Let $A$ be an arbitrary Banach algebra and $varphi$ a homomorphism from $A$ onto $Bbb C$. Our first purpose in this paper is to give some equivalent conditions under which guarantees a $varphi$-mean of norm one. Then we find some conditions under which there exists a $varphi$-mean in the weak$^*$ cluster of ${ain A; |a|=varphi(a)=1}$ in $A^{**}$.

Hexagrid structural system is an innovated system with structural behavior which is similar to a tubular system. In this paper, a numerical study is conducted to estimate the seismic performance of horizontal hexagrid concerning the combined horizontal and vertical hexagrid, tubular and diagrid structural systems. First 30 and 50 story buildings are modeled using ETABS, then pushover and nonlin...

energy conservation in buildings plays a vital role for sustainable development of societies and nations. although, newer buildings in developing nations are being constructed using energy conservation approach, existing buildings have higher energy demand to meet the desired comfort. excessive energy demand for cooling the built environment is a major problem over most of the arid climatic zon...