Suzuki-Miyaura cross-coupling reactions of halo derivatives of 4H-pyrido[1,2-a]pyrimidin-4-ones

The palladium-catalyzed Suzuki-Miyaura cross-coupling reactions of halo derivatives of 4H-pyrido[1,2-a]pyrimidin-4-one with (het)arylboronic acids allow easy access to (het)aryl and vinyl derivatives of this bicycle in good to excellent yields, even from chloro derivatives. The sequence of reactivity of the halogen in the different positions of the ring system was also investigated. 6-Phenyl-4H-pyrido[1,2-a]pyrimidin-4-one could be prepared by thermal cyclization of isopropylidene (6-phenylpyrid-2-ylamino)methylenemalonate, together with a small amount of 7-phenyl-1,4-dihydro-1,8-naphthyridin-4-one.     

Novel electrochemical deoxygenation reaction using diphenylphosphinates

The electrochemical reduction of diphenylphosphinate esters leads smoothly and in high yields to the corresponding deoxygenated products. In comparison with the previously developed methodologies, the electrolysis could be performed at lower temperature and with a higher current density, resulting in a shorter reaction time.     

Discrete maximum principles for FE solutions of nonstationary diffusion‐reaction problems with mixed boundary conditions

In this article, we derive and discuss sufficient conditions for providing validity of the discrete maximum principle for nonstationary diffusion‐reaction problems with mixed boundary conditions, solved by means of simplicial finite elements and the θ time discretization method. The theoretical analysis is supported by numerical experiments. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Unexpected preparation of (Z)-chloromethyleneketals and their sulfur analogues by a novel three-component condensation

A novel multicomponent condensation, leading to the rare (Z)-chloromethyleneketals and their sulfur analogues, has been discovered. The mechanism of this reaction has been studied in some detail and subsequent modifications were performed on the adducts, leading to unusual Umpolung transforms.     

Comparison of two regulatory results on functional equations with few parameters

Two methods to prove regularity properties of the linear functional equation $$f(x)=h_0(x,y)+\sum_{j=1}^n h_j(x,y)f(x+g_j(y)), $$ where ${(x,y) \in D \subset \mathbb{R}^r \times \mathbb{R}^s}$ , ${x \in \mathbb{R}^r}$ and ${y \in \mathbb{R}^s}$ , with few parameters i.e. allowing 1 ?? s < r are examined. It is proved that??under certain conditions, for some class of equations and in some sense??they are equivalent.     

On the regularization effect of space-time white noise on quasi-linear parabolic partial differential equations

Summary We show that an existence and uniqueness and a comparison theorem hold if we add a space time white noise to a quasi-linear parabolic equation in one space dimension, even if the nonlinearity is only measurable and not even locally bounded.Research supported by the Hungarian National Foundation of Scientific Research No. 2290. Université de Provence (Aix-Marseille I), Mathématiques Case 64, Place Victor Hugo, 13331 Marseille, Cedex 3 (for the academic year 1991/92)Partially supported by DRET under contract 901636/A000/DS/SR     

Combinatorial synthesis of carbon nanotubes by the catalytic chemical vapor deposition method

Summary Bimetallic (Fe-Co) catalyst samples prepared from different precursors over various supports were tested in carbon nanotube (CNT) production. In order to quicken the evaluation of the performance of the catalysts a combinatorial arrangement was used.</o:p>     

Approximation and support theorems in modulus spaces

Summary We prove an approximation theorem for stochastic differential equations, under rather weak smoothness conditions on the coefficients, when the driving semimartingales are approximated by continuous semimartingales, in probability, and the solutions are considered in several Banach spaces, defined in terms of different types of the modulus of continuity. Hence Stroock-Varadhan's support theorem is obtained in these spaces, in particular, in appropriate Besov and Hölder spaces.Partially supported by the Foundation of National Research n° 2290Partially supported by the DGICYT grant n^o PB 90-0452