Conjugate points at infinity in infinite dimensional teichmüller spaces

We show in this article that there exists conjugate points at infinity in infinite dimensional Teichmüller spaces.     

Sobolev H1 geometry of the symplectomorphism group

For a closed symplectic manifold $(M,\omega )$ with compatible Riemannian metric g we study the Sobolev $H^1$ geometry of the group of all $H^s$ diffeomorphisms on M which preserve the symplectic structure. We show that, for sufficiently large s, the $H^1$ metric admits globally defined geodesics and the corresponding exponential map is a non-linear Fredholm map of index zero. Finally, we show that the $H^1$ metric carries conjugate points via some simple examples.     

Recent advances in asymmetric reactions catalyzed by chiral phosphoric acids

The very recent advances in chiral phosphoric acids (CPAs) catalyzed asymmetric reactions are discussed.     

On duality concepts in fractional programming

The paper (Part I) describes an approach to duality in fractional programming on the basis of another kind of conjugate functions. The connections to some duality concepts (the Lagrange-duality and duality concepts of Craven and Schaible) are investigated and some new proofs of strong duality theorems are given.     

Kinetic Investigation of Poly(ethylene glycol) Hydrogel Formation via Perfusion‐Based Frontal Photopolymerization: Influence of Free‐Radical Polymerization Conditions on Frontal Velocity and Swelling Gradients

Poly(ethylene glycol) diacrylate (PEGDA) hydrogels are extensively used as scaffolds in tissue engineering. The ability to spatially control hydrogel properties is critical for designing scaffolds that direct cell behavior and tissue regeneration. To this end, we have recently developed a polymerization technique, perfusion‐based frontal photopolymerization, to generate tunable gradients in PEG hydrogels. This study explores the effects of polymerization conditions on the velocity of the propagating front and its influence on gradients in hydrogel swelling. Alterations in photoinitiator perfusion rate result in the largest variations in frontal velocity and in the magnitude of the swelling gradient among all polymerization conditions investigated.

     

Conjugate Addition of a Silyl Ketene Acetal to α,β‐Unsaturated Lactones

Abstract

Conjugate addition of a silyl ketene acetal [Me₂C?C (OMe)OSiMe₃] to α,β‐unsaturated lactones (namely, 5,6‐dihydro‐2H‐pyran‐2‐one, 2(5H)‐furanone as Michael acceptor) occurs efficiently at room temperature in the presence of a nucleophilic catalyst, tetra‐n‐butyl ammonium bibenzoate (TBABB), in THF as well as Lewis acid catalysts such as Yb(OTf)₃ and I₂ in CH₂Cl₂, giving the corresponding 1,4‐adducts in excellent yields.     

Asymmetric syntheses of dihydroxyhomoprolines via doubly diastereoselective lithium amide conjugate addition reactions

The asymmetric syntheses of novel dihydroxyhomoprolines have been achieved using the doubly diastereoselective conjugate additions of the antipodes of lithium N-benzyl-N-(α-methylbenzyl)amide to a set of four chiral α,β-unsaturated esters (derived from d-pentoses) as one of the key steps. A full account of the diastereoselectivity observed in these conjugate additions is presented and the stereochemical outcomes of these reactions have been established unambiguously via a combination of hydrogenolytic chemical correlation and single crystal X-ray diffraction analyses. A tandem hydrogenolysis/intramolecular reductive amination reaction was then used to create the corresponding enantiopure pyrrolidines, providing access to (2′S,3′S,4′R)-dihydroxyhomoproline and (2′S,3′R,4′S)-dihydroxyhomoproline after deprotection.     

Palladium(II)-catalyzed tandem annulation reaction of o-alkynylbenzoates with methyl vinyl ketone for the synthesis of isocoumarins

A palladium(II)-catalyzed highly regioselective tandem reactions of o-alkynylbenzoates with methyl vinyl ketone for the synthesis of isocoumarins was developed. It is a convenient, mild and environmentally benign reaction with moderate to high yield. The reaction is initiated by the Pd(II) species and regenerate the Pd(II) species to complete the catalytic cycle without the necessity of a redox system.     

CONJUGATE ADDITION OF AMINES TO SUGAR DERIVED OLEFINIC ESTERS: SYNTHESIS OF GLYCOSYLATED AMINO ESTERS AS DNA TOPOISOMERASE-II INHIBITORS

Conjugate addition of amines to olefinic esters derived from sugars leading to formation of glycosylated amino esters in a stereoselective manner is described. Some of the synthesized compounds possess DNA topoisomerase-II enzyme inhibitory activities at low concentrations.     

Odorless Preparation of Thioglycosides and Thio‐Michael Adducts of Carbohydrate Derivatives

A general, odorless, one‐pot methodology has been developed for the preparation of 1,2‐trans‐thioglycosides and thio‐Michael addition products of carbohydrate derivatives through triphenyl phosphine‐mediated cleavage of disulfides and reaction of the thiolate formed in situ with glycosyl bromides and glycosyl conjugated alkenes.