Application of the network equivalent concept for external system representation for power system transient analysis is well known. However, the challenge to utilize an equivalent network, approximated by a rational function, is to guarantee the passivity of the corresponding model. In this regard, special techniques are required to enforce the passivity of the equivalent model through a post processing approach that minimizes its impact on the original model characteristics. In this paper, the passivity is enforced by expressing the problem in terms of a convex optimization problem that guarantees the global optimal solution. The convex optimization problem is efficiently solved by recently developed numerical interior–point methods. This passivity enforcement is also global which indicates that the passivity enforcement in one region does not lead to passivity violation in other regions.

A new geometric notion on a nonempty and convex pair of subsets of a convex metric space X, called semi-normal structure, is introduced and used to investigate the existence of best proximity pairs for a new class of mappings, called strongly noncyclic relatively C-nonexpansive. We also study the structure of minimal sets of strongly noncyclic relatively C-nonexpansive mappings in the setting of convex metric spaces.

The conic structure of the convex cone of non-negative operator convex functions on (0,¥) (also on (−1, 1)) is clarified. We completely determine the extreme rays, the closed faces, and the simplicial closed faces of this convex cone.

Nowadays, the fundamental role of having a purpose for life in physical and mental health has been confirmed. According to victor frankl, presence of a purpose in life gives life a meaning and increases resilience against pains and traumas. The importance of the purpose in life construct reveals the need for a reliable and valid tool to measure it. Crumbaugh and Maholick's purpose in life questionnaire is the first and one of the most applied tools for the assessment of life's purposefulness. The aim of this research is to determine the factor structure of purpose in life questionnaire. The questionnaire was administered on 206 students who were selected through random stratified sampling at Ferdowsi University of Mashhad. Exploratory factor analysis showed that there are two factors "comprehension" and "purpose" and this finding were confirmed by confirmatory factor analysis. Altogether results of this research showed factor validity of the purpose in life questionnaire with a two factor pattern