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.

We extend the work presented in [7, 8] to a regions-based, twodimensional, Euclidean theory. The goal is to recover the classical continuum on a point-free basis. We first derive the Archimedean property for a class of readily postulated orientations of certain special regions, “generalized quadrilaterals” (intended as parallelograms), by which we cover the entire space. Then we generalize this...

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...

In this article we present a fuzzy logic based method for the construction of thoughts of artificial animals (animats). Due to the substantial increase of the processing power of personal computers in the last decade there was a notable progress in the field of animat construction and simulation. Regardless of the achieved results, the coding of the animat’s behaviour is very inaccurate and can...

We introduce a model of bargaining among groups, and characterize a family of solutions using a Consistency axiom and a few other invariance and monotonicity properties. For each solution in the family, there exists some constant α ≥ 0 such that the "bargaining power" of a group is proportional to cα, where c is the cardinality of the group. Subject classification: JEL C71, C78

Hilbert (David Hilbert, 1862-1943 a.d) is a well-known German mathematician. He introduced 23 of the most important problem for twentieth century mathematicians to study, this is the famous “Hilbert problems”. Hilbert’s sixth mathematical conjecture has attracted the attention many over past century. Traditional Chinese Philosophy (TCP) differs from Western philosophy mainly in that TCP co...