A ecessary and Sufficient Condition for The Stability of General molecular Systems

We study here the binding of atoms and molecules and the stability of general molecular systems including molecular ions. This is the first paper of a series devoted to the study of these general problems. We obtain here a general necessary and sufficient condition for the stability of general molecular ststem in the context of thomasz-Fermi-Von Weiasäcker, Thomas-Fermi-Dirac-Von Weizsaäcker, Hartree or Hartree-Fock theories

SUMARY OF PART 1

1.Introduction.

II.Presentation of the models

III.Diatomic molecular systems and hartree-Fock theory

IV.Diatomic molecular systems and Hartree or Thomas-Fermi theories

V.General molecular systems

Appendix 1: Hartree-Fock models when Z > N ― 1

Appendix 2: Dichotomy yields equal Lagrange multipliers

Appendix 3: The problem at infinty for the TRDW model     

On the locus of curves with automorphisms

Sunto Si descrivono le componenti del luogo delle curve con automorfismi non banali all'interno dello spazio dei moduli delle curve algebriche di genere maggiore o uguale a tre. Si descrivono poi le componenti del luogo singolare dello spazio dei moduli delle curve di genere maggiore o uguale a due.

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Durante questa ricerca l'autore ha usufruito di un finanziamento del Ministero della Pubblica Istruzione.

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An erratum to this article is available at .     

Una maggiorazione a priori dal punto di vista variazionale

Summary A class of linear second order ordinary differential operators is considered, with bounded measurable coefficients. An optimal a priori estimate for such operators is determined, using variational techniques.

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Entrata in Redazione il 12 febbraio 1975.

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Lavoro eseguito nell'ambito del G.N.A.F.A. del C.N.R.     

Sulla stabilità asintotica parziale

Summary In this paper the well known theorems of E.A. Barbaschin-N.N. Krasovskij and J. P. LaSalle on asymptotic statility and instability are extended to partial stability. An application is given for a class of non-holonomic dissipative mechanical systems.

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A Bruno Finzi nel suo70 ^mo compleanno.

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Lavoro svolto nell'ambito dei Gruppi di Ricerca del Comitato per la Matematica del C.N.R.

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Entrata in Redazione il 23 marzo 1970.     

Punti esplosivi (radianti o vibranti) delle equazioni differenziali ordinarie del 2o ordine

Summary It is given in § 1.

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All'amicoDario Graffi nel suo 70^o compleanno

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Entrata in Redazione il 3 aprile 1975.     

Un teorema di esistenza per controlli ottimi di sistemi definiti da equazioni integrali di Urysohn

Summary In this paper an existence theorem is proved for optimal control problems described by Urysohn systems, with pointwise constraints on controls and states. An example of application of the existence theorem is given.

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Entrata in Redazione il 15 marzo 1978.

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Lavoro eseguito nell'ambito della mia attività di ricerca come borsista C.N.R., presso l'Università di Genova.     

Extremal Prime Filters and Universality of Some Categories

Abstract

Due to the existence of constants, classical topological categories cannot be universal in the sense of containing each concrete category as a full subcategory. In the point-free case, this obstruction vanishes and the question of universality makes sense again. The main problem, namely that as to whether the category of locales and localic morphisms is universal is still open; we prove, however, the universality of the following categories:

- pairs (locale, sublocale) with the localic morphisms preserving the distinguished sublocales,

- frames with frame homomorphisms reflecting the maximal prime ideals,

- Priestley spaces with f-maps preserving the maximal elements.     

On the brauer group of a designularization of a normal surface 1

If ‰ : ? S → is a desingularization of the norm3 surface S, then it is shown that the induced map H² _et:(S, G_m) → H^2: _et(?, G_m) is surjective. It

follows that if all of the singularities of S are rational, the Brauer group

map B(S) → B(?) is surjective. An example is given to show that this

property fails if the dimension of S ≥ 3.     

La diffraction des ondes électromagnetiques par des ondes gravitationnelles. Sur une nouvelle méthode de détection des ondes gravifiques

Summary A new method for the detection of gravitational waves is proposed. It is based on an assumed diffraction of electromagnetic waves produced by a pattern of stationary gravitational waves.

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A Dario Graffi, pour son 70-ème anniversaire

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Entrata in Redazione il 1 luglio 1975.     

Sulla propagazione di onde elettromagnetiche in una colonna di plasma cilindrica circolare indefinita,soggetta ad agitazione termica elettronica e a un campo magnetico assiale uniforme

Summary A study is made about the ways of propagation of electromagnetic waves in a cylindrical plasma column subject to termic and electronic agitation and to an axial uniform field; and it is put in evidence the possibility for four ways of propagation of waves according to the cylinder's axis. Then it is examined a particular case in which the ways of waves propagation are reduced to two.

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A Bruno Finzi nel suo 70^mo compleanno.

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Lavoro svolto nell'ambito del Gruppo di ricerca n. 3 del Comitato per la Matematica del C.N.R.

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Entrata in Redazione il 26 gennaio 1970.     

Studio di una disequazione quasi-variazionale relativa ad un problema di filtrazione in tre dimensioni

Summary A 3-dimensional problem related to the theory of fluid flow through porous media is translated into a quasi-variational inequality: an existence theorem is proved.

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Entrata in Redazione il 17 marzo 1976.

