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The existence of solution is studied for a class of second - order periodic boundary value problems with first applying Leray - Schauder fixed point theorem, two exislence theorems are established.

考察了一类非线性项含有一阶导数的二阶周期边值问题的解的存在性，其中非线性项是Carathèodory函数。通过构造非线性项的高度函数并且利用Leray-Schauder不动点定理建立了两个存在定理。

Of mathematical theorems to study the self-questioning approach: This theorem is presented in the context of how come?

对数学定理学习的自我提问方式：这个定理是在怎样的背景下提出来的？

In this paper, new theorems of the generation of the nonlinear semigroup of Lipschhitz-αoperator are established.

本文仔细研究了这种半群，并给出了它的一种生成元的存在性定理。

In additional, we connect with semiorder to get a series existence theorems of multiple fixed points about quasimonotone increasing operator.

此外，我们还与半序结合，得到了一系列拟单调增算子的多个不动点的存在定理。这一章与第一章的联系比较密切。

In this paper, based on the domestic and overseas existing research results, the elastic shakedown analysis and the plastic shakedown theorems are summarized.

在阅读大量国内外相关文献的基础上总结了弹性安定分析和塑性安定分析的理论，同时归纳了影响安定分析的多种因素。

Fundamental Content of the similarity theory contains definition, theorems, type and methods of similitude.

相似论基本内容包括相似定义，相似定理，相似类型和相似方法。

In thesequel,the definition of singular point is given,and then the Laurent's expansionof a LR regular function with isolated singular points is obtained in the corre-sponding Laurent domain,after that,we introduce the definition of residue,andthe residue theorems are obtained.

虽然这仅仅讨论的是在Clifford分析中的较为特殊的Riemann边值问题与奇异积分方程，但它仍然改进了以前文献的结果，从而也为更进一步地解决Clifford分析中一般的Riemann边值问题与奇异积分方程提供了基本的解决思想。

As a result, we establish the theorems of its solvability according to the known theory.

最后，提出了一类实轴上的双解析函数Riemann边值逆问题。

Then some theorems of π-solvable group are obtained.

得到了关于π可解群的一些定理。

Some properties and convergence theorems of the Henstock variational integral for stochastic process with respect to canonical Brownian motion are probed.

讨论了关于布朗运动的随机积分用Henstock变差逼近的方法所定义的积分的一些性质和收敛定理。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。