（K1（x），K2（x））-有限伸张映射

该文首先给出(K1(x),K2(x))一有限伸张映射的定义,然后研究其自我提高的可积性性质.最后利用Caccioppoli型不等式得到可去奇异性结果.     

Nanomechanical characteristics of SnO2:F thin films deposited by chemical vapor deposition

The nanoindentation characterizations and mechanical properties of fluorine-doped tin oxide (SnO₂:F) films deposited on glass substrates, using chemical vapor deposition (CVD) method, were studied, which included the effects of the indentation loads, the loading time and the hold time on the thin film. The surface roughness, fractal dimension and frictional coefficient were also studied by varying the freon flow rates. X-ray diffraction (XRD), atomic force microscopy (AFM) and frictional force microscopy (FFM) were used to analyze the morphology of the microstructure. The results showed that crystalline structure of the film had a high intensity (1 1 0) peak orientation, especially at a low freon flow rate. According to the nanoindentation records, the Young's modulus ranged from 62.4 to 75.1 GPa and the hardness ranged from 5.1 to 9.9 GPa at a freon flow rate of 8000 sccm. The changes in measured properties were due to changing loading rate.     

Parseval Theory of Complex Wavelet Transform for Wavelet Family Including Rotational Parameters

A rotational parameter Rθ has been introduced to complex wavelet transform （CWT）. The rotational CWT （RCWT） corresponds to a matrix element 〈φ｜U2（θ;μ;κ）[F〉 in the context of quantum mechanics, where U2（θ;μ;κ） is a two-mode rotational displacing-squeezing operator in the 〈η｜ representation. Based on this, the Parseval theorem and the inversion formula of RCWT have been proved. The concise proof not only manifestly shows the merit of Dirac＇s representation theory but also leads to a new orthogonal property of complex mother wavelets in parameter space.     

A Novel Rule Induction Algorithm

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　　Ｋｎｏｗｌｅｄｇｅｄｉｓｃｏｖｅｒｙｉｎｄａｔａｂａｓｅｓ (ＫＤＤ)ｉｓｃｏｎｃｅｒｎｅｄｗｉｔｈｅｘｔｒａｃｔｉｎｇｕｓｅｆｕｌｉｎｆｏｒｍａｔｉｏｎｆｒｏｍｄａｔａｂａｓｅｓ.Ｔｈｅｔｅｒｍｄａｔａｍｉｎｉｎｇｈａｓｈｉｓｔｏｒｉｃａｌｌｙｂｅｅｎｕｓｅｄｉｎｔｈｅｄａｔａｂａｓｅｃｏｍｍｕｎｉｔｙａｎｄｉｎｓｔａｔｉｓｔｉｃｓ (ｏｆｔｅｎｉｎｔｈｅｌａｔｔｅｒｗｉｔｈｎｅｇａｔｉｖｅｃｏｎｎｏｔａｔｉｏｎｓｔｏｉｎｄｉｃａｔｅｉｍｐｒｏｐｅｒｄａｔａａｎａｌｙ…     

Control of the microstructure of polymer network and effects of the microstructures on light scattering properties of UV‐cured polymer‐dispersed liquid crystal films

Polymer‐dispersed liquid crystals (PDLC) films were prepared from ultraviolet (UV) irradiation‐induced polymerization of the photopolymerizable monomers in photopolymerizable monomers/nematic liquid crystal (LC) mixtures. The effects of the composition of the mixtures, the curing temperature, and the UV light intensity on the microstructure of the polymer network in the PDLC films were investigated. Furthermore, the effects of the microstructures on the light scattering properties of the PDLC films in the wavelength region of 300–2500 nm were studied experimentally and theoretically based on the combination of three kinds of classical light scattering theories: the Rayleigh‐Gans (RG) approach, the anomalous diffraction (AD) approach, and the geometrical optics (GO) approach. It was found that the sizes of LC domain in PDLC films increased with the increase of the LC content as well as the decrease of the UV curing intensity, while increased at first and then decreased with the increase of the curing temperature. Moreover, smaller LC domain sizes could exhibit strong scattering properties in a smaller VIS wavelength region and the transmittance in NIR region (especially in the wavelength range of 1300–2500 nm) obviously decreased with the increasing sizes of LC domain. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2090–2099, 2008     

