Extendible elements of the alternating groups

An element σ of A_n, the Alternating group of degree n, is extendible in S_n, the Symmetric group of degree n, if there exists a subgroup H of S_n but not A_n whose intersection with A_n is the cyclic group generated by σ. A simple number-theoretic criterion, in terms of the cycle-decomposition, for an element of A_n to be extendible in S_n is given here.     

Tracking poles and representing Hankel operators directly from data

Summary We propose and analyse a method of estimating the poles near the unit circleT of a functionG whose values are given at a grid of points onT: we give an algorithm for performing this estimation and prove a convergence theorem. The method is to identify the phase for an estimate by considering the peaks of the absolute value ofG onT, and then to estimate the modulus by seeking a bestL ² fit toG over a small arc by a first order rational function. These pole estimates lead to the construction of a basis ofL ² which is well suited to the numerical representation of the Hankel operator with symbolG and thereby to the numerical solution of the Nehari problem (computing the bestH , analytic, approximation toG relative to theL norm), as analysed in [HY]. We present the results of numerical tests of these algorithms.Partially supported by grants from the AFOSR and NSF     

The synthesis of 1,4-diazacycl[3,2,2]azine

The diazaanalog of “cycl[3,2,2]azine”, “1,4-diazacycl[3,2,2]azine” (1,4,7b-triazacyclopent-[cd]indene) and its 2-methyl derivative were prepared. These compounds are subject to facile acid-catalyzed hydrolysis affording substituted imidazo[1,2-a]pyridines.     

Complex II from a structural perspective

The super-macromolecular complex, succinate:quinone oxidoreductase (SQR, Complex II, succinate dehydrogenase) couples the oxidation of succinate in the matrix / cytoplasm to the reduction of quinone in the membrane. This function directly connects the Krebs cycle and the aerobic respiratory chain. Until the recent first report of the structure of SQR from Escherichia coli (E. coli) the structure-function relationships in SQR have been inferred from the structures of the homologous QFR, which catalyses the same reaction in the opposite direction. The structure of SQR from E. coli, analogous to the mitochondrial respiratory Complex II, has provided new insight into SQR's molecular design and mechanism, revealing the electron transport pathway through the enzyme. Comparison of the structures of SQR, QFR and other related flavoproteins shows how common amino acid residues at the interface of two domains facilitate the inter-conversion of succinate and fumarate. Additionally, the structure has provided a possible explanation as to why certain organisms utilise both SQR and QFR despite the fact that both can catalyse the inter-conversion of succinate and fumarate, in vitro and in vivo. Here we review how this structure has advanced our knowledge of this important enzyme and compare the structural information to other members of the Complex II superfamily and related flavoproteins.