ON THE DISTRIBUTION OF VALUES AND DEFICIENT FUNCTION OF A GENERAL RANDOM INTEGRAL FUNCTION

We consider the random power serie8aoIw(z) = ZX.(w)z", (1)n =Owhere {Xn} is a 8equence of complex random variables in a probability spare (Q, F, P).Lemma 1 Supose that {Xn) is independent ai1d that there exists a positive coustallt crsuch thatVn 2 l, o'a: = a'ElXn l' S E'lX.l < oo. (2)Then for w e n, there exists a natural nunther N(w) a.s. such that for n > N(w)IXn(w)l 5 nrrn. (3)If {X.* } is any subsequence Of {X.}, thenP (ltL(lXn*l 2;rru*) = l. (4)Proof When ny = 0,X. = 0 a.s. …     

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.     

Synthesis,growth and characterization of organic nonlinear optical bis-glycine maleate (BGM) single crystals

A new organic compound of bis-glycine maleate was synthesized in the alkaline medium of 10% ammonium hydroxide solution. The bulk single crystals of Bis-Glycine Maleate (BGM) have been grown by slow cooling method. The grown crystals were characterized by employing single crystal and powder X-ray diffraction, Fourier transform infrared, optical absorption spectral studies and thermo gravimetric analysis. The microhardness studies confirmed that the BGM has a fairly high Vicker’s hardness number value (41 kg mm⁻²) in comparison to other organic NLO crystals. Second harmonic generation efficiency of the crystal measured by Kurtz–Perry powder method using Nd:YAG laser is found to be comparable to that of potassium dihydrogen phosphate (KDP). Frequency dependent dielectric studies were carried out along the major growth axis.     

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.     

Flux growth and characterizations of NdPO4 single crystals

Neodymium phosphate single crystals, NdPO₄, have been grown by a flux growth method using Li₂CO₃-2MoO₃ as a flux. The as-grown crystals were characterized by X-ray powder diffraction(XRPD), differential thermal analysis (DTA) and thermogravimetric analysis (TG) techniques. The results show that the as-grown crystals were well crystallized. The crystal was stable over the temperature range from 26 to 1200 °C in N₂. The specific heat of NdPO₄ crystal at room temperature was 0.41 J/g °C. The absorption and the fluorescence spectra of NdPO₄ crystal were also measured at room temperature.     

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.     

Ca3N2 as a flux for crystallization of GaN

In this work Ca₃N₂ was investigated as a potential flux for crystallization of GaN. Melting temperature of the potential flux at high N₂ pressure evaluated by thermal analysis as 1380 °C is in good agreement with the theoretical prediction. It is shown that Ca₃N₂ present in the liquid gallium in small amount (1 at%) dramatically accelerates synthesis of GaN from its constituents. On the other hand, it does not influence significantly the rate of GaN crystallization from solution in gallium in temperature gradient for both unseeded and seeded configurations. However the habit and color of the spontaneously grown GaN crystals change drastically. For 10 mol% Ca₃N₂ content in the liquid Ga it was found that the GaN thick layer and GaN crystals (identified by micro-Raman scattering measurements) were grown on the substrate. For growth from molten Ca₃N₂ (100%) with GaN source, the most important observations were (i) GaN source material was completely dissolved in the molten Ca₃N₂ flux and (ii) after experiment, GaN crystals were found on the sapphire substrate.     

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.     

Hydrothermal synthesis of Bi2Te3 nanowires through the solid-state interdiffusion of Bi and Te atoms on the surface of Te nanowires

Polycrystalline Bi₂Te₃ nanowires were prepared by a hydrothermal method that involved inducing the nucleation of Bi atoms reduced from BiCl₃ on the surface of Te nanowires, which served as sacrificial templates. A Bi–Te alloy is formed by the interdiffusion of Bi and Te atoms at the boundary between the two metals. The Bi₂Te₃ nanowires synthesized in this study had a length of 3–5 μm, which is the same length as that of the Te nanowires, and a diameter of 300–500 nm, which is greater than that of the Te nanowires. The experimental results indicated that volume expansion of the Bi₂Te₃ nanowires was a result of the interdiffusion of Bi and Te atoms when Bi was alloyed on the surface of the Te nanowires. The morphologies of Bi₂Te₃ are strongly dependent on the reaction conditions such as the temperature and the type and concentration of the reducing agent. The morphologies, crystalline structure and physical properties of the product were analyzed by X-ray diffraction (XRD), field-emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM), selected area electron diffraction (SAED) and X-ray photoelectron spectroscopy (XPS).