ON NUMEROV SCHEME FOR NONLINEAR TWO-POINTS BOUNDARY VALUE PROBLEM

1.IntroductionInstudyingsomeproblemsarisinginelectromagnetism,biology)astronomy,bound-arylayerandothertopics,weoftenmeetnonlineartwo--pointsboundaryproblem,i.e.,findingyECo[0,11nC2(0,1)suchthatwhereor,garecertainconstants,andf(x,z)EC'(0,1)xC'(--co,co).Undersomeconditionsonf(x,z),wecanusetheframeworkof[1]toinvestigatetheexistenceanduniquenessofitssolutions.Alsotherearealotofliteratureconcerningitsnumericalsolutio.s[2--'].Inparticular,N..ero.15]proposedafamousfinitedifferenceschemewiththeaccu…     

金属基陶瓷复合材料的激光热冲击破坏效应

 研究了激光热冲击条件下静态受拉Sic颗粒增强6061铝合金材料的热断裂行为。热冲击用的激光束的脉宽分别为1.0ms和250μs, 激光束辐照在缺口的根部附近。对于热冲击下裂纹的产生及扩展进行细致的宏、微观观察,发现裂纹的产生和扩展的机制是不相同的。     

四元Heisenberg群上次拉普拉斯算子的m幂次的基本解

本文研究了四元Heisenberg群上次拉普拉斯算子的m幂次的基本解，该结论是Heisenberg群上结果的推广.本文利用了四元Heisenberg群上的Fourier变换理论构造了该群上次拉普拉斯算子的m幂次的基本解，并且给出了基本解的积分表示.     

Thermodynamics of wurtzite GaN from first-principle calculation

The density function perturbation theory (DFPT) is employed to study the linear thermal expansion and heat capacity at constant pressure (with the quasiharmonic approximation) for wurtzite GaN. The calculated results of linear thermal expansion coefficient and heat capacity at constant pressure are compared with the available experimental data in a wide temperature range. Generally these properties calculated agree well with experimental data except at high temperature, thus it suggests the thermal expansion and heat capacity can be well calculated from this first-principle approach.     

矩形校正公式的误差分析

This paper presents truncation errors among Corrector Formula for left Rectangular rule and Corrector Formula for middle Rectangular rule respectively.It also displays an analysis on convergence order of compound corrector formulas for rectangular rule.Examples of numerical calculation have validated theoretical analysis.     

Observability of elastic vibrations of a beam

The observability problem for beam vibrations described by a fourth-order partial differential equation with various boundary conditions is considered. Dynamic observability problems are solved in terms of boundary conditions and observations of the beam state at certain fixed instants of time.     

Asymptotic expansions of the Robbins-Monro process

Assume that the function values f(x) of an unknown regression function f: ℝ → ℝ can be observed with some random error V. To estimate the zero ϑ of f, Robbins and Monro suggested to run the recursion X _n+1 = X _n − a/n Y _n with Y _n = f(X _n ) − V _n . Under regularity assumptions, the normalized Robbins-Monro process, given by (X _n+1 − ϑ)/√Var(X _n+1, is asymptotically standard normal. In this paper Edgeworth expansions are presented which provide approximations of the distribution function up to an error of order o(1/√n) or even o(1/n). As corollaries asymptotic confidence intervals for the unknown parameter ϑ are obtained with coverage probability errors of order O(1/n). Further results concern Cornish-Fisher expansions of the quantile function, an Edgeworth correction of the distribution function and a stochastic expansion in terms of a bivariate polynomial in 1/√n and a standard normal random variable. The proofs of this paper heavily rely on recently published results on Edgeworth expansions for approximations of the Robbins-Monro process.      

光的衍射法测量金属的线胀系数

给出测量金属线胀系数的一种新方法．利用光的衍射法可以较精确地测量长度变化这一特点，对黄铜的线胀系数进行了测量．     

Extremal Problems in the Class of Delta-Subharmonic Functions of Finite Order in a Half-Plane

We obtain exact lower bounds of the upper limits of ratios of the Nevanlinna characteristics of a delta-subharmonic function in the upper half-plane.     

动态冷原子吸收法快速测定地球化学样品中微量汞

本文介绍了动态冷原子吸收法快速测定地球化学样品中微量汞的方法。本文研究采用了新型的汞蒸气发生器，并对气泡的干扰进行了研究。线性范围为0.2-12ng/mL，标准回收率为97％－106％，相对标准偏差为3.6%，相关系数为0.9997，试验结果表明此方法简便、快速、准确。