分布，它具有良好的性质，在峰态的表征方面较为简单而直观，可用以比较一些其他分布的峰态，由此引出峰度当量的概念．     

若干矩阵Г分布的相关分布

本文研究了与矩阵Г分布相关的若干分布的密度函数，利用矩阵Г分布的特征函数和它的Bartlett分解等方法，获得了与矩阵Г分布相关的几个分布的密度函数解析表达式，它们包括Г分布随机矩阵的子矩阵、行列式、迹和特征根的分布密度，进一步还得到了相关系数矩阵的分布密度函数形式．     

椭球等高矩阵分布的条件分布

本文给出了椭球等高矩阵分布的条件分布的随机表示，证明了椭球等高矩阵分布的条件分布仍是椭球等高分布。     

幂分布

讨论了一类新的统计分布——幂分布,它具有良好的性质,在峰态的表征方面较为简单而直观,可用以比较一些其他分布的峰态,由此引出峰度当量的概念.     

若干矩阵Γ分布的相关分布

本文研究了与矩阵Γ分布相关的若干分布的密度函数,利用矩阵Γ分布的特征函数和它的Bartlett分解等方法,获得了与矩阵Γ分布相关的几个分布的密度函数解析表达式,它们包括Γ分布随机矩阵的子矩阵、行列式、迹和特征根的分布密度,进一步还得到了相关系数矩阵的分布密度函数形式.     

不同参数几何分布和的分布

针对一个具体实例说明按定义计算随机变量数字特征可能会遇到的困难,并介绍将随机变量分解成若干独立的随机变量之和以简化其数字特征计算的方法.推广所引实例,并用简化方法得出带有多个独立参数的几何分布的分布列的数字特征.     

Estimation of the measure of the image of the ball

Under study is the class of ring Q-homeomorphisms with respect to the p-module. We establish a criterion for a function to belong to the class and solve a problem that stems from M. A. Lavrentiev [1] on the estimation of the measure of the image of the ball under these mappings. We also address the asymptotic behavior of these mappings at a point.     

On the distributions of the ratios of the extreme roots to the trace of the Wishart matrix

In this paper, the authors cosider the derivation of the exact distributions of the ratios of the extreme roots to the trace of the Wishart matrix. Also, exact percentage points of these distributions are given and their applications are discussed.     

On the rational approximation of the sum of the reciprocals of the Fermat numbers

Let $\mathcal{G}(z):=\sum_{n\geqslant0} z^{2^{n}}(1-z^{2^{n}})^{-1}$ denote the generating function of the ruler function, and $\mathcal {F}(z):=\sum_{n\geqslant} z^{2^{n}}(1+z^{2^{n}})^{-1}$ ; note that the special value $\mathcal{F}(1/2)$ is the sum of the reciprocals of the Fermat numbers $F_{n}:=2^{2^{n}}+1$ . The functions $\mathcal{F}(z)$ and $\mathcal{G}(z)$ as well as their special values have been studied by Mahler, Golomb, Schwarz, and Duverney; it is known that the numbers $\mathcal {F}(\alpha)$ and $\mathcal{G}(\alpha)$ are transcendental for all algebraic numbers α which satisfy 0<α<1. For a sequence u, denote the Hankel matrix $H_{n}^{p}(\mathbf {u}):=(u({p+i+j-2}))_{1\leqslant i,j\leqslant n}$ . Let α be a real number. The irrationality exponent μ(α) is defined as the supremum of the set of real numbers μ such that the inequality |α?p/q|<q ^?μ has infinitely many solutions (p,q)∈?×?. In this paper, we first prove that the determinants of $H_{n}^{1}(\mathbf {g})$ and $H_{n}^{1}(\mathbf{f})$ are nonzero for every n?1. We then use this result to prove that for b?2 the irrationality exponents $\mu(\mathcal{F}(1/b))$ and $\mu(\mathcal{G}(1/b))$ are equal to 2; in particular, the irrationality exponent of the sum of the reciprocals of the Fermat numbers is 2.     

