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...

This list is a short overview of some of my results. One can nd a more detailed description in my Research Statement or at 1. Simple associative algebras with nite Z-grading. Here, R is a simple algebra with a nite Z-grading over a commutative ring. A description of all such algebras was given 18]. As a corollary, it was proved that every (not necessarily nite dimensional) simple Lie algebra of...

Explicit formulae for asymptotic expansions of Feynman diagrams in typical limits of momenta and masses with external legs on the mass shell are presented. E-mail: [email protected]

In symbolic data analysis, the values of the variables can be, among others, intervals. The algebraic structure of these variables leads us to adapt dissimilarity ones to be able to study them. The Kolmogorov-Smirnov criterion is used as a test selection metric for decision tree induction. For this criterion, the values taken by the explanatory variables have to be ordered. We have been interes...

and Applied Analysis 3 Now we recall definitions and some properties of the Smirnov class, the Privalov class, the Bergman-Privalov class, and the Zygmund F-algebra on Bn or D. The space of all holomorphic functions on X Bn or D is denoted by H X . For each 0 < p ≤ ∞, the Hardy space is denoted by H X with the norm ‖ · ‖p. 2.1. Smirnov Class N∗ X Let X ∈ {Bn, Dn}. The Nevanlinna class N X on X ...