By Ulam’s conjecture every finite graph G can be reconstructed from its deck of vertex deleted subgraphs. The conjecture is still open, but many special cases have been settled. In particular, one can reconstruct Cartesian products. We consider the case of k-vertex deleted subgraphs of Cartesian products, and prove that one can decide whether a graph H is a kvertex deleted subgraph of a Cartesi...

The weak-* topology is seen to play an important role in the study of various finiteness conditions one may place on a coalgebra C and its dual algebra C*. Here we examine the interplay between the topology and the structure of ideals of 0*. The basic theory has been worked out for the commutative and almost connected cases (see [2]). Our basic tool for reducing to the almost connected case is ...

‎Let $D$ be an integral domain with quotient field $K$‎, ‎$E$ be a $K$-vector space‎, ‎$R = D propto E$ be the trivial extension of $D$ by $E$‎, ‎and $w$ be the so-called $w$-operation‎. ‎In this paper‎, ‎we show that‎ ‎$R$ is a $w$-FF ring if and only if $D$ is a $w$-FF domain; and‎ ‎in this case‎, ‎each $w$-flat $w$-ideal of $R$ is $w$-invertible.

Steganography is the art of hiding the fact that communication is taking place, by hiding information in other information. Many different carrier file formats can be used, but digital images are the most popular because of their frequency on the Internet. For hiding secret information in images, there exists a large variety of steganographic techniques some are more complex than others and all...

A hypergraph is color-critical if deleting any edge or vertex reduces the chromatic number; a color-critical hypergraph with chromatic number k is k-critical. Every k-chromatic hypergraph contains a k-critical hypergraph, so one can study chromatic number by studying the structure of k-critical (hyper)graphs. There is vast literature on k-critical graphs and hypergraphs. Many references can be ...

We study the -server problem when the off-line algorithm has fewer than servers. We give two upper bounds of the cost WFA of the Work Function Algorithm. The first upper bound is OPT OPT , where OPT denotes the optimal cost to service by servers. The second upper bound is OPT OPT for . Both bounds imply that the Work Function Algorithm is -competitive. Perhaps more important is our technique wh...

Kaon Physics is a very complicated blend of Ultraviolet and Infrared effects which still defies complete physical understanding. The problem consists in the large enhancement (≈ 20) of the ∆I = 12 amplitude with respect to the ∆I = 32 one. Being a process involving hadrons, Kdecay must be treated non-perturbatively, so that lattice discretization is the ideal tool to deal with this problem. In ...