查询词典 finite difference approximation

In this thesis the process of constructing the non-perturbative Hamiltonian theory is de-scribed and is applied to estimate the vacuum condensate. It contains the following contents:At the very beginning, by using the path integral method and eliminating the gluon freedom, aGCM action 〓 of current quarks including lower order current-current coupling was derivedfrom the QCD Lagrangian and the effective Hamiltonian operator that could hardly be doneby the normal methods was derived. After doing this, the broken vacuum is introduced whichincludes quark-antiquark condensate through the generalized Bogoliubov-Valatin transformation,the effective Hamiltonian of constituent quark was derived. The detailed formulas containingthe spatial current-current coupling term for the effective Hamiltonian and gap equations wasworked out by parameterizing the correlation kernel as a quadratic potential. And then, the gapequation was solved and the quark-antiquark condensate of vacuum was studied both in the casesof instantaneous interaction and retarded interaction. In the end, the effective Hamiltionian withtwo-body quark-quark interaction was derived with one-body approximation, and with the helpof the functional integral method the coupling non-linear dynamic equations for systems withnuclear matter was derived. Finally, these equations were solved by selfconsistent method andthe effect of nuclear matter on vacuum condensate was studied. The spatial current-current coupling term is too difficult to handle, hence the correlationkernel is assumed to be not important and usually omitted in the pure vacuum condensate, andthe instantaneous interaction generally is adopted. Retaining the spatial current-current termand partial retardation effect, the quark pairs condensate in pure vacuum was studied, and theeffect of quark mass was also studied. At present, little study is focused in the case with nuclearmatter and spatial current-current term also omitted. Under the approximation with partialspatial current-current term, the effect of nuclear matter on vacuum condensate was studied.

本论文描述了量子色动力学整体色对称模型哈密顿量方法的构建过程，得到了反映正反夸克对凝聚真空结构的关于组分夸克的有效哈密顿量算符，它隐含了胶子作用，并且准确至流-流耦合项；接着，通过参数化哈密顿量中的夸克作用关联核，导出平方禁闭势参数化选择的哈密顿量的具体公式和能隙方程；随后，应用公式，编程求解，考察了瞬时作用下和部分延迟作用下真空的正反夸克对凝聚，在计算中保留了空间流-流耦合作用；之后，导出瞬时势和延迟势下包含二体作用项的哈密顿量公式，并采用单体化近似，通过泛函变分方法得到核物质存在时耦合的非线性动力学方程；在保留部分空间双流耦合作用的近似下，求解核物质的动力学方程，考察核物质密度对真空凝聚的影响，以往考察真空凝聚，对关联核的选用，由于空间流-流耦合项不易处理，也认为作用不大，常忽略该项，并且常采用瞬时作用；本文保留空间双流项和部分延迟作用，考察了真空情形的夸克对凝聚，还考察了夸克质量对纯真空凝聚的影响，以往对核物质存在情形的真空凝聚考察很少，也都忽略空间流-流项，本文在考虑部分空间流-流项近似下，考察了核物质存在对真空凝聚的影响。

The main procedures are as following: to generate small increment of parameters automatically and to calculate the FE several times and obtain the sensitivity of objective function to the parameters, and then form a Hermite polynomial approximation, the calculation of FE solutions are substitute by the calculation of polynomial approximation, so time cost decreases dramatically.

用n维埃尔米特插值技术建立设计变量在可行域上的目标函数的逼近函数；将局部寻优的梯度算法和全局寻优的随机算法结合起来，大幅度地降低寻优过程中电磁场的计算次数。

First the approximation problems are obtained by approximation to the initial datum.

第三部分研究基本半导体方程混合初边值问题解的整体性质。

There are substantial relation between the interpolation and approximation of functions.The interpolation polynomial is regarded as the important tool of achieving approximation of function.

函数插值与函数逼近有着密切的联系，插值多项式可看作实现函数逼近的一种重要工具。

And several rough set operation algorithms are also offered in this paper,such as upper approximation set,lower approximation set,intersection, cardinal number and so on.

通过讨论二进制与粗糙集之间的内在联系，提出基于二进制的粗糙集运算理论，并借助二进制的位运算操作，给出粗糙集的上近似集和下近似集、等价类的交、集合的基数的运算算法。

The objective function of the QP problem is a quadratic function which is an approximation of the Lagrangian function of the constrained problem and the constraints of the QP problem are linear approximation of the constraints of the constrained problem.

这些二次规划子问题的目标函数是原约束最优化问题的Lagrange函数的某种二次近似，其约束条件是原约束条件的线性逼近。

By applying the concept of "dominant input",the existence of both the approximation error and external disturbance which are supposed to have unknown boundaries is considered.What's more,the adaptive law utilizes two types of errors in the adaptive fuzzy systems,the tracking error and approximation error.

该方法应用"主导输入"的概念，同时考虑了函数逼近误差和系统外扰的存在，假设了该系统逼近误差和系统外扰有界但界未知的情况；并探讨了自适应模糊控制器的参数自适应律由跟踪误差和逼近误差共同进行调节。

However, the generalized moving least squares approximation makes require least squares approximation with regard to functional and its derivative value on all nodes.

而广义移动最小二乘近似要求近似函数及其导数在所有节点处的误差的平方和最小。

Secondly three kinds of approaches of function approximation are discussed which are the interpolation with radial basis function, moving least squares and approximate approximation. And the correlative theories are proved.

在此之后介绍了求解偏微分方程数值解的两种无网格方法：无网格伽辽金方法和无网格局部Petrov-Galerkin方法。

This dissertation focuses on the spherical wavelet expansion of the earth gravity field and its application. Based on the concept of the integration approaches and radial basis functions the spherical wavelet is put forward, with that the earth gravity field is described in a new way, and some other researches are conducted, they are: spherical wavelet regularization, multiscale approximation of satellite gravity measurement, down continuation of airborne geavimetry data, the least squares properties of geopotential wavelet approximation, the spherical wavelet solution of two kinds of BVP and spherical selective multiscale reconstruction.

本文围绕地球重力场的球面小波展开及其应用进行研究，在积分逼近与径向基函数概念的基础上引入了球面小波，利用球面小波对重力场展开进行了重新表示，在此基础上进行了球面小波正则化、卫星重力多尺度逼近、航空重力数据向下延拓、重力场球面小波逼近的最小范数性质、两类边值问题的球面小波实用解、球面选择多尺度去噪方法等方面的研究。

We have something to do in the new stage.

在这段崭新的时期中，我们有一些要做的。

The difference between tourism decision-making under uncertainty and risky tourism decision-making is indistinctive.

其中不确定性旅游决策和风险旅游决策的界线比较模糊，两者的区分是相对的。