Unexpected formation of benzaldehydes by the reactions of dithioacetals derived from cinnamaldehydes with 2,3-dichloro-5,6-dicyano-p-benzoquinone in aqueous solvents

1,3-Dithianes 1 , 1,3-dithiolanes 2 , and diphenyl dithioacetals 3 derived from cinnamaldehydes reacted with 2,3-dichloro-5,6-dicyano-p-benzoquinone in aqueous solvents to give benzaldehydes 4 . Hydride transfer from 1–3 to 2,3-dichloro-5,6-dicyano-p-benzoquinone followed by hydrolysis and oxidative carbon-carbon bond cleavage would produce benzaldehydes 4 .     

Parallel preconditioned conjugate gradient algorithm on GPU

We propose a parallel implementation of the Preconditioned Conjugate Gradient algorithm on a GPU platform. The preconditioning matrix is an approximate inverse derived from the SSOR preconditioner. Used through sparse matrix–vector multiplication, the proposed preconditioner is well suited for the massively parallel GPU architecture. As compared to CPU implementation of the conjugate gradient algorithm, our GPU preconditioned conjugate gradient implementation is up to 10 times faster (8 times faster at worst).     

Thermoresponsive behavior of charged <Emphasis Type="Italic">N</Emphasis>-isopropylacrylamide-based hydrogels containing gold nanostructures

We report the synthesis of N-isopropylacrylamide-based hydrogels containing either an anionic (acrylic acid) or cationic ([2-(acryloyloxy)ethyl]trimethylammonium chloride) co-monomer. These hydrogels were cross-linked with a cleaveable (N,N′-cystaminebisacrylamide) and/or inert (N,N′-methylenebisacrylamide) molecule in four combinations. Gold nanostructures were then synthesized within these hydrogel matrices by in situ reduction of a metal ion precursor. The resulting eight nanocomposites and their non-gold-containing (native) analogs were characterized with several analytical methods. UV–visible and infrared spectroscopy revealed differences among the samples based largely on the concentration and identity of cross-linking agent. Equilibrium swelling masses and phase transition behavior point to differences among samples on charge of the hydrogel backbone, cross-linker type, and presence or absence of gold nanostructures. A molecular level explanation for these observations is described.     

Uzawa block relaxation domain decomposition method for a two-body frictionless contact problem

We propose a Uzawa block relaxation domain decomposition method for a two-body frictionless contact problem. We introduce auxiliary variables to separate subdomains representing linear elastic bodies. Applying a Uzawa block relaxation algorithm to the corresponding augmented Lagrangian functional yields a domain decomposition algorithm in which we have to solve two uncoupled linear elasticity subproblems in each iteration while the auxiliary variables are computed explicitly using Kuhn–Tucker optimality conditions.     

Photoformation of (Z)-Isomers in Diarylazomethines. Part IV. Direct and sensitized photoisomerization of pyridyl analogues of benzylidene-aniline and absorption spectra of their (Z)-isomers

UV irradiation of solutions of the (E)-isomers of five (out of the possible six) monopyridyl analogues at reduced temperatures results in extensive (80–90%) conversion into the corresponding (Z)-isomers. The process is reversible both thermally and photochemically. The (Z)-isomers are stable at temperatures below ?80°, and their absorption spectra were estimated. Biacetyl-photosensitized (E)(Z) isomerization was observed, with (Z)-contents of ca. 70% at the photo-stationary state.     

Parallel Uzawa Method for Large-Scale Minimization of Partially Separable Functions

A parallel Uzawa-type algorithm, for solving unconstrained minimization of large-scale partially separable functions, is presented. Using auxiliary unknowns, the unconstrained minimization problem is transformed into a (linearly) constrained minimization of a separable function.The augmented Lagrangian of this problem decomposes into a sum of partially separable augmented Lagrangian functions. To take advantage of this property, a Uzawa block relaxation is applied. In every iteration, unconstrained minimization subproblems are solved in parallel before updating Lagrange multipliers. Numerical experiments show that the speed-up factor gained using our algorithm is significant.     

Planarity, Symmetry and Counting Tilings

We axiomatize the geometrical properties of T-tetromino to what we call generalised k-T-tetromino. Using this set of axioms, we show that the number of tilings of a 2kn × 2km rectangular region is given by T(L _n,m ; 3, 3) if and only if the tile is a k-T-tetromino. This generalizes a result of Korn and Pak (Theor Comp Sci 319:3–27, 2004).