乘积积分

The background component must be calculated by integration of the product of aerodynamic force covariance and influence function, instead of mode superimposition, while the resonant component only consider the contribution of the 1st mode.

前者不能按振型分解法求解，而应通过对气动力协方差与影响函数乘积积分的方法来计算；后者可只考虑一阶振型的贡献，两者应按平方和开方的原则组合得到脉动风致响应的峰值。

With help of product integration theory this paper gives the necessary and suffient conditions for finite determinacy of smooth map-germs under some subgroups of and .

本文利用乘积积分理论给出了映射芽在和的一些子群下有限决定的充分必要条件。

By studying measure theory, the students are asked to understand σ-algebras, measure, measurable functions, integral, the measure theory of product spaces, Fubini theorem, and the representation theory of Boolean algebras.

通过本课程学习，使学生掌握σ-代数、测度、可测函数、积分，初步掌握乘积测度空间的构造及Fubini定理，以及布尔代数的表示理论。

Integral comparison criterion, product of absolutely convergence series.

积分判别法；无穷乘积

During the simulation, surface current from primary electrode is computed. Taking rectangular triangle as the mesh unit, the integral formula of surface current can be simplified to a product of a difference expression and the surface area. So the computation complexity of FEM will be decreased and the time-cost will be cut down greatly.

在模拟过程中，需要计算主电极表面电流，通过选用直角三角形作为离散单元，将表面电流的二重积分表达式简化为一个差商表达式与主电极表面积的乘积，极大地降低了有限元分析的复杂度，减少了计算时间。

The 3-D thermal weight function method was proposed, in which the works ussually done for finite element stress analyses for every time instants could be avoided, and the transient stress intensity factor of a body subjected to thermal shock can be calculated through direct integration of products of temperature fields and TWF.

在国际上首次以三维热权函数法为核心，绕过对每一时刻有限元应力分析这一步，直接通过温度场与热权函数的乘积的积分来计算热冲击应力强度因子K的过渡过程，极大地提高了计算效率。

In this project, we study the theory of higher order differential equations in Banach spaces and related topics. We solve an open problem put forward by two American Mathematicians and two Italian Mathematicians concerning wave equations with generalized Weztzell boundary conditions, introduce an existence family of operators from a Banach space $Y$ to $X$ for the Cauchy problem for higher order differential equations in a Banach space $X$, establish a sufficient and necessary condition ensuring $ACP_n$ possesses an exponentially bounded existence family, as well as some basic results in a quite general setting about the existence and continuous dependence on initial data of the solutions of $ACP_n$ and $IACP_n$. We set up quite a few multiplicative and additive perturbation theorems for existence families governing a wide class of higher order differential equations, regularized cosine operator families, regularized semigroups, and solution operators of Volterra integral equations, obtain classical and strict solutions having optimal regularity for the inhomogeneous nonautonomous heat equations with generalized Wentzell boundary conditions, gain novel existence and uniqueness theorems,which extend essentially the existing results, for mild and classical solutions of nonlocal Cauchy problems for semilinear evolution equations, present a new theorem with regard to the boundary feedback stabilization of a hybrid system composed of a viscoelastic thin plate with one part of its edge clamped and the rest-free part attached to a visocelastic rigid body. Also we obtain many other research results.

在本研究中，我们对Banach空间中的高阶算子微分方程的理论以及相关理论进行了深入研究，解决了由美国和意大利的四位数学家联合提出的一个关于广义Wentzell边界条件下的波动方程适定性的公开问题，恰当地定义了Banach空间中的高阶算子微分方程Cauchy问题的算子存在族及唯一族，建立了齐次和非齐次高阶算子微分方程Cauchy问题适定性的判别定理，获得了关于高阶退化算子微分方程的算子存在族、正则余弦算子族、正则算子半群、Volterra积分方程解算子族的乘积扰动和混合扰动定理，得到了关于以依赖于时间的二阶微分算子为系数的一大类非自治热方程非齐次情形下的时变广义Wentzell动力边值问题的古典解、严格解的最大正则性结果，获得了半线性发展方程非局部Cauchy问题广义解和经典解存在唯一的判别条件，从实质上推广了现有的相关结果；得到了一部分边缘固定而另一部分附在一粘弹性刚体上的薄板构成的混合粘弹性系统的边界反馈稳定化的新稳定化定理，还建立了一系列其他研究结果。

The residual parts are surface integrations whose integrands are the products of the scalar Green's function and fields or their derivatives. The high order singularity of integrands in the integral equation is reduced to one order, making for program implementation.

剩下的部分是关於标量Green函数与场强值或与它们的一阶导数值乘积的面积分，这样积分方程的被积函数高阶奇异性被降到一阶，有利於计算机的程序实现。

In order to obtain more exact analytical solution to study the output characteristics of double-clad fiber lasers,according to the continuous-wave rate equations of fiber lasers,using typical parameters of double-clad fiber lasers,the contribution of the re-emission effect arising from the interaction between the upper-level atoms and pump light was estimated.Taking into account the predominant part of the re-emission to improve the accuracy of the integration approximated rate equations,the integration of the product of the loss and radiation should be found and explicit analytical expressions for the output of the DCFLs and gradient efficiency of the pump radiation,were deduced,and certain issues of concern were discussed.

为了求得用于研究双包层光纤激光器输出特性的更为精确的解析解，根据稳态速率方程组，针对典型的双包层光纤激光器参量，在估计了上能级粒子再发射项和抽运光产生的影响后，采用保留再发射贡献主导部分的办法以提高可积分近似方程的精确度，明确地提出了要获得光纤激光器输出功率的解析表达式的关键在于求出损耗系数与光场乘积的积分值，简洁地求得了输出功率和抽运光斜线效率的显函数解析表达式，并对其相关问题进行了讨论，以915nm，920nm和975nm的抽运光为例，当输出激光为1090nm时，得出975nm抽运光产生的斜率效率最高并可高达约87%。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了