Spazi di Sobolev con peso e problemi ellittici in un angolo. (I)

Summary This work, which consists of three parts, is concerned with boundary value problems for linear partial differential equations of elliptic type in a plane sector. They have been investigated within suitable Sobolev weight spaces. In this first part of the work Sobolev weight spaces are studied. Duality, embedding and trace theorems have been proved.

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Lavoro eseguito con contributo del C.N.R. nell'ambito del Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni.

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Entrato in Redazione il 28 novembre 1972.     

Near varieties of idempotent generated completely simple semigroups

Algebra universalis - Completely simple semigroups form a variety if we consider them as algebras with multiplication and inversion. A near variety of idempotent generated completely simple...     

Solute-Solvent interactions in water-rich mixtures. II. Ionic conductances in water-dimethylsulfoxide mixtures at 25°C

Conductances of sodium bromide, iodide, and perchlorate, potassium chloride, and tetraphenylboride (BPh ₄ ^– ) as well as triisoamyl-n-butylammonium iodide (i-Am₃BuNI) have been measured in aqueous mixtures containing up to 20 mole percent dimethylsulfoxide (DMSO) at 25°C. Experimental data were analyzed by the 1965 Fuoss-Onsager-Skinner (FOS) equation. Single-ion limiting equivalent conductances were calculated by assuming that ₀ (i–Am ₃ BuN ⁺=₀ (BPh ₄ ^– ). The variations of the limiting ionic Walden products are discussed on the basis of acid-base type interactions for cations, and on the basis of structural effects for anions.     

Second-order optical nonlinearity in bulk PbO/B2O3 glass

By investigating the second-harmonic generation (SHG) of the bulk PbO/B₂O₃ glass samples with different compositions after thermal poling, it was found that there was an optimal poling temperature for each sample with different compositions and there was also a relation between optimal poling temperature and glass transition temperature. At their own optimal poling temperatures, the samples had different frequency doubling efficiencies with the same applied voltage. We also found that the frequency doubling efficiency of PbO/B₂O₃ glass increased with the increase of poling voltage. An induced dipole model was proposed to explain the super-quadratic relation between the SHG intensity and the poling voltage.     

Synthesis of 4-acyl-2,3-dihydro-4H-1,4-oxazines

The synthesis of 4-acyl-2,3-dihydro-4H-1,4-oxazines ( 6a-h ) via acid dehydration of 4-acyl 2- and 3-morpholinols is described. During dehydration of 2-morpholinols 3d,e , N-alkylisoquinolones 7a-e were also isolated.     

A convenient one-pot procedure for the selective reduction of ketones in the presence of aldehydes

The title process has been accomplished by a three-step sequence involving protection of aldehyde as the imine, $\text{in situ}$ reduction of ketone with lithium tri-$\text{tert}$-butoxyaluminohydride, and regeneration of aldehyde on hydrolytic work-up.     

Comparative borazarobenzenes calculations following different methods

Borazarobenzenes are studied with different approaches, some treating only electrons and others including all valence electrons. The importance of the total net electronic density for interpreting the chemical behaviour of the molecules is stressed. All methods agree in assigning fairly high values to dipole moments. Disagreeing conclusions about other properties in the different methods are analyzed.

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Zusammenfassung Die Borazarobenzol-Isomeren werden mit verschiedenen Methoden untersucht, die entweder nur die -Elektronen oder alle Valenzelektronen behandeln. Die Wichtigkeit der Gesamt-Elektronen-dichte für die Erklärung des chemischen Verhaltens der Moleküle wird hervorgehoben. Alle Methoden stimmen in dem Ergebnis recht hoher Werte für die Dipolmomente überein. Unterschiedliche Ergebnisse bei der Anwendung der verschiedenen Methoden werden analysiert.

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Résumé On étude les borazarobenzènes suivant de diverses méthodes; les unes traitent seulement les électrons et les autres impliquent tous les électrons de valence. On souligne l'importance des charges nettes totales pour interpréter le comportement chimique des molécules. Toutes les méthodes s'accordent en attribuer des valeurs assez hautes au moment dipolaire. On analyse des conclusions discordantes sur d'autres propriétés prévues par les différents méthodes.

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One of us (M. G.) wishes to thank the Consiglio Nazionale delle Ricerche for making possible his stay in Italy.     

A convenient synthesis of 2-chromonecarboxylic acids

Knoevenagel condensation of the β-ketosulfinyl intermediate II with butyl glyoxylate afforded the butyl 2-hydroxy-4-(2-hydroxyphenyl)-3-methylsulfinyl-4-oxobutyrates (III). Compounds III are versatile intermediates for the synthesis of either 2-chromonecarboxylates (V) or 2-carboxy-methylene-3-coumaranone esters (VII).