The Borel directions of algebroidal function and its coefficient functions

In this article, the relationship between the Borel direction of algebroidal function and its coefficient functions is studied for the first time. To begin with, several theorems of algebroidal functions in unit disk are proved. By these theorems, some interesting conclusions are obtained.     

EFFICIENT NUMERICAL ALGORITHMS FOR THREE-DIMENSIONAL FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

This paper detailedly discusses the locally one-dimensional numerical methods for ef- ficiently solving the three-dimensional fractional partial differential equations, including fractional advection diffusion equation and Riesz fractional diffusion equation. The second order finite difference scheme is used to discretize the space fractional derivative and the Crank-Nicolson procedure to the time derivative. We theoretically prove and numerically verify that the presented numerical methods are unconditionally stable and second order convergent in both space and time directions. In particular, for the Riesz fractional dif- fusion equation, the idea of reducing the splitting error is used to further improve the algorithm, and the unconditional stability and convergency are also strictly proved and numerically verified for the improved scheme.     

具有任意方向的扇形滤波器及其在图像方向检测中的应用

扇形滤波器在图像的方向检测中是非常重要的.本文基于极傅里叶变换和一个楔形滤波器,设计出具有任意方向的二维扇形滤波器.首先,楔形滤波器被变换到极傅里叶域,再利用极傅里叶变换的旋转特性,楔形滤波器可以通过将其极傅里叶变换沿着水平方向进行移动来实现旋转,得到一系列具有任意方向导向的扇形滤波器,它们能够检测图像中所包含的任意方向信息.由于整个设计过程不涉及二维优化,因此所提出的设计方法具有设计简单的优点.为了验证扇形滤波器的方向敏感性,将所设计的扇形滤波器应用于图像的纹理方向检测,结果表明,具有任意方向的扇形滤波器在图像纹理方向检测中具有很大的潜能.     

国家自然科学基金工程热物理与能源利用学科研究方向与关键词修订

2021年国家自然科学基金委员会工程与材料科学部工程热物理与能源利用学科对学科代码下的研究方向和关键词进行了梳理和修订,调整了学科资助布局,合并了相近的研究方向,删除了不恰当的研究方向,增加了反映新趋势的研究方向,精炼了各研究方向下的关键词,使研究方向和关键词更加全面合理.通过本次修订进一步厘清了学科的内涵和外延,有利...     

船舶运动状态下风速风向测量补偿与数字仿真

为了研究船舶运动状态下的风速风向精确测量,设计了一种船舶风速风向动态测量及误差补偿的数字仿真系统。通过对船舶航行状态下的风速风向测量原理进行分析,建立了船舶平面运动的相对风速风向和真风风速风向的解算模型,并根据船舶空间运动的风速风向测量及其误差补偿算法,对船舶横摇、纵摇状态下的风速风向的动态测量和误差补偿进行了数字仿真。数字仿真结果表明,该方法能够消除船舶航行时的运动姿态对风速风向测量带来的影响,为船舶的操纵控制和航行安全提供了精确和可靠的风速风向数据信息。     

一个基于张量火车分解的张量填充方法及在图像恢复中的应用

低秩张量填充在数据恢复中有广泛应用, 基于张量火车(TT) 分解的张量填充模型在彩色图像和视频以及互联网数据恢复中应用效果良好。本文提出一个基于三阶张量TT分解的填充模型。在模型中, 引入稀疏正则项与时空正则项, 分别刻画核张量的稀疏性和数据固有的块相似性。根据问题的结构特点, 引入辅助变量将原模型等价转化成可分离形式, 并采用临近交替极小化(PAM) 与交替方向乘子法(ADMM) 相结合的方法求解模型。数值实验表明, 两正则项的引入有利于提高数据恢复的稳定性和实际效果, 所提出方法优于其他方法。在采样率较低或图像出现结构性缺失时, 其方法效果较为显著。     

A modified Newton direction for unconstrained optimization

In this article, a modification on Newton's direction for solving problems of unconstrained optimization is presented. As it is known, a major disadvantage of Newton's method is its slowness or non-convergence for the initial point not being close to optima's neighbourhood. The proposed method generally guarantees the decrement of the norm of the gradient or the value of the objective function at every iteration, contributing to the efficiency of Newton's method. The quadratic convergence of the proposed iterative scheme and the enlargement of the radius of convergence area are proved. The proposed algorithm has been implemented and tested on several well-known test functions.     

Simplified versions of the conditional gradient method

ABSTRACT

We suggest simple modifications of the conditional gradient method for smooth optimization problems, which maintain the basic convergence properties, but reduce the implementation cost of each iteration essentially. Namely, we propose an adaptive step-size procedure without any line-search and inexact solution of the direction finding subproblem. Preliminary results of computational tests confirm efficiency of the proposed modifications.