The Gaussian Free Field and SLE<Subscript>4</Subscript> on Doubly Connected Domains

The level lines of the Gaussian free field are known to be related to SLE₄. It is shown how this relation allows to define chordal SLE₄ processes on doubly connected domains, describing traces that are anchored on one of the two boundary components. The precise nature of the processes depends on the conformally invariant boundary conditions imposed on the second boundary component. Extensions of Schramm’s formula to doubly connected domains are given for the standard Dirichlet and Neumann conditions and a relation to first-exit problems for Brownian bridges is established. For the free field compactified at the self-dual radius, the extended symmetry leads to a class of conformally invariant boundary conditions parametrised by elements of SU(2). It is shown how to extend SLE₄ to this setting. This allows for a derivation of new passage probabilities à la Schramm that interpolate continuously from Dirichlet to Neumann conditions.     

Effect of Side Chains on Charge Transfer in Quaterthiophene-Naphthalene Diimide Based Donor-Bridge-Acceptor Dyads

We have probed the effect of side chains on the charge transfer dynamics in dyads containing quaterthiophene (QT) donor and naphthalene diimide (NDI) acceptor. The donor and the acceptor are covalently linked using a flexible linker. Four dyads (1–4) were synthesized with the quaterthiophene bearing hexyl side chain and the naphthalene diimide bearing hydrocarbon, fluorocarbon, branched or polar side chains. The UV-Vis spectra for these dyads showed the existence of a donor-acceptor complex. The time-resolved fluorescence (TRF) decay studies show a rapid quenching of fluorescence in all the dyads upon excitation of the donor. We found that the side chains on the NDI did not alter the quenching rates in solution.     

On Triangularizability of a Group of Operators

Let ${\mathcal{G}}$ be a group of invertible linear transformations on a finite-dimensional vector space over an algebraically closed field. We show that if ${\mathcal{G}=\mathcal{H}\vee\mathcal{K}}$ , where ${\mathcal{H}}$ is a normal subgroup consisting of singleton spectrum operators and ${\mathcal{K}}$ is a triangularizable subgroup, then ${\mathcal{G}}$ is triangularizable.     

An experimental and theoretical investigation of the regio- and stereoselectivity of the polar [3+2] cycloaddition of azomethine ylides to nitrostyrenes

The regio- and stereochemical polar [3+2] cycloaddition of the azomethine ylides, which were generated in situ by the reaction of isatin derivatives and proline, with trans-β-nitrostyrene and (E)-1-phenyl-2-nitropropene were studied using experimental and theoretical methods. In comparison with trans-β-nitrostyrene, when the reactions were performed with (E)-1-phenyl-2-nitropropene, a remarkable inversion in the regioselectively was observed. The regioselectivity of the reactions was investigated using global and local reactivity indices and frontier molecular orbital (FMO) analysis at the B3LYP/6-31G(d,p) level of theory. The effects of the electronic and steric factors on the regioselectivity of the reactions were discussed. The inspection of geometries and energetics of transition states revealed the importance of weak interactions in regioselectivity of the cycloaddition reactions.     

Palladium(II) acetate‐catalyzed reduction of imines to the corresponding amines by triethylsilane

Reduction of a variety of imine compounds with triethylsilane in the presence of catalytic amounts of palladium(II) acetate in ethanol resulted in the formation of the corresponding amines in excellent yields after short reaction times. Copyright © 2013 John Wiley & Sons, Ltd.     

Casimir energy–momentum tensor for curved boundaries in de Sitter space-time

In the present paper, we study Casimir effect for a conformally coupled scalar field propagating on background of \(4+1\)-dimensional de Sitter (dS) space-time. The field is supposed to obey Dirichlet boundary condition on two 4-dimensional curved boundaries. Technically, we accomplish our calculations using an indefinite field quantization scheme, which already has been successfully applied to the dS minimally coupled massless scalar field and the dS linear gravity to obtain a causal and fully covariant quantum field on dS space-time.     

Me3SiCl and Et3SiI‐promoted one‐pot synthesis of 1,4‐dihydropyridine derivatives

An efficient synthesis of 1,4‐dihydropyridine derivatives has been achieved by the one‐pot cyclocondensation reaction of methyl 3‐aminocrotonate and a range of aldehydes in the presence of chlorotrimethylsilane as a promoter under solvent‐free conditions. The cyclocondenstion reaction requires a very short time and takes place in good to excellent yields. Furthermore iodotriethylsilane, generated in situ by the reaction of triethylsilane and methyl iodide in the presence of palladium chloride, has been investigated for the synthesis of 1,4‐dihydropyridine derivatives. This facile and efficient method affords high yields for the preparation of 1,4‐dihydropyridines at room temperature and short reaction times. Copyright © 2009 John Wiley & Sons, Ltd.