比较定理

We give several sufficient conditions of NA and NSD properties of random variables, compare the closeness of distribution functions of order statistics between NA and independent rv's, investigate properties of NSD defined by supermodular functions, study the dependence structure of stationary Markov process and order statistics and their spacings from two samples, establish stochastic comparisons of order statistics of heterogeneous rv's in the hazard rate and the reversed hazard rate orders, and give the first analytic proof of the closure property of the up shifted likelihood ratio order under convolution.

给出判定一组随机变量NA性质的几个充分条件，并给出NA和独立随机变量的次序统计量之间"贴近性"的比较，系统地研究基于特殊函数类所定义的NSD负相依概念，给出一些判别NSD性质的结构定理和一些有用概率不等式。系统研究平稳马氏过程的相依结构。研究两样本次序统计量及其问题隔的相依结构。在失效率、反向失效率序和似然序意义下给出非齐次随机变量次序统计量的比较。给出上漂移似然序卷积封闭性的第一个解析证明。

In the following, we list the main works in our paper:(1) We introduce briefly the concepts of fuzzy mathematics and three fundamental principles—decomposition theorem, representation theorem and extension theorem. We also present the concepts of fuzzy number and some simple properties.

本文主要内容包括以下几个方面：(1)简要地介绍了模糊数学中基本概念和三大基本定理--分解定理，表现定理和扩展定理，模糊数的概念、性质以及比较两个模糊数的方法。

There is a relatively complete style of homogeneous function about the boundary condition in the problem of sure resolution of unhomogeneous boundary condition,which is based on the summarizing of mass former experiences and is proved in this article.

通过对非齐次边界条件的定解问题的讨论，引出了本文的论题，对非齐次边界条件定解问题的边界条件齐次化函数提出了一种比较一般和标准的形式，并提出了一个定理。对该定理进行了证明，证明了它的正确性。

This article compared the integrand of infinite integral and unbounded function integral by comparing the infinitesimal with the infinity, obtained the corresponding equivalence theorem of criterion of convergence of abnormal integral, and gave out the proof.

将无穷积分及无界函数积分的被积函数运用无穷小和无穷大比较的方法进行比较，得到了相应的反常积分敛散性极限审敛法的等价定理，并给予证明，从而可运用等价定理灵活的判断反常积分的敛散性。

This mean value theorem of the introduction and in the example on the other the application of proven methods to illustrate the mean value theorem to prove some of the infinitive is very simple.

本文将通过对中值定理的介绍和在例题上的与其他证明方法的比较应用，来说明中值定理对一些不定式的证明是相当简单的。

Missirlis in article [1]. At the same time, a sufficient condition for convergence of the PSD method is given to be compared when the coefficient matrix A of the linear system Ax = b is a symmetric, positively defective matrix. In §3.2, an example is given to state that the range of our sufficient condition is wider than theorem 3.3 of article [1]. On the other hand, following a.n analogous approach of [14] and starting the functional relationshipwe have a perfect analysis for the PSD method to converge and optimum valves for the involved parameters under different conditions.Under the assumptions that A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are real,we get necessary and sufficient conditions for the PSD method to convergence.The result is equal to theorem 1 of article [9].Under the same condition, we can see the optimal parameter and of corresponding spectral radius of thePSD method in [8]:(2)When A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are imaginary or zero,we get necessary and sufficient conditions for the PSD method to convergence.In chapter 3, the optimal parameter and of corresponding spectral radius of the PSD method are given by table 3.3. Moreover, under the assumption 0

Missirlis在文献[1]中定理3.3的不准确，同时给出了当线性方程组Ax=b的系数矩阵A为对称正定阵时，PSD迭代法收敛的一个充分条件与之比较，并且在§2.3中用实例说明了对于一部分矩阵而言本文得到的充分条件广于[1]中定理3.3的充分条件；另一方面，按照文献[14]的方法，我们从PSD迭代法的特征值λ与其Jacobi迭代矩阵B的特征值μ的关系式：出发，在不同条件下对PSD迭代法的收敛性和最优参数以及最优谱半径进行了完整的分析：(1)在系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为实数的条件下，给出了PSD迭代法收敛的充分必要条件，此结果与[9]中的定理1等价，此时最优参数及最优谱半径由[8]得：(2)第三章表3.3中给出了，当系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为纯虚数或零时的PSD迭代法的收敛范围和最优参数，并且我们可以得到当0

Regarding the extinction of every kind of scatter, the results of the sum of scattering and absorption coefficient, and that from forward scattering theory are compared and discussed.

关于各类散射体的衰减，本文比较了散射系数和吸收系数之和，与前向散射定理的结果，并对前向定理的适用性进行了讨论。

A comparison is made between the electrostatic field and universal gravitation field to find out the very similarities between them.

在比较静电场与万有引力场相似性的基础上，归纳出相似性的本质，进而根据相似性由静电场中已有的公式、定理及解题方法推导出万有引力场中与此相似的公式、定理及解题方法。

Using the new comparative method, the variation of constants formula, M-matrix theory, integral differential inequality, new theoretical results on global exponential stability of neural networks with bounded time-varying delays and Lipschitz continuous activation functions have been obtained.

利用新的比较方法的思想，改进了一维线性和非线性纯时滞微分系统的3/2稳定性定理，推广了Yorke条件到具两个时滞项的情形，将Yorke等人的3/2稳定性定理推广到具两个时滞项的线性和非线性纯时滞微分系统，进一步还推广到N维纯时滞微分系统，为纯时滞神经网络的研究打下理论基础。

Definition, formulary, theorematic go against definition, formulary, theorem is being applied directly in be being used in maths to solve a problem is a kind of commonner method, but its are converse application often is ignored.

定义、公式、定理的逆用在数学解题中直接运用定义、公式、定理是一种比较常见的方法，但其逆向应用往往被忽视。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。