Hopf代数上的扭曲模和(斜)余配对Hopf模

本文第一部分主要把扭曲的方法运用到模上,从而得到扭曲模．作为特例,我们构造了H  M的Smaush模和量子模．当K是有限维Hopf代数,证明K*  M是一个右D(K)-Hopf模,因此得到了一个基本同构定理．第二部分主要把斜余配对双代数进行推广,得到了斜余配对Hopf模,并且给出判断斜余配对Hopf模的一个充要条件．     

Guaranteed-accuracy approximation of reachable sets for a linear dynamic system subject to impulse actions

A method is proposed for approximating the reachable set of a dynamic system with a state space dimension no higher than six-eight considered on a finite time interval. The system is governed by linear differential equations with piecewise constant coefficients and impulse actions specified at prescribed times. The method is based on guaranteed-accuracy polyhedral approximations of reachable sets at researcher-specified times. Every approximation is constructed using the preceding one. A procedure is described for choosing parameters of the method that ensure the required accuracy with close-to-minimal time costs.     

Pd (II)‐catalyzed vinyl addition polymerization of novel functionalized norbornene bearing dimethyl carboxylate groups

Three novel functionalized polynorbornenes (PNB) with pendant dimethyl carboxylate group (carboxylates—acetate, propionate, and butyrate) are synthesized as a vinyl‐type with a palladium (II) catalyst in high yield. The effects of size of substitutents, molar ratio of monomer to catalyst, solvent polarity, reaction time, and temperature on the polymerization of exo‐norbornene dimethyl propionate were systematically investigated. The low molar ratio and temperature, as well as high polarity of solvent, and long reaction time, are favorable for the enhancement of the monomer conversion, especially, the solvent have an obvious effect on the catalyst activity. The resulting poly(cis‐norbornene‐exo‐2,3‐dimethyl carboxylates) (PNB‐dimethyl carboxylates) show good solubility in common organic solvent and high thermal stability up to 360 °C. The glass transition temperature was detected by DMA at 331, 324, and 318 °C for acetate, propionate, and butyrate, respectively. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3391–3399, 2007     

Szász型算子线性组合的同时逼近

本文利用ω^2r_φλ(f,t)代替ω^r_φλ(f,t)给出了Szász-Kantorovich算子线性组合同时逼近的估计。     

黄芪成分F3新制剂的工艺监测

对黄芪成分F3新制剂中多糖、蛋白质进行了工艺监测，多糖提取达99．2％，蛋白质≤0．2％，符合黄芪成分F3的质量标准要求，达到了选择最佳提取工艺的目的，结果令人满意。     

Fluoride-assisted trifluoromethylation of aromatic thiones with (trifluoromethyl)trimethylsilane

In the presence of a stoichiometric amount of Bu₄NF·3H₂O, (trifluoromethyl)trimethylsilane reacts with aromatic thiones in both thiophilic and carbophilic ways to deliver, in medium yield, a mixture of (trifluoromethylthio)diarylmethane and 1,1-diaryl-2,2,2-trifluoroethanethiol, the former product being the major one.     

Depth profiling of latex blends of fluorinated and fluorine‐free acrylates with laser‐induced secondary mass spectrometry

We explored phase separation and self‐assembly of perfluoroalkyl segments at the surface of polymer films obtained from latices of semifluorinated acrylate copolymers and the corresponding latex blends of nonfluorinated and semifluorinated polyacrylates. With laser‐induced secondary mass spectrometry the fluorine distribution was measured after annealing above the minimum film‐forming temperature of the polymers up to a depth of several micrometers. Depth profiles of a semifluorinated acrylate homopolymer and latex blends thereof with fluorine‐free alkylacrylates with 25, 50, and 75 mol % semifluorinated acrylate as well as a copolymer comprised of alkyl acrylate and semifluorinated acrylate (50/50 mol %) were investigated. In the case of latex blends containing both semifluorinated polyacrylates and fluorine‐free or low‐fluorine polymers, self‐assembly accounted for enrichment of the perfluoroalkyl segments at the surface. Coatings exhibiting low surface energy and having a substantially reduced total fluorine content were obtained. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 360–367, 2003     

On the Exceptional Zeros of Rankin–Selberg L-Functions

The main objects of study in this article are two classes of Rankin–Selberg L-functions, namely L(s,f×g) and L(s, sym²(g)× sym²(g)), where f,g are newforms, holomorphic or of Maass type, on the upper half plane, and sym²(g) denotes the symmetric square lift of g to GL(3). We prove that in general, i.e., when these L-functions are not divisible by L-functions of quadratic characters (such divisibility happening rarely), they do not admit any LandauSiegel zeros. Such zeros, which are real and close to s=1, are highly mysterious and are not expected to occur. There are corollaries of our result, one of them being a strong lower bound for special value at s=1, which is of interest both geometrically and analytically. One also gets this way a good bound onthe norm of sym²(g).     

线性二次型最优控制的并行算法和软件

构造了线性二次型最优控制的并行算法，介绍了这个并行算法在武汉大学“ＷＵＤＰ９１”并行分布式处理系统上试算的数值应用软件的框图．本软件适用于既定动态系统的平衡问题．对于经济系统，可通过政策控制变量来调节和改善其状态和响应．对于自治系统可找出最优控制使得消耗函数达到最小值．通过对一系列例子进行试算，结果证实，所构造的并行算法和相应的数值软件是有效的，其加速比约为７．     

Problems of an additional experiment

In some situations estimates of unknown parameters must be corrected by additional measurements. It is in principle no problem to calculate the corrected estimates, however, it is of more interest to find formulae for correction itself. The formulae enable us to design an additional experiment and to judge its usefulness. The aim of the paper is to find such formulae for several situations. Supported by the grant of the Council of Czech Government MSM 6 198 959 214.