Inf-dif-stability of oblique perturbation

Laurent and Rockafellar have studied certain problems of perturbation and of stability in convex minimization problems. Laurent has discussed inf-dif-stability conditions respectively for horizontal perturbation and for vertical perturbation. In this paper, we generalize some results of Laurent^[1] by giving several inf-dif-stability conditions of oblique perturbation.Project supported by the National Natural Science Foundation of China.     

Numerical-perturbation analysis of edge effect in bending laminated plate

In this paper, we consider a bending laminated plate. At first, the dimensionless variables are used to transform the equilibrium equations of any layer to perturbation differential equations. Secondly, the composite expansion is used and the solution domain is divided into interior and boundary layer regions and the mathematical models for the outer solution and the inner solution are yielded respectively. Then, the inner solution is expressed with the boundary intergral equation.Project Supported by the National Science Foundation of China.     

Direct Spectroscopic Evidence for 1ΔgO2 Production from the Photolysis of Vanadium(V)-Peroxo Complexes in Aqueous Solution

The chemiluminescence of ¹DL_gO₂ expelled from the UV photolysis of vanadium(V)-peroxo (VP) complexes in aqueous solution was observed for the first time. Using phenalenone photosensitization as a standard reference, the ¹O₂ quantum yields from the photolysis of 12 VP complexes were measured. No good correlation was found between the relative DNA-photocleavage activities and the ¹O₂ quantum yields of these complexes. This lack of correlation underscores the significant contribution of the complex-DNA binding interaction in determining the observed DNA-photocleavage activity of the complex. The small ¹O₂ quantum yields observed in these complexes were interpreted in terms of the minor ¹O₂ pho-toelimination channel relative to other more efficient relaxation processes.     

Numerical analysis of a mixed finite element method for a flow-transport problem

We consider a generic flow-transport system of partial differential equations, which has wide application in the waste disposal industry. The approximation of this system, using a finite element method for the brine, radionuclides, and heat combined with a mixed finite element method for the pressure and velocity, is analyzed. Optimal order error estimates in H¹ and L² are derived. The error analysis is given with no restriction on the diffusion tensor. That is, we have included the effects of molecular diffusion and dispersion. © 1996 John Wiley & Sons, Inc.     

Numerical study of vortex shedding from a rotating cylinder immersed in a uniform flow field

A numerical study is made of the unsteady two‐dimensional, incompressible flow past an impulsively started translating and rotating circular cylinder. The Reynolds number (Re) and the rotating‐to‐translating speed ratio (α) are two controlled parameters, and the influence of their different combinations on vortex shedding from the cylinder is investigated by the numerical scheme sketched below. Associated with the streamfunction (ψ)–vorticity (ω) formulation of the Navier–Stokes equations, the Poisson equation for ψ is solved by a Fourier/finite‐analytic, separation of variable approach. This approach allows one to attenuate the artificial far‐field boundary, and also yields a global conditioning on the wall vorticity in response to the no‐slip condition. As for the vorticity transport equation, spatial discretization is done by means of finite difference in which the convection terms are handled with the aid of an ENO (essentially non‐oscillatory)‐like data reconstruction process. Finally, the interior vorticity is updated by an explicit, second‐order Runge–Kutta method. Present computations fall into two categories. One with Re=10³ and α≤3; the other with Re=10⁴ and α≤2. Comparisons with other numerical or physical experiments are included. Copyright © 2000 John Wiley & Sons, Ltd.     

Improvement of M-plane GaN thin film grown on pre-annealing β-LiGaO2 (100) substrate

In this paper, we report the growth of M-plane GaN thin films on LiGaO₂ (100) substrates pre-annealed in vacuum and in air ambient. The surface of M-plane GaN film grown on the LiGaO₂ (100) substrate pre-annealed in air ambient was significantly improved. X-ray diffraction data showed that the M-plane GaN thin film grown on the LiGaO₂ (100) substrate pre-annealed in air ambient has better crystal quality than that grown on the LiGaO₂ (100) substrate pre-annealed in vacuum. In addition, the strain generated between GaN thin film and LiGaO₂ substrate was relaxed when the GaN thin film grew on the LiGaO₂ substrate pre-annealed in air ambient. It revealed that the thermal annealing LiGaO₂ substrate in air ambient can suppress the formation of lithium-rich surface effectively, and then one can grow a high quality M-plane GaN thin film on the LiGaO₂ substrate.     

In-plane free vibration of a single-crystal silicon ring

In this paper the natural frequencies and the associated mode shapes of in-plane free vibration of a single-crystal silicon ring are analyzed. It is found that the Si(1 1 1) ring is two-dimensionally isotropic in the (1 1 1) plane for elastic constants but three-dimensionally anisotropic, while the Si(1 0 0) ring is fully anisotropic. Hamilton’s principle is used to derive the equations of vibration, which is a set of partial differential equations with coefficients being periodic in polar variable. Expressing the radial and tangential displacements in sinusoidal form with non-predetermined amplitudes, and through the integration with respect to the circumferential variable, the original governing equations in partial differential form can be converted into the amplitude equations in ordinary differential form. The exact expressions for frequencies and mode shapes are obtained. It is found that for Si(1 0 0) rings the frequencies of a pair of modes, which are equal for an isotropic ring, split due to the anisotropic effect only for the second in-plane vibration mode. The phenomena of frequency splitting and degenerate modes can be proved either based on the conservation of averaged mechanical energy or by the concept of crystallographic symmetry groups. When the single-crystal silicon is replaced by the polycrystalline silicon, which is isotropic in elastic constants, the derived equations for frequencies correctly predict the vanishing of the phenomenon of frequency splitting.     

Synthetic Applications of 3‐(Phenylsulfinyl)‐3‐sulfolene

The title compound 2 was readily prepared by MCPBA oxidation of the sulfide 1. Thermal desulfonylation of 2 gave the sulfoxide‐substituted diene 3. The Diels‐Alder reactions of 3 with various dienophiles gave the cyclized products 4‐9 in good yields. The regiochemistry was found to be dominated by the phenylsulfinyl group, but could be reversed by the presence of a Lewis acid. Deprotonation of 2 by BuLi, followed by the reaction with alkyl halides, gave the substituted 2‐sulfolenes 10. A synthetic application of 10 was demonstrated by converting 10e to the bicyclic product 11.