可微的

The exact form of exterior boundary value problems for plane potential problem is established with variational principle.

使用变分法确立平面 Laplace外问题的确切形式；在此基础上，为了避免使用无限区域上的 Green公式，通过构造紧支集上的无穷可微函数，获得满足非齐次控制微分方程的特解的重要结果。

Furthermore,we obtain a sufficient and necessary condition about continuity of functional series and integral with parameter,and show the sufficient condition about differential .

将数学分析中一致收敛性的概念加以推广，分别对函数项级数和含参量积分引入次一致收敛的概念，证明了函数项级数、含参量非正常积分连续性的充要条件和可微性的充分条件，推广了数学分析中的相应结

In these algorithms, because of no requirements on the continuity and differentiability of the objective function, they have strong adaptability for the uncertain data and the traits of agility, strong intuitiveness and randomness; they have been put into applications broadly in a short time so as to become active approaches for solving optimization problems.

由于这些方法不要求目标函数连续可微、对计算数据的不确定性有很强的适应能力，且具有灵活性好、直观性和随机性强等特点，因此在很短的时间内就得到了广泛应用，成为解决优化问题的一种有力工具，并展示出方兴未艾的强劲发展势头。

The main aim of this thesis is to extend some results of classical convex analysis to notions of Carnot groups, which contain the inequalities of Hadamard type, the Lipschitz continuity, the comparison principle and the second order derivatives for convex functions on Carnot groups G and regularity of quasiconvex functions on G.

本文的主要目的是推广欧氏空间凸分析中的一些结果到Carnot群上凸分析的情形，其中包括Carnot群上凸函数的Hadamard型不等式、Lipschitz连续性、比较原理、二阶可微性及拟凸函数的正则性问题。

This article uses the implicit function theorem and the properties of analytic functions,with less limitations for the uniqueness,continuity,continuous differentiability of the implicit functions,and gets the sufficient and necessary conditions of the existence of implicit functions by simplifying them.

从常用隐函数存在性定理出发，放宽对隐函数唯一、连续、连续可微等性质的限制，利用解析函数的性质将其展拓，得到广义隐函数存在的充分必要条件和广义隐函数的分布特征。

Institute of Statistics and Actuary, Shandong Economic UniversityAbstract We consider the risk process perturbed by diffusion under interest force in this article. The integral expressions, continuities, twice continuous differentiability and integro-differential equations about $F_{\delta}$, the distribution of the surplus immediately before ruin, and $H_{\delta}$, the joint distribution of the surplus immediately before ruin and the deficit at ruin are obtained.

我们考虑既带有随机干扰又带有确定投资回报的风险过程，得到了破产前瞬间盈余的分布$F_{\delta}$及破产前瞬间盈余和破产时赤字的联合分布$H_{\delta}$所满足的积分表达，连续性及二次连续可微性和积分--微分方程。

By weakening the premise of the convexity of the objective function required in paper[7], we prove the sufficient desent property and the global convergence with the strong Wolfe line search.

在第二章中，我们参照文献[7]中的方法，提出了一类与HS算法相关的共轭梯度算法，并减弱了文[7]中要求目标函数二阶连续可微且为凸的前提条件，采用强Wolfe线搜索，在较弱的条件下证明了这一类算法具有充分下降性和全局收敛性。

Finally, we study the eventual differentiability of a C_0-semigroup associated to a waveequation with boundary dissipation.

最后，我们讨论了一类具边界耗散的线性双曲型方程生成的算子半群的最终可微性，并利用这个结果得到了方程的解具有最终正则性以及半群满足谱决定增长条件。

For a class of nondifferentiable generalized fractional programming problems with the norm \$‖Bx‖\-p\$ in the objective function involving, a new incomplete Lagrange function is given, and the saddle point optimal criteria are proven by using the existing necessary optimality conditions, under the assumptions of the class of generalized (\$F,α,ρ,d\$)-convexity.

对于一类目标函数中含范数‖Bx‖p的非可微广义分式规划，给出了一个新的非完全Lagrange函数，并利用已有的最优性必要条件，在一类广义-凸性的条件下，证明了鞍点最优性准则。

The research of these problems has not been vended in the publication by now and the conclusions are not only brief and practicable but also the generation involving optimality conditions of Fritz John.

这些问题的研究至今为止还没有学者在刊物上公开发表过，所得到的结论不仅简洁、可行性强，而且是在可微情形下Fritz John最优性条件的推广。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。