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).     

X-ray structure and UV spectroscopic studies of (adenmato-N9)triethylphosphinegold(I)

The preparation, characterization, and X-ray structure analysis of (adeninatoN9)triethylphosphinegold(I) is reported. The crystal structure consists of discrete molecules, the adeninate anion coordinates via the N(9) atom with a Au-N(9) bond distance of 2.057(5) Å and the linear geometry about the Au atom is completed by the P atom of a disordered Et₃P ligand; the Au-P(1) bond distance is 2.238(2) Å and the N(9)-Au-P(1) bond angle is 178.8(2)°. The crystals are orthorhombic, space groupPbca, with unit cell dimensionsa=8.528(1),b=17.797(3),c=18.526(2) Å andZ=8. The structure was refined by a full-matrix least-squares procedure to finalR=0.030 andR _w =0.033 for 1749 reflections withI>2.5a(I). The electronic spectrum of the complex dissolved in water in the near ultraviolet is consistent with essentially separate -electron systems of the adenine and phosphinegold moieties; a conclusion which corroborates the X-ray structural results.     

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.     

The search for a new model structure of β-Factor XIIa

We present the search for a new model of -factor XIIa, a blood coagulation enzyme, with an unknown experimental 3D-structure. We decided to build not one but three different models using different homologous proteins as well as different techniques and different modellers. Additional studies, including extensive molecular dynamics simulations on the solvated state, allowed us to draw several conclusions concerning homology modelling, in general, and -factor XIIa, in particular.