All regular polytopes are Ramsey

In this paper it is shown that all regular polytopes are Ramsey. In the course of this proof all convex quasi-regular polyhedra are proved to be Ramsey.     

On the approximability of the maximum induced matching problem

In this paper we consider the approximability of the maximum induced matching problem (MIM). We give an approximation algorithm with asymptotic performance ratio d−1 for MIM in d-regular graphs, for each d3. We also prove that MIM is APX-complete in d-regular graphs, for each d3.     

Transition between regular and Mach reflection of shock waves: new numerical and experimental results

New numerical and experimental results on the transition between regular and Mach reflections of steady shock waves are presented. The influence of flow three-dimensionality on transition between steady regular and Mach reflection has been studied in detail both numerically and experimentally. Characteristic features of 3D shock wave configuration, such as peripheral Mach reflection, non-monotonous Mach stem variation in transverse direction, the existence of combined Mach-regular-peripheral Mach shock wave configuration, have been found in the numerical simulations. The application of laser sheet imaging technique in streamwise direction allowed us to confirm all the details of shock wave configuration in the experiments. Close agreement of the numerical and experimental data on Mach stem heights is shown. Received 23 November 2000 / Accepted 25 April 2001     

Maximally differential ideals in regular local rings

It is shown that ifA is a regular local ring andI is a maximally differential ideal inA, thenI is generated by anA-sequence.     

Sequential convergence of regular measures on prehilbert space logics

This paper investigates Nikodym-type and Cafiero-type convergence theorems for regular charges in the general set-up of projection logics of prehilbert spaces. For this aim we also characterize bounded regular charges.     

Dieudonné's theorem for non-additive set functions

A Cafiero type criterion and an extension of the classical Dieudonné's theorem for a class of non-additive set functions valued into a complete Hausdorff uniform space are established.     

On Approximation of Laplacian Eigenproblem over a Regular Hexagon with Zero Boundary Conditions

In my earlier paper [4], an eigen-decompositions of the Laplacian operator is given on a unit regular hexagon with periodic boundary conditions. Since an exact decomposition with Dirichlet boundary conditions has not been explored in terms of any elementary form.In this paper, we investigate an approximate eigen-decomposition. The function space,corresponding all eigenfunction, have been decomposed into four orthogonal subspaces.Estimations of the first eight smallest eigenvalues and related orthogonal functions are given. In particulary we obtain an approximate value of the smallest eigenvalue λ1～29/40π^2= 7.1555, the absolute error is less than 0.0001.     

Series solutions of coupled differential equations with one regular singular point

We consider two linear second-order ordinary differential equations. r=0 is a regular singular point of these equations. Applying the classical Method of Frobenius, we do not obtain any indicial equation and therefore no solution, because the differential equations are coupled.

In this paper, we present an extended Method of Frobenius on a coupled system of two ordinary differential equations. These equations come from the micropolar theory, which is one of the three kinds of the new 3M physics.