查询词典 theorems for limits

On the basis of the researching the neural network theory, presenting the neural network model (N-SearCut model) for searching for minimal cutset of a graph, proving the stability of this model, analyzing the dynamic behavior of this model, deducing a series of corresponding theorems and affording an academic fundaments for solving optimization problem based on this model.

在研究人工神经元网络理论基础之上，提出了搜索图最小割集的神经网络模型——N-SearCut模型，证明了该模型的稳定性，分析了该模型的动态特性，导出了一系列的定理，为运用该模型进行优化问题的求解提供了理论依据。

In the present paper, some theorems for variational inequalities and minimax inequality are obtained in hyperconvex metric spaces.

文章给出了超凸度量空间中的一些变分不等式定理和极大极小不等式定理。

The abstract result contains several concrete results in the literature and can also be used to deal with some new cases for resonant differential equations.In the introduction, we briefly introduce the development process of the variational methods. In Chapter 2, we list some basic knowledges refering to the variational methods, including the Sobobev space,—△ operator, the weak solution and the minimizing sequence methods and some minimax theorems. In Chapter 3, we introduce the research process of Hamiltonian system of second order and the semilinear elliptic problems, using the methods introduced previously. In Chapter 4, we prove the main theorem of the thesis, and apply it to the problems in the previous Chapter, and can also be applied to some new resonant cases.

在前言中，简要介绍了变分法的产生、发展过程，在第二章中我们介绍了有关变分法的一些基本知识，包括Sobolev空间，—△算子，弱解，极小化序列方法和一些极小极大定理，在第三章中我们介绍了非线性项有界或满足次线性条件，以及它满足推广的Ahmad-Lazer-Paul条件时，二阶Hamiltonian系统和半线性椭圆问题的研究历程，最后在第四章中我们证明了本论文的主要定理，并把它应用到第三章的问题中，使得前面的几种共振的情形都可以统一到这个抽象的结果中。

And also,the Holder"s, Minkowski"s,Young-type inequalities and four interpolation theorems,which are hold on the Lebesgue spaces,are established on the homogeneous Morrey-Herz spaces MK_~ and the weak homogeneous Morrey-Herz spaces WMK_~.These results on the cor-responding homogeneous Herz space K_q~and the weak homogeneous Herz spaces WK_q~are also new.

同时把Lebesgue空间上成立的Holder、Minkowski、Young不等式以及四个插值定理推广到了齐次Morrey-Herz空间及弱Morrey-Herz空间WMK_~上，而这些结果在相应的齐次Herz空间K_q~和弱齐次Herz空间WK_q~上也是新的。

Until now, there are many kinds of machine language systemwhich are use to prove mathematical theorems, and several of them are recognized bythe mathematician and computer experts, such as HO1, Mizar, PVS, coq etc.

迄今为止，世界已有多种可用来进行数学命题证明和逻辑推理的机器语言系统，但其中只有少数几种语言可被普遍接受并受到数学家与计算机专家的认可，如HOL、Mizar、PVS、Coq等，它们各自的初衷不同，却有一个共同的特征：人类使用机器语言书写、计算、逻辑推理和证明文本性质的数学问题，并由计算机自动验证其正确性。

In the point of view of interacting forces among micro-particles in liquid pure substance and according to argon model and theorems and rules in semi-metal structure theory of organic molecules created by one of authors, a new theoretical equation of the liquid molar volume V at the normal boiling point to pure substance is proposed.

从液体纯质中的微观粒子间的相互作用力方面考虑，按照作者创立的氮模型理论和有机分子的半金属结构理论中的定理定则，导出液体纯质在正常沸点下的摩尔体积V理论方程，给出了理论方程成立的数学证明。

In the proof,the tools of the conditional moment generating function and the differentiation on a net for the study on strong limit theorems in the random selection system are applied.

在证明中采用了一种把网微分法与条件矩母函数相结合应用于随机选择系统强极限定理研究的一种途径。

Some limit properties of the multivariate function sequences of the nonnegative integer-valued random variables are studied by using the differentiation of measures on a net and the conditional moment generating function s, and some strong limit theorems related to the conditional expectations are obtained.

利用测度关于网的微分法和条件矩母函数的工具研究非负起值随机变量多元函数序列的极限性质，得到了若干与条件数学期望有关的强极限定理

According to theorems of momentum and moment of momentum and helmholtzs equation, motion quations of the tethered system are obtained.

根据动量定理、动量矩定理和Helmholtz方程建立了系统动力学方程。

In this paper, by using the cone theory and mixed monotone iterative technique, the fixed point theorems for a class of mixed monotone multivalued operators in Banach spaces without continuity and compactness are invetigated. The results presented here develop some known ones.

利用锥理论和混合单调迭代序列技术，在不要求任何紧性和连续性的情况下，证明了Banach空间中的一类混合单调集值算子不动点定理，并应用到一阶集值方程中，推广了某些已知结果。

The shaping method of noncircular part and the tool holder's radial motion characters in noncircular turning process are discussed in detail in the thesis.

论文详细研究了非圆零件的成型方法和加工过程中刀架的径向运动规律。

I have not really liked him,I do not like his this kind of disposition.

我没有真的喜欢他，我不喜欢他的这种性格。