Motivated by Benney’s general theory, we propose new models for short wave long wave interactions when the long waves are described by nonlinear systems of conservation laws. We prove the strong convergence of the solutions of the vanishing viscosity and short wave long wave interactions systems by using compactness results from the compensated compactness theory and new energy estimates obtain...

Article history: Received 1 September 2013 Available online xxxx

In this paper, it is shown that an n-variable rotation symmetric Boolean function f with n even but not a power of 2 admits a rotation symmetric function g of degree at most e ≤ n/3 such that the product gf has degree at most n− e− 1.

A 1 2 -arc-transitive graph is a vertexand edgebut not arc-transitive graph. In all known constructions of quartic 1 2 -arc-transitive graphs, vertex stabilizers are isomorphic to Z 2,Z 2 2 or to D8. In this article, for each positive integer m ≥ 1, an infinite family of quartic 1 2 -arctransitive graphs having vertex stabilizers isomorphic to Z m

In this article we perform von Neumann analysis of the difference equations that arise as a result of loop quantum gravity being applied to models of cosmology and black holes. In particular, we study the numerical stability of Bianchi I LRS (symmetric and non-symmetric constraint) and Schwarzschild interior (symmetric constraint) models, and find that there exist domains over which there are i...

We produce a one-parameter family of hyperplane arrangements that are counterexamples to the conjecture of Saito that the complexified complement of a free arrangement is K(n, 1 ). These arrangements are the restriction of a one-parameter family of arrangements that arose in the study of tilings of certain centrally symmetric octagons. This other family is discussed as well. I. Definitions and ...

We prove that there does not exist a non-square quadratic polynomial with integer coefficients and an axis of symmetry which takes square values for N consecutive integers for N = 7 or N ≥ 9. At the opposite, if N ≤ 6 or N = 8 there are infinitely many.

A regular graph is called semisymmetric if it is edge transitive but not vertex transitive It is proved that the Gray graph is the only cubic semisymmetric graph of order p where p is a prime

In [12], Stanley associated with a graph G a symmetric function XG which reduces to G’s chromatic polynomial XG(n) under a certain specialization of variables. He then proved various theorems generalizing results about XG(n), as well as new ones that cannot be interpreted on the level of the chromatic polynomial. Unfortunately, XG does not satisfy a Deletion-Contraction Law which makes it diffi...