展开系数

The application of Karhunen-Loeve expansion to simulating the soil parameters random field is researched;and the characteristics of the KL decomposition are analyzed;and the Galerkin finite element method is adopted to solve the integral equation numerically in the irregular region and for arbitrary covariance function and to simulate the anisotropic conductivity field.

研究了Karhunen-Loeve展开在土性参数随机场模拟中的应用，分析了KL展开的特点，针对不规则区域和任意类型协方差函数提出了积分方程的Galerkin数值解法，模拟了土壤渗透系数各向异性随机场。

Since the multiple scattering should be considered, the scattering problem of many-cylinders is more complicated than single cylinder. By using scattering matrix method to solve the scattering problem of many-cylinders, first we have to express the incident fieldand scattered field by special function（for example, Bessel function and Hankel function）under cylindrical coordinate, then use the addition theorem of special function to get a linear system of equations to relate the incident field coefficients and scattered field coefficients. The incident and scattered field coefficients for every cylinder can be solved from the linear equations by matching electromagnetic boundary condition pointwisely.

单颗圆柱散射体的散射场解析解很早就被解出，而多个圆柱阵列的散射场问题因为涉及到入射光在圆柱与圆柱间的多重散射，故散射行为较单颗圆柱的散射复杂，因此圆柱阵列的多重散射问题需要利用加法定理来处理；散射矩阵法的主要精神即是先用圆柱座标下的特殊函数对平面波和圆柱散射体的内外域电磁场做无穷级数展开，再藉由特殊函数的加法定理将所有圆柱散射体的展开中心移到同一个展开中心，最后可以得到一组连结整个散射系统的入射电磁场系数及散射电磁场系数的线性方程组，将该组线性方程配合电磁场在散射体边界的连续条件，便可分别求出圆柱阵列中各个圆柱体的内部电磁场与外部散射场，再利用线性叠加原理即可求得整个圆柱系统的全域电磁场分布。

In this paper, applications of theJacobi elliptic function expansion method and F-expansion method in constantand variable coe?cient nonlinear evolution equation are considered.

本文主要讨论了Jacobi椭圆函数展开法和F-展开法在求解常系数和变系数非线性波动方程中的应用。

Thus LES is proved to be suitable to simulate the flow and temperature fields of large scale vortices with complex geometric boundaries. LES cooperated with the second order full extension ETG finite element method is applied to simulate the forced convection heat transfer around two square cylinders arranged side by side. While the boundary conditions are symmetrical, the time history and power spectrums of drag coefficient, lift coefficient, averaged Nusselt number at the wall, and the streamwise velocity and temperature on the symmetrical points are calculated. The results show that the power spectrums are all almost symmetrical.

应用大涡模拟与二阶全展开ETG有限元离散格式相结合的方法对间距比为1.5的条件下横掠并列双方柱强制对流换热问题进行了数值模拟，通过边界条件对称时，对并列双方柱对称点上的速度和温度以及方柱的阻力系数、升力系数和壁面平均Nu数进行的时域分析和频域分析，得到了在对称边界条件下并列双方柱对称点上的速度和温度以及方柱的阻力系数、升力系数和壁面平均Nu数的功率谱均基本对称的结论。

In this paper, a high order accuracy difference method is presented for solving unsteady convection diffusion equation by using Implicit Perturbation Finite Difference scheme.

本文利用摄动差分思想，对定常对流扩散方程中的空间微商系数进行摄动展开，展开幂级数系数通过消去摄动格式修正微分方程的截断误差项求出，由此获得方程的隐式摄动差分格式，将此方法应用于非定常对流扩散方程，并加以修正，得到该方程的修正隐式摄动差分格式。

In this paper, a high order accuracy difference method is presented for solving unsteady convection diffusion equation by using Implicit Perturbation Finite Difference scheme. Firstly, we use the steady convection diffusion equation, the constant coefficients of this equation are expanded to power series of grid-spacings, then the high-order Perturbation Finite Difference scheme is obtained by determining the coefficients of the power series. Put this scheme on unsteady convection diffusion equations and modified it, the IPFD scheme is constructed.

本文利用摄动差分思想，对定常对流扩散方程中的空间微商系数进行摄动展开，展开幂级数系数通过消去摄动格式修正微分方程的截断误差项求出，由此获得方程的隐式摄动差分格式，将此方法应用于非定常对流扩散方程，并加以修正，得到该方程的修正隐式摄动差分格式。

Themethod is based on a decomposition of atomic wavefunction〓 into a product of a correlation factor 〓,partially describing the wavefunctioncharacteristics,and the other factor 〓,which is stillexpanded in the symmetric basis function of 〓permutation group.

