A Dual Photoredox- and Cp2TiCl2-Catalyzed Approach for the Direct Access to α-Vinyl-β-hydroxy Esters

For the first time, a dual photoredox- and titanocene-catalyzed methodology for the regioselective access to α-vinyl-β-hydroxy esters towards aldehyde allylation with 4-bromobut-2-enoate is reported. The protocol is based on the Barbier-type properties of the inexpensive and available Cp₂TiCl₂ in catalytic amount (5 mol%). The developed mild reaction conditions gave access to a library of differently functionalized α-vinyl-β-hydroxy esters in moderate diastereoselectivity, employing the commercially available ethyl 4-bromobut-2-enoate and both aromatic and aliphatic aldehydes. The reaction was realized under visible light irradiation, in the presence of an organophotocatalyst (3DPAFIPN, 2 mol%) combined with Hantzsch's ester as the sacrificial reductant. In contrast to other Barbier-type reactions employing ethyl 4-bromobut-2-enoate, the photoredox system ensures a better regioselectivity. Moreover, the use of preformed organometallic nucleophilic species (e. g., dienolborinates), and the need of metal reductants or stoichiometric amount of transition metals in low oxidation state for Barbier-type reactions, is avoided. To support the experimental evidence, a detailed photophysical study shed light on the mechanism of the reaction.     

New solvable dynamical systems

New solvable dynamical systems are identified and the properties of their solutions are tersely discussed.     

Dynamics of Robertson–Walker spacetimes with diffusion

We study the dynamics of spatially homogeneous and isotropic spacetimes containing a fluid undergoing microscopic velocity diffusion in a cosmological scalar field. After deriving a few exact solutions of the equations, we continue by analyzing the qualitative behavior of general solutions. To this purpose we recast the equations in the form of a two dimensional dynamical system and perform a global analysis of the flow. Among the admissible behaviors, we find solutions that are asymptotically de-Sitter both in the past and future time directions and which undergo accelerated expansion at all times.     

THE CRYSTAL AND MOLECULAR STRUCTURE OF THE POTENTIAL ANTIBACTERIAL AGENT 2-PYRIDYL-PHENYL SULPHONE

Abstract

Crystals of 2-pyridyl-phenyl sulphone are monoclinic, space group P2₁/c, with eight molecules in the unit cell of dimensions a = 11.781, b = 5.903, c = 29.748 Å and B = 94.13°. The dihedral angles between the best planes of the two aromatic rings are significantly different in two crystallographically independent molecules (88.4° and 71.9° for molecule A and molecule B, respectively), as well as those between the CSC plane and the pyridine ring (59.4° and 67.4°) and between the CSC plane and the phenyl ring (51.7° and 81.8°). The average bond distances of interest include C?S 1.77(1) and S?O 1.44(1) Å; among the bond angles there are CSO = 108.1(7), CSC = 105.0(6) and OSO = 118.7(6)°. The packing of the molecule in the crystal is determined by the van der Waals interactions and by two intermolecular H?O contacts of 2.43 and 2.49 Å. The observed conformation in the solid state agrees well with results of previous investigations, in the solution state, by means of dipole moment method and theoretical M.O. calculations, for the analogous di-2-pyridyl sulphone.     

<Emphasis Type="Italic">ϕ</Emphasis>-pairs and common fixed points in cone metric spaces

In this paper we introduce a contractive condition, called ϕ-pair, for two mappings in the framework of cone metric spaces and we prove a theorem which assures existence and uniqueness of common fixed points for ϕ-pairs. Also we obtain a result on points of coincidence. These results extend and generalize well-known comparable results in the literature. The authors are supported by Università degli Studi di Palermo, R. S. ex 60%.     

Best proximity points for cyclic Meir–Keeler contractions

We introduce a notion of cyclic Meir–Keeler contractions and prove a theorem which assures the existence and uniqueness of a best proximity point for cyclic Meir–Keeler contractions. This theorem is a generalization of a recent result due to Eldred and Veeramani.