广义C-R组的性质及两个边值问题

本文考虑广义C-R组^[1](H)的解f=u iv jw∈C^2的一些性质，提出与之相关的两个边值问题，用积分方程方法和调和函数性质证明了边值问题解的存在唯一性，并写出解的积分表达式．     

New functionalized polyesters to achieve controlled architectures

Following our continued interest in the production of bioerodible and biodegradable functional polymers for biomedical applications, we synthesized and characterized new unsaturated polyesters. The presence of functional groups in the polymer backbone provided sites for chemical modification, and through a variation in the structure, the physical properties, such as the hydrophilicity and solubility, could be affected. With 1,1-di-n-butyl-stanna-2,7-dioxacyclo-4-heptene as the initiator in the ring-opening polymerization of polyesters, a new set of functionalized polyesters was created. The polymerization of ϵ-caprolactone resulted in poly(ϵ-caprolactone) with a double bond incorporated into the structure. The polymers were obtained in a controlled manner with low molecular dispersities. The double bond was previously incorporated into L -lactide polymers, and the two reactions were compared in this study. The conversion of ϵ-caprolactone, with a degree of polymerization of 50, was completed within 140 min, whereas for L -lactide, only a 45% conversion took place in the same period of time. The dispersities were somewhat higher with ϵ-caprolactone because of the higher reaction rate and, therefore, lower selectivity. The incorporated CC double bond in the polyesters provided a variety of opportunities for further modifications. In this case, the double bond of the L -lactide macromonomers was oxidized into epoxides. Epoxidation was carried out with m-chloroperoxybenzoic acid as a chemical reagent. The conversion of the double bonds into epoxides was completed, and the obtained yields were good (>95%). As a result of the mild reaction conditions, the epoxidation of the double bond was carried out quantitatively without any side reactions. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 444–452, 2004     

高精度的光纤衰减系数测试系统的设计

利用常规仪器设备，设计了一套集光、机、电为一体的光纤衰减测量,实现了数字化监测显示，并可与微机接口；采用双光路法，消除了由于光源光强不稳定产生的误差。     

Isothermal crystallization kinetics of poly(3‐hydroxybutyrate)/layered double hydroxide nanocomposites

Poly(3‐hydroxybutyrate) (PHB)/layered double hydroxides (LDHs) nanocomposites were prepared by mixing PHB and poly(ethylene glycol) phosphonates (PEOPAs)‐modified LDH (PMLDH) in chloroform solution. Both X‐ray diffraction data and TEM micrographs of PHB/PMLDH nanocomposites indicate that the PMLDHs are randomly dispersed and exfoliated into the PHB matrix. In this study, the effect of PMLDH on the isothermal crystallization behavior of PHB was investigated using a differential scanning calorimeter (DSC) and polarized optical microscopy. Isothermal crystallization results of PHB/PMLDH nanocomposites show that the addition of 2 wt % PMLDH into PHB induced more heterogeneous nucleation in the crystallization significantly increasing the crystallization rate and reducing their activation energy. By adding more PMLDH into the PHB probably causes more steric hindrance of the diffusion of PHB, reducing the transportation ability of polymer chains during crystallization, thus increasing the activation energy. The correlation among crystallization kinetics, melting behavior and crystalline structure of PHB/PMLDH nanocomposites can also be discussed. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3337–3347, 2006     

A new method for constructing infinite families of k-tight optimal double loop networks

The double loop network (DLN) is a circulant digraph with n nodes and outdegree 2. DLN has been widely used in the designing of local area networks and distributed systems. In this paper, a new method for constructing infinite families of k-tight optimal DLN is presented. For k = 0,1,…,40, the infinite families of k-tight optimal DLN can be constructed by the new method, where the number nk(t,a) of their nodes is a polynomial of degree 2 in t and contains a parameter a. And a conjecture is proposed.     

正交变换在重积分中某些应用

正交变换是代数学的基本内容 ,其用途十分广泛 .重积分的计算往往存在技术性的困难 ,若利用“正交变换”的有关理论去解决某些重积分的计算问题是颇有功效的 .本文将以“正交变换”为工具 ,简洁的处理重积分的某些问题     

Evaluation formulas for Tornheim's type of alternating double series

In this paper, we give some evaluation formulas for Tornheim's type of alternating series by an elementary and combinatorial calculation of the uniformly convergent series. Indeed, we list several formulas for them by means of Riemann's zeta values at positive integers.

     

On the limit cycles of a quintic planar vector field

This paper concerns the number and distributions of limit cycles in a Z_2-equivariant quintic planar vector field.25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation.It can be concluded that H(5)≥25=5~2, where H(5)is the Hilbert number for quintic polynomial systems.The results obtained are useful to study the weakened 16th Hilbert problem.     

A computational study into the reactivity of epichlorohydrin and epibromohydrin under basic conditions in the gas phase and solution

Ab initio molecular orbital calculations were carried out on epibromohydrin (EBH) and epichlorohydrin (ECH) in an attempt to elucidate their reactivity with respect to a hard nucleophile, hydroxide. These systems were modeled in both the gas phase and a polar solvent under basic conditions. In the gas phase, it was determined that a direct displacement mechanism (nucleophilic attack at the C1 position) was operative for EBH, while an indirect pathway (nucleophilic attack at the C3 position and subsequent intramolecular displacement) was followed for ECH. In an acetone solution, only the indirect displacement mechanism was found to occur. An electrostatic argument is advanced to account for this behavior in polar solution. Copyright © 2007 John Wiley & Sons, Ltd.     

The construction of infinite families of any k-tight optimal and singular k-tight optimal directed double loop networks

The double loop network(DLN)is a circulant digraph with n nodes and outdegree 2.It is an important topological structure of computer interconnection networks and has been widely used in the designing of local area networks and distributed systems.Given the number n of nodes,how to construct a DLN which has minimum diameter?This problem has attracted great attention.A related and longtime unsolved problem is:for any given non-negative integer k,is there an infinite family of k-tight optimal DLN?In this paper,two main results are obtained:(1)for any k≥0,the infinite families of k-tight optimal DLN can be constructed,where the number n(k,e,c)of their nodes is a polynomial of degree 2 in e with integral coefficients containing a parameter c.(2)for any k≥0, an infinite family of singular k-tight optimal DLN can be constructed.