三次自然样条函数的凸性条件

提出了在等距情形下三次自然样条函数一系列凸性的充分条件，在某定之下，还得到了一些三次自然样条函数凸性的必要条件。     

Analysis of Matrix-Convex Functions

The properties of matrix-convex functions, which may take values from an expanded numerical axis, are analyzed. Matrix convexity is specified by a pair of matrices, a final set of matrices, or an infinite family of matrices. The results obtained are used in the theory of differential games.     

Epoxy‐functionalized polyhedral oligomeric silsesquioxane/cyanate ester resin organic–inorganic hybrids with enhanced mechanical and thermal properties

A series of cyanate ester resin (CE) based organic–inorganic hybrids containing different contents (0, 5, 10, 15 and 20 wt%) of epoxy‐functionalized polyhedral oligomeric silsesquioxane (POSS‐Ep) were prepared by casting and curing. The hybrid resin systems were studied by the gel time test to evaluate the effect of POSS‐Ep on the curing reactivity of CE. The impact and flexural strengths of the hybrids were investigated. The micromorphological, dynamic mechanical and thermal properties of the hybrids were studied by SEM, dynamic mechanical analysis (DMA) and TGA, respectively. Results showed that POSS‐Ep prolonged the gel time of CE. CE10 containing 10 wt% POSS‐Ep displayed not only the optimum impact strength but the optimum flexural strength. SEM results revealed that the improvement of mechanical properties was attributed to the large amount of tough whirls and fiber‐like pull‐outs observed on the fracture surfaces of CE10. DMA results indicated that POSS‐CE tended to decrease E′ of the hybrids in the glassy state but to increase E′ of the hybrids in the rubbery state. TGA results showed that CE10 also possesses the best thermal stability. The initial temperature of decomposition (T_i) of CE10 is 426 °C, 44 °C higher than that of pristine CE. © 2013 Society of Chemical Industry     

POSS-based hybrid thermosets via photoinduced copper-catalyzed azide–alkyne cycloaddition click chemistry

An efficient approach for the preparation of inorganic/organic hybrid thermosets via photoinduced copper-catalyzed azide–alkyne cycloaddition click chemistry is established. Highly cross-linked thermoset polymers have been practically obtained by this technique using multifunctional compounds, tri-alkyne (1,1,1-tris[4-(2-propynyloxy) phenyl]-ethane) with octakis-azido-POSS or tri-azide (3,3′-((2-((3-azido-2-hydroxypropoxy)methyl)-2-ethylpropane-1,3-diyl)bis(oxy))bis(1-azidopropan-2-ol)) in the presence of Cu(II)Br₂/N,N,N′,N″,N?-pentamethyldiethylenetriamine/2-dimethoxy-2-phenyl acetophenone. The homogeneously distributed POSS nanoparticles are clearly detected in the TEM micrographs; whereas the TGA analysis shows that the obtained hybrid thermosets are thermally stable up to 360 °C and begin to lose weight at higher temperatures with a char yield of 23–50% at 800 °C.     

轴承滚子凸度轮廓的最小二乘拟合与误差评定

为了实现对轴承滚子凸度轮廓误差的精确评定,依据圆弧修正型轴承滚子凸度素线轮廓的几何特征和形状误差的定义,基于最小二乘原理,研究了轴承凸度轮廓(两段圆弧和一段直线)的最小二乘拟合和误差评定方法。首先利用各测量点的曲率差值确定了圆弧段与直线段的相切参考点;其次分别选取两个参考点临近的测量点作为辅助相切参考点,并与对应的圆弧段测量点一起拟合出一系列的最小二乘圆弧并计算拟合误差;然后基于直线与两段圆弧相切的原则确定出一系列的直线方程并计算对应的直线度误差;通过比较判断最终确定出圆弧修正型轴承滚子凸度轮廓的最小二乘拟合及误差评定。实例结果表明:圆弧修正型凸度轮廓曲线的总误差0.020 9mm与文中设定标准凸度轮廓曲线引入的法向误差0.02mm相差4.5%。本方法可以有效的实现轴承凸度轮廓的拟合与误差评定,为平面多段曲线的最小二乘拟合提供了一种新的思路。     

