Optimal L∞-error estimates for nonconforming and mixed finite element methods of lowest order

Summary For second order linear elliptic problems, it is proved that theP ₁-nonconforming finite element method has the sameL -asymptotic accuracy as theP ₁-conforming one. This result is applied to derive optimalL -error estimates for both the displacement and the stress fields of the lowest order Raviart-Thomas mixed finite element method, and a superconvergence result at the barycenter of each element.Performed in the research program of Istituto di Analisi Numerica of C.N.R. of PaviaPartially supported by MPI, GNIM of CNR, ItalySupported by Consejo Nacional de Investigaciones Cientificas y Técnicas, Argentina     

Improved activity in acidic media of immobilized lysozyme

Polyethylene glycols (PEGs) of various chain length were used to crosslink lysozyme onto an insoluble support such as oxirane. A very high degree of modification and no inactivation of lysozyme were obtained with PEG 20000, but enzymatic activity increased up to 20 times at pH 3.0, at which point the activity of the native enzyme was lower when using Leuconostok oenus as a macromolecular substrate.     

The transport of amino acids by 18-crown-6 through liquid membranes

The possibility of separating in cationic form some -amino acids (L-Methionine, L-Leucine, L-Isoleucine, L-Valine, L-Phenylalanine, L--Alanine and L-Cysteine) from mixtures in the presence of picrate anion has been investigated by means of active transport assisted by a pH gradient through liquid membranes. 18-Crown-6 in 1,2-dichloroethane has been used as a selective carrier. The effect of stirring rates at different volumes of the membrane, suggests a diffusional rate-limiting process of the amino acid transport.     

Asymptotics for thenth-degree Laguerre polynomial evaluated atn

Summary We investigate the asymptotic behaviour of _n (n),n where _n (x) denotes the Laguerre polynomial of degreen. Our results give a partial answer to the conjecture _n (n)>1 forn>6, made in 1984 by van Iseghem. We also show the connection between this conjecture and the continued fraction approximants of .Work sponsored by the Consiglio Nazionale delle Ricerche and by the Ministero dell'Università e della Ricerca Scientifica e Tecnologica of Italy     

Heterocyclic variants of the 1,5-benzodiazepine system. VIII. Reaction of 4(7)-aminobenzimidazole with ethyl 2-alkylmalonates

Reaction of 4(7)-aminobenzimidazole with ethyl 2-alkylmalonates gave the novel 4,5,6,7-tetrahydro-5-alkyl-imidazo[1,5,4-ef][1,5]benzodiazepine-4,6-diones, and the 2-alkyl-4(7)-(2′-ethoxycarbonyl)acetamido-benzimidazoles. The structure of all the products was corroborated by ir, mass spectrometry and ¹H-nmr.     

Expeditious synthesis of new 1,2,3-thiadiazoles and 1,2,3-selenadiazoles from 1,2-diaza-1,3-butadienes via Hurd-Mori-type reactions

Alpha-substituted hydrazones obtained from 1,2-diaza-1,3-butadienes and methylenic or methinic activated substrates gave rise to a wide range of cyclic compounds. In particular, in the presence of thionyl chloride as solvent-reagent, they were transformed into 1,2,3-thiadiazoles,(1) with selenium oxychloride in new 4-substituted 2,3-dihydro-1,2,3-selenadiazoles, while with selenium dioxide, they were transformed into 4-substituted 1,2,3-selenadiazoles. We have also examined the nucleophilic behavior of 1,2,3-thiadiazole 4a in the reaction with 1,2-diaza-1,3-butadienes that produced, under basic conditions, 4-hydrazono-1-(1,2,3-thiadiazolyl)pentane derivatives. This event represents an interesting example of stereoselective synthesis because it leads exclusively to the formation of the RR/SS racemic mixture. These latter compounds, treated with thionyl chloride, gave the corresponding 1,3-di-1,2,3-thiadiazolylpropane derivatives, while with sodium methoxide they afforded 1,2,3-thiadiazolyl-2-oxo-2,3-dihydro-1H-pyrrole systems.     

Light intensity effects on photoinduced charge separation parameters in a molecular triad based on an Iridium(III) bis(terpyridine) unit.

The effect of photon flux on the yield and lifetime of charge separation over the extreme components of a D-Ir-A triad, where D is a triphenyl amine electron donor, A is a naphthalene bis(imide) electron acceptor and Ir is an Ir(III) bis(terpyridine) complex, has been investigated. In usual laboratory conditions, with nanosecond and picosecond laser pulses in the 4-8 mJ range, biphotonic processes take place. Biphotonic products and their evolution can introduce complications in reaction mechanisms and their interpretation but can also drastically reduce the yield and the lifetime of the charge-separated state. In the present case, after discussion of several possible mechanisms, the process detrimental to charge separation is ascribed to absorption of a photon by the photogenerated charge-separated state D(+)-Ir-A(-).     

Sulle funzioni fortemente continue a valori in un gruppo topologico

In una nota del 1976 C. Constantinescu [2], fa osservare che per una misura μ, definita in un δ-anelloR, a valori in un gruppo topologico e non verificante la countable chain condition, i μ-atomi non sono identificati, come nel caso classico, da particolari elementi diR ma sono parti diR godenti di opportu vista è ripreso in [3] da A. B. d’Andrea e P. de Lucia per lo studio degli atomi di una funzione finitamente addittiva in un anello. Nella presente nota si fa vedere che (n. 2), dando un’opportuna definizione di insieme μ-atomico, un μ-atomo può sempre essere individuato da un elemento diR e si stabiliscono poi (n. 3) delle relazioni fra le funzioni fortemente continue e le funzioni prive di atomi. Nel n. 4, infine, sono dimostrate alcune proprietà delle funzioni a due valori.     

Variable strategy toward carbasugars and relatives. 6. Diastereoselective synthesis of 2-deoxy-2-amino-5a-carba-beta-L-mannopyranuronic acid and 2-deoxy-2-amino-5a-carba-beta-L-mannopyranose

Efficient, total syntheses of novel 2-deoxy-2-amino-5a-carba-beta-L-mannopyranuronic acid (1) and 2-deoxy-2-amino-5a-carba-beta-L-mannopyranose (2), a positional stereoisomer of validamine, have been achieved in 28% and 24% overall yields and in 12 steps and 13 steps, respectively, from 2-[(tert-butyldimethylsilyl)oxy]furan (3) and (2S)-2,3-O-isopropylideneglyceraldehyde N-benzyl imine (4) via two highly diastereoselective Mukaiyama aldol-related chemical maneuvers. The strategy, which furnishes the targeted carbasugars in enantiopure forms, allows for complete control of the configuration at all five contiguous stereocenters of the targets by utilizing the sole element of chirality present in the aldimine progenitor 4.