微分

Based on the characteristics of product provisions in local market, here developed 3 models using binomial tree, partial differential equation, term structure and Monte Carlo simulation.

在归纳国内产品关键条款的基础上，借助二叉树、偏微分方程、利率期限结构和Monte Carlo模拟算法，建立了三种可转债定价模型。

Key words: biomathematics; optimal harvesting problem; stochastic differential equation; mutualism model; harvesting cost

关键 词：生物数学；最优捕获问题；随机微分方程；互惠模型；捕获费用

A class of nonlinear two species competition singularly perturbed initial-boundary-value problems in a reaction-diffusion system in biomathematics was studies using the modern method of differential equation.

利用微分方程的近代方法研究了生物数学中一类非线性两种群竞争模型的反应扩散系统奇摄动问题。

The approximation of the parabolic integro-differential equations is studied with anisotropic biquadratic finite element.

摘要研究具有各向异性特征的双二次元对抛物积分微分方程进行了逼近。

There is model error except differential model. The bisection model and equal turning angle model are equivalent each other.

除微分模型外，其它三种模型均存在模型误差，其中等分模型和等转角模型是等价模型。

The author points out: if lots of the conflicts of philosophical foundation the 20th century's quantum mechanics faced with, well-known to everybody, should be logically attributed to the confusions of the some fundamental concepts in the classical electromagnetic field theory, the series of logic inconsistencies implied in the classical electromagnetic theory and the forms of difficulties the modern computational electromagnetism encounters while solving time-varying electromagnetic field should be also logically attributed to an anomalous fact that series of fundamental mathematical propositions relating with bispinor differential operator, which naturally appears in the formal expression about dynamic electromagnetic field, have not be solved really while the related complete mathematic physical models or well posed boundary value problems have not been built.

著者指出：如果说20世纪的量子力学之所以面对哲学基础众所周知的矛盾，在逻辑上最终不能不归咎于经典电磁场理论体系的一些基本概念并没有真正得到澄清的话，那么，经典电磁场理论体系隐含的众多逻辑不自洽问题与目前计算动态电磁场所面对的困境，则必须逻辑地归咎于与双旋度微分算子相关的一系列基本数学命题并没有解决，而相关的恰当数学物理模型至今没有真正建立起来的缘故。

It is impossible to describe this complex flow with a single method. Specially to transition flow, there is no suitable theory. The equation that fits it is Boltzmann equation, but the solution of it is almost impossible.

特别是对于过渡领域的流动，目前尚无完善的理论，与之相对应的数学方程是完全的Boltzmann方程，它是一个非常复杂的非线性的积分-微分方程，除了极其简单的情形，它的求解根本是不可能的。

The sequential Cireut model with fuzzy border is set up on the bases of Boolean defferetial and fuzzy border set.

在布尔微分及乏晰边沿集合两个基础上，建立了乏晰边沿的时序电路模型。

The thesis is organized as follows:In Chapter 1,a new partial differential equation model for Spontaneous Potential log in heterogeneous formations is introduced.At the same time,the existence and uniqueness of weak solution to the problem are proved,and the problem of resistance identification in SP log is studied.Furthermore,a jump condition capturing finite difference scheme is proposed and applied to solve such elliptic interface problems.The effects of various factors on SP response,which include objective layers resistivity,bed thickness,bore-hole diameter,invasion and water-flooded zones and so on,are investigated quantitatively by the proposed method, and satisfactory results are obtained.

具体安排如下：第一章首先建立复杂地层中自然电位测井的偏微分方程数学模型，证明了该边值问题弱解的存在唯一性，在此基础上研究了自然电位测井电阻率识别问题：然后发展了用于求解椭圆交界面问题的间断捕捉有限差分方法，利用该方法定量分析了目的层电阻率、地层厚度、井径、侵入带和水淹层等因素对自然电位测井响应的影响，取得了满意的结果。

Developed in 1990's, the distorted wave Born approximation methodwhich deal with the problem of three bodies of interaction in the collision betweenelectron and atom provide the theoretical criterion to calculate the tripledifferential cross section of the (e,2e) reaction.

二十世纪九十年代发展起来的处理电子—原子碰撞三体相互作用问题的畸变波玻恩近似方法，为计算原子的(e，2e)反应的三重微分截面提供了理论标准。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。