矩阵方程AX=B,XC=D的定秩解

本文研究了一类矩阵方程组解的秩的范围.利用矩阵的奇异值分解以及Frobenius范数的特征,得到了解的极值秩以及解的通式,并就这些问题的特殊情况进行了讨论,得到了一些结果.     

Czochralski-growth of germanium crystals containing high concentrations of oxygen impurities

Oxygen-containing germanium (Ge) single crystals with low density of grown-in dislocations were grown by the Czochralski (CZ) technique from a Ge melt, both with and without a covering by boron oxide (B₂O₃) liquid. Interstitially dissolved oxygen concentrations in the crystals were determined by the absorption peak at 855 cm⁻¹ in the infrared absorption spectra at room temperature. It was found that oxygen concentration in a Ge crystal grown from melt partially or fully covered with B₂O₃ liquid was about 10¹⁶ cm⁻³ and was almost the same as that in a Ge crystal grown without B₂O₃. Oxygen concentration in a Ge crystal was enhanced to be greater than 10¹⁷ cm⁻³ by growing a crystal from a melt fully covered with B₂O₃; with the addition of germanium oxide powder, the maximum oxygen concentration achieved was 5.5×10¹⁷ cm⁻³. The effective segregation coefficients of oxygen in the present Ge crystal growth were roughly estimated to be between 1.0 and 1.4.     

Hydride vapor phase epitaxy of GaN boules using high growth rates

The boule-like growth of GaN in a vertical AIXTRON HVPE reactor was studied. Extrinsic factors like properties of the starting substrate and fundamental growth parameters especially the vapor gas composition at the surface have crucial impact on the formation of inverse pyramidal defects. The partial pressure of GaCl strongly affects defect formation, in-plane strain, and crystalline quality. Optimized growth conditions resulted in growth rates of 300–500 μm/h. GaN layers with thicknesses of 2.6 and of 5.8 mm were grown at rates above 300 μm/h. The threading dislocation density reduces with an inverse proportionality to the GaN layer thickness. Thus, it is demonstrated that growth rates above 300 μm/h are promising for GaN boule growth.     

Growth and shape control of orthorhombic Fe5(PO4)4(OH)3·2H2O single crystalline dendrites

Orthorhombic Fe₅(PO₄)₄(OH)₃·2H₂O single crystalline dendritic nanostructures have been synthesized by a facile and reproducible hydrothermal method without the aid of any surfactants. The influences of synthetic parameters, such as reaction time, temperature, the amount of H₂O₂ solution, pH values, and types of iron precursors, on the crystal structures and morphologies of the resulting products have been investigated. The formation process of Fe₅(PO₄)₄(OH)₃·2H₂O dendritic nanostructures is time dependent: amorphous FePO₄·nH₂O nanoparticles are formed firstly, and then Fe₅(PO₄)₄(OH)₃·2H₂O dendrites are assembled via a crystallization-orientation attachment process, accompanying a color change from yellow to green. The shapes and sizes of Fe₅(PO₄)₄(OH)₃·2H₂O products can be controlled by adjusting the amount of H₂O₂ solution, pH values, and types of iron precursors in the reaction system.     

Template-based fabrication of Ag–ZnO core–shell nanorod arrays

We report a simple, versatile, two-step fabrication technique for synthesizing a core–shell nanorod array whose architecture is specifically suited for use as an electrode in a dye sensitized solar cell (DSSC). The particular structure fabricated by us consists of a parallel array of 5 μm long and 150–200 nm wide Ag nanorod cores, each coated with a 15–20 nm thick ZnO shell. Importantly, the shell thickness is roughly uniform throughout the length of the rods, which are free standing but distinctly separated from each other. This would allow the dye to penetrate freely and cover the ZnO surface completely in a DSSC.     

线性唯象传热定律下光驱动发动机的最优路径

以存在热漏、摩擦等不可逆性,以双分子反应系统2SO3FS2O6F2为工质的光驱动发动机为研究对象,考虑工质与环境之间传热服从线性唯象传热定律[q∝Δ(T-1)],分别以输出功最大和熵产生最小为目标对整个循环活塞运动的最优路径进行研究.利用最优控制理论得出了活塞运动路径及工质温度的最优构型,给出了最优构型的数值算例,并与牛顿传热定律[q∝Δ(T)]下的最优构型进行了比较.     

“Click polyester”: Synthesis of polyesters containing triazole units in the main chain via safe and rapid “click” chemistry and their properties

Click Cu(I)‐catalyzed polymerizations of diynes that contained ester linkages and diazides were performed to produce polyesters (click polyesters) of large molecular weights [(～1.0–7.0 ) × 10⁴], that contained main‐chain 1,4‐disubstitued triazoles in excellent yields. Incorporation of triazole improved the thermal properties and magnified the even‐odd effect of the methylene chain length. We also found that, by changing the positions of the triazole rings, the thermal properties of the polyesters could be controlled. The use of in situ azidation was a safe reaction, as explosive diazides are not used. In addition, the microwave heating was found to accelerate the polymerization rates. This is the first study that has applied click chemistry for the synthesis of a series of polyesters. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 4207–4218, 2010