酸度对CeCl3·nH2O晶体热分解过程的影响研究

采用热重-差式扫描量热法（TG—DSC）分析了不同酸度的盐酸-水合氯化铈饱和溶液中生成的CeCl3·nH2O晶体在空气氛围热分解脱水的过程，热分析表明酸度对CeCl3·nH2O晶体结晶形式有影响，氯化铈饱和溶液在盐酸中生成的CeCl3·nH2O晶体较商品CeCl3·nH2O晶体的热分解多一个恒温脱水失重的过程．X射线粉末衍射（XRD）结果表明此商品CeCl3·nH2O晶体为CeCl3·7H2O，盐酸-水合氯化铈饱和溶液中生成的CeCl3·nH2O晶体为含有不同个数结晶水的混合物．     

Preparation and properties of covalently cross-linked sulfonated copolyimide membranes containing benzimidazole groups

A series of sulfonated copolyimides containing benzimidazole groups (SPIs) were synthesized by random copolymerization of 1,4,5,8-naphthalenetetracarboxylic dianhydride (NTDA), 2-(4-aminophenyl)-5-aminobenzimidazole (APABI), 4,4′-diaminodiphenyl ether-2,2′-disulfonic acid (ODADS) and 9,9-bis(4-aminophenyl)fluorene (BAPF) in m-cresol in the presence of benzoic acid and triethylamine at 180 °C for 20 h. Membranes with good mechanical properties were prepared by solution cast method. Proton exchange treatment resulted in ionic cross-linking and the membranes were further covalently cross-linked by treating them in polyphosphoric acid (PPA) at 180 °C for 6 h. The covalently cross-linked membranes displayed slightly lower ion exchange capacities (IECs) and proton conductivities than the corresponding covalently uncross-linked ones because small part of the sulfonic acid groups had been consumed during the cross-linking process. Fenton’s test (3% H₂O₂ + 3 ppm FeSO₄, 80 °C) revealed that benzimidazole groups played an important role in the radical oxidative stability of the membranes, while the cooperative effect of benzimidazole groups and covalent cross-linking led to much more significant enhancements in the radical oxidative stability of the membranes than each alone. The membrane 4 (ODADS/APABI/BAPF = 2/1/1, by mol), for example, after covalent cross-linking could maintain membrane form within 8 h measurement, which was much longer than that (3 h) before covalent cross-linking under the same conditions. The membrane 5 (ODADS/BAPF = 3/1, by mol) without benzimidazole groups, however, after covalent cross-linking started to break into pieces after 85 min measurement, which was only slightly longer than that (60 min) before cross-linking under the same conditions.     

An X‐shaped π‐conjugated polymer comprising of fluorene units and anthracene units with high efficiency. Synthesis and optical and electrochemical properties

A new X‐shaped π‐conjugated monomer comprising of fluorene units and anthracene units was synthesized, and it was used to fabricate the new X‐shaped π‐conjugated polymers and investigate the properties of the new polymers. Using different molar ratios between such monomer and a fluorene monomer gave three polymers that showed higher absolute PL quantum yields than the linear polyfluorene (PF) in the solid state. After thermal annealing at 200 °C for 4 h, the linear PF showed an additional bathochromic emission at about 550 nm, whereas such red‐shifted emission was fully eliminated for the X‐shaped polymers. The electroluminescent devices based on the X‐shaped polymers with a configuration of ITO/PEDOT:PSS/polymer/LiF/Ca/Al displayed blue emission with low turn‐on voltage and high brightness. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5616–5625, 2008     

从$A^{p}_{\alpha}$到$A^{\infty}(\varphi)$的加权复合算子

设$u \in H(D), \ \phi$为$D$上的解析自映射,定义$H(D)$上的加权复合算子为$u C_{\phi}(f)=$$uf\circ\phi$, \ $f\in H(D)$.本文得到了从$A^{p}_{\alpha}$到$A^{\infty}(\varphi)\ (A_{0}^{\infty}(\varphi))$的加权复合算子$u C_{\phi}$的有界性和紧性的充要条件.