Syntheses of Theaspirone and Vitispirane via Palladium(II)-Catalyzed Oxaspirocyclization

Total syntheses of theaspirone (A and B) and vitispirane (A and B) are described. The key step in the syntheses is the palladium(II)-catalyzed intramolecular oxaspirocyclization of diene alcohol 4 to either vitispirane or the allylic alcohol 9. The outcome of the oxaspirocyclization is very much dependent on the solvent employed. In water-acetic acid (4:1) a 1:1 mixture of the diastereomeric alcohols 9A and 9B was exclusively formed. In water with 8 equiv of a strong non-nucleophilic acid, vitispiranes A and B (1:1) were obtained. An alternative procedure to obtain vitispirane with the use of LiCl and K(2)CO(3) is described. In the latter reaction vitispirane B is formed preferentially. This result is explained by an equilibrium between the two possible pi-allyl complexes 5A and 5B, the kinetically favored 5B being transformed into vitispirane 3B before isomerization to 5A occurs.     

Synthesis, Conformational Studies, X-ray Structures, and Complexation Properties of Semirigid Macrocyclic Phosphonamides

The semirigid phosphonamide ligands 1-5 have been synthesized from the macrocyclic precursors 6-9 by reaction with 1,3-propanediol ditosylate or 1,2-dichloroethane. For the thiophosphoryl compounds 1 and 2, and the phosphoryl derivative 5, the reactions were carried out in biphasic aqueous NaOH solutions. The phosphoryl derivatives 3 and 4 were better obtained from NaH in anhydrous tetrahydrofuran. The conformations of the hosts in solution were deduced from low-temperature NMR and NOE difference experiments. Conformational equilibria between exo and endo forms are observed for the 18-membered macrocycles 1 and 3. The exo conformer predominates in solution for the 21-membered macrocycle 2, whereas 4 exists as rapidly exchanging conformers. The X-ray crystal structures of macrocycles 1, 2, and 5 have been determined as well as the complexes 1.Hg(SCN)(2) and 5.LiNO(3). In the Hg(2+) complex the metal ion is located out of the macrocyclic cavity and is coordinated to the thiophosphoryl unit. In 5.LiNO(3)()()the Li(+) cation is located inside the macrocyclic cavity and is coordinated to a tetrahedral array of oxygen donors. Free energies of complexation (DeltaG degrees ) of the phosphorylated ligands 3-5 with alkali metal and ammonium cations were determined in CHCl(3) saturated with H(2)O by picrate extraction experiments. The -DeltaG degrees values are greatest for 4 complexing K(+) and NH(4)(+) (7.3 and 8.0 kcal/mol, respectively). The relationships between structure and binding are discussed.     

Crystallographic evidence of hexacoordination at phosphorus via intramolecular coordination of donor groups on phosphane and phosphane sulphide

The X-ray structure analysis of bis(8-dimethylamino-l-naphthyl)phenylphosphane (3) and of the corresponding sulphide 4 has revealed hexacoordination at phosphorus in both cases, the N … P separations being less than the sum of the van der Waal radii. Furthermore, in both cases the overall geometry corresponds to a distorted bicapped tetrahedron. The optimum geometry calculated for 4 via the program developed by Autodesk (MM + method) suggests that the structure of the molecule is a function not only of steric requirements but also of electronic effects.     

Enantioseparation of chiral N-imidazole derivatives by electrokinetic chromatography using highly sulfated cyclodextrins: mechanism of enantioselective recognition

Baseline separation of ten new substituted [1-(imidazo-1-yl)-1-phenylmethyl)] benzothiazolinone and benzoxazolinone derivatives, with one chiral center, was achieved by CD-EKC using highly sulfated CDs (alpha, beta, gamma highly S-CDs) as chiral selectors. The influence of the type and concentration of the chiral selectors on the enantioseparations was investigated. The highly S-CDs exhibit a very high enantioselectivity power since they allow excellent enantiomeric resolutions compared to those obtained with the neutral CDs. The enantiomers were resolved with analysis times inferior to 2.5 min and resolution factors R(s) of 3.73, 3.90, 1.40, and 4.35 for compounds 1, 2, 3, and 5, respectively, using 25 mM phosphate buffer at pH 2.5 containing either highly S-alpha-CD, highly S-beta-CD, and highly S-gamma-CD (3 or 4% w/v) at 298 K, with an applied field of 0.30 kV/cm. The determination of the enantiomer migration order for the various analytes and the study of the analyte structure-enantioseparation relationships display the high contribution of the interactions between the analytes phenyl ring and the CDs to the enantiorecognition process. The thermodynamic study of the analyte-CD affinities permits us to improve our knowledge about the enantioseparation mechanism.     

Critical duality

We look for a general framework in which the Ekeland duality can be formulated. We propose a scheme in which the parameter sets are provided with a coupling function which induces a conjugacy. The decision spaces are not supposed to have any special structure. We examine several examples. In particular, we consider some special classes of generalized convex functions.     

Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems

Numerous planning problems can be formulated as multi-stage stochastic programs and many possess key discrete (integer) decision variables in one or more of the stages. Progressive hedging (PH) is a scenario-based decomposition technique that can be leveraged to solve such problems. Originally devised for problems possessing only continuous variables, PH has been successfully applied as a heuristic to solve multi-stage stochastic programs with integer variables. However, a variety of critical issues arise in practice when implementing PH for the discrete case, especially in the context of very difficult or large-scale mixed-integer problems. Failure to address these issues properly results in either non-convergence of the heuristic or unacceptably long run-times. We investigate these issues and describe algorithmic innovations in the context of a broad class of scenario-based resource allocation problem in which decision variables represent resources available at a cost and constraints enforce the need for sufficient combinations of resources. The necessity and efficacy of our techniques is empirically assessed on a two-stage stochastic network flow problem with integer variables in both stages.     

Genericity of Well-Posedness, Perturbations and Smooth Variational Principles

We show that three important topics in nonlinear analysis and optimization are intimately related: the theory of perturbations, the notion of well-posedness and variational principles in the sense of Ekeland, Borwein–Preiss and Deville–Godefroy–Zizler. The concept of genericity and the new notion of flexible perturbation play a key role in these connections. This notion enables one to consider topologies on spaces of functions which have been introduced recently. A link between the Asplund and Ekeland–Lebourg methods and the Palais–Smale condition, another important topic in nonlinear analysis, is pointed out.     

Embedding of Biological Regulatory Networks and Property Preservation

In the course of understanding biological regulatory networks (BRN), scientists usually start by studying small BRNs that they believe to be of particular importance to represent a biological function, and then, embed them in a larger network. Such a reduction can lead to neglect relevant regulations and to study a network whose properties can be very different from the properties of this network viewed as a part of the whole. In this paper we study, from a logical point of view, on which conditions concerning both networks, properties can be inherited by BRNs from sub-BRNs. We give some conditions on the nature of the network embeddings ensuring that dynamic properties on the embedded sub-BRNs are preserved at the level of the whole BRN.