Algorithms for generalized fractional programming

A generalized fractional programming problem is specified as a nonlinear program where a nonlinear function defined as the maximum over several ratios of functions is to be minimized on a feasible domain of ⁿ . The purpose of this paper is to outline basic approaches and basic types of algorithms available to deal with this problem and to review their convergence analysis. The conclusion includes results and comments on the numerical efficiency of these algorithms.This research was supported by NSERC (grant A8312) and Cooperation franco-québécoise (projet 20-02-13). Paper presented at Workshop on Mathematical Programming Catholic University of Rio de Janeiro, Brazil, October 10–14, 1988.     

Sur les séries de Taylor et les transformations de Möbius

Given a non-empty closed subsetF of the unit circle |z|=1, and a Möbius transformationM(z) of the unit disc |z|1, such thatM(0)0, there exists a functionf(z) holomorphic in the unit disc,F being the singular set at the boundary, whose Taylor coefficients tend to zero while the Taylor coefficients off(M(z)), do not tend to zero.     

Structure, 31P and 13C chemical shift anisotrophy of (CH3)3P, (CH3)3PO, (CH3)3PS and (CH3)3PSe as determined by liquid crystal NMR spectroscopy

The ¹³P and ¹³C spectra of the triply ¹³C labelled molecules (CH₃)₃P, (CH₃)₃PO, (CH₃)₃PS and (CH₃)₃PSe oriented in a nematic phase are reported. The CPC bond angles have been measured. The ¹³P chemical shift tensor shows a large anisotropy except in the case of (CH₃)₃P. The abnormal large value observed for the PSe bond length suggests a large anisotropy of the ¹J(PSe) spin coupling.     

Acylation des β-énaminoesters: Regio et stéréoformation des β-énaminoesters N- ou C-acylés

The reaction of acyl chlorides with cyclic five-membered β-enaminoesters gave exclusively N-acylated products while reaction of acyl chlorides with cyclic seven-membered β-enaminoesters gave only C-acylated products. In the case of cyclic six-membered β-enaminoesters, the reaction of acyl chlorides gave a mixture of N-acylated and C-acylated products.     

Use of gel-permeation chromatography in the determination of the composition of two-polymer mixtures

The possibility of evaluating with acceptable accuracy the composition of a two-polymer mixture which is well separated by GPC, was studied by using mixtures of high molecular weight polybutadiene (M?_w = 4.5 × 10⁵) and low molecular weight polyiso-butylene (M?_n in the range of 10³). It was concluded that a satisfactory evaluation of the composition of a polymer mixture can be achieved, provided that the variations of the refractive index with the molecular weight are taken into account for the low molecular weight polymer (the polyisobutylene).     

An Efficient Strategy to Orthogonally Protected (R)- and (S)-alpha-Methyl(alkyl)serine-Containing Peptides via a Novel Azlactone/Oxazoline Interconversion Reaction

A novel strategy for the synthesis of (R)- and (S)-alpha-methyl(alkyl)serine-containing peptides is presented. Using (S)-phenylalanine cyclohexylamide 6 as chiral auxiliary, the optically pure azlactones (R)- and (S)-2 were synthesized via a novel azlactone/oxazoline interconversion reaction (Figures 3 and 6). These azlactones constitute fully protected and activated synthetic equivalents of (R)- and (S)-alpha-methylserine and can be directly incorporated into peptides without further protective group manipulations. Like other alpha,alpha-dialkylated glycines, optically pure alpha-alkylserines can be used to stabilize beta-turn and alpha-helical conformations in short peptides.     

Improved access to 19-nor-7β, 8β-methylene-taxoids and formation of a 7-membered C-ring analog of doxetaxel by electrochemistry

A new route to semisynthetic 19-nor-7β, 8β-methylene taxoids, such as compound 8, from the 7-O-trifluoromethanesulfonyl derivative 6 is reported. Evidence for a dissociation of the triflate to form a carbocation at C-7 under the reaction conditions is presented. Electrochemical reduction of the cyclopropane taxoid 8 gives, besides the expected 10-dehydroxy-cyclopropane analog 10, the 7-membered C-ring derivative 11.     

Total synthesis of phytoprostane F1 and its 16 epimer

The first synthesis of the two enantiomers of phytoprostane F₁ methyl ester 1 and 2 is described using the syn-anti-syn alcoxy ester 3 as starting material.     

Octasubstituted metal-free phthalocyanine as core of phosphorus dendrimers: a probe for the properties of the internal structure

The synthesis of a new family of phosphorus dendrimers built from an octasubstituted metal-free phthalocyanine core is described up to generation 5. This core is used as a sensor and a probe for analyzing the properties of the internal structure and the influence of each structural part (core, branches, surface) upon the whole structure. UV-visible spectra show both a hyperchromic and bathochromic effect on the Q-bands with increasing generation, indicating that the chromophore is more isolated, and that the dendritic shell mimics a highly polar solvent. There is no evidence for aggregation, except for generation 0, showing again the isolation of the core. However, the dendritic shell is permeable to aqueous acids and bases, as demonstrated by the reversible splitting of the Q-band in an acidic medium (neutral form of the phthalocyanine) and the single Q-band in a basic medium (dianionic form), even for generation 4. The fluorescence quantum yield for the neutral form increases with increasing generation. The dianionic form of generation 0 is poorly fluorescent, whereas generations 3 and 4 (G3 and G4) exhibit better fluorescence. The cores of G3 and G4 are highly sensitive optical sensors for H3O+ and OH-. These experiments are carried out in THF/water mixtures, and the influence of water on the structure has been checked. The hydrodynamic radius of generation 4 is measured by NMR diffusion (pulse gradient spin-echo) experiments. R(H) varies from 35.4 A at 4 mol % of water to 32.5 A at 64 mol % of water in THF, indicating the hydrophobic nature of these dendrimers.     

Phosphorus-Containing Dendrimers: Synthesis and Properties

Several series of phosphorus-containing dendrimers have been designed to study the variation of their properties, depending on the type, the location (surface, branches, core, and cavities), and the number of functions implied.