Sopra una classe di equazioni ellittiche a coefficienti misurabili

Sunto Si considera una equazione lineare a derivate parziali di tipo ellittico del secondo ordine, a coefficienti reali misurabili. Con una ipotesi conveniente sugli autovalori della forma quadratica associata, si dimostrano una limitazione a priori per soluzioni dotate di derivate seconde di quadrato sommabile, e un teorema di esistenza-unicità per il problema di Dirichlet. Questo lavoro fa parte dell'attività del gruppo di ricerca n. 23 del C. N. R., a. a. 1964–1965.     

Derivations of differential forms on jet bundles

Summary The theory of derivations of differential forms, originally formulated by Frölicher and Nijenhuis [2], is generalized to include derivations which connect differential forms on two different manifolds. This generalized theory is then used to analyze derivations of direct limits of exterior algebras of forms on jet bundles. Such derivations have found applications in the analysis of Lie equations [3], [4] and in the inverse problem of the calculus of variations [6], [7], [8], [9].

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Résumé On présente une généralization de la théorie des dérivations des formes extérieures, formulée par Frölicher et Nijenhuis [2], au cas des dérivations qui relient les formes extérieurs sur deux variétés différentes. On utilize ensuite cette théorie généralizée pour étudier les dérivations des limites directes des algèbres des formes extérieures sur les fibrés des jets. Ces dérivations ont été appliquées dans l'analyse des équations de Lie [3], [4] et dans le problème inverse du calcul des variations [6], [7], [8], [9].

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This work is a part of a program conducted jointly with ProfessorBenenti at Istituto di Fisica Matematica «J. L. Lagrange» of Torino. The authors are greatly indebted to the Director of the Institute Professor D.Galletto for his interest and encouragement.This work has been supported by Gruppo Nazionale per la Fisica Matematica del Consiglio Nazionale delle Ricerche.     

Separation and quantitation of urinary trypsin inhibitors by reversed-phase high-performance liquid chromatography

Summary Human urines contain a family of trypsin inhibitors (UTIs) in small quantities, which seem to be involved in important biological processes. A procedure for separation and quantitative determination of such endogenous inhibitors in human urine has been developed. The urine sample is adjusted to pH 8.3 and percolated through a trypsin-Sepharose 4B column: the inhibitors are eluted with acid solution. The eluate (1000 l) is analysed by RP-HPLC with programmed elution and ultraviolet detection (200 nm). Three principal peaks have been evidenced: they are due to the elution of urinary trypsin inhibitors (UTIs) having apparent m.w. of ca. 6000, 72000, 18000 daltons, respectively. Characteristics of the procedure are: limited sample volume (ca. 200 ml) and recovery of the global inhibition activity (95%). For each UTI determination reproducibility and linearity ranges are reported.

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Trennung und Bestimmung von Trypsin-Inhibitoren im Harn durch Umkehrphasen-HPLC

     

Multicharged particle emission in the disintegration of aluminium induced by 800 mev electrons

The disintegration of aluminium nuclei by 800 MeV electrons is studied using plastic detectors. Angular and energy distributions of emitted Li, Be and B isotopes are presented. The compatibility of the results with a two-stage process (cascade and evaporation) is studied with the aid of a Monte Carlo calculation.     

Conformation of bicyclo[n.1.0] derivatives: Part 2. Norcarane and cyclohexene epoxide

The conformation al geometries and the possible interconversion paths for bicyclo[4.1.0] heptane (norcarane) and cyclohexene epoxide have been studied by both quantum mechanical and molecular mechanics calculations. The half-chair conformation is the most stable in the two compounds even if conformational equilibria with other forms cannot be excluded. Theoretical results are compared with the experimental data of molecular geometry, heat of formation, rotational constants, dipole moment, molar Kerr constant and proton coupling constants. The results obtained by the force-field method are satisfactory and consequently the extension of the method to derivatives of this kind seems possible.     

On a paper by A. G. Ramm

Si migliorano i risultati di [7].     

Carboxylation and acylation of 4,7-dimethoxyindoles and a study of the corresponding dealkylated derivatives

Treatment of 4,7-dimethoxyindoles 1 and 9 with ethylmagnesium bromide and ethyl chloroformate in refluxing dry ether gives the corresponding indole-1-carboxylic acid ethyl esters 3 and 10 as major products, together, with minor amounts of indole-3-carboxylic acid ethyl esters 2 and 11 . Similar treatment of 4,7-dimethoxyindole ( 1 ) with ethylmagnesium bromide and chloroacetyl chloride affords the related 3-chloroacetyl derivative 13 . All of the new 4,7-dimethoxyindole compounds were dealkylated with anhydrous aluminium chloride in refluxing dry benzene. Transformation of these demethylated indoles into other interesting derivatives, in view of possible antimicrobial activity is also reported.     

A modified Eguchi-Kawai model

A modified version of the Eguchi-Kawai model is proposed. We show that this modified model is equivalent to U(N) gauge theory in the infinite volume when N → ∞. The argument is based on investigations both in the continuum and on a lattice. We show that our modified model does not suffer from the notorious spontaneous symmetry breaking.