Convergence of an Ishikawa type iterative scheme for asymptotically quasi-nonexpansive mappings

In convex metric spaces, the Ishikawa iteration process and the Ishikawa iteration process with errors is defined for asymptotically quasi-nonexpansive mappings. It is proved some sufficient and necessary conditions for the iterative scheme converges to the fixed point of the asymptotically quasi-nonexpansive mappings. These results generalize and unify many important known results in recent literature.     

免修整的端面砂轮去毛刺机构设计

针对"合金钢材质的中心有凸台的热后精冲板状小零件的四周表面均有高低不同的毛刺,需要一次性快速自动去除干净"这一课题,设计一种全新的端面免修整的砂轮行星平动磨削去毛刺机构。对其主要部分的结构进行了创新设计和分析。     

中凸变椭圆机床夹具设计与仿真分析

我国大型船舶、重型机车、汽车、航空航天、工程机械等国民经济重要领域急需的大功率船用柴油机活塞加工用变椭圆车床亟待研发。设计一种用于加工大直径活塞的车床专用夹具,并对其进行了三维建模与有限元仿真分析,证明该夹具设计合理,能够满足工作需要。     

凸体几何光谱解混研究进展及若干问题浅析

高光谱图像在高维特征空间中的凸体特性是凸体几何类光谱解混方法的理论依据，这类光谱解混方法具有直观性强、复杂度低、效率高等优点，是高光谱图像光谱解混方法研究的一个重要分支。本文旨在对国内外基于凸体几何理论的光谱解混方法进行回顾，指出这类方法研究中需要特别关注的若干问题，并着重对：①数据降维对凸体几何端元提取方法的影响，②两类经典的单形体体积衡量标准，③3个单形体体积计算公式及其关系3个问题进行简要分析，得到初步分析结果。     

A customized low-rank prior model for structured cartoon–texture image decomposition

The mathematical characterization of the texture component plays an instrumental role in image decomposition. In this paper, we are concerned with a low-rank texture prior based cartoon–texture image decomposition model, which utilizes a total variation norm and a global nuclear norm to characterize the cartoon and texture components, respectively. It is promising that our decomposition model is not only extremely simple, but also works perfectly for globally well-patterned images in the sense that the model can recover cleaner texture (or details) than the other novel models. Moreover, such a model can be easily reformulated as a separable convex optimization problem, thereby enjoying a splitting nature so that we can employ a partially parallel splitting method (PPSM) to solve it efficiently. A series of numerical experiments on image restoration demonstrate that PPSM can recover slightly higher quality images than some existing algorithms in terms of taking less iterations or computing time in many cases.     

Maximum Likelihood Coordinates

Any point inside a d-dimensional simplex can be expressed in a unique way as a convex combination of the simplex's vertices, and the coefficients of this combination are called the barycentric coordinates of the point. The idea of barycentric coordinates extends to general polytopes with n vertices, but they are no longer unique if n > d+1. Several constructions of such generalized barycentric coordinates have been proposed, in particular for polygons and polyhedra, but most approaches cannot guarantee the non-negativity of the coordinates, which is important for applications like image warping and mesh deformation. We present a novel construction of non-negative and smooth generalized barycentric coordinates for arbitrary simple polygons, which extends to higher dimensions and can include isolated interior points. Our approach is inspired by maximum entropy coordinates, as it also uses a statistical model to define coordinates for convex polygons, but our generalization to non-convex shapes is different and based instead on the project-and-smooth idea of iterative coordinates. We show that our coordinates and their gradients can be evaluated efficiently and provide several examples that illustrate their advantages over previous constructions.     

一种凸多面体的阴影生成方法

阴影生成是使三维场景具有真实感的重要方式之一。以往的阴影生成算法是对点和面进行处理的,而该文中的阴影生成算法只针对点进行处理。由于任何物体都可以分解成若干个凸多面体,所以凸多面体的阴影生成很有研究价值。该文将凸壳技术应用于三维场景的阴影生成中,形成一种凸多面体的阴影生成方法,并用OpenGL技术实现。该文简述了OpenGL技术和阴影生成技术的基本原理,用OpenGL生成的三维场景模型进行检验,并叙述了场景的组织结构和阴影生成的实现过程,最后生成了较真实的阴影。     

A Linear-Time Approximation Scheme for Maximum Weight Triangulation of Convex Polygons

In this paper we present a linear-time approximation scheme for determining the maximum weight triangulation of a convex polygon. Our algorithm is simple and can be implemented easily.