下降函数

Each weight function is a composite function of a generalized Chebyshev polynomial and a linear function, only algebraic calculation is needed, and no requirement is involved for the calculation such as the steepest descent-like algorithms or matrix calculation.

权函数是广义Chebyshev多项式和线性函数的复合函数，只需要通过代数计算就可以求得，不需要梯度下降计算或者矩阵计算。

Each weight function is a composite function of a generalized Chebyshev polynomial and a linear function, only algebraic calculation is needed, and no requirement is involved for the calculation such as the steepest descentlike algorithms or matrix calculation.

权函数是广义Chebyshev多项式和线性函数的复合函数，只需要通过代数计算就可以求得，不需要梯度下降计算或者矩阵计算。

The application of an appropriate apodization film to an ordinary lens makes the point amplitude response asymptotic to a Dirac-delta function, or causes an arbitrarily narrow depth of focus. This implicates that we may achieve lateral or axial superresolution through implementing an apodization film.

运用适当形式的光瞳滤波器可以改变成像系统点振幅响应的分布，使其具有类似于冲击函数(Dirac-delta函数)的形式，这样就有可能实现光学超分辨，但变迹术的运用往往会因其强烈的旁瓣效应而导致成像系统对比度的急剧下降。

The research shows that gas concentration shows generally an increasing tendency along the working face airflow direction, from 0.095% to 0.18%, under the effect of gas drainage points, up-and-down changing locally; gas distribution in a transect of working face is unequal, under the effect of gas emission, ventilation and drainage, the gas concentration near coal wall is larger than that near goaf, which is a concave function distribution within a distance of 1876.5 m from the inlet of working face, after greater than 76.5m, which is a decreasing distribution from coal wall to goaf.

研究表明，该工作面瓦斯体积分数沿风流方向总体呈逐渐增加趋势，介于0.095%~0.18%之间，受瓦斯抽放点的影响，局部有起伏变化；工作面横断面瓦斯体积分数分布不均匀，受瓦斯涌出、通风和抽放的影响，靠近煤壁侧瓦斯体积分数要高于采空区侧，在距离进风口约18~76.5 m范围内为凹函数分布，大于76.5 m之后，从煤壁至采空区为单调下降函数分布。

The decreasing conditions of an energy function are investigated by the use of convex function. By utilization of the primal convex function, the conditions are analyzed under which its conjugate function minus a quadratic function is also convex.

利用凸函数的定义研究了能量函数下降的条件，根据凸函数的性质分析它的共轭函数减去二次函数之差仍为凸函数的条件。

The decreasing conditions of an energy function are investigated by the use of convex function.

利用凸函数的定义研究了能量函数下降的条件，根据凸函数的性质分析它的共轭函数减去二次函数之差仍为凸函数的条件。

That is, the average size of scattering grains (the correlative interval at the first minimum point of autocorrelation function), the descending curve of the autocorrelation and the rectilinear asymptote of the autocorrelation at the large correlated interval changed regularly with the differential roughness of the scattering screen.

即当散射屏粗糙度改变时，散斑颗粒(自相关函数的第一个极小点所对应的相关间隔)的平均大小、散斑的自相关函数曲线的下降趋势和散斑自相关函数在大的相关间隔处的渐近值等都按一定的规律变化。

The NEF method is potential in developing new efficient tools for on-line security analysis and control. In study of the method of damping system low-frequency oscillations, this project has proposed the control strategy of oscillation energy function descent.

项目研究中还应用归一化暂态能量函数对电力系统振荡机理进行分析，设计了增加阻尼平抑电力系统振荡的方法，提出了振荡能量函数的概念，得出"振荡能量函数下降法"的控制策略。

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。

We transforms the special linear system of strict inequalities into three kinds of minimax problems, and then solves it with the aggregate function method assisted with some corresponding method. At last the numerical experiment is done under the environment of matlab.

我们将其转化为三种形式的Minimax问题，对转化后的三种Minimax问题，用凝聚函数法分别将其目标函数光滑化，并分别用带Armijo不精确线搜索的最速下降法、带自适应参数修正的凝聚函数法以及既约梯度法来求解。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。