求解过程

When solving IK, we use position constraint of the knee joint to decide the swivel angle. The result obtained in this way can preserve the continuousness and the detail signal of the original data.

在求解IK的过程中，使用膝关节的位置约束来确定旋转角φ，求解结果保持了解的连续性和原始数据的细节信号。

Then,the cosine value of central angle between the spacecraft and the descending node is solved by using cosine theorem of spherical geometry to avoid the cumbersome solving process by judging the flight direction of a satellite and the latitude of sub-satellite point in an original calculation model of image motion speeds.

通过球面几何的余弦定理直接求解航天器与降交点相对地心夹角的余弦值，避开了原像移速度计算模型中通过判断卫星飞行方向和星下点纬度来求解航天器与降交点相对地心夹角余弦值这一过程。

With the investigation of the domestic and foreign literature systematically, the bases on the domestic and foreign present research and the comprehensive utilizations of the various knowledge of fluid mechanics in porous medium, reservoir engineering, mathematical physics, perforation completion, numerical simulation and so on, this article takes numerical simulation of gas reservoir of water solubility as the research aim which has completed following research works and obtained the corresponding research results: it analyzes the nature of the Water-soluble gas and formation water as well as the influent factors of the solubility through the study of massive materials; It establishes mathematical models three-dimension, the dual medium, the gas-water phase through the way of finite difference in the migration of water-soluble gas, which describes the entire process of release, migration and production in formation, where it considered the problems of variable bubble point; According to the numerical models of gas reservoir of water solubility it provides solution procedure that based on black oil model; It discovers that there will obtain the good effects in the lowly speed of development through simulation; the reinjection of formation water may largely enhance the produce degree of water-soluble gas when we consider reinjection in simulator; It considered the influence of perforated completion on development so as to increase the simulator"s versatility, It discovers that the simulator may reflect the conditions of development when we exanimate he simulator"s reliability with the empirical datum.

本文以水溶性气藏数值模拟研究为研究目标，在系统调研国内外文献、深入分析国内外研究现状的基础上，综合利用渗流力学、油气藏工程、数学物理方法、射孔完井以及数值模拟理论等多方面的知识，完成了以下研究工作并取得相应的研究成果；①通过对大量的资料调研，分析了水溶气、地层水性质、储层地质性质以及影响气体在水中溶解度的因素。②考虑到由于高压产生的大量水力裂缝，采用有限差分方法建立水溶气运移的三维、双重介质、气-水两相全隐式数学模型，该模型描述了水溶气在地层中的释放、运移和采出的整个过程。③在原有黑油模型的基础上，根据水溶性气藏数值模型编制了该数值模型的求解程序，该程序可以求解单重、双重介质两种情况。④通过模拟不同开采速度对水溶气开发效果的影响，发现开采速度较慢的时候可以取得较好的开采效果。⑤在模拟器中考虑了注水对水溶性气藏开发的影响，地层水回注可以大幅度提高水溶气的采出程度。⑥为增加模拟器的通用性，在模拟器中考虑了射孔完井方式对开采的影响。⑦检验模拟器计算的可靠性，发现在使用实验数据对水溶性气藏进行模拟时，模拟器可以很好的反映气藏开发的状态。

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。

In the present work,the existence and uniqueness results aboutperiodic boundary value problems for different kinds of the nonlin-ear periodically perturbed nonconservative systems are establishedthrough the discretization technique,under suitable assumptions,by using global inverse function theorem and result about the ex-istence and uniqueness of periodic solution for nonhomogeneouslyfirst order linear periodic boundary value problem.

本文的第一章概述了在讨论原问题解的存在唯一性过程中以及构造和分析相关的数值求解方法时将要用到的全局反函数定理、有关矩阵特征值的若干重要引理、线性常微分方程非齐次周期问题解的存在唯一性定理和单参数影射方法及有关结论，并简单回顾了已有的证明非线性微分方程周期边值问题解的存在唯一性的方法，其中包括谱理论、最大最小化形式方法、摄动技术和全局反函数理论方法，最后，介绍了两类数值求解非线性微分方程问题的方法。

Here pis 1 or 2.In chapter 8. we extend the Runge-Kutta methods to variable delay differentialalgebraic system. It is proved that if the Runge-Kutta method which is algebraicallystable and diagonally stable is consistent with order p , the extended Runge-Kuttamethod with Lagrange interpolation procedure is D_A-convergence with order M. HereM=min{p, u + q + 1 }, and u + q is the degree of Lagrange interpolation polynomial.

第八章将求解常微分方程的Runge-Kutta方法改造后用于求解变延迟微分代数系统，并且证明如果代数稳定且对角稳定的Runge-Kutta方法对于常微分方程初值问题在经典意义下是p阶相容的，那么具有Lagrange插值过程的该方法是M阶D_A-收敛的，M=min{p，u+q+1}，u+q为Lagrange插值多项式的次数。

The processing of the middle point incremental method of resolution in particular is discussed.

论述了求解非线性有限元方程的方法，主要讨论了中点增量法求解的具体过程。

Establish the steady-state and transient model using the three hydrodynamics equations (Continuity equation, Momentum equation and Energy equation). By comparing different state equation, it selects the BWRS state equation which is considered the most accurate state equation in current natural gas measurement. It calculates compression factor, density and other Thermal parameters based on BWRS state equation. In Numerical solution of the steady-state and transient model, compression factor, friction coefficient and all the other Thermal parameters are recalculated in each small time step to reduce the numerical calculation error.

在稳态模型的建立上，利用流体力学三大方程(连续性方程、运动方程和能量方程)，通过比较不同的状态方程选用了目前被认为最精确的用于天然气计量的BWRS状态方程，并以此方程为基础进行压缩因子、密度等热物性参数的计算；在稳态模型的求解上，选用容易计算，精度较高的标准型龙格—库塔(Runge-Kutta)法进行数值求解，并且在迭代过程的每一小步都重新计算燃气的压缩因子，摩阻系数等所有的计算参数，以减少数值计算的误差。

As well, ACA outperforms GA in performance on average. 2. Through the analysis and studying of Ant colony algorithm and Flow shop scheduling problem, a construction graph is introduced. Two ant colony algorithms are proposed and analyzed for solving the flow shop scheduling problem with the objective of minimizing the flowtime. The Initialization of parameters and updating of trail intensities and probability is described respectively and a newly local search technique is proposed. Last is the experiment and the comparison shows that the PACA performs better than the FACA in the case of relatively large-sized problems than in the case of relatively small-sized problems.

通过对基本蚁群算法的实现过程和流水调度问题进行研究，给出了求解流水调度问题的解构造图，提出了两种蚁群算法来求解以总流程时间最小为目标的流水调度问题-FACA 蚁群算法和PACA 蚁群算法，分别给出了FACA 蚁群算法和PACA 蚁群算法的参数初始化方式、相对应的信息素更新方法和概率分布规则，并提出了局部搜索模式，最后进行模拟试验，对这两种算法进行比较，试验结果表明：对于较大规模的问题，PACA 蚁群算法要优于FACA 蚁群算法，而对于较小规模的问题，FACA 蚁群算法优于PACA蚁群算法。

And combining finite element method and periodic boundary conditions,this article has provided the solution process for asymptotic homogenization equation and the predicting effective mechanics properties method in engineering.

本文利用渐进均匀化理论，详细叙述了求解具有周期性细观单元结构的复合材料有效力学性能的方法，并结合有限元理论和周期性边界条件，给出了求解渐进均匀化方程的过程，为实际工程问题提供了预测材料力学性能的方法。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新