Biquartic C-surface splines over irregular meshes

C¹-surface splines define tangent continuous surfaces from control points in the manner of tensor-product (B-)splines, but allow a wider class of control meshes capable of outlining arbitrary free-form surfaces with or without boundary. In particular, irregular meshes with non-quadrilateral cells and more or fewer than four cells meeting at a point can be input and are treated in the same conceptual frame work as tensor-product B-splines; that is, the mesh points serve as control points of a smooth piecewise polynomial surface representation that is local and evaluates by averaging. Biquartic surface splines extend and complement the definition of C¹-surface splines in a previous paper (Peters, J SLAM J. Numer. Anal. Vol 32 No 2 (1993) 645–666) improving continuity and shape properties in the case where the user chooses to model entirely with four-sided patches. While tangent continuity is guaranteed, it is shown that no polynomial, symmetry-preserving construction with adjustable blends can guarantee its surfaces to lie in the local convex hull of the control mesh for very sharp blends where three patches join. Biquartic C¹-surface splines do as well as possible by guaranteeing the property whenever more than three patches join and whenever the blend exceeds a certain small threshold.     

An improved condition for the convexity of Bernstein-Bézier surfaces over triangles

A sufficient condition which is superior to that of Chang and Davis for the convexity of the Bernstein-Bézier polynomials of degree n over triangles is presented. The condition is proved to be necessary also for n = 2 and n = 3.     

基于连通性转换的三维多面体快速变形

研究了连通性转换方法,并将其应用于多面体快速变形.采用优先权控制函数控制模型特征,且可以实现点和边的同步处理.通过预先安排连通性转换提高了变形速度,通过解一个稀疏线性方程组缩短变形片的嵌入时间.之后,矫正特征点以及边界处理得到平滑变形序列.用该方法和传统变形方法分别演示了三维多面体模型的变形实例,并对实验结果和相关数据进行了分析比较.实验结果表明,该变形方法可快速实现平滑变形.     

笼状纳米化合物八乙烯基倍半硅氧烷的合成及表征

以无水三氯化铁和浓盐酸为催化剂，甲醇-石油醚-二氯甲烷为溶剂，乙烯基三氯硅烷水解缩合得到了笼状八乙烯基多面体低聚倍半硅氧烷.该方法反应时间短，产率高（34.7％）.通过1H、13C和29Si核磁共振光谱、红外光谱、元素分析和凝胶渗透色谱等对产物的结构进行了表征，表明产物是笼状的八乙烯基倍半硅氧烷.采用TGA对OvPOSS的热稳定性进行了研究.结果表明，OvPOSS初始分解温度(失重5％)为278.5 ℃，热稳定性良好.对反应条件的研究发现，温度对OvPOSS产率影响不大，而适度延长反应时间或提高溶剂中甲醇的质量分数均可以提高OvPOSS的产率.     

Constraint Networks of Topological Relations and Convexity

This paper studies the expressivity and computational complexity of networks of constraints of topological relations together with convexity. We consider constraint networks whose nodes are regular regions (a regular region is one equal to the closure of its interior) and whose constraints have the following forms: (i) the eight base relations of [12], which describe binary topological relations of containment and adjacency between regions; (ii) the predicate, X is convex. We establish tight bounds on the computational complexity of this language: Determining whether such a constraint network is consistent is decidable, but essentially as hard as determining whether a set of comparable size of algebraic constraints over the real numbers is consistent. We also show an important expressivity result for this language: If r and s are bounded, regular regions that are not related by an affine transformation, then they can be distinguished by a constraint network. That is, there is a constraint network and a particular node in that network such that there is a solution where the node is equal to r, but no solution where the node is equal to s.     

Ultralight and Low Thermal Conductivity Polyimide–Polyhedral Oligomeric Silsesquioxanes Aerogels

The research on rapid growing, organic, and ultralight cross‐linking polyimide aerogels is receiving significant interest. In this work, poly(aminophenyl) silsesquioxanes (PAPSQ) are introduced as a cross‐linker into the polymide (PI) aerogel. A comparative aerogel is prepared, using 1,3,5‐triaminophenoxybenzene (TAB) as a cross‐linker. The aerogels are characterized in terms of their micro‐ and nanostructures, density, shrinkage, thermal conductivity and insulation, and mechanical properties. It is found that the PI‐PAPSQ aerogel have lower density, smaller shrinkage, lower thermal conductivity, higher thermal stability and insulation, and higher compression strength than the PI‐TAB aerogel. The 1.1 wt% PI‐PAPSQ shows the lowest aerogel density (0.010 g cm^?3) and the 2.2 wt% PI‐PAPSQ has a lower thermal conductivity (22.90 mW (m K)^?1 than air. A model of the PI‐TAB and PI‐PAPSQ cross‐linking networks are proposed to explain the excellent performance of the PI‐PAPSQ aerogel.     

凸性数据的样条修匀及其应用

借助于样条技术 ,给出了利用先验信息对初始估计进行修正的新方法 .这些先验信息可以包含数据的凸性以及增减性 .同时讨论了这种数据处理方法在生存分析尤其是精算等领域中的应用 .     

Non‐convex model for sensor network localization based on connectivity

In this paper, a new model utilizing all the information derived from connectivity‐based sensor network localization is introduced. The connectivity information between any pair of nodes is modeled as convex and non‐convex constraints. The localization problem is solved by searching for a solution that would satisfy all the constraints established in the problem. A two‐objective evolutionary algorithm called Pareto Archived Evolution Strategy (PAES) is used to solve the localization problem. The solution can reach the most suitable configuration of the unknown nodes because the information on both convex and non‐convex constraints related to connectivity has been utilized. From simulation results, a relationship between the communication range and accuracy is obtained. Furthermore, a two‐level range connectivity‐based sensor network localization method is proposed to enrich the connectivity information. The two‐level range/indication of connectivity between each pair of nodes would indicate three levels of connectivity: strong, weak, or nil. A comparison on accuracy between the one‐level and two‐level ranges of connectivity is carried out by simulation using six different topological networks all containing 100 nodes. Simulation results have shown that better solution can be obtained by using two‐level range connectivity compared with the usual one‐level range connectivity‐based localization. Copyright © 2012 John Wiley & Sons, Ltd.     

笼型倍半硅氧烷(POSS)/环氧树脂有机无机杂化材料的热性能

为了提高环氧树脂(EP)的性能,采用具有氨基官能团的笼型倍半硅氧烷(POSS)改性.首先通过POSS与EP发生化学反应,形成有机无机杂化树脂;然后固化杂化树脂,得到POSS/EP有机无机杂化材料.文中研究了杂化树脂的凝胶特性和杂化材料的热性能,包括热变性温度(HDT)、玻璃化转变温度(Tg)和高温热分解性能.研究结果表...     

笼型倍半硅氧烷(POSS)合成的研究进展

笼型倍半硅氧烷(POSS)是一类引人注目的新型纳米材料。POSS独特的有机无机杂化结构赋予其许多优异的性能,如高的耐热性、力学性能、良好的介电性能及光学性能等,展示出广泛的应用前景。文中首先介绍了POSS的结构和性能特点,然后详细综述了笼型倍半硅氧烷(POSS)合成方面的研究进展,将笼型倍半硅氧烷的合成方法分成三官能团硅烷的水解缩聚反应法、顶端-带帽法、硅氢化反应法、侧基转化法和POSS的结构重排法等5种合成方法。