The aim of the present paper is to efficiently describe the membrane potential dynamics of neural populations formed by species having a high density difference in specific brain areas. We propose a hybrid model whose main ingredients are a conductance-based model (ODE system) and its continuous counterpart (PDE system) obtained through a limit process in which the number of neurons confined in...

In this paper, we establish new convergence theorems and best proximity point theorems for a pair of nonlinear non-self mappings in metric spaces. Mathematics Subject Classification: 41A17, 41A65

The notion of generalized Berinde type contraction non-self maps in partially ordered metric spaces is introduced, and some best proximity point theorems for this class are established. Mathematics Subject Classification: 47H10, 54H25

We verify that the best-known nonstandard set theories: IST, BST, and HST, with the Axiom of Choice deleted, are conservative extensions of ZF + Boolean Prime Ideal Theorem. 2010 Mathematics Subject Classification 26E35 (primary); 03E25, 03E70, 03H05 (secondary)

We describe the Nash equilibria set as an intersection of graphs of players’ best responses. The problem of Nash equilibria set construction for three-person extended 2× 2× 2 games is studied. Mathematics Subject Classification 2000: 90C05, 90C10, 90C29, 90C31.

We describe the Nash equilibria set as an intersection of best response graphs. The problem of Nash equilibria set construction for two-person mixed extended 2× 3 games is studied. Mathematics Subject Classification 2000: 91A05, 91A06, 91A10, 91A43, 91A44.

The notion of generalized almost Geraghty type contraction non-self maps in partially ordered metric spaces is introduced, and some new best proximity point theorems for this class are established. Mathematics Subject Classification: 47H10, 54H25

In this paper we established some of the results of the best simultaneous approximation in the context of linear 2-normed space. 2000 Mathematics Subject Classification: 41A50, 41A52, 41A99, 41A28.

We give upper and lower bounds estimates for the best constant which appears in a multidimensional integral inequality, in the particular case of homogeneous weights. 2000 Mathematics Subject Classification: 26D15, 26B99