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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。

In chapter one, by using a competely continuous operator on cone and the Krasnoselskii fixed point theorem, we study the existence of positive periodic solutions of differential equations with impulses and delays, and some sufficient conditions will be given.

第一章讨论了一类具脉冲时滞微分方程周期正解的存在性，通过建立锥上的全连续算子，利用Krasnoselskii不动点定理，得到了存在周期正解的若干充分条件。

Faraday's law is that when the flux in the conductor loop changes, it produces electromotive force in the conductor loop, and obeys to contour integral law , Maxwell Curl Theory is that when the magnetic intensity of a certain point in ether space changes, there produces electric field at that point in ether space, which is the field mutual production theory of "electric field produces magnetic field and magnetic field produces electric field" in the free space which everybody is familiar with, and it obeys differential law , Lorentz magnetic force is that when metal electrons cut magnetic lines, metal electrons forced by move along the conductor to form inductive current, in fact, it doesn't matter whether coil moves or magnet moves, only if there exists relative motion between magnetic field and conductor, metal electrons must cut magnetic lines, which is,"coil stills while magnet moves to the left" and "magnet stills while coil moves to the right" these two situations are the same, which both belong to metal electrons having cut magnetic lines.

法拉第定律指导体环路里的磁通量发生变化时，在导体环路上产生电动势，而且服从围线积分律；麦克斯韦旋度理论指以太空间某点的磁场强度发生变化时，在以太空间的该点产生电场，即大家熟知的自由空间里"电场生磁场与磁场生电场"之互生场理论，而且服从微分律；洛伦兹磁力指金属电子切割磁力线时，金属电子受力沿着导体漂移而形成感应电流，其实，无论线圈运动或是磁铁运动，只要磁场与导体存在相对运动，则金属电子必然切割磁力线，即，"线圈静止而磁铁向左运动"与"磁铁静止而线圈向右运动"这两种情况是一样的，都属于金属电子切割了磁力线。

Be aimed at ordinary control system, the curvilinear theory in using differential geometry put forward appearance variable, be accused the concept such as appearance contrail curve and appearance contract control.

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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。

In Chapter 4,we study the controllability of differential systems with de-lay.

第四章中，我们研究了时滞系统的能控性问题。

In this dissertation, we discuss the controllability and regularity for some control systemsgoverned by partial differential equations.

本文研究了几类偏微分方程支配的系统的能控性和正则性问题。

Therefore, it is significant to study the existence and controllability of multivalued functional differential equations and integrodifferential equations.

因此，对多值泛函微分方程和积分微分方程存在性和可控性的研究具有重要意义。

Our results indicate that not only the poloidal convection patterns in uppermost mantle have good correlations to surface tectonic motion, but also the toroidal ones reveal important information of their horizontal motion and rotation for the first time. There is a SEE_NWW strong convection zone close to the equator in toroidal convection patterns, which probably correlates with the large_scale shear zone near the equator and is the deep dynamic background of strong earthquake occurrence in this zone. The opposite rotating large_scale convection rolls in the Southern and Northern hemispheres suggest that maybe there is differential rotation between them.

研究结果表明，不但地幔浅部的极型场对流图像显示出了与大地构造运动的相关性并揭示了其深部动力学过程，更重要的是，地幔浅部的环型场对流图像首次为我们认识和理解板块构造的水平与旋转运动提供了重要的信息：环型场速度剖面中在赤道附近存在一条大致南东东—北西西向的强对流条带，可能与环赤道附近大型剪切带的形成相关，进而表明可能是该带强震发生的深部动力学背景；在南北半球存在的旋转方向相反的对流环表明它们整体上可能存在差异旋转。

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。