Q-matrix recognition via secondary and universal polytopes

T (Mx+q)=0, Mx+q≥0, x≥0 has a solution. We explain how one can use the polyhedral structure of the set of all triangulations of a finite point set to determine if an n×n matrix M is a Q-matrix. Our implementation of the algorithm is practical for deciding the Q-nature for all M with n≤8. Received May 30, 1997 / Revised version received June 12, 1998 Published online November 24, 1998     

聚乙烯熔体的离散松弛时间谱与熔融指数的关系

该文通过动态线性小振幅剪切震荡实验所得的聚乙烯熔体储能模量Ｇ′（ω）和耗能模量Ｇ″（ω）数据,采用最小二乘法线性回归、正则法和非线性回归法分别计算得到离散松弛时间谱,比较三种方法得到结果的差别,讨论计算参数、温度和材料对离散松驰时间谱影响．     

Cyclic star products and universalities in symbolic dynamics of trimodal maps

Cyclic star products for the triple superstable kneading (TSSK) sequences are presented for symbolic dynamics of trimodal maps of endomorphisms on the interval. Feigenbaum’s metric universalities in unimodal maps are generalized to trimodal maps. Four equal-value universal convergent rates {δ_a,δ_c,δ_η,δ_a,c,η} and three universal scaling factors {_C,_D,_E} are first obtained.     

Polarization interferometer as a proximity sensor

A simple interferometric phasemeter which can be used as a proximity sensor is described. It is based on the measurement of the phase shift between the p- and s- components of a field caused by the processes of attenuation in total internal reflection. The role of the interferometer is to restore the p- and the s- components from the resultant totally reflected field, with minimum amplitude and phase distortions and to let them interfere. The phase shift as a function of the attenuation of the total internal reflection can be determined from the interference signal. The interferometer is of a common path polarization shearing type, consisting of Rochon beamsplitter and a linear polarizer. An experiment for measuring the distance between glass plane surface and a plane attenuater made of Si mono-crystal is described. A good agreement between theory and experiment for separations less than 300 nm is observed. This device can be applied in research and metrology. After further modifications, the optical system could be used for proximity sensing, surface geometry control, variable optical retarders, contamination monitoring, etc.     

有序分子系统的线性与非线性光谱学的简化描述

A simplified formulation for treating the linear and nonlinear spectroscopy of ordered molecular systems is presented,in order to help experimentalists to have an explicit physical picture and quantitative tool on using linear and nonlinear spectroscopy to study molecules in ordered molecular systems. This formulation is expended from our recent quantitative orientational and polarization treatment on second-order nonlinear spectroscopic techniques in interface studies,namely,the Second Harmonic Generation（SHG）and Sum Frequency Generation-Vibrational Polarization Spectroscopy（SFG-VPS）. The key to this formulation is to simplify the effective linear or nonlinear molecular susceptibility and construct the general orientational functional with a clear approach to calculate the orientational and intensity parameters from the experimental parameters,which determines the orientational and polarization behavior of the general orientational functional in a particular experimental configuration. Also discussed are the advantages of coherent spectroscopic techniques over incoherent ones for the accurate measurement of orientation and ordering of ordered molecular system.     

非线形嵌段共聚物的合成

主要介绍了非线形嵌段共聚物,如星型嵌段共聚物、杂臂星型共聚物、梳型聚合物等的合成方法,包括多官能团引发剂法、大分子引发剂法等。各种活性聚合方法,如阳离子开环聚合、原子转移自由基聚合(ATRP)和氮氧稳定自由基聚合等都可以用于合成非线形嵌段共聚物。     

Star factorizations of graph products

A k‐star is the graph K_1,k. We prove a general theorem about k‐star factorizations of Cayley graphs. This is used to give necessary and sufficient conditions for the existence of k‐star factorizations of any power (K_q)^s of a complete graph with prime power order q, products C × C ×··· × C of k cycles of arbitrary lengths, and any power (C_r)^s of a cycle of arbitrary length. © 2001 John Wiley & Sons, Inc. J Graph Theory 36: 59–66, 2001     

Star‐Shaped Polyaromatic Ethers Coordinated to Redox‐Active Cyclopentadienyliron Moieties

This communication is focused on the controlled design of star‐shaped aromatic ethers with pendent cyclopentadienyliron moieties. A trimetallic core was prepared, which was then reacted with a number of oligomeric ether complexes to give star‐shaped polymers with six, nine, twelve and fifteen pendent cationic cyclopentadienyliron moieties. Cyclic voltammetric studies showed reduction of the iron centers between –0.99 and –1.41 V. Thermogravimetric analysis showed that loss of the metallic moieties occurred between 225 and 284°C.     

On the Contraction Factor of Star‐Branched Polymers with Flory‐Distributed Arms

More than fifty years ago, Zimm and Stockmayer calculated the average contraction factor of star‐branched polymers (stars) with uniformly distributed arms to be 6f/{(f + 1)(f + 2)}. Since then this contraction factor has also been used for stars with other arm distributions. In this paper we determine the (probability) density function of the contraction factor of stars with arms with a Flory (most probable) distribution and conclude that this function is equal to that for stars with uniformly distributed arms. Other arm distributions, however, lead to different contraction factor density functions. The moments of the contraction factor distribution were precisely determined with the aid of a recursion method. The stochastical behavior of the contraction factor of stars was applied to size‐exclusion chromatography (SEC) analysis and showed that upward correction of the crude SEC data is necessary to determine the proper molecular‐mass distribution of stars.     

模糊Delta算子系统的鲁棒镇定

研究一类基于Delta算子描述的T-S模糊模型状态反馈镇定设计问题。首先将全局模糊模型按隶属函数划分成若干子空间,并被表示成不确定系统的形式;采用分段Lyapunov函数法,得到鲁棒稳定化控制律存在的充分条件．该条件被进一步等价表示成一组线性矩阵不等式的可解性问题。克服了以往设计法中需要求解一公共正定矩阵P的不足,也无需求解繁琐的Riccati方程。所得结果可将连续和离散模糊系统的有关结论统一到Delta算子框架内。