( 2) The primitive formation of ODE in the process of founding calculus are studied.

Ode techniques and applications in Computational Mechanics

常微分方程技术及其在固体力学计算中的应用

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This paper deals with generalized Cauchy-Riemann system in even dimensions, which is transformed to an equation similar to the ones in the plane by using the theory of governing equations.

研究了偶数维空间上的广义Cauchy Riemann方程组，利用有限伸张映射的控制偏微分方程组理论，将偶数维空间上的广义Cauchy Riemann方程组转化为一个类似于平面上的方程的形式。

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The author and his research group have combined the Energy Casimir method with the a prior estimate method innovatively and have attained outstanding achievements.

我们将能量Casimir方法与现代非线性偏微分方程理论中的非线性先验估计方法有创新性地结合起来，在该领域取得了突出的成果。

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On the Necessary and Sufficient Conditions of the Uniqueness of the Solution of the Dirichlet Problem for a Class of Elliptic Partial Differential Systems of Second Order with Constant Coefficients

一类常系数二阶椭圆型偏微分方程组Dirichlet问题解唯一的充分必要条件

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As a direct result a partial differential equation determining the optimal loss-function J ( x) is found and the connection between function J ( x) and optimal vector control function u ( x) is also stated.

导出了求算最优损耗函数J（x）的偏微分方程，以及这一函数与最优控制函数u（x）的关系。

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Boundary and boundary conditions are an important aspect of numerical solutions of partial differential equations where the element free Galerkin method have had to surmount many initial difficulties due to the lack of a finite-element-like Kronecker Delta conditions.

边界和边界条件是偏微分方程求解中的一个重要方面。由于无单元的近似函数不像有限元一样满足可罗内克尔Delta条件，所以基本边界条件的引入是无单元方法中的一个难点。

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In this paper we employ Euler's Transformation to discuss the solvability for a class of LPDOs with varible coefficients. Global solvability for this kind of LPDOs is obtained.

本文应用Euler变换讨论一类变系数线性偏微分方程的可解性，得到了全局可解性。

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Secondly, the differential game proved to have a unique value function, and a partial differential equation is obtained for the value function.

其次，证明了该微分对策模型存在唯一的值函数，并根据微分对策理论推导出了值函数满足的IB偏微分方程；

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Based on regressing the curves of average relative permeability in single well, that the oil saturation distribution, permeability ( K) and average formation pressure have been gotten through seeking numerical solution to this two equations.

在回归出单井平均相对渗透率曲线的基础上，通过求两个偏微分方程的数值解，求出了径向上的含油饱和度分布、地层渗透率K和平均地层压力；

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The key technologies of super-resolution restoration for underground mine surveillance images are researched by using of the theory of partial differential equation, non local means, fuzzy set and Markov random field.

论文利用偏微分方程、非局部均值滤波、模糊集、Markov随机场等理论对煤矿井下监控图像超分辨率复原关键技术进行研究。

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The Galerkin approach is employed to deduce a two-degree-of-freedom nonlinear system under the combination of the parametric and external excitations from the governing partial differential equations.

采用Galerkin法对偏微分方程进行离散，得到包含外激励和参数激励的二自由度控制方程。

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The properties of Quasi shannon wavelet was studied in this paper, and a wavelet collocation method for partial differential equations was conducted.

第一、研究了拟Shannon小波的性质，构造了求解偏微分方程的拟Shannon小波配置法，同时将外推法引入小波配置法，进一步改善了该方法的计算效率和计算精度。

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Concerning the defects of Logarithmic Image ProcessingTotal Variation ( LIP_TV) denoising model, an improved Partial Differential Equation ( PDE) image denoising method based on LIP was proposed.

针对对数图像处理-全变分（LIP TV）去噪模型存在的不足，提出一种改进的LIP偏微分方程去噪方法。

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Discussed the augment lagrange multiplier algorithm for a class optimal control problems governed by PDEs gave the finite element discretization and its parallel implementation.

讨论了一类由偏微分方程导出的最优控制系统的增广Lagrange乘于算法，给出了有限元逼近及其并行实现算法。

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Mart is a network-based PSE for solving partial differential equations ( PDEs). It is a Java-based protocol.

Mart是一种新的基于网络的、用来求解偏微分方程的PSE，是一种基于Java的协议。

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Jacobi elliptic function is very useful for solving nonlinear partial differential equation ( s).

Jacobi椭圆函数在求解非线性偏微分方程（组）中具有重要作用。

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Partial differential equation ( PDE) has become an important tool in image processing and analysis.

偏微分方程（PDE）已成为图像处理与分析中的重要工具。

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The Construction of Analytic Solutions for Cauchy Problem with System of Third Order Linear Partial Differential Equations

三阶线性偏微分方程组Cauchy问题解析解的结构

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Applications of Expansion Method About the Jacobi Elliptic Function of Nonlinear Partial Differential Equations

Jacobi椭圆函数展开法在求解非线性偏微分方程组中的应用

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Then the author describes an algorithm of surface reconstruction based on the PDE method.

接着，重点描述了一种根据偏微分方程曲面造型的特点，利用PDE方法进行散乱数据曲面重构的方法。

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