Structures and electronic properties of stoichiometric hydrogenated aluminum clusters

The lowest-energy geometries and electronic-structure properties have been obtained for Al_nH_n (n=1-10) clusters within the density-functional theory using the generalized gradient approximation for the exchange correlation potential. The resulting geometries show that the hydrogen atoms tend to occupy outside positions and no hollow positions are found. The subunit Al_n of Al_nH_n (n=1-5) have little distortion, in comparison with corresponding pure Al_n cluster, whereas the subunit Al_n have large distortion from n=6. The stability has been investigated by analyzing the binding energy per atom and the second difference in energy, indicating that Al₈H₈ exhibit higher stability than others. The bonding property has been analyzed by calculating the Mulliken charges and Al–H distances. The calculated energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO-LUMO), the vertical ionization potential, and the vertical electron affinity also confirm that Al₈H₈ is a stable cluster. The density of states (DOS) shows that Al_nH_n exhibit changes from molecular-like (Al₁H₁) to band-like structure (Al₁₀H₁₀) as n increases.     

Numerical study on InGaAsN/GaAs multiple-quantum-well laser with GaAsP and GaAsN barriers

In this work, the multiple-quantum-well InGaAsN laser structures with indirect-GaAsP and direct-GaAsN barriers are investigated by using LASTIP simulation program. We vary the quantum-well number, from 1 to 5, to find appropriate barrier material for InGaAsN laser structures. The simulation results show that InGaAsN laser structure has higher characteristic temperature regardless of what quantum-well number is if the indirect-GaAsP barrier is utilized. Furthermore, for InGaAsN laser structure, the usage of indirect-GaAsP barrier is beneficial for reducing the threshold current when the quantum-well number is from 1 to 2 and the usage of direct-GaAsN barrier is beneficial for reducing the threshold current when the quantum-well number is from 3 to 5.     

Equilibrium of drops on inclined fibers

Why is it that drops do not slip down inclined thin fibers or spider silks? The possible explanation is based on the existence of fiber size, which causes a sustaining force that pins these drops. Following this explanation, the drop remains in equilibrium until a critical value of the sustaining force is reached. We suggest an alternative analyses, from the point of view of the inclined fiber at which the drop slips down is predicted. This result does not depend explicitly on silk surface roughness, but only on the drop size and surface tensions.     

Sulfonylation of arenes with sulfonamides

In the presence of triflic anhydride, sulfonylation of arenes with sulfonamides proceeded smoothly in Cl₂CHCHCl₂ at 80-140 °C, which gave rise to the desired products in good to excellent yields.     

On analytical solutions of the Black–Scholes equation

This work presents a theoretical analysis for the Black–Scholes equation. Given a terminal condition, the analytical solution of the Black–Scholes equation is obtained by using the Adomian approximate decomposition technique. The mathematical technique employed in this work also has significance in studying some other problems in finance theory.     

Compressible navier-stokes equations with density-dependent viscosity, vacuum and gravitational force in the case of general pressure

This is a continuation of the article（Comm.Partial Differential Equations 26（2001）965）.In this article,the authors consider the one-dimensional compressible isentropic Navier-Stokes equations with gravitational force,fixed boundary condition,a general pressure and the density-dependent viscosity coefficient when the viscous gas connects to vacuum state with a jump in density.Precisely,the viscosity coefficient μ is proportional to ρ^θ and 0〈θ〈1/2,where ρ is the density,and the pressure P=P（ρ）is a general pressure.The global existence and the uniqueness of weak solution are proved.     

Strong convergence of an iterative method for nonexpansive mappings with new control conditions

The purpose of this paper is to study the convergence problem of an iterative method for nonexpansive mappings in Banach spaces under some new control conditions on parameters.     

甲基氯化锡的核磁共振波谱研究

定性和定量测定甲基氯化锡,文献上报道的方法较多。有薄层色谱,气相色谱,极谱法等。但测定方法麻烦,重现性较差。我们采用核磁共振波谱的方法,利用溶剂化效应对化学位移的影响,分别定性定量测定了水溶液中的SnCl_4,(CH_3)_2SnCl_2和CH_3SnCl_3。并结合薄层分离和原子吸收分光光度法进行了比较,结果较为满意。     

参数曲线的全局凸性判别条件

基于平面曲线的二次微商,导出了二重点的判别条件,结合参数曲线的局部凸性条件,得到了参数闭曲线的充要条件。给出了参数曲线的拐点判别条件,从而得到了参数曲线局部凸的充要条件。