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WEAK AMENABILITY OF THE LAU PRODUCT OF BANACH ALGEBRAS DEFINED BY A BANACH ALGEBRA MORPHISM
Ramezanpour, Mohammad Korean Mathematical Society 2017 대한수학회보 Vol.54 No.6
Let A and B be two Banach algebras and $T:B{\rightarrow}A$ be a bounded homomorphism, with ${\parallel}T{\parallel}{\leq}1$. Recently, Dabhi, Jabbari and Haghnejad Azar (Acta Math. Sin. (Engl. Ser.) 31 (2015), no. 9, 1461-1474) obtained some results about the n-weak amenability of $A{\times}_TB$. In the present paper, we address a gap in the proof of these results and extend and improve them by discussing general necessary and sufficient conditions for $A{\times}_TB$ to be n-weakly amenable, for an integer $n{\geq}0$.
Experimental investigation on optimal shear strengthening of RC beams using NSM GFRP bars
Ramezanpour, M.,Morshed, R.,Eslami, A. Techno-Press 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.67 No.1
Several techniques have been developed for shear strengthening of reinforced concrete (RC) members by using fiber reinforced polymer (FRP) composites. However, debonding of FRP retrofits from concrete substrate still deemed as a challenging concern in their application which needs to be scrutinized in details. As a result, this paper reports on the results of an experimental investigation on shear strengthening of RC beams using near surface mounted (NSM) FRP reinforcing bars. The main objective of the experimentation was increasing the efficiency of shear retrofits by precluding/postponing the premature debonding failure. The experimental program was comprised of six shear deficient RC beams. The test parameters include the FRP rebar spacing, inclination angle, and groove shape. Also, an innovative modification was introduced to the conventional NSM technique and its efficiency was evaluated by experimental observation and measurement. The results testified the efficiency of glass FRP (GFRP) rebars in increasing the shear strength of the test specimens retrofitted using conventional NSM technique. However, debonding of FRP bars impeded exploiting all retrofitting advantages and induced a premature shear failure. On the contrary, application of the proposed modified NSM (MNSM) technique was not only capable of preventing the premature debonding of FRP bars, but also could replace the failure mode of specimen from the brittle shear to a ductile flexural failure which is more desirable.
ON ACTION OF LAU ALGEBRAS ON VON NEUMANN ALGEBRAS
Mohammad, Ramezanpour Korean Mathematical Society 2015 대한수학회보 Vol.52 No.2
Let $\mathbb{G}$ be a von Neumann algebraic locally compact quantum group, in the sense of Kustermans and Vaes. In this paper, as a consequence of a notion of amenability for actions of Lau algebras, we show that $\hat{\mathbb{G}}$, the dual of $\mathbb{G}$, is co-amenable if and only if there is a state $m{\in}L^{\infty}(\hat{\mathbb{G}})^*$ which is invariant under a left module action of $L^1(\mathbb{G})$ on $L^{\infty}(\hat{\mathbb{G}})^*$. This is the quantum group version of a result by Stokke [17]. We also characterize amenable action of Lau algebras by several properties such as fixed point property. This yields in particular, a fixed point characterization of amenable groups and H-amenable representation of groups.
Experimental investigation on optimal shear strengthening of RC beams using NSM GFRP bars
M. Ramezanpour,R. Morshed,A. Eslami 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.67 No.1
Several techniques have been developed for shear strengthening of reinforced concrete (RC) members by using fiber reinforced polymer (FRP) composites. However, debonding of FRP retrofits from concrete substrate still deemed as a challenging concern in their application which needs to be scrutinized in details. As a result, this paper reports on the results of an experimental investigation on shear strengthening of RC beams using near surface mounted (NSM) FRP reinforcing bars. The main objective of the experimentation was increasing the efficiency of shear retrofits by precluding/postponing the premature debonding failure. The experimental program was comprised of six shear deficient RC beams. The test parameters include the FRP rebar spacing, inclination angle, and groove shape. Also, an innovative modification was introduced to the conventional NSM technique and its efficiency was evaluated by experimental observation and measurement. The results testified the efficiency of glass FRP (GFRP) rebars in increasing the shear strength of the test specimens retrofitted using conventional NSM technique. However, debonding of FRP bars impeded exploiting all retrofitting advantages and induced a premature shear failure. On the contrary, application of the proposed modified NSM (MNSM) technique was not only capable of preventing the premature debonding of FRP bars, but also could replace the failure mode of specimen from the brittle shear to a ductile flexural failure which is more desirable.
Weak amenability of the Lau product of Banach algebras defined by a Banach algebra morphism
Mohammad Ramezanpour 대한수학회 2017 대한수학회보 Vol.54 No.6
Let $A$ and $B$ be two Banach algebras and $T:B\to A$ be a bounded homomorphism, with $\|T\|\leq 1$. Recently, Dabhi, Jabbari and Haghnejad Azar (\textit{Acta Math. Sin. $($Engl. Ser.$)$} \textbf{31} (2015), no. 9, 1461--1474) obtained some results about the $n$-weak amenability of $A\times_T B$. In the present paper, we address a gap in the proof of these results and extend and improve them by discussing general necessary and sufficient conditions for $A\times_T B$ to be $n$-weakly amenable, for an integer $n\geq0$.