Let R be a ring with involution. An additive mapping T : R → R is called a left ∗-centralizer (resp. Jordan left ∗-centralizer) if T (xy) = T (x)y∗ (resp. T (x2) = T (x)x∗) holds for all x, y ∈ R, and a reverse left ∗-centralizer if T (xy) = T (y)x∗ holds for all x, y ∈ R. The purpose of this paper is to solve some functional equations involving Jordan left ∗-centralizers on some appropriate su...

0

In [11] the author proved that every quasiconformal harmonic mapping between two Jordan domains with C, 0 < α ≤ 1, boundary is biLipschitz, providing that the domain is convex. In this paper we avoid the restriction of convexity. More precisely we prove: any quasiconformal harmonic mapping between two Jordan domains Ωj , j = 1, 2, with C, j = 1, 2 boundary is bi-Lipschitz.

We present a general framework whereby analysis of interior-point algorithms for semidefinite programming can be extended verbatim to optimization problems over all classes of symmetric cones derivable from associative algebras. In particular, such analyses are extendible to the cone of positive semidefinite Hermitian matrices with complex and quaternion entries, and to the Lorentz cone. We pro...

begin{abstract} If $F,D:Rto R$ are additive mappings which satisfy $F(x^{n}y^{n})=x^nF(y^{n})+y^nD(x^{n})$ for all $x,yin R$. Then, $F$ is a generalized left derivation with associated Jordan left derivation $D$ on $R$. Similar type of result has been done for the other identity forcing to generalized derivation and at last an example has given in support of the theorems. end{abstract}

Generi programming allows you to write a fun tion on e, and use it many times at di erent types. A lot of good foundational work on generi programming has been done. The goal of this paper is to propose a pra ti al way of supporting generi programming within the Haskell language, without radi ally hanging the language or its type system. The key idea is to present generi programming as a ri her...