Sequential and parallel synchronous alternating iterative methods

The so-called parallel multisplitting nonstationary iterative Model A was introduced by Bru, Elsner, and Neumann [Linear Algebra and its Applications 103:175-192 (1988)] for solving a nonsingular linear system Ax = b using a weak nonnegative multisplitting of the first type. In this paper new results are introduced when A is a monotone matrix using a weak nonnegative multisplitting of the second type and when A is a symmetric positive definite matrix using a P -regular multisplitting. Also, nonstationary alternating iterative methods are studied. Finally, combining Model A and alternating iterative methods, two new models of parallel multisplitting nonstationary iterations are introduced. When matrix A is monotone and the multisplittings are weak nonnegative of the first or of the second type, both models lead to convergent schemes. Also, when matrix A is symmetric positive definite and the multisplittings are P -regular, the schemes are also convergent.

Synthesis of Dihydroisobenzofurans via Palladium-Catalyzed Sequential Alkynylation/Annulation of 2-Bromobenzyl and 2-Chlorobenzyl Alcohols under Microwave Irradiation

The palladium-catalyzed synthesis of dihydroisobenzofurans has been performed by sequential Sonogashira cross-coupling/cyclization reactions between terminal alkynes and 2-(hydroxymethyl)bromo- and chlorobenzenes in methanol as solvent at 130 °C under microwave irradiation. A 4,4′-dichlorobenzophenone oxime-derived chloro-bridged palladacycle is an efficient pre-catalyst to perform this tandem process using 2-dicyclohexylphosphanyl-2′,4′,6′-triisopropylbiphenyl (Xphos) as ancillary ligand and potassium hydroxide as base in the absence of a copper cocatalyst. Under these conditions, functionalized 2-bromo- and 2-chlorobenzaldehydes are also suitable partners in the domino process affording phthalans in good yields. All the reactions can be performed under air and employing reagent-grade chemicals under low loading conditions (1 mol% Pd).

A Sequential Algorithm for the Rigorous Design of Thermally Coupled Distillation Sequences

A sequential design method is presented for the design of thermally coupled distillation sequences. The algorithm starts by selecting a set of sequences in the space of basic configurations in which the internal structure of condensers and reboilers is explicitly taken into account and extended with the possibility of including divided wall columns (DWC). This first stage is based on separation tasks (except by the DWCs) and therefore it does not provide an actual sequence of columns. In the second stage the best arrangement in N-1 actual columns is performed taking into account operability and mechanical constraints. Finally, for a set of candidate sequences the algorithm try to reduce the number of total columns by considering Kaibel columns, elimination of transfer blocks or columns with vertical partitions. An example illustrate the different steps of the sequential algorithm.