We show that for every connected analytic subvariety V there is a pseudoconvex set Ω such bounded matrix-valued holomorphic function on extends isometrically to Ω. prove if two discs intersecting at one point, scalar valued Ω, then so does function. In the special case symmetrized bidisc, we this cannot be done by finding linear isometric extension from functions vanish point.

In that paper, the fuzzy nonlinear programming problem is discussed. In order to obtain more accurate solution, the properties of fuzzy set and fuzzy number with linear membership function and fuzzy maximum decision maker is utilized to fuzzifying the crisp problem. In the illustration, we have given a refinement to obtain this solution.

We study linear functions on the space of n × matrices over a field which preserve or strongly each Green's equivalence relations ( L , R H and J ) corresponding pre-orders. For these we are able to completely describe all preservers an algebraically closed (or more generally, in every polynomial degree has root), strong bijective any field. Over general field, non-zero -preservers coincide wit...