将Li原子的波函数ψ分解为两项之积，即ψ=Xφ，X=exp-α（〓；而φ仍向〓群的对称基展开，得出超球径耦合微分方程，〓（1）其中，〓和〓为方阵，〓为对角阵，〓（2）再利用广义Laguerre函数展开法对其求解，得到系数矩阵的递推关系式。

The conductivity field and hydraulic field are represented by Karhunen-Loeve expansion and polynomial expansion, respectively. The original stochastic partial differential equation is transformed into a series of deterministic equation at the collocation points.

其渗透系数场和水头场分别被表示为Karhunen-Loeve展开和多项式展开的形式；初始随机偏微分方程被转化为在相应配点上的确定性方程。

The conductivity field and hydraulic field are represented by Karhunen-Loeve expansion and polynomial expansion , respectively. The original stochastic partial differential equation is transformed into aseries of deterministic equation at the collocation points.

其渗透系数场和水头场分别被表示为 Karhunen-Loeve 展开和多项式展开的形式；初始随机偏微分方程被转化为在相应配点上的确定性方程。

With the support of a major research grant of Zhejiang Province (No. 001101027) and the Plan of Promoting Education of Excellence of Zhejiang University in the 21st Century, this dissertation is devoted to address the above problems and fabricate an L-band EDFA with low cost, high performance and technological innovation.First the mechanism of an erbium doped fiber amplifier is introduced. Various theoretical models based on classical rate propagation equations are summarized and compared for their applications. We use a modified numerical model based on the Giles model, which agrees with the experimental results well. This serves as the theoretical base for the whole thesis and will be used to optimize the characteristics of EDFAs. A novel method based on a map of noise figure and gain is proposed to analyze efficiently the dependence of the noise figure and gain for EDFAs on the EDF length and the pump power. The characteristics of various EDFAs are studied and compared.Secondly, some important parameters are introduced to describe the characteristics of EDFAs. The methods and the experimental setups for measuring the gain and noise figure of an EDFA are emphasized. We introduce how to measure the characteristics of each component of an EDFA, especially the gain and absorption coefficient of an erbium doped fiber.Thirdly, four types of simple and novel L-band EDFA structures with low noise, high gain and low gain ripple are proposed to satisfy the requirement of a DWDM system. They can be classified into two categories. In the first category, a single ASE pumping is served asa secondary pump. This category includes the following three types. Type: a new construction using a fiber Bragg grating in an unpumped EDF section at the input side. Type: a new structure of L-Band EDFA with two-stage pumps, which utilizes the forward ASE as a second pump.

本论文本着科技创新、服务于生产实践的精神，以设计价格低廉，性能优越、结构合理简单的L-band EDFA为目标，依托浙江省科技厅重大科学基金资助项目(001101027)和浙江大学振兴教育计划资助的全光网络的搭建—《光通信技术》课程实验建设项目，展开了如下工作：首先，介绍了掺铒光纤放大器的工作原理，归纳总结了基于速率方程基础的EDFA的各种理论模型，分析比较了各个模型的特点和适用场合，最终选择完善的Giles理论模型作为本论文分析设计EDFA的理论基础；针对实际实验条件提出了修正的EDFA模型的数值计算方法；创新地提出了增益—噪声系数全局分析法，直观有效地分析了EDFA的增益和噪声系数与掺铒光纤长度和泵浦功率的依赖关系，并对各种EDFA的性能作了全面的比较；第二，介绍了掺铒光纤放大器特性参数的定义与测量方法，重点介绍了噪声系数和增益系数的测量方法及实验装置；介绍了组成掺铒光纤放大器各组件的特性测量方法，重点介绍了测量掺铒光纤参数的方法和实验装置；第三，针对WDM系统对L-band EDFA谱平坦、低噪声、高增益的要求，我们创新地提出了四种不同的L-band EDFA结构，按设计思路可以分为两大类：一类是基于单抽运二级泵浦法，这一类包括在未泵浦掺铒光纤的输入端插入一根布拉格光纤光栅的两段L-band的EDFA的新结构；基于前向ASE光作为二级泵浦源推动下一级EDF工作的泵浦分配、两段级联L-band的EDFA的新结构；基于单根光纤光栅、泵浦分配、两段级联的EDFA；另一类则是基于同时应用前后向C-band ASE作二级泵浦源的双抽运法，如基于前后向ASE光作为二级泵浦源的三段级联L-band的EDFA的新结构。

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