晶体学与准晶体学点群的母子群关系

依据群论，得出了准晶体学点群的直积或半直积推导算式；依据结晶学理论，绘出了五角、八角、十角和十二角晶系各点群的极赤投影图.据此推导出了每一个准晶体学点群的全部最大子群，从而推导并绘制出了三维晶体学和准晶体学点群之间的母子群关系(60个点群的“家谱”).该“家谱”以最大子群链的图解形式直观地给出了每个点群的最小母群和最大子群. 关键词： 准晶体 晶体 点群 最大子群 最小母群 群链     

Atomistic packing models for experimentally investigated swelling states induced by CO2 in glassy polysulfone and poly(ether sulfone)

Atomistic packing models have been created, which help to better understand the experimentally observed swelling behavior of glassy polysulfone and poly (ether sulfone), under CO₂ gas pressures up to 50 bar at 308 K. The experimental characterization includes the measurement of the time‐dependent volume dilation of the polymer samples after a pressure step and the determination of the corresponding gas concentrations by gravimetric gas‐sorption measurements. The models obtained by force‐field‐based molecular mechanics and molecular dynamics methods allow a detailed atomistic analysis of representative swelling states of polymer/gas systems, with respect to the dilation of the matrix. Also, changes of free volume distribution and backbone mobility are accessible. The behavior of gas molecules in unswollen and swollen polymer matrices is characterized in terms of sorption, diffusion, and plasticization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1874–1897, 2006     

Approximation of Matrices and a Family of Gander Methods for Polar Decomposition

Two matrix approximation problems are considered: approximation of a rectangular complex matrix by subunitary matrices with respect to unitarily invariant norms and a minimal rank approximation with respect to the spectral norm. A characterization of a subunitary approximant of a square matrix with respect to the Schatten norms, given by Maher, is extended to the case of rectangular matrices and arbitrary unitarily invariant norms. Iterative methods, based on the family of Gander methods and on Higham’s scaled method for polar decomposition of a matrix, are proposed for computing subunitary and minimal rank approximants. Properties of Gander methods are investigated in details. AMS subject classification (2000) 65F30, 15A18     

Surface free energy of CrNx films deposited using closed field unbalanced magnetron sputtering

CrN_x thin films have attracted much attention for semiconductor IC packaging molding dies and forming tools due to their excellent hardness, thermal stability and non-sticking properties (low surface free energy). However, few data has been published on the surface free energy (SFE) of CrN_x films at temperatures in the range 20-170 °C. In this study CrN_x thin films with CrN, Cr(N), Cr₂N (and mixture of these phases) were prepared using closed field unbalanced magnetron sputtering at a wide range of Cr⁺² emission intensity. The contact angles of water, di-iodomethane and ethylene glycol on the coated surfaces were measured at temperatures in the range 20-170 °C using a Dataphysics OCA-20 contact angle analyzer. The surface free energy of the CrN_x films and their components (e.g., dispersion, polar) were calculated using the Owens-Wendt geometric mean approach. The influences of CrN_x film surface roughness and microstructure on the surface free energy were investigated by atomic force microscopy (AFM) and X-ray diffraction (XRD), respectively. The experimental results showed that the lowest total SFE was obtained corresponding to CrN at temperature in 20 °C. This is lower than that of Cr(N), Cr₂N (and mixture of these phases). The total SFE, dispersive SFE and polar SFE of CrN_x films decreased with increasing surface temperature. The film roughness has an obvious effect on the SFE and there is tendency for the SFE to increase with increasing film surface roughness.     

A mathematical model of the ring-spinning process

This paper develops a mathematical model of the ring-spinning process that takes into account its non-stationary nature. A complex system of differential equations is obtained, which from a mathematical point of view constitutes a ‘free-boundary’ problem. Its solution involves definition of suitable boundary conditions related to the mechanical characteristics of the process and of the spinning machine itself. The boundary conditions which determine the solution are pointed out. A numerical solution of the system of differential equations can be obtained by the Finite-Segments method, as shown in an example.     

The effect of crystallinity on chain mobility and free volume in the amorphous regions of a miscible polycarbonate/polyester blend

Homopolymers and blends of polycarbonate/ThermX have been investigated by differential scanning calorimetry, dynamic mechanical analysis, density measurements, and positron annihilation lifetime spectroscopy. The study focuses on the chain mobility and free volume in the amorphous miscible regions of the blends and how this mobility and free volume are affected by increasing crystallinity. It is proposed that judicious annealing, which results in increasing crystallinity (while avoiding ageing or transesterification), induces a constraint on the amorphous region leading to an increase in T_g and coalescence of free volume sites. © 1994 John Wiley & Sons, Inc.     

There exist no 2-type surfaces in E 3 which are images under stereographic projection of minimal surfaces in S 3

In this paper we deal with the following particular case of a weaker conjecture by B. Y. Chen: Are there 2-type Willmore surfaces in E ³? In particular we prove that the above question has a negative answer when the surface is the image under stereographic projection of a minimal surface in S ³.     

带有边集限制的最均匀支撑树问题

本在无向网络中，建立了带有边集限制的最均匀支撑树问题的网络模型．中首先解决最均匀支撑树问题，并给出求无向网络中最均匀支撑树的多项式时间算法；然后，给出了求无向网络中带有边集限制的最小树多项式时间算法；最后，在已解决的两个问题的基础上解决了带有边集限制的最均匀支撑树问题．     

A Theta Lift for Spin7

We establish an example of a functorial lift from generic cuspidal representations of a similitude group of the type A ₁×C ₂ to generic representations of Spin₇. Our construction uses the theta correspondence associated to the dual pair of the type (A ₁×C ₂ B ₃) inside E ₇. We also consider another theta correspondence associated to the dual pair of type (A ₁×C ₂ A ₁×A ₁) in D ₆ and show that these two pairs fit into a tower and the standard properties of a tower of theta correspondences hold.     

Trichloroisocyanuric acid as a novel oxidizing agent for the oxidation of 1,3,5-trisubstituted pyrazolines under both heterogeneous and solvent free conditions

Trichloroisocyanuric acid is used as an effective oxidizing agent for the oxidation of 1,3,5-trisubstituted pyrazolines to their corresponding pyrazoles under both heterogeneous and also solvent free conditions with good yields at room temperature.