Effect of the properties of the components and the geometric characteristics of the structure on the thermal-conductivity coefficients of glass-reinforced plastics

A method is proposed for estimating the thermal-conductivity coefficients of orthotropic composite glass-reinforced plastics with a structure composed of continually repeating units, in which the contours of the reinforcing elements can be described by a sinusoidal law. The arguments in the formulas are the relative content and thermophysical characteristics of the components and the parameters of the microstructure of the materials considered.Mekhanika Polimerov, Vol. 4, No. 1, pp. 18–23, 1968     

On the minimization of the product of the powers of several integrals

This paper considers the minimization of the product of the powers ofn integrals, each of which depends on a functiony(x) and its derivative . The necessary conditions for the extremum are derived within the frame of the Mayer-Bolza formulation of the calculus of variations, and it is shown that the extremal arc is governed by a second-order differential equation involvingn undetermined multipliers related to the unknown values of the integrals. After the general solution is combined with the definitions of the multipliers and the end conditions, a system ofn+2 algebraic equations is obtained; it involvesn+2 unknowns, that is, then undetermined multipliers and two integration constants.The procedure discussed here can be employed in the study of shapes which are aerodynamically optimum at supersonic, hypersonic, and free-molecular flow velocities, that is, wings and fuselages having the maximum lift-to-drag ratio or the minimum drag. The problem of a slender body of revolution having the minimum pressure drag in Newtonian hypersonic flow is developed as an example. First, a general solution is derived for any pair of conditions imposed on the length, the thickness, the wetted area, and the volume. Then, a particular case is treated, that in which the thickness and the wetted area are given, while the length and the volume are free; the shape minimizing the pressure drag is a cone.This research, supported by the Office of Scientific Research, Office of Aerospace Research, United States Air Force, Grant No. AF-AFOSR-828-67, is a condensed version of the investigation described in Ref. 1. The author is indebted to Messrs. H. Y. Huang, J. C. Heideman, and J. N. Damoulakis for analytical and numerical assistance.     

用常微分方程模型分析预防和隔离措施对SARS发病率的影响

通过建立常微分方程模型 ,分析了预防和隔离措施对 SARS发病率的影响 ,并把计算结果与实际统计数据进行了比较 ,结果表明 ,及时高效的预防和隔离措施能够有效地控制 SARS的传播 .     

Investigation of the nonunifcrmity of the acoustic properties of the human tibia

Mechanics of Composite Materials - A method is proposed for determining the propagation velocity and coefficient of attenuation of ultrasonic vibrations in both the whole diaphysis of the human...     

Interpreting the Action of the Endomorphism Monoid of the Rationals

Algebra and Logic - In a first order language we interpret the action of the monoid M of embeddings of (?,&lt;) on the set ? inside (M,°). A similar result is proved for the...     

Effect of the incompressibility condition on the stability of the solutions of ill-posed problems of the theory of elasticity

One considers the energy functional with density depending only on the first invariant of the strain tensor. Under natural constraints on the density and in the absence of exterior actions, the zero displacements yield a minimum to the energy functional both for the compressible and the incompressible media. In the paper one proves the isolation of this minimum for incompressible media and its nonisolation for compressible media.Translated from Problemy Matemticheskogo Analiza, No. 10, pp. 62–71, 1986.     

Investigation of the nonuniform distribution of the elastic and strength characteristics over the cross section of the diaphysis of the human tibia

The elastic, deformation, and strength properties of six different zones of the cross section of the diaphysis of the human tibia have been experimentally investigated. It is shown that when the compact bone tissue is stressed in tension all these properties differ significantly from zone to zone. The greatest values of the initial modulus of elasticity and the tensile strength correspond to the frontal-outer zones of the bone. The nonlinear stress-strain curves are analytically approximated. The secant and tangent moduli are shown to depend on the stress intensity.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 940–946, September–October, 1971.