Generalized Global Monotonicity of Generalized Derivatives

The gradient and the several kinds of its generalizations provide a very efficient tool in characterizing important properties of functions. Convexity and generalized convexity, which are central properties in many branches of Operational Research, can also be characterized by special properties (monotonicity and generalized monotonicity) of the gradient map in the smooth case (Karamardian and Schiable, 1990. JOTA , Vol. 66, pp. 37–46) and by that of the Dini derivatives in the nonsmooth case (Komlosi, 1991. Working paper, Janus Pannonius University; 1992a. Nonsmooth Optimization: Methods and Applications; Proceedings of the IVth International Workshop on Generalized Conuexity , in press; Luc, 1991. Subgradients of quasiconvex functions). It is shown in this paper how quasiconvexity, pseudoconvexity and (strict) pseudoconvexity of lower semicontinuous functions can be characterized via quasimonotonicity and (strict) pseudomcnotonicity of different types of generalized derivatives, including the Dini, Dini-Hadamard, Clarke and Rockafellar derivatives.     

在线手绘投影线图的端点融合

针对现有3D手绘投影图端点融合方法的不足，提出通过变系数容差带进行端点融合的方法．首先利用容差半径计算变系数容差带，通过将二次曲线求交转化为直线段与二次曲线求交确定节点；然后按线元为棱线还是转向轮廓线，依据聚类点类型和融合规则分别给出其端点融合方法；最后结合完整线图和3D重建技术进行端点规整．通过算例对文中方法予以验证并与现有方法进行比较．实验结果证明该方法能得到满意的3D手绘投影图规整效果．     

一种保凸曲线的设计方法

针对计算机图形学和计算机辅助设计中的一类基本问题，即通过一组给定的数据（Ｘｉ，Ｙｉ）作一光滑的三次曲线（ｉ＝１，２．．．，ｎ，且有Ｘ１＜Ｘ２＜．．．＜Ｘｎ），应用分段三次插值，提出了曲线保凸的一种方法，对某些不能够保凸的区间，作法是在该区间上插入一结点，用两段三次插值曲线实现保凸，并推导了整个曲线在插入点二阶导数连续的条件，最后举例说明了这种方法的应用。     

二元函数的一个磨光算子

给出了一个新的二元函数磨光公式。与文［１］中所给出的逼近阶０（ｈ＾２＋ｌ＾２）的公式相比较，逼近精度大大提高，在相同节点及计算量情形下，达到０（ｈ＾４＋ｌ＾４）阶，具有保凸性质。     

局部凸空间的弱局部一致凸性与局部一致凸性

本文引进了局部凸空间的弱局部一致凸和局部一致凸的概念,同时得到了几个与赋范线性空间几何理论中相应定理平行的结论。     

Polyhedral studies for minimum-span graph labelling with integer distance constraints

This paper studies the polytope of the minimum‐span graph labelling problems with integer distance constraints (DC‐MSGL). We first introduce a few classes of new valid inequalities for the DC‐MSGL defined on general graphs and briefly discuss the separation problems of some of these inequalities. These are the initial steps of a branch‐and‐cut algorithm for solving the DC‐MSGL. Following that, we present our polyhedral results on the dimension of the DC‐MSGL polytope, and that some of the inequalities are facet defining, under reasonable conditions, for the polytope of the DC‐MSGL on triangular graphs.     

关于特殊函数ma(r)的广义凹凸性及不等式

函数的广义凹凸性是获取函数不等式的一种重要的工具.利用广义凹凸函数(MN-凹凸函数)判别方法-广义凹凸性与单调性之间的关系,揭示了特殊函数ma(r)及由ma(r)与初等函数复合而成的复合函数的广义凹凸性.同时,利用这些结果获得相关的几个不等式.     

关于Bézier曲面的凸性

本文讨论了几个能形成凸的Bezier曲面的空间网格的充分条件。讨论了它们的解析表达式及几何意义。还讨论了平行网格的特例,得出了几个有用的结论。并用反例说明网格凸与曲面凸互不为充分条件。     

Nonwetting,nonrolling, stain resistant polyhedral oligomeric silsesquioxane coated textiles

Cotton/polyester fabric surfaces were modified using nanostructured organic‐inorganic polyhedral oligomeric silsesquioxane (POSS) molecules via solution dip coating. Surface wetting characteristics of coatings prepared from two chemically and structurally different POSS molecules, a closed cage fluorinated dodecatrifluoropropyl POSS (FL‐POSS) and an open cage nonfluorinated trisilanolphenyl POSS (Tsp‐POSS), were evaluated with time and compared with Teflon. Surface analysis, including Atomic Force Microscopy, SEM/EDAX, and NMR revealed the presence of POSS aggregates on the fabric surface leading to a spiky topography, high roughness, and hysteresis. POSS coated fabrics showed complete reversal of surface wetting characteristics with contact angles higher than the benchmark Teflon surface. Water contact angle measured as a function of time showed equivalent or better performance for POSS‐coated surfaces in comparison to Teflon. Furthermore, FL‐POSS coated fabric exhibited exceptional stain and acid resistance along with a 38% reduction in relative surface friction. Additionally, “nonsliding” and high surface adhesion behavior of water droplets on the FL‐POSS coated fabric are reported. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010