条件方程

In order to imitate the unbounded space wave propagation,the non local boundary condition is used as the absorption boundary condition to cut off the computation domain,and the problems of plane wave incidence at different angles are calculated with the high order PE algorithm.

文章通过引入Padé逼近构造高阶抛物线方程算法，用非局部边界条件作为吸收边界条件，截断计算区域以模拟无界空间波的传播，结合高阶PE算法分别计算不同角度平面波的入射问题。

As we well know, the symmetry reduction methods related to group theory, such as the Lie point symmetry method, conditional symmetry, generalized conditional symmetry and etc, are effective tools to study the exact solutions of the nonlinear partial differential equations.

众所周知，与群论有关的对称约化方法，如李点对称方法，条件对称方法，一般条件对称方法等，是研究非线性偏微分方程精确解的有效方法。

This article that focuses on the systematic and in-depth research in the current primal problem about abnormal burst pressure reservoir depress burst pressure has procured following main fruits:1 It forms the method which could obtain massive vertical static state mechanics parameters.2 In a foundation of acquisition of rock mechanics parameters,apply bent lamella that as mechanical model along with characteristic of actual geologic characteristics to analysis curvature for anticlinal strcture, get homologous tectonic stress value throug relation between the curvature and stress and different principal curvature in anticlinal structure,consequently set up laminational stress model for anticline reservoir. The block lamination for existed fracturing date has formed method of setting up mechanical model of lamination terrestrial stress by abtaining the block tectonic stress coefficients which are got by complex utilization test, laboratory test and fracturing date playback.3 Analysesing the main reason which lead to high burst pressure by considering the characteristic of reservoir geology,reservoir,and rock mechanics and reservoir damage,etc.Establishing burst pressure quantitative prediction model which provide gist for depressing construction risk and optimizing construction craft under the condition of open hole completion ,gun-perforated completion and damaged reservoir.4 Provding theoretical basis for interpreting acidification pretreatment which could depress busrt pressure by finding the relation between the influencing factors and rock machanics parameters and analysing the factors that have effect on rock mechanics parameters. Expounding the mechanism of reaction of mixed monomineral and acid from the angle of microcosmic element, evaluating quantitatively acid sensilility of different kinds of mineral effectively, and determing the first-order reaction dynamical equation of each mineral.5 Revealing rock mechanics property chage as a result of acid flooding in different condition by sandstone traumata experiment in different temperatures which combined with rock mechanics triaxial stress experiment.6 Associating damage mechanics with sandstone acidizing, established sandstone damage mechanics model in the foundation of the recognition on the rock mechanics parametric variation which is caused by acid-rock reaction in both macroscopic view and microscopic view ,also demonstrated those processes and quantitative estimated the acid busrt pressure to direct the site operation.

本文针对目前异常破裂压力储层降低破裂压力的主要问题展开较为系统和深入的研究，取得了以下主要成果：1形成了利用测井资料，结合室内岩芯测试结果，获取静动岩石力学参数的相关性特征，从而获得纵向上大量静态力学参数的方法。2在获取了岩石力学参数的此基础上，利用弯曲薄板作为力学模型，结合区块实际地质特征对背斜构造进行曲率分析，通过曲率与应力的关系，利用背斜构造不同部位的主曲率求得相应的构造应力值，从而建立起背斜储层的分层应力模型；对已有压裂资料的区块分层，形成了综合利用测试、室内实验、压裂资料反演获得该区块构造应力系数，建立起分层地应力的力学模型的方法。3综合考虑储层地质、油藏、岩石力学特性和储层伤害等因素，分析造成高破裂压力的主要原因，综合利用岩石力学、弹性力学等知识，建立了裸眼完井、射孔完井条件下以及储层受到伤害后的储层破裂压力定量预测模型，为降低施工风险和优化施工工艺提供了依据。4完成了物性、岩性影响岩石力学参数的因素分析，找出了各影响因素和岩石力学参数之间的关系，为从机理上解释酸化预处理降低破裂压力提供了理论基础；从微观元素的角度阐述了单矿物与酸反应的机理；并在此基础上，有效评价了各种矿物的酸敏感性，定量确定了岩石中各矿物的一级反应动力学方程。5完成了不同温度下的酸液类型、酸液浓度、注酸量等一系列砂岩损伤实验，结合岩石力学三轴应力实验，系统揭示了在不同条件下注酸而引起的岩石力学性质变化。6将损伤力学与砂岩酸化相结合，在宏观、微观两个方面认识酸岩反应引起岩石力学参数变化基础上，建立了砂岩损伤力学模型，并对其进行验证，在此基础上定量计算酸化后的破裂压力，有效指导现场施工

Firstly, with the thermal conduction equations of second homogeneous boundary and non-homogeneous boundary condition,we gained the temperature distribution in and after the heating process of the absorbing cavity.

