流形上各种算子(如偏微分算子)的研究。
Study of all kinds of operators (such as partial differentia operators) on manifolds.
这个是符号化的向量算子，其中它的分量是偏微分算子。
That was this symbolic vector operator in which the components are the partial derivative operators.
由此得出了判别重特征线性偏微分算子亚椭园性和局部可解性的若干充分条件。
From this, we obtain some sufficient conditions for hypoellipticity and local solvability of those operators.
基于双曲型线性偏微分算子理论，引入并研究了具有非零初始值的拟线性双曲型方程的定解问题。
Based on theory of hyperbolic linear partial differential operator, the initial value problem of a kind of quasi-linear hyperbolic equations with non-zero initial values was introduced and studied.
本文从连续图像出发，将二阶偏微分算子应用于影像函数，利用多重网格算子能得到近似影像的性质，得出一种多分辨影像分解的方法，经过图像重建过程得到融合影像。
Using the so-called approximation of image property by a multi-grid operator, we can derive a method of multi-resolution decomposition of the image, thus the fusion image is formed by reconstructing.
众所周知，分数次积分算子是调和分析中以偏微分方程为背景的一种重要算子。
It is well-known that fractional integral operator is one of the important operators in harmonic analysis with background of partial differential equations.
本文研究了系数为强单调算子的椭圆型偏微分方程，得到了解的梯度的几乎处处收敛性。
In this paper, we study the elliptic partial differential Cquation whose coefficients are strongly monotony operators, and obtain the everywhere convergence of the gradients of solutions.
脉冲双曲型偏微分方程振动性高阶Laplace算子。
Impulse hyperbolic partial differential equation oscillation higher order Laplace operator.
介绍了微分算子级数法在微分方程求解中的应用，给出了方程的微分算子级数解的根据及解偏微分、常微分方程的实例。
The method of differentiator series and its simple application in partial (or ordinary) differential equation is introduced. Some formulae of differentiator series and examples are given.
因此，本文主要致力于对偏微分方程的改进，在该方程基础上加上一个冲击滤波算子，冲击滤波算子的主要作用是在检测到边缘信息时产生一个冲击，使边缘细节信息得到增强。
Therefore, we emphasize on the improvement of the PDE by adding a shock filter operator. The shock filter's main function is creating a shock when detecting an edge to enhance the edge information.
因此，本文主要致力于对偏微分方程的改进，在该方程基础上加上一个冲击滤波算子，冲击滤波算子的主要作用是在检测到边缘信息时产生一个冲击，使边缘细节信息得到增强。
Therefore, we emphasize on the improvement of the PDE by adding a shock filter operator. The shock filter's main function is creating a shock when detecting an edge to enhance the edge information.
应用推荐