we introduce some new concepts of topological spaces which say α − separable topologicalspace and o-topological group, α − first axiom, α − second axiom, and we find some relations betweenthem with some applications in normed spaces.

The taxonomic and systematic history of the South American silversides has changed significantly since Campos (1984) review. As a result of phylogenetic studies of the subfamilies Menidiinae (Chernoff, 1986b), Atherinopsinae (White, 1985; Crabtree, 1987; Dyer 1997, 1998) and of the order Atheriniformes (Saeed et al., 1994; Dyer and Chernoff, 1996) the taxonomy and classification of silversides ...

The Chernoff bound is a tail bound for sums of independent real variables.

In this article we prove that Axiom A is a necessary condition for structural stability of C1 nonsingular endomorphisms of the circle.

We construct a variety of inner models exhibiting features usually obtained by forcing over universes with large cardinals. For example, if there is a supercompact cardinal, then there is an inner model with a Laver indestructible supercompact cardinal. If there is a supercompact cardinal, then there is an inner model with a supercompact cardinal κ for which 2κ = κ+, another for which 2κ = κ++ ...

We discuss a model, in which two agents may distribute finitely many objects among themselves. The conflict is resolved by means of a market procedure. Depending on the specifications, this procedure serves to implement bargaining solutions such as the discrete Raiffa solution, the Kalai-Smorodinsky solution and the Perles-Maschler solution. The latter is axiomatized using the superadditivity a...