in this study, aluminosilicate mcm-41 has been found to be an efficient catalyst for reaction betweendifferent benzaldehyde derivatives and 5,5-dimethyl-1,3-cyclohexanedione to give open chain analogue of1,8-dioxo-octahydroxanthene in excellent yields. no evidence for the formation of cyclization products wasobserved. the catalyst can be used several times after recovery.

Abstract We study the thermodynamics and criticality of su( m | n ) Haldane–Shastry chain BC N type with a general chemical potential term. first derive complete description spectrum this model in terms -type motifs, from which we deduce representation for partition function as trace product site-dependent transfer matrices. In thermodynamic limit, formula yields simple expression free energy p...