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Lavoro svolto nell'ambito del ? Gruppo Nazionale per l'Analisi Funzionale e le sue applicazioni ? e del ? Laboratorio di Analisi Numerica ? di Pavia del C.N.R.     

A criterion for non-integrability of Hamiltonian systems with nonhomogeneous potentials

A necessary condition for integrability is presented for two degrees of freedom Hamiltonian systems with nonhomogeneous potentials. This is based on a theorem of Ziglin and gives also an efficient criterion for non-integrability. As an application, it is used to single out integrable cases among the Hénon-Heiles Hamiltonians.

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Résumé On démontre une condition nécessaire pour l'intégrabilité de systèmes hamiltoniens à deux degrés de liberté qui possèdent des potentiels inhomogènes. La démonstration repose sur un théorème de Ziglin et l'on obtient aussi un critère de non-integrabilité. Comme application, on s'en sert pour trouver des cas intégrables dans les hamiltoniens de Hénon-Heiles.

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Dedicated to Prof. Yoshikazu Hirasawa on his 60th birthday

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This research was partially supported by Grant-in-Aid for Scientific Research (No. 60740069), Ministry of Education. Japan.

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Staying at Forschungsinstitut für Mathematik, ETH-Zentrum, Zürich until the end of August, 1987.     

Approximation of the eigenvectors of a positive compact operator and estimate of the error

Sunto. Vengono date formule per calcolare l'errore nella approssimazione degli autovettori di un operatore compatto e positivo mediante il metodo di Rayleigh-Ritz.

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A Dario Graffi nel Suo 70^o compleanno

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Entrata in Redazione il 30 giugno 1975.     

Sulla instabilità gravitazionale secondo Jeans di un plasma dissipativo in presenza di effetto Hall

Summary In this paper we study Jeans' gravitational instability of a dissipative Hall plasma, i.e., of a viscous, heat-conducting plasma with finite electrical conductivity, described by the magnetofluiddynamic equations in the presence of the Hall effect. The critical value of the wavelength is determined and the condition for the gravitational instability is discussed. Several noteworthy particular cases are then examined.

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Facoltà di Ingegneria dell'Università.

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Entrata in Redazione il 7 settembre 1977.     

Information theoretic interpretation of Forte's entropy for the grand canonical ensemble

Summary Forte's characterization of the entropy of a grand canonical ensemble in statistical mechanics has a natural interpretation in information theory. This entropy is also shown to be finite under the natural assumption that the average message length be finite. In the proof, an analogue of a well-known inequality of Shannon is obtained.

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Riassunto La caratterizzazione di Forte dell'entropia di un insieme gran canonico in meccanica statistica viene interpretata in teoria dell'informazione. Si mostra anche che questa entropia è finita nell'ipotesi naturale che la lunghezza media del messaggio sia finita. Nella dimostrazione si ottiene una disuguaglianza analoga a quella ben nota di Shannon.

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The author is a member of G.N.A.F.A. of the Italian C.N.R.

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An erratum to this article is available at .     

Proper holomorphic self-maps of smooth bounded Reinhardt domains in ℂn

It is proved that every proper holomorphic self-map of a smooth bounded Reinhardt domain of D’Angelo finite type in ℂⁿ (n1) is an automorphism.

     

A characterization of the entropy functionals for grand canonical ensembles. The discrete case

Summary ? Natural ? properties lead to a representation theorem for the entropy functional of a grand canonical ensemble. In addition to the classical Boltzmann term, the representation contains three more terms that seem to be meaningful in statistical mechanics.

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Sunto Da proprietà ? naturali ? imposte al funzionale entropia di un insieme gran canonico si deduce un teorema di rappresentazione per esso. In aggiunta al termine classico di Boltzmann, la rappresentazione mette in luce tre ulteriori termini che sembrano significativi in meccanica statistica.

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A Dario Graffi per il suo 70° compleanno

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Entrata in Redazione il 17 marzo 1976.

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While on sabbatical leave of absence from the University of Waterloo, Canada, Department of Applied Mathematics.

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Research supported in part by National Research Council of Canada, grant A-7677 and IBM-Italia.     

Onn-dimensional extensions of Fatou's lemma

Different extension of Fatou's Lemma to several dimensions are discussed and compared. The connection of those results with integral of set-valued mapping is underlined.

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Resumé On discute et compare différentes extensions du Lemma de Fatou au cas de plusieurs variables. La relation de ces résultats avec l'intégrale d'une application multivoque est soulignée.

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Dedicated to H. Knobloch on the occasion of his 60th birthday

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Ce rapport a été publié en partie grâce á une subvention du Fonds FCAR pour l'aide et le soutien á la recherche.     

Sui problemi al contorno per le equazioni ellittico-paraboliche di ordine 2m

Summary In this note a theorem of existence and uniqueness for a boundary value problem for a class of 2m-order elliptic-parabolic operators is proved.

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Entrata in Redazione il 15 settembre 1976.

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

Sulla propagazione delle onde elettromagnetiche nei mezzi di Toupin e Rivlin

Summary The propagation of an ordinary plane wave in a medium of Toupin and Rivlin is here considered, limitedly to the instances of an external electric or magnetic field acting on the medium. In particular, the conditions for the propagation of T.E. and T.M. or T.E.M. waves are determined.

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A Dario Graffi nel suo 70^o compleanno

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Entrata in Redazione il 4 giugno 1976.

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Lavoro eseguito nell'ambito dei gruppi di ricerca del C.N.R. per la Fisica Matematica.