火工品可靠性试验数据的综合分析方法

升降法试验数据和固定刺激量下的成败型试验数据,是两种最常见的火工品可靠性试验数据．我们应用Markov链,研究了升降法试验数据下,感度分布参数的极大似然估计的特性．在此基础上,应用Bootstrap方法和Bayes方法,给出了综合分析两种试验数据的方法．最后,将该方法应用于520底火的可靠性鉴定,得出了有益的结论．     

随机泛函微分方程的渐近稳定性

应用多个Liapunov函数讨论了随机泛函微分方程解的渐近行为,建立了确定这种方程解的极限位置的充分条件,并且从这些条件得到了随机泛函微分方程渐近稳定性的有效判据,使实际应用中构造Liapunov函数更为方便．同时也说明了该结果包含了经典的随机泛函微分方程稳定性结果为其特殊情况．最后给出的结果在随机Hopfield神经网络中的应用．     

微积分在数列中的应用

随着新一轮教改的实施,微积分已走进了高中课堂．它在函数方面的应用已人所尽知,但在数列方面的应用还不多见．笔者通过观察和研究发现,如果把微积分应用在数列的求和及求通项公式上,能减少运算量,提高准确率,达到事半功倍的效果．     

关于在概率统计课程中改进教学方法的若干思考

通过结合教学实践与理论,阐述了概率统计教学改革的几点看法．提出了在教学过程中加强数学美学教育,应用情景教学法和适当应用反例教学与软件教学．     

解线性方程组的预条件Gauss-Seidel型迭代法

给出了解线性方程组的预条件Gauss-Seidel型方法,提出了选取合适的预条件因子．并讨论了对Z-矩阵应用这种方法的收敛性,给出了收敛最快时的系数取值．最后给出数值例子,说明选取合适的预条件因子应用Gauss-Seidel方法求解线性方程组是有效的．     

半渗透涨缩管道内微极性流动解析求解

分析了半渗透涨缩管道内的微极性流体的流动．应用合适的相似变换,将控制方程转化为常微分方程组．为了得到该问题的解析解,应用同伦分析方法得到该问题的速度表达式．并且用图形分析了各个不同参数,特别是膨胀系数对速度场和微旋转角速度的影响．     

具有可利用服务员的M/G/1排队模型

本文考虑了具有可利用服务员的M／G／1有有限容量的排队模型．当工作量超过k(k是常数或者随机变量),可利用服务员参与工作,一直到工作量少于或等于k．可利用服务员的速率依赖于目前工作量．应用Level-crossing方法,获得了工作量的平稳分布．应用Kolmogorov向后微分方程方法,构造更新方程以获得忙期的Laplace变换．     

“以静制动”——另辟蹊径解决线性规划问题

1．问题的背景与提出 高中新课标数学十分注重引导学生体会数学的应用价值,发展学生的应用意识．线性规划是直线方程的一个简单应用,这一内容无疑增加了数学知识的工具性和实用性．线性规划是用数学知识来研究在一定的人、材、物、时、空等资源条件下,如何进行合理安排,用最少的资源,取得最大的经济效益的数学工具．根据美国《财富》杂志对全美前500家大公司的调查表明,线性规划的应用程度名列前茅,有85％的公司频繁地使用线性规划,并取得了提高经济效益的显著效果．     

带自由液面粘性流体运动的最小二乘有限元模拟

给出了一种求解带自由液面流体运动的数值方法．流体运动的Navier-Stokes方程应用最小二乘有限元进行离散,有限差分法用来进行时间推进．采用Lagrange方法描述网格．将模型的计算结果与二维矩形和三维圆柱形坝溃的实验结果进行了对比．计算得到的时间历程与实验结果十分吻合,验证了最小二乘有限元在此类问题中应用的可能性．     

Lagrange-Maxwell方程与发电机组磁饱和参数共振

推广了Lagrange-Maxwell方程,使之适用于分析发电机组磁饱和振动问题．应用机电分析动力学方法和电机学理论,找到了考虑磁饱和时发电机气隙磁场能,建立了发电机组电磁激发振动的非线性常微分方程组．发现在磁饱和状态下发电机电磁干扰力包括倍频参数激励成分．应用平均法求得系统主参数共振时的解,分析了发电机组电磁参数对共振特性的影响,揭示了一些新现象．     

