Solutions en dualité pour les gaz sans pression

We introduce the notion of duality solution for the system of pressureless gases, which ensures existence for the Cauchy problem, and uniqueness under optimal conditions on initial data.     

Optimization of eigenvalue bounds for the independence and chromatic number of graph powers

The $k^{\text{th}}$ power of a graph $G=(V,E)$, $G^k$, is the graph whose vertex set is V and in which two distinct vertices are adjacent if and only if their distance in G is at most k. This article proves various eigenvalue bounds for the independence number and chromatic number of $G^k$ which purely depend on the spectrum of G, together with a method to optimize them. Our bounds for the k-independence number also work for its quantum counterpart, which is not known to be a computable parameter in general, thus justifying the use of integer programming to optimize them. Some of the bounds previously known in the literature follow as a corollary of our main results. Infinite families of graphs where the bounds are sharp are presented as well.     

A family of projective two-weight linear codes

Designs, Codes and Cryptography - Projective two-weight linear codes are closely related to finite projective spaces and strongly regular graphs. In this paper, a family of q-ary two-weight linear...     

Multivariate quadrature rules on crosslet sparse grids

Numerical Algorithms - We introduce a new configuration of node sets: crosslet grids for high-dimensional numerical integration, and develop symmetric quadrature rules on the unit cube of the...     

Construction of Normal Bimagic Squares of Order 2u

Acta Mathematicae Applicatae Sinica, English Series - An n × n matrix A consisting of nonnegative integers is a general magic square of order n if the sum of elements in each row, column, and...     

Cubic Semisymmetric Graphs of Order 2qp2

Acta Mathematicae Applicatae Sinica, English Series - A regular edge-transitive graph is said to be semisymmetric if it is not vertex-transitive. Let p be a prime. By Folkman [J. Combin. Theory 3...     

A lattice isomorphism theorem for cluster groups of mutation-Dynkin type An

Each quiver appearing in a seed of a cluster algebra determines a corresponding group, which we call a cluster group, which is defined via a presentation. Grant and Marsh showed that, for quivers appearing in seeds of cluster algebras of finite type, the associated cluster groups are isomorphic to finite reflection groups. As for finite Coxeter groups, we can consider parabolic subgroups of cluster groups. We prove that, in the type $A_n$ case, there exists an isomorphism between the lattice of subsets of the defining generators of the cluster group and the lattice of its parabolic subgroups. Moreover, each parabolic subgroup has a presentation given by restricting the presentation of the whole group.