On Finite and Strong Convergence of a Proximal Method for Equilibrium Problems

We introduce the notions of conditioning and well-posedness for equilibrium problems. Using these concepts, we obtain finite and strong convergence results for the proximal method that improve, develop, and unify several theorems in optimization and nonlinear analysis.     

Well-behaved asymptotical convex-concave functions

Recently Auslender & Crouzeix introduced a well-behaved asymptotical notion for convex functions. The aim of this work is to extend this notion to the saddle case     

A partial complement method for approximating solutions of a primal dual fixed-point problem

We study the convergence of the Mann Iteration applied to the partial complement of a firmly nonexpansive operator with respect to a linear subspace of a Hilbert space. A new concept considered here. A regularized version is also proposed. Furthermore, to motivate this concept, some applications to robust regression procedures and location problems are proposed.     

Synthesis of purine-acridine hybrid molecules related to artificial endonucleases

In the course of a program devoted to the synthesis of artificial endonucleases, we have previously reported a series of hybrid molecules in which a purine is linked to an intercalating drug by a polyamino chain. These molecules recognize and cleave selectively abasic sites in DNA with very high efficiency. In order to get insight into the mechanism of recognition and cleavage, we have prepared a new series of molecules in which the purine is linked to an amino-acridine by an aliphatic chain containing amido or/and amino groups. The key intermediates are -halo-ω-amino polyaza which may be of general use as linkers in bioconjugate chemistry.     

The Synthesis of Natural Acetylenic Compounds from Stereum hirsutum

The regioselective synthesis of two new acetylenic compounds, sterehirsutinal ( 1 ) and sterehirsutinol ( 2 ), isolated recently from culture medium of the fungus Stereum hirsutum, is reported.     

Computational study of sulfur atom-transfer reactions from thiiranes to ER3 (E = As, P; R = CH3, Ph)

Computational estimates have been made for the P=S and As=S bond strengths in triphenylphosphine sulfide and triphenylarsine sulfide, on the basis of G3 calculations for the methyl analogues and isodesmic-exchange reactions. Also, with the performance of the G3 method level for related compounds taken into consideration, the best estimates are 82 and 68 kcal/mol, respectively. While the value for triphenylarsine sulfide is within 2 kcal/mol of the single experimental estimate, that for triphenylphosphine sulfide is lower by 6 kcal/mol. (Capps, K. B.; Wixmerten, B.; Bauer, A.; Hoff, C. D. Inorg. Chem. 1998, 37, 2861-2864.) Despite virtually identical electronegativities of P and As, it is found that there is greater charge separation in the P=S bond. It is found that S atom transfer from thiiranes to arsines is exothermic.     

A posteriori error estimator for finite volume methods

In this paper, first we discuss a technique to compare finite volume method and some well-known finite element methods, namely the dual mixed methods and nonconforming primal methods, for elliptic equations. These both equivalences are exploited to give us a posteriori error estimator for finite volume methods. This estimator is explicitly given, easy to compute and asymptotically exact without any regularity of the solution in unstructured grids.     

DISCONTINUOUS FINITE ELEMENT METHOD FOR CONVECTION-DIFFUSION EQUATIONS

1. IlltroductionThe finite element approximation of the convection--diffusin equations has been investigated using several different approaches (see e.g. [3] [4] and the references therein).Previous analysis in primal formulation of these problems was done for two types ofapproximation schemes: one which produces a continuous piecewise polynomial approximation and one which produces a piecewise polynomial approximation which arecontinuous for certain number of moments accross interelement edge…     

Synthesis of Unprecedented Sulfonylated Phosphono‐exo‐Glycals Designed as Inhibitors of the Three Mycobacterial Galactofuranose Processing Enzymes

This study reports a new methodology to synthesize exo‐glycals bearing both a sulfone and a phosphonate. This synthetic strategy provides a way to generate exo‐glycals displaying two electron‐withdrawing groups and was applied to eight different carbohydrates from the furanose and pyranose series. The Z/E configurations of these tetrasubstituted enol ethers could be ascertained using NMR spectroscopic techniques. Deprotection of an exo‐glycal followed by an UMP (uridine monophosphate) coupling generated two new UDP (uridine diphosphate)‐galactofuranose analogues. These two Z/E isomers were evaluated as inhibitors of UGM, GlfT1, and GlfT2, the three mycobacterial galactofuranose processing enzymes. Molecule 46‐(E) is the first characterized inhibitor of GlfT1 reported to date and was also found to efficiently inhibit UGM in a reversible manner. Interestingly, GlfT2 showed a better affinity for the (Z) isomer. The three enzymes studied in the present work are not only interesting because, mechanistically, they are still the topic of intense investigations, but also because they constitute very important targets for the development of novel antimycobacterial agents.     

Debenzylative Cycloetherification: An Overlooked Key Strategy for Complex Tetrahydrofuran Synthesis

Tetrahydrofuran (THF) is a major structural feature found in many synthetic and natural products displaying a variety of biological properties. This review summarizes the main synthetic approaches that have been developed to construct tetrahydrofuran moieties involving debenzylative cycloetherification reactions (DBCE). Interestingly, this reaction is regio‐ and stereoselective without the requirement of a selective protection/deprotection strategy. Many applications of this process have been reported, including carbafuranoside synthesis, regioselective deprotection of the benzyl group positioned γ to an alkene, and total synthesis of natural products. The stereochemical outcome and the mechanism of these interesting transformations are also discussed.