积分公式

Let D be a bounded domain with C(1) boundary in Cn . The authors use the locally finite open coverring of the countable strictly pseudoconvex to define a new partitions of unity of σpoint finite local holomorphic , constructed a generalized Cauchy integral formula with discrete local holomorphic kernel on the bounded domain D and applied it to solving the 52equation.

设D 是Cn 空间中具有C(1)边界5D 的有界域，本文利用D 上一个局部有限的可数强拟凸开复盖，定义了D上一个新的局部全纯的σ点有限的单位分解，建立了D上一个更一般的具有离散局部全纯核的Cauchy积分公式并获得D 上52 方程的具有离散核的解的积分表示。

Secondly,we firstly study the properties of functions with values in a uni-versal Clifford algebra 〓,and we obtain the following very important basictheorems in universal Clifford analysis:Cauchy's integral formula,Cauchy's inte-gral theorem,the mean value theorem,the three versions of the maximum mod-ulus theorem,the Taylor's expansion,the Laurent's expansion and the residuetheorem etc..All of these results generalized the classical results.

第二，本文所讨论的各种函数性质以及所得的结果都在泛Clifford代数〓上所做的工作，它一方面包含了从前在泛Clifford代数〓上所做的工作，所得到的结果更广泛、更漂亮、更自然，另一方面，本文也是迄今为止第一次建立起来了在泛Clifford分析中与经典函数论相对照处基础地位的LR正则函数在特异边界上的Cauchy积分公式、Cauchy积分定理、平均值定理、极大模原理的三种表达形式、Taylor展式、Laurent展式留数定理等深刻的结果。

Property 2 (Term-by-Term Integration) Suppose that is the sum of a power series on interval ;that is,Then, if is interior to ,and the radius of convergence of the integrated series is the same as for the orginal series.

性质 2 幂级数的和函数在其收敛域上可积，并有逐项积分公式，，逐项积分后所得到的幂级数和原级数有相同的收敛半径。

In order to meet the required simulation precision and meet the real-time simulation in ballistic simulation calculation,this paper analyzes the selection method of the simulation step,and then introduces variable step integration methods in Runge-Kutta to Adams and educes Adams variable step integral formulas,and then put forwards a method by seeking zero of condition function in discontinuous nonlinear system of the ballistic simulation.

在弹道仿真计算中，为了既达到要求的仿真精度又能满足实时仿真，分析了仿真步长的选择方法，然后在龙格－库塔转阿当姆斯法中引入变步长积分方法，推导了阿当姆斯变步长积分公式，同时对弹道仿真中的间断非线性系统提出条件函数求零的方法来解算弹道。

The new method applies quadratic spline function to interpolate thenonharmonic function in Duhamel's integral.

本方法是利用二次样条函数对Duhamel积分中的非振荡型函数进行插值，导出了相应的数值积分公式。

First of all, Newton-Cotes integral formula is used to calculate the special solution of nonhomogeneous equation in Duhamel integral form for linear system.

首先对于线性问题，利用等步长的Newton-Cotes积分公式计算非齐次方程Duhamel积分形式的特解。

Based on Fresnel Kirchhoff diffraction integral equation, a mathematical model on the diffraction of nonlinear optical media to Gaussian beam is established.

从菲涅耳基尔霍夫衍射积分公式出发，建立了非线性光学介质对高斯光束的衍射模型，通过数值积分，得到了与实验现象符合的计算结果。

By the theory of natural boundary reduction, the natural integral equation and the Poisson integral formula of the problem considered are obtained, and the numerical method of the natural integral equation is given.

通过自然边界归化，获得了该问题的自然积分方程和Poisson积分公式，给出了自然积分方程的数值解法，并通过数值例子以示本文方法的可行性与有效性。

As we know,the integration by parts reveals the direct relationsbetween the integration of a function and that of its derivative.

我们知道，微积分中的分部积分公式给出了一个函数的积分与其导函数积分的联系。

In addition,the recursive summation method for programming the kirchhoff's integral formulation is discussed in detail.

详细论述了将Kirchhoff积分公式程序化的循环累加法；并着重分析了不同积分面及其网格划分对积分精度的影响。

This paper analyzes the compound attractor structure of a new three-dimensional autonomous chaotic system.

分析了一种新的三维自治混沌系统吸引子的复合结构。

ON shut rivals out of their transmission systems and shy away from reinvesting their profits in network improvements.

ON将竞争者挡在了其输送体系之后，并不愿将其收益再投资于网络改建工作。