Abstract Only one allusion to the phrase “the faith once delivered saints” (Jude 3) survives from early church, in Book 10 of Origen’s Commentary on John . This article establishes that Origen is offering a close paraphrase this saying, and suggests it appears as slogan, possibly reflecting use by other Christians, favour overriding implications spiritual reading 2.20–22. It shows how interpret...

Image smoothing is a fundamental procedure in applications of both computer vision and graphics. The required properties can be different or even contradictive among tasks. Nevertheless, the inherent nature one operator usually fixed thus cannot meet various requirements applications. In this paper, we first introduce truncated Huber penalty function which shows strong flexibility under paramet...

Let $A$ and $B$ be two unital $C^{*}$-algebras and $varphi:A rightarrow B$ be a linear map. In this paper, we investigate the structure of linear maps between two $C^{*}$-algebras that preserve a certain property or relation. In particular, we show that if $varphi$ is unital, $B$ is commutative and $V(varphi(a)^{*}varphi(b))subseteq V(a^{*}b)$ for all $a,bin A$, then $varphi$ is a $*$-homomorph...

Let A and B be n × m matrices. The matrix B is said to be g-row majorized (respectively g-column majorized) by A, if every row (respectively column) of B, is g-majorized by the corresponding row (respectively column) of A. In this paper all kinds of g-majorization are studied on Mn,m, and the possible structure of their linear preservers will be found. Also all linear operators T : Mn,m ---> Mn...