条件方程

In the Gaussian sum filter-Kalman filter algorithm, the conditional linear state equation is first inserted into the measurement equation, which fuses the linear State process noise and the original measurement noise. And the GSF is applied to the new measurement and nonlinear state equations to estimate the nonlinear states. Then the estimations of the nonlinear states are inserted into the linear state equation and the original measurement equation to estimate the linear states by the KF.

算法将模型中的条件线性状态方程代入观测方程，并融合线性状态的过程噪声和观测噪声，再与非线性状态方程联立，由高斯和滤波器(Gaussian sum filter， GSF)获得非线性状态的估计；然后将估计值代入线性状态方程与观测方程，由卡尔受滤波器(Kalman Filter， KF)获得线性状态的估计。

In this paper, a least-square collocation formulation for solving Helmholtz equation with Dirichlet and Neumann boundary conditions was established.

对于Helmholtz方程问题，其微分方程和边界条件可表示为法应用于Helmholtz方程问题的研究，建立了 Helmholtz方程问题的最小二乘配点格式，分别研究了Hdmholtz方程的波传播问题和边界层问题。

In chapter 3,we study the Zakharov-Kuznetsov-Modified Equal-Width equation by employing the extended Jacobi elliptic function expansion method and obtain some new solutions of Jacobi elliptic function type of the ZK-MEW equation.;Secondly,using sn-cn method,we study K(m,n,1) equation and obtained some new exact solutions when k=s=3,especially obtained abundand solitary solutions and trigonometric function solutions when m→0 and m→1;In chapter 4,Painleve singular analysis was applied to nonlinear PDE with variable coefficients.

第四章将Painleve奇性分析方法应用到带阻尼项的变系数Burgers方程中，并得到了该类Burgers方程具有Painleve性质的条件，给出了该类Burgers方程的Backlund变换，用所得Backlund变换得到了若干精确孤立波解，包括奇异孤立波解，这些解不等同于行波型孤立波解；用齐次平衡法得到了对数型DBM方程的Backlund变换，并获得了DBM方程的各种孤立波解，包括尖峰孤立波解和奇异尖峰孤立波解。

On the basis of gas migration equation -Darcy Law,coal seam gas content equation -parabola equation ,ideal gas state equation and the continuity equation s of the gas flow,a dynamic model of gas unilateral flow in the coal seam is set .

根据基本假设，对煤层瓦斯流动规律进行了研究，运用瓦斯运动方程—达西定律、煤层瓦斯含量方程—抛物线方程、理想气体状态方程以及气体流动的连续性方程，建立了煤层单向瓦斯流动的动力学模型，并根据边界条件和初始条件，对动力学模型进行了求解，推导出煤壁单位面积的瓦斯涌出量的计算公式，分析了瓦斯涌出量的影响因素，利用测得的数据，进行了实例计算，并用vc编制了计算机程序。

By introducing reasonable fundamental assumptions and the Green strain in orthogonal curvilinear coordinates,geometric equations expressed by the Green strain tensor for solving thin shells with large deformation are derived in this paper.

将正交曲线坐标下的格林应变张量引入到薄壳大变形分析，通过建立恰当的基本假设，直接导出了用格林应变张量表示的壳体变形几何方程，将该方程代入到本构方程，由能量原理得到了小应变非线性变形平衡方程、内力方程和边界条件，在此基础上提出了大应变变形的简化分析方法。

Based on modern optimization theory and optimal control theory, this dissertation studies some questions as follows:1. The optimization model of parameter identification of three-dimensional geologic history numerical simulation, algorithm and its applicationGeologic history numerical simulation is a basic content of basin numerical simulation, and the porosity is the major parameter in the evolution and development process of oil-bearing basin. According to the sedimentation and burial mechanism, the physical and chemical principles of oil geology, the mudstone porositys non-linear parabolic partial differential equation has been established.