Synthesis of 3,13-diglycidyloxypropyloctaphenyl double-decker polyhedral oligomeric silsesquioxane and the thermal reaction properties with thermosetting phenol-formaldehyde resin

3,13-Diglycidyloxypropyloctaphenyl double-decker silsesquioxane (EP-DDSQ) was synthesized by process of alkaline hydrolysis condensation of phenyltrimethoxysilane and corner capping reaction of methyldichlorosilane, followed by hydrosilylation with allyl glycidyl ether, and the resultant structure was confirmed by fourier transform infrared spectrometer (FTIR) and nuclear magnetic resonance (NMR), respectively. The thermosetting phenol-formaldehyde (PF) resin was then modified by EP-DDSQ, and the reactivity of PF resin with EP-DDSQ and thermal pyrolysis of modified cured resin were investigated by differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). The surface morphologies of modified resins at high temperature were characterized with field emission scanning electron microscope (FESEM), and chemical structure of modified resins was analyzed through X-ray photoelectron spectrometer (XPS). The results showed that the appropriate addition of EP-DDSQ did not affect the curing temperature of the PF resin itself, but could improve the heat resistance of the system. When the amount of EP-DDSQ added was 10%, the initial degradation temperature of PF resin was increased by 49.31°C, and when the amount of EP-DDSQ added was 16%, the char yield of which was reached up to 61.39%, compared with that of pure PF resin (TGA_1,000°C of 57.62%) at Ar atmosphere. More importantly, the modified resin formed a regular and dense layer of SiC and SiO_x ceramic on the surface after ablation in the muffle furnace at 800°C air atmosphere, which is very important for ablative resistant materials.     

笼型倍半硅氧烷（POSS）的功能化改性 及应用研究进展

有机/无机杂化材料的改性及应用是目前材料科学中最富有活力的研究领域之一。其中笼型倍半硅氧烷（Polyhedral oligomeric silsesquioxane,POSS）在分子水平上实现了有机组分与无机组分的结合,结构呈硅氧骨架连接的立体笼型,具有优异的反应活性、耐热阻燃性、多孔性和纳米尺寸效应等特性,通过化学改性可将其应用在多个领域。本文主要从官能团改性、聚合改性和配位改性三个方面阐述了POSS的改性方法,综述了POSS在耐热材料、阻燃材料、增强材料和多孔材料等领域的应用研究进展,并对POSS今后的研究方向提出了展望。可从POSS的构效关系、改性方法以及安全性等方面进行更加深入和系统的研究,以促进POSS材料更广泛的应用。     

POSS及其改性聚合物的研究进展

介绍了多面体倍半硅氧烷（POSS）的合成方法,综述了POSS改性聚合物的一些优异性能,总结了近3年国内的研究成果,展望了POSS改性聚合物的研究前景。     

Exploring local regularities for 3D object recognition

In order to find better simplicity measurements for 3D object recognition, a new set of local regularities is developed and tested in a stepwise 3D reconstruction method, including localized minimizing standard deviation of angles(L-MSDA), localized minimizing standard deviation of segment magnitudes(L-MSDSM), localized minimum standard deviation of areas of child faces (L-MSDAF), localized minimum sum of segment magnitudes of common edges (L-MSSM), and localized minimum sum of areas of child face (L-MSAF). Based on their effectiveness measurements in terms of form and size distortions, it is found that when two local regularities: L-MSDA and L-MSDSM are combined together, they can produce better performance. In addition, the best weightings for them to work together are identified as 10% for L-MSDSM and 90% for L-MSDA. The test results show that the combined usage of L-MSDA and L-MSDSM with identified weightings has a potential to be applied in other optimization based 3D recognition methods to improve their efficacy and robustness.     

功能化POSS对硅橡胶力学性能的影响及机理研究

研究了八聚笼型倍半硅氧烷(POSS)功能化侧基的种类和用量对硅橡胶力学性能的影响。结果表明,POSS的加入使硅橡胶的拉伸强度和断裂伸长率均下降,硬度均提高。乙烯基POSS的加入显著延长了硅橡胶的正硫化时间。POSS的加入能显著降低硅橡胶的压缩永久变形,乙烯基POSS的效果比甲基POSS好;且乙烯基含量越高,压缩永久变形越小。分析了功能化POSS对硅橡胶力学性能的影响机理。