We deal with two classes of locally compact sober spaces, namely, the class of locally spectral coherent spaces and the class of spaces in which every point has a closed spectral neighborhood (CSN-spaces, for short). We prove that locally spectral coherent spaces are precisely the coherent sober spaces with a basis of compact open sets. We also prove that CSN-spaces are exactly the locally spec...

The aim of this paper is to introduce a new class of sets called (i,j) r^g closed sets and a new class of maps called D^(i,j) continuous maps and D^(i,j)irresolute maps in bitopological spaces. Also we introduce some new spaces called (i,j) – T^1/2 , (i,j) ^T 1/2 ,*T^1/2, ^T*1/2 and ^Trg and obtain their basic properties. Mathematics Subject Classification: 54A10

We re-examine measure-category duality by a bitopological approach, using both the Euclidean and the density toplologies of the line. We give a topological result (on convergence of homeomorphisms to the identity) obtaining as a corollary results on in…nitary combinatorics due to Kestelman and to Borwein and Ditor. As a by-product we give a uni…ed proof of the measure and category cases of Unif...

We introduce an analog of the Maxwell operator on a q-Minkowski space algebra (treated as a particular case of the so-called Reflection Equation Algebra) and on certain of its quotients. We treat the space of ”quantum differential forms” as a projective module in the spirit of the Serre-Swan approach. Also, we use ”braided tangent vector fields” which are q-analogs of Poisson vector fields asso...

SOBER-128 is a stream cipher designed by Rose and Hawkes in 2003. It can be also used for generating Message Authentication Codes (MACs) and an authenticated encryption. The developers claimed that it is difficult to forge MACs generated by both functions of SOBER128, though, the security assumption in the proposal paper is not realistic in some instances. In this paper, we examine the security...