一个带Hardy项的椭圆方程的多重解

通过对偶变分方法证明了一个带Hardy项和临界非线性的非线性椭圆方程的非平凡解的存在性和多重性.     

解整数线性规划中选择割平面的一个方法

本指出了[4]的一个错误。用最速下降规则，给出了选择割平面的一个新方法。一个复杂的例子说明，该方法有一定的实用价值。     

Slosh dynamics of inviscid fluids in two‐dimensional tanks of various geometry using finite element method

This paper brings into focus some of the interesting effects arising from the motion of the liquid free surface due to sloshing in partially filled containers of several geometrical shapes in two dimensions. The slosh characteristics that include frequencies, free surface profiles and the hydrodynamic pressure over the container walls have been reported in this study. The equations of motion of the fluid, considered inviscid, are expressed in terms of the pressure variable alone. It is assumed that the frequency of the exciting oscillation is not in the immediate neighborhood of the natural slosh frequency, so that the slope of the free surface is small. Simple harmonic oscillation and earthquake excitations are used as the prescribed boundary conditions. A finite difference‐based iterative time‐stepping technique is employed to advance the solution in the time domain. The paper presents numerical solutions for rectangular, vertically mounted annular cylindrical, trapezoidal and horizontal circular cylindrical containers. Numerical results obtained are compared with the available existing solutions to validate the code developed. The parametric study of the slosh dynamic systems shows the importance of the nature of excitation, fluid height and the geometry of the container. Copyright © 2007 John Wiley & Sons, Ltd.     

Small non‐embeddable quasi‐derived designs

We establish the existence of non‐embeddable quasi‐derived 2‐designs with the parameters (13, 4, 3), (15, 6, 5), and (16, 6, 5). © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 364–372, 2008     

Extensions of the potential reduction algorithm for linear programming

In this work, we study several extensions of the potential reduction algorithm that was developed for linear programming. These extensions include choosing different potential functions, generating the analytic center of a polytope, and finding the equilibrium of a zero-sum bimatrix game.     

Study of the Heterocyclic-Substituted Platinum-1,2-Enedithiolate 3ILCT Excited States by Transient Absorption Spectroscopy

The photoluminescent 1,2-enedithiolate complexes, (dppe)Pt{S₂C₂(2-quinoxaline)(H)}, [L₂Pt{S₂C₂(2-pyridinium)(H)}]⁺ where L₂ = dppm and dppe, [L₂Pt{S₂C₂(4-pyridinium)(H)}]⁺, [L₂Pt{₂C₂(N-Methyl-4-pyridinium)(H)}]⁺ and [L₂Pt{S₂C₂(CH₂CH₂-N-2-pyridinium)}]⁺ where L₂ = dppm, dppe, and dppp are room temperature dual emitters where the emissions have thiolate to heterocycle * intraligand charge transfer character (ILCT) singlet and triplet character. The pyridinium complexes have strong triplet-triplet absorption bands at approximately 400, 520 and 630 nm with a weaker band at 800 nm while (dppe)Pt{S₂C₂(2-quinoxaline)(H)} has strong triplet-triplet absorption bands at 385 and 550 nm with weaker bands at 610 and 805 nm. By fitting the decay of the transients to single exponential kinetics, the ³ILCT* lifetimes of the pyridinium complexes where determined to be 0.7 to 15.9 s (DMSO) while the ₃ILCT* lifetime of (dppe)Pt{S₂C₂(2-quinoxaline)(H)} was determined to be 2.8 s (CH₃CN). The transient absorption spectra of the complexes is affected by the appended heterocycle rather than the bulk of ancillary phosphine ligand or whether the heterocycle is protonated or alkylated.     

On d-Dimensional Dual Hyperovals

d-dimensional dual hyperovals in a projective space of dimension n are the natural generalization of dual hyperovals in a projective plane. After proving some general properties of them, we get the classification of two-dimensional dual hyperovals in projective spaces of order 2. A characterization of the only two-dimensional dual hyperoval which is known in PG(5,4) is also given. Finally the classification of 2-transitive two-dimensional dual hyperovals is reached.     

Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier-Stokes equations

SUPG methods were originally developed for the scalar advection-diffusion equation and the incompressible Navier-Stokes equations. In the last few years successful extensions have been made to symmetric advective-diffusive systems and, in particular, the compressible Euler and Navier-Stokes equations. New procedures have been introduced to improve resolution of discontinuities and thin layers. In this paper a brief overview is presented of recent progress in the development and understanding of SUPG methods.     

Electrical resistivity studies of certain quasi one-dimensional organic systems at high pressures and low temperatures

We report the electrical resistivity studies of six quasi one-dimensional organic systems under high pressures up to 8 GPa and temperatures down to 77K. The room temperature resistivity of these complexes lies in the wide range from 10⁸ ohm cm to 0.05 ohm cm, but they have common features under high pressures. The possible interpretations of these behaviours have also been discussed.