In this paper we define a discrete subset family of a topological space and basis sigma locally finite and sigma discrete. First, we prove an auxiliary fact for discrete family and sigma locally finite and sigma discrete basis. We also show the necessary condition for the Nagata Smirnov theorem: every metrizable space is T3 and has a sigma locally finite basis. Also, we define a sufficient cond...

We study to which extent the family of pairs of subspaces of a vector space related to each other via intersection properties determines the vector space. In another language, we study to which extent the family of vertices of the building of a projective space related to each other via several natural respective conditions involving the Weyl distance and incidence determines the building. Thes...

We present a superfield Lax formalism of superspace sigma model based on the target space G/H and show that a one-parameter family of flat superfield connections exists if the target space G/H is a symmetric space. The formalism has been related to the existences of an infinite family of local and non-local superfield conserved quantities. Few examples have been given to illustrate the results....

The Data Encryption Standard (DES) defines an indexed set of permutations acting on the message space M = (0,l)". If this set of permutations were closed under functional composition, then DES would be vulnerable to a known-plaintext attack that runs in 228 steps, on the average. It is unknown in the open literature whether or not DES has this weakness. We describe two statistical tests for det...

We introduce a new kind of hypergraphs and hyperedge replacement grammars, where nodes are associated types. We use them to adapt the abstraction framework Juggrnaut presented by us in [7, 8] – for the verification of Java Bytecode programs. The framework is extended to handle additional concepts needed for the analysis of Java Bytecode like null pointers and method stacks as well as local and ...

The classical Krein-Naimark formula establishes a one-to-one correspondence between the generalized resolvents of a closed symmetric operator in a Hilbert space and the class of Nevanlinna families in a parameter space. Recently it was shown by V.A. Derkach, S. Hassi, M.M. Malamud and H.S.V. de Snoo that these parameter families can be interpreted as so-called Weyl families of boundary relation...

we show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. further we study the preservation of diagonal conditions, which characterize approach spaces. it is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...