Convergence of interval-type algorithms for generalized fractional programming

The purpose of this paper is to analyze the convergence of interval-type algorithms for solving the generalized fractional program. They are characterized by an interval [LB _k , UB _k ] including*, and the length of the interval is reduced at each iteration. A closer analysis of the bounds LB _k and UB _k allows to modify slightly the best known interval-type algorithm NEWMODM accordingly to prove its convergence and derive convergence rates similar to those for a Dinkelbach-type algorithm MAXMODM under the same conditions. Numerical results in the linear case indicate that the modifications to get convergence results are not obtained at the expense of the numerical efficiency since the modified version BFII is as efficient as NEWMODM and more efficient than MAXMODM.This research was supported by NSERC (Grant A8312) and FCAR (Grant 0899).     

Synthesis of 3-formyltetronic acid and enamine derivatives

The first reported synthesis of 3-formyltetronic acid and its conversion to enamine derivatives is described. 3-Dimethylaminomethylene-2,4-dioxotetrahydrofuran derivatives were also prepared by treatment of tetronic acids with dimethylformamide diethyl acetal. Nmr spectral studies are included.     

(1-Adamantanethio)pyridines and tetrahydropyridines from the reaction of 1-adamantanethiol with pyridine I-oxide in acetic anhydride

The reaction of pyridine 1-oxide with 1-adamantanethiol in acetic anhydride produced a mixture of 2- and 3-(1-adamantanethio)pyridines, 1-aeetyl-2-(1-adamantanethio)-3-hydroxy-4-acetoxy-1,2,3,4-telrahydropyridine and the corresponding 3-acetoxyderivative. Pure substances were separated by means of column chromatography on alumina. The tetrahydropyridines were identified by means of their proton magnetic and mass spectra. 4-(1-Adamantanethio)pyridine was synthesized from 4-chloropyridinc and 1-adamantanethiol. The three isomeric (1-adamantanethio)-pyridines were, each, cleaved by concentrated hydrochloric acid to give 1-chloroadamantane and the corresponding pyridinethiol.     

Role of pyridine in the catalytic activation of sodium hypochlorite in the presence of manganese porphyrin

Steric and electronic influences of various substituted pyridines support the hypothesis of the coordination of pyridine in the manganese porphyrin-catalysed epoxidation of olefins with sodium hypochlorite solution.     

Calculation of Franck-Condon factors including anharmonicity: simulation of the C2H4+X2B3u<--C2H4X1A(g) band in the photoelectron spectrum of ethylene

Our new simple method for calculating accurate Franck-Condon factors including nondiagonal (i.e., mode-mode) anharmonic coupling is used to simulate the C2H4+X2B3u<--C2H4X1A(g) band in the photoelectron spectrum. An improved vibrational basis set truncation algorithm, which permits very efficient computations, is employed. Because the torsional mode is highly anharmonic it is separated from the other modes and treated exactly. All other modes are treated through the second-order perturbation theory. The perturbation-theory corrections are significant and lead to a good agreement with experiment, although the separability assumption for torsion causes the C2D4 results to be not as good as those for C2H4. A variational formulation to overcome this circumstance, and deal with large anharmonicities in general, is suggested.     

Peroxisome Proliferator-Activated Receptors target family landscape: A chemometrical approach to ligand selectivity based on protein binding site analysis

The Peroxisome Proliferator-Activated Receptors (PPARs) are nuclear receptors which over the last couple of years have been the focus of considerable research efforts aiming to identify compounds with well-defined selectivity profiles for the treatment of metabolic diseases. The ligand binding domains (LBD) of the three known PPAR subtypes exhibit between 60 and 70% sequence identity. To gain insight into the structural determinants of selectivity for the PPAR subtypes, a set of 13 crystal structures of PPAR LBD were classified, using the GRID/CPCA approach. As a result, nearly all of the crystal structures of each different PPAR subtype were found clustered in different regions of the CPCA score plots, and hydrophobic as well as steric interactions were identified as the major determinants of PPAR subtypes selectivity. Furthermore, interpretation of the GRID/CPCA model in structural terms led to the identification of LBD regions which could be targeted to improve the selectivity for a given PPAR subtype. Our findings are consistent with published structure-activity relationships for PPAR ligands as well as with site-directed mutagenesis results.