本文应用现代最优化及最优控制理论，对如下一些问题进行了研究： 1、三维地史数值模拟的参数辨识优化模型、算法及应用地史模拟是盆地数值模拟的一个基础性的研究内容，地层孔隙度是含油气盆地地史演化发育过程中的重要参数，根据地层沉积埋藏机理和石油地质的物理化学原理，通过引入数学物理方程概念，建立了泥岩三维孔隙度场方程，根据问题的特点，给出了方程的定解条件，对方程的动边界也给出了处理方法，并且证明了解的存在性与惟一性，在此基础上建立了以当今实测数据为拟合准则的三维地史数值模拟的参数辨识优化模型，这是一个含有二阶偏微分方程约束的泛函极值问题。

Thirdly, according to the development of the frozen soil, the coupling model of single freezing pipe of axial symmetry of temperature field, stress field and moisture migration is put forward firstly. Then, by means of the progressing principle of potential field, the coupling model of temperature field, stress field and moisture migration which is under the condition of the multi-freezing pipes is extended. At last, the energy balance equation, stress balance equation, quality balance equation, geometric equation, physical equation, initial and boundary conditions etc are adopted to give the analytic solution to the problem of plane axial symmetry of single freezing pipe.

第三，在对室内试验和现场实测结果研究的基础上，分析了土体冻结过程中温度场、应力场、水分场耦合原理，并按照冻土体形成发展过程，首先建立了单一冷源冻结轴对称温度、应力、水分场耦合模型；接着利用势场的迭加原理，将单一冷源情况的三场耦合问题推广到多冷源情况的三场耦合；最后根据能量守恒平衡方程、应力平衡方程、质量守恒平衡方程、几何方程、物理方程、初始及边界条件，解出了单一冷源平面轴对称问题的解析解。

The asymptotical properties of KdV equation and KP equation exhibit the soliton behavior when some conditions are satisfied, and in some cases the parameter matrices describing the interaction between two solutions is quite simple. Two kinds of solutions of the second coupled equations of AKNS hierarchy are provided and applied to NLS equation. A systemical way of construction of special solutions is also tried for DS equation. Most of the results on a scalar equation can often be directly generalized to some matrix equation, and the difference between the ω in scalar form and ω in matrix form lies only in the replacement of vector p, q by matrices p, q.

对KdV方程和KP方程渐近性质的讨论显现出解在一定条件下的孤子特性，从而使得一些情形下，同类解的相互作用体现在参数矩阵上变的较简单；我们给出了AKNS方程的两类不同解，并约化到NLS；对DS方程，我们从另一个方面初步探讨了形式化推导矩阵方程特解的方法；把这些有关标量ω的结果推广到ω为矩阵上往往只要把p，q变为矩阵即可，进而可以再推广到方程组上。

In spherical polar coordinates, DRSC potential have supersymmetry and shape invariance for θ and r coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schrodinger equation with double ring-shaped Coulomb potential are presented. The normalized angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained.

本文研究了双环形Coulomb势Schrdinger方程的束缚态精确解，所采用的方法是首先对双环形Coulomb势的Schrdinger方程在球坐标系中进行分离变量，得到相应的角向方程和径向方程；证明双环形Coulomb势在角向和径向具有超对称性和形不变性；根据超对称性和形不变性的性质，获得了角动量量子化条件和束缚态的能谱方程，并将归一化角向波函数用Jacobi多项式表示，将归一化径向波函数用Laguerre多项式函数表示。

Neutral differential equations with variable sign coefficients are separated into neutral differential equations with positive and negative coefficients by transformation. According to the characteristic of these equations, a real number set with supremum is constructed, and sufficient conditions for oscillation of all solutions to neutral equations with variable sign coefficients are obtained.

通过变换将具有变号系数的中立型微分方程分解为具有正负系数的中立型微分方程；分析具有正负系数中立型微分方程的特征，构造存在上确界的实数集；并对中立型微分方程的解作细致分析，得到了具有变号系数中立型微分方程所有解振动的充分条件。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。