An algorithm for solving linear Volterra integro-differential equations

An efficient numerical procedure for solving linear second order Volterra integro-differential equations is presented herein. The scheme is based on B-spline collocation and cubature formulas. Analysis is accompanied by numerical examples. Results confirm reliability and efficiency of the proposed algorithm.     

Arithmétique fonctorielle des topologies de Grothendieck

Riassunto Il punto di partenza di questo lavoro è l'interpretazione delle topologie di Grothendieck nel linguaggio dei sistemi relazionali (cfr. [5]); ciò permette uno studio aritmetico di tali topologie. Attraverso nuove tecniche, qui introdotte, si ottengono risultati non privi di interesse, tra i quali una caratterizzazione degli spazi topologici noetheriani, ed ulteriori strutture topologiche di tipo locale (siti tangenti), per le quali vengono dimostrate numerose proprietà. Vengono, infine, date alcune applicazioni alla teoria degli schemi, utilizzando il funtore inviluppo affine.

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Summary The starting point of this paper is the interpretation of Grothendieck's topologies in the language of relational systems (cfr. [5]); this permits an arithmetical study of these topologies. By applying new techniques introduced here, we have achieved interesting results. These include a new characterization of Noetherian topological spaces, and further topological structures of local type (tangent sites) for which we have shown numerous properties. Finally, we have used the affine-envelope functor to illustrate some applications to the theory of schemes.

     

A Numerical Algorithm for Cubature by Bivariate Splines on Nonuniform Partitions

We have studied the numerical integration 2D based on bivariate C ¹ local polynomial splines with a criss–cross triangulation of nonuniform rectangular partition. We have constructed the cubature formula and proved the convergence properties and error bounds. The paper includes some numerical tests that illustrate the performance of the corresponding algorithm. In the appendix there are explicit expressions of the quadratic polynomial restrictions of the B-splines related to every triangular cell.     

Green synthesis and antibacterial activity of chalcogenoesters

Herein, we present a new variation for an eco-friendly methodology for the synthesis of chalcogenoester in good-to-excellent yields in a short time, with an easy work-up/purification step, and in a greenest methodology, affording the minimum generation of solid and liquid waste, in comparison to that described in the literature. Additionally, some selected compounds were evaluated as antimicrobial agents, showing moderate activity against a variety of microorganisms including the K. pneumoniae, P. aeruginosa and also some selected fish pathogenic bacteria.     

Methyl 4-Carbomethoxy-3-Hydroxy-5-Methyl-Phenyl-Acetoacetate from the Disilylated Dianion of Methyl Acetoacetate

Recently, Chaley and Chan¹ reported a novel synthesis of methyl olivetolate (3a) from the annelation of 1,3-bis(trimethylsiloxy)-1-methoxybuta-1,3-diene (1) with the acid chloride 2a and titanium tetrachloride at room temperature. In view of their success, we attempted to apply this methodology for a convenient synthesis of isotopically labelled orsellinic acid in order to unravel its biosynthesis to cyclopentanoids.     

Thermotropic liquid crystalline polymers with low thermal transitions. II. Low melting thermotropic liquid crystalline homo- and co-polyesters

Thermotropic liquid crystalline (TLC) polymers with low melt transitions are useful for imaging technologies. This is the first report describing thermotropic liquid crystalline copolyesters of low melt transitions comprised of a mesogen with up to three different spacer moieties. We have noted that the smectic mesophase range decreased with increasing amounts of different spacer moieties, without altering the isotropic transition and thereby leading to a broader nematic range. © 1995 John Wiley & Sons, Inc.     

Synthesis of 4-substituted glutarimides by free radical addition of iodoacetamide to α,β-unsaturated esters

Free radical addition of either methyl bromoacetate or iodoacetamide to an α,β,-unsaturated ester gave the 4-substituted glutarate or glutarimide respectively, whereas the radical cyclisation of N-bromoacetyl crotonamide gave the 2-substituted succinimide.