Hydromagnetic stability of plane Couette flow of an upper convected Maxwell fluid

Hydrodynamic stability of plane Couette flow of an upper convectedMaxwell fluid is investigated in presence of a transverse magneticfield assuming that the magnetic Prandtl number is sufficientlysmall. The resulting equation is a modified Orr–Sommerfeldequation. The equations of stability are solved numericallyusing Chebyshev collocation method with QZ algorithm. The criticalvalues of Reynolds number, wave number and wave speed are computedand the results are shown through the neutral curves. By increasingthe amount of elasticity to a certain value, it is shown that,as the Hartmann number increases, the minimum critical Reynoldsnumber decreases and it does not increase again in contrastto the Newtonian case.     

Geometry and Algebra of Prime Fano 3-folds of Genus 12

The connection between these Fano 3-folds and plane quartic curves is explained.     

Numerical-analytical method to determine the stress state of an elastic rectangular plate

A numerical-analytical method for solving the plane problem of elasticity is proposed. Systems of nonorthogonal functions are used. The method involves the minimization of a quadratic form that is equal to the integral of the sum of squared residuals of the solution and given forces. An explicit expression for stresses is derived. Bessel's inequality and the convergence of the solution are proved. The accuracy of the boundary conditions is estimated. The stress and strain distribution in the plate depending on the maximum magnitude of distributed forces and the size of their localization area is analyzed numerically. New quantitative and qualitative features of the stress distribution in the plate are established __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 1, pp. 90–98, January 2008.     

Modeling of the polarization behavior of elliptical surface-relief VCSELs

We undertake a theoretical study of the polarization behavior and mode structure of Vertical-Cavity Surface-Emitting Lasers (VCSELS) with an elliptical surface relief. The aim of the relief is twofold, first to enhance the single mode operation by introducing spatially distributed losses, and second, to enhance polarization stability by making these losses anisotropic. First, we use an analytical variational approach, for the two fundamental VCSEL modes within a Gaussian and weak guidance approximation. As a second approach we use a more refined numerical technique based on vectorial plane wave decomposition with periodic boundary conditions, which we formulate to include material anisotropy. Our studies show that whereas the polarization direction is governed by the orientation of the index ellipsoid, the selection of the lasing LP mode is mainly determined by the anisotropy in the mirror losses introduced by the elliptical surface relief.     

Some subsets of points in the plane associated to truncated Reed-Muller codes with good parameters

We gives some examples of subsets of points in the projective plane associated to truncated generalized projective Reed-Muller codes with good parameters, of dimensions 6 and 10 over GF(7), GF(8) and GF(9).     

弹性体内平面波

由胡克定律直接得到弹性体内平面波波动方程.     

点与平面相关位置的进一步探讨

本文利用平面到点的离差对点与平面的相关位置作了进一步的探讨 ,得到了一系列判定结果 .     

Solving variational inequalities defined on a domain with infinitely many linear constraints

We study a variational inequality problem whose domain is defined by infinitely many linear inequalities. A discretization method and an analytic center based inexact cutting plane method are proposed. Under proper assumptions, the convergence results for both methods are given. We also provide numerical examples to illustrate the proposed methods. The work of S. Wu was partially supported by the National Science Council, Taiwan, ROC (Grant No. 19731001). S.-C. Fang’s research has been supported by the US Army Research Office (Grant No. W911NF-04-D-0003) and National Science Foundation (Grant No. DMI-0553310).