用第二非齐次边界条件和第二齐次边界条件的热传导方程分别建立了吸收腔在激光加热过程中和激光加热结束后的温度分布，利用模拟实验对激光照射吸收腔的过程进行模拟，得到内、外壁温度差的实验数据。

On the basis of Nagumo′s existence theorem for the singular case, we obtain the existence of solutions of singular equations satisfying nonlinear boundary value conditions and periodic boundary value conditions by means of approximations.

在Nagumo型存在定理的基础上，我们应用逼近的方法给出了奇性方程满足非线性边值条件和周期边值条件的解的存在性。

The major implementations of the developed model include: Pseudo-spectral and finite-difference schemes are employed to approximate the spatial-differential operators in the horizontal and vertical directions, respectively. A second-order Runge-Kutta method is adopted to integrate in time for the velocity field and the free-surface elevation. The solenoidal condition of the velocity field is satisfied by solving the transformed pressure Poisson equation. A modified secant method is used to accelerate the iterative solution of the non-separable Poisson equation.

模式的主要数值方法包括：分别以拟频谱法以及二阶有限差分法近似控制方程与边界条件中的水平与垂直导数；以二阶Runge-Kutta法进行非稳态的自由液面位移与流场速度的时间积分；利用改良式割线叠代法求解计算区间中不可分离的压力Poisson方程式，以满足不可压缩流条件。

If the neighborhood of equation solution is solvable and meets the point- by-point Lipschitz condition, stable boundary could be obtained as the convergence of the difference method is realized, and thus the stability is ensured.

方程解的邻近如果可解并具备逐点Lipschitz条件，则差分法收敛必有稳定界存在，从而差分格式收敛性保证其稳定性，因此可以放弃线性这一重要条件。

According to Shilnikov Theorem, on the condition that satisfies the basic characteristics of heteroclinic orbit, Shilnikov inequality and the eigenvalue equation, by finding a heteroclinic orbit consist of three geometric invariant sets, namely unstable manifold, heteroclinic point, and stable manifold, a set of real parameters accordance with the condition of existing heteroclnic orbit is obtained in this chaotic system.

根据Shilnikov定理，在满足异宿轨道基本特性、Shilnikov不等式和特征方程条件下，通过寻找该系统中一条由不稳定流形、异宿点和稳定流形三个几何不变集构成的异宿轨道，在分段Sprott系统中导出了存在异宿轨道时该系统中各个参数应符合的条件，并找到了一组对应的实参数，由此证明了异宿轨道的存在性。

As the main part of this thesis, based on RSJ model, a symmetric DC SQUID is theoretically studied through two-dimensional Fokker-Planck equations, by using the "potential condition" in the case of steady state, the stationary probability distribution function of this system is obtained firstly in the accurate theory, meanwhile, the expressions of all the SQUID characteristics functions are obtained, for example, the circulating current, total normalized voltage and transfer function.

作为本论文的主体工作，我们以RSJ模型为基础，利用二维Fokker—Planck方程从理论上研究了对称型双结超导量子干涉器件，利用定态条件下的"势条件"得到了系统定态概率分布的精确解析表达式，进而得到了该系统所有特性函数如环路电流、总电压、调制函数的统计表达式，利用数值计算讨论了各种参数对DC SoL71D系统特性的影响。

With the idea of smoothing Newton method, we propose a new class of smoothing Newton methods for the nonlinear complementarity problem based on a class of special functions. In this paper, complementarity problem is converted into a series of smoothing nonlinear equations and a modified smoothing Newton algorithm is used to solve the equations. We use Newton direction and Gradient direction together in the algorithm which guarantees that our method is globally convergent. Also using another smoothing function, we reformulate the generalized nonlinear complementarity problems defined on a polyhedral cone as a system of smoothing equations and a smooth unconstrained optimization problem. Theoretical results that relate the stationary points of the merit function to the solution of the generalized nonlinear complementarity problems are presented, we use the modified smoothing Newton algorithm in generalized nonlinear complementarity problems, under mild hypothesis, a global convergence is proved.

本文一方面基于现有的各种光滑Newton法的思想和半光滑理论，利用著名的F-B互补函数的光滑形式，首先将互补问题的求解转化为求解一系列光滑的非线性方程组，然后给出了一种修正的光滑Newton法，该方法不仅放宽对函数F的要求，在Newton方程不可解时引入初始效益函数的最速下降方向，而且光滑因子的选择也比较简单可行，同时在适当的条件下，证明了其算法具有全局收敛性；另一方面，借助另一种F-B光滑函数，将多面体锥上的广义互补问题转化为一种光滑形式，讨论了优化问题的稳定点与广义非线性互补问题的解之间的理论关系，并将这种修正的光滑Newton法用于求解广义非线性互补问题中，在适当的条件下，该算法同样具有全局收敛性。

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