Characteristics of invariant weights related to code equivalence over rings

The Equivalence Theorem states that, for a given weight on an alphabet, every isometry between linear codes extends to a monomial transformation of the entire space. This theorem has been proved for several weights and alphabets, including the original MacWilliams’ Equivalence Theorem for the Hamming weight on codes over finite fields. The question remains: What conditions must a weight satisfy so that the Extension Theorem will hold? In this paper we provide an algebraic framework for determining such conditions, generalising the approach taken in Greferath and Honold (Proceedings of the Tenth International Workshop in Algebraic and Combinatorial Coding Theory (ACCT-10), pp. 106–111. Zvenigorod, Russia, 2006).     

Existence d'une mesure de Sinai—Ruelle—Bowen pour des systèmes non uniformément hyperboliques

Let M be a smooth Riemannian manifold, and ƒ be a Csu1 + α-diffeomorphism of M onto itself Let Λ be a Pesin's set (see [5]). We prove that under some assumptions on Λ, and if the system (M, ƒ) is conservative for the Lebesgue measure, then there exists a SRB-measure, ƒ -invariant and σ-finite.     

Continuous facility location on graphs

Mathematical Programming - We study a continuous facility location problem on undirected graphs where all edges have unit length and where the facilities may be positioned on the vertices as well...     

Persistent Homology to Quantify the Quality of Surface-Supported Covalent Networks

Covalent networks formed by on-surface synthesis usually suffer from the presence of a large number of defects. We report on a methodology to characterize such two-dimensional networks from their experimental images obtained by scanning probe microscopy. The computation is based on a persistent homology approach and provides a quantitative score indicative of the network homogeneity. We compare our scoring method with results previously obtained using minimal spanning tree analyses and we apply it to some molecular systems appearing in the existing literature.     

An integral test for a critical multitype spatially homogeneous branching particle process and a related reaction-diffusion system

An integral test (Theorem 5) is established for the dichotomy concerning local extinction and survival (even persistence) at late times for critical multitype spatially homogeneous branching particle systems in continuous time. Our conditions on the branching mechanism are close to the ones known from “classical” processes without motion component. This generalizes and complements results of López-Mimbela and Wakolbinger [LMW96] and others. Our approach is based on some genealogical tree analysis combined with the study of the long-term behavior of L ¹-norms of solutions of related systems of reaction-“diffusion” equations, which is perhaps also of some independent interest. Received: 13 August 1997 / Revised version: 12 May 1998 / Published online: 14 February 2000     

Sum-free sets in abelian groups

We show that there is an absolute constant δ>0 such that the number of sum-free subsets of any finite abelian groupG is