可微分性

In this paper, we consider the properties of so_called N_analytic functions , integral formula of Cauchy type and the problem of Riemann boundary value.

研究了N 解析函数的性质、Cauchy型积分公式及相应的Riemann边值问题，然后将其结果应用到一类奇异微分—积分复方程的可解性理论中，建立了其特征方程解的积分表示式。

In section 2, the integral expression, continuity and twice continuous differentiability and integro-differential equation satisfied by the expected discounted penalty at ruin Ф〓 are derived.

在第二节，我们得到了Ф〓的积分表达，连续性及二次连续可微性和积分-微分方程。

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。

The first part is the preparatory knowledge, introducing the contracting mapping principle which through the basis of vector and matrix norm, derivative and differential theorem of mean to thorough understanding the nature of soluble for nonlinear equations.

第一部分为预备知识，重点介绍压缩映象原理。通过引入向量与矩阵范数，导数与微分中值定理，以求深入理解非线性方程组可解性的基本理论。

Firstly,by using the estimating methodfor the compact embedding operators(from weighted Sobolev space to the weighted〓space),we obtain a necessary and sufficient condition for the discreteness of thespectrum of certain differential operators.Secondly,based on the property of thespectrum of difinitizable operators on the Krein space,we consider the left definitedifferential equations with middle deficiency indices,and give a completecharacterization for self-adjoint(J-self-adjoint)differential operators in theindefinite inner product space 〓.Especially,we prove that all the J-self-adjoint differential operators are definitizable.

我们首先运用加权Sobolev空间到加权〓空间嵌入算子紧性的判别方法，证明一类加权自伴微分算子具有离散谱的充要条件；然后，基于Krein空间上可定化算子谱的性质，对于具中间亏指数的左定型微分方程，建立其相应的微分算式在不定度规空间〓上所生成自伴算子的完备性刻画（特别证明了J-自伴微分算子具有可定化性）。

Discusses the multipliers integrability of second order linear differential equation by the numbers.

系统地讨论了二阶线性微分方程的乘子可积性。

Wear degree decreases, and the wear particle distribution curves become protrusive and precipitous gradually in the initial stage.

通过分析铜合金销与碳钢盘在干摩擦条件下相互对磨所产生的磨粒群和销试样磨损量，发现磨粒的累积分布和微分分布特性随磨损时间的变化而变化：在磨损开始阶段，磨损程度逐渐减小，磨粒群分布曲线由平缓变得逐渐凸、陡；达到磨损平衡状态后，磨损率达到最小，磨粒群微分布曲线的幅值达到最大，横向宽度达到最小；随着销与盘间互适性变弱，磨损程度增大，磨粒分布曲线变得越来越平缓，横向宽度逐渐增大；磨粒分布曲线随磨损时间的变化规律与磨损率随磨损时间的变化规律有明显的对应关系，可为科学诊断和预测摩擦学系统状态提供有用信息。

Based on the existence condition of the solution for singular ordinary differential systems,the existence condition of the solution of the degenerate neutral differential system as well as the general solution are obtained by defining the solvable matrix pair and fundamental solution and using Laplace transformation.

讨论了对于退化矩阵E不是方阵情形的一般退化中立型微分系统的解，基于退化的常微分系统解的存在性条件，通过定义可解阵对和基础解以及利用拉普拉斯变换，给出了一般退化中立型微分系统解的存在性条件以及通解表达式。

This chapter proposes three conceptions, i.e., Kernelled quasidiferential, star-kernel and star-diferential, and establishes their operational properties. A sufficient theorem and a sufficent and necessity theorem for a quasi-kernel being a kernelled quasidiferential are proven. Both the existence of star-kernel for a quasidiferentiable function and the existence of star-differential for a direnction-ally diferentiable function are established.

在这一章里，首先给出核拟微分，星核与星微分的定义及其它们的运算性质；然后证明了拟核微分的一个充分条件定理及一个充要条件定理；最后讨(来源：A27BC论文网www.abclunwen.com)论拟可微函数星核的存在性及方向可微函数星微分的存在性以及Penot-微分与上下导数之间的关系。

Thischapter proposes three concepts,i.e.,kernelled quasidifferential,star-kerneland star-differential,and establishes their operational properties.A sufficiencytheorem and a sufficiency and necessity theorem for a quasi-kernel being a ker-nelled quasidifferential are proven.Both the existence of star-kernel for a qua-sidifferentiable function and the existence of star-differential for a directionallydifferentiable function are established.The relationships between sub-and su-per derivatives and Penot differentials are discussed as well.

这一章我们引入了三个概念，即核拟微分，星核与星微分并建立了它们的运算性质；证明了拟核为核拟微分的一个充分条件定理及一个充分与必要条件定理；建立了拟可微函数星核的存在性及方向可微函数星微分的存在性并讨论了Penot微分与上、下导数的关系。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。