条件方程

Applying the Euler method to the equation and particularly using the interpolation technique on variable delay, the Euler approximation is obtained. The discrete Euler approximation is extended to the continuous Euler approximation. It is proved that the Euler numerical solutions will converge strongly to the true solution under the local Lipschitz condition.

对方程应用欧拉方法，特别地对变延迟部分运用插值技巧进行数值离散后，将离散的欧拉格式延拓为连续的欧拉格式，从而得到欧拉格式在局部Lipschitz条件下强收敛到解析解。

Gerber and Shiu (1998a) and Tsai and Willmot (2002) all consider the renewal equation for the expected discounted penalty function at ruin Ф and its decomposition in this risk process. In their proceeding, they assumed the twice continuous differentiability of Ф,Ф〓,Ф〓 as a premise but its proof isn't obvious.

Gerber and Landry（1998）及Tsai andWillmot（2002）考虑了此模型下的破产时罚金折现期望Ф所满足的更新方程及其分解后的因子Ф〓和Ф〓，但它们的推导过程都是在假定Ф，Ф〓，Ф〓连续且二次连续可微的前提条件下进行的，但实际上此前提假定的成立并非显然。

This paper is to research singular transport equations with anisotropic continuous energy homogeneous slab geometry for periodic boundary condition in slab geometry.

在Lp1周期边界条件下各向异性、连续能量、均匀介质的奇异迁移方程，证明了其相应的奇异迁移算子产生C0半群和该C0半群的Dyson-Phillips展开式的二阶余项是紧的，从而该算子的谱在区域Γ中由具有限重的离散本征值组成等结果。

The objective of this paper is to research singular transport equations with anisotropic continuous energy homogeneous slab geometry for perfect reflecting boundary condition in slab geometry.

在L1空间上研究了板几何中一类具完全反射边界条件下各向异性、连续能量、均匀介质的奇异迁移方程。

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。

With considering of the risk, and through analyzing effective equations, the paper gains the generation company's supply curve and the power distribution company's demand curve of contract thus finds the effective bargaining section, and establishes the relations between the transaction capacity and price.

研究了双边合同谈判的动态形成过程。在风险规避的条件下，通过效用方程分析得到发电公司的合同供给曲线和配电公司的合同需求曲线，并确定了合同的有效谈判区间，从而建立了合同数量和价格的谈判关系。

By improving the Holder condition which the divided differences of order one satisfy,we obtain radius of convergence ball the uniqueness ball.All the theoretical conclusions are tested and verified by a numerical example.

通过改进一阶差商所满足的Holder连续条件，得到了两点弦截法的收敛球半径和方程具惟一解的球半径，并用数值例子验证了理论结果。

Fourthly, Broyden iterative method is studied to solve nonlinear equation with parameters and the existence and convergence theorem is also given.

第四章的主要结果：研究用Broyden迭代求解带参数非线性方程，在弱条件下给出Broyden迭代格式的存在性和收敛性定理。

Further, it is proved that the semi-implicit Euler method is convergent with order 1/2 in mean square sense for the linear test equation by virtue of properties of the conditional expectation.

在此基础上由条件期望的性质证明了半隐式Euler方法应用于线性试验方程时在均方意义下是l／2阶收敛的。

The boundary conditions, written in the Time Domain, yield a convolution equation.

在时域中描绘的边界条件使克林-高登方程以卷积形式出现。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新