On several new Hilbert-type inequalities involving means operators

In this paper, we establish several new Hilbert-type inequalities with a homogeneous kernel, involving arithmetic, geometric, and harmonic mean operators in both integral and discrete case. Such inequalities are derived by virtue of some recent results regarding general Hilbert-type inequalities and some well-known classical inequalities. We also prove that the constant factors appearing in established inequalities are the best possible. As an application, we consider some particular settings and compare our results with previously known from the literature.     

Extensions of Heinz-Kato-Furuta inequality

We give an extension of Lin's recent improvement of a generalized Schwarz inequality, which is based on the Heinz-Kato-Furuta inequality. As a consequence, we can sharpen the Heinz-Kato-Furuta inequality.

     

一个对偶的Hardy-Hilbert不等式及其推广

本文给出一个对偶的具有最佳常数因子的Hardy-Hilbert不等式,它是Hilbert不等式的具有(p,q)-参数形式的新推广,还考虑了它的更为推广的单参数形式及一个等价不等式。     

Laeng-Morpurgo-Type Uncertainty Inequalities for the Laguerre Transform

In this work,we prove Clarkson-type and Nash-type inequalities for the Laguerre transform■on M=[0,∞)×R.By combining these inequalities,we show Laeng-Morpurgo-type uncertainty inequalities.We establish also a local-type uncertainty inequalities for the Laguerre transform■,and we deduce a Heisenberg-Pauli-Weyl-type inequality for this transform.     

反向Dresher不等式

配合使用Houlder不等式和Minkowski不等式,得到了反向Dresher不等式。     

A note on Hardy-type inequalities

We use a theorem of Cartlidge and the technique of Redheffer's ``recurrent inequalities" to give some results on inequalities related to Hardy's inequality.

     

φ形式Khintchine不等式不成立

本文论证了龙顺潮、王键建立的φ形式的Khintchine 不等式不成立,他们的不等式如下:φ- 1 ∑n1φ(｜aj｜) ≤C 12n ∑ε1…∑εn｜ε1a1+ …+ εnan｜,其中φ(x)为满足φ(a+ b)≥φ(a)+ φ(b) (a,b≥0),其反函数φ- 1(x)单调增加的函数,C为常数,εi= ±1,∑ε1…∑εn对所有(ε1…εn)取值,a1,…,an 为任意复数.     

On Variance and Covariance for Bounded Linear Operators

In this paper we initiate a study of covariance and variance for two operators on a Hilbert space, proving that the c-v (covariance-variance) inequality holds, which is equivalent to the Cauchy-Schwarz inequality. As for applications of the c-v inequality we prove uniformly the Bernstein-type inequalities and equalities, and show the generalized Heinz-Kato-Furuta-type inequalities and equalities, from which a generalization and sharpening of Reid's inequality is obtained. We show that every operator can be expressed as a p-hyponormal-type, and a hyponormal-type operator. Finally, some new characterizations of the Furuta inequality are given. Received April 9, 2000, Revised July 20, 2000, Accepted August 8, 2000     

REFINEMENTS OF THE FAN－TODD‘S INEQUALITIES

51. IntroductionIn recent years, refinements or interpolations have played an important role on severaltypes of inequalities with new results deduced as a consequence. Please refer to the papers[2, 8, 9, 12], etc. The aim of this paper is to furnish refinements of the Cauchy's and Bessel'sinequalties as shown in Section 2, and also refinements of the Fan-Todd's inequality and theFan-Todd's determinantal inequality in Sections 3 and 4, with an improved condition forequality derived.First of…     

Two new forms of half-discrete Hilbert inequality

In this paper, we introduce two new forms of the half-discrete Hilbert inequality. The first form is a sharper form of the half-discrete Hilbert inequality and is related to Hardy inequality. In the second one, we give a differential form of this inequality.