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.     

Geometrische Beziehungen in der Aerodynamik kompressibler Medien

There are investigated and discussed relations between the stream-function-surface and the pressure-surface in the theory of the two-dimensional isentropic steady flow in gasdynamics.

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A Bruno Finzi nel suo 70^mo compleanno.

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Entrata in Redazione il 19 gennaio 1970.     

Propriétés Asymptotiques des Groupes Linéaires

Let G be a reductive linear real Lie group and be a Zariski dense subgroup. We study asymptotic properties of through the set of logarithms of the radial components of the elements of : we prove that the asymptotic cone of this set is a convex cone with non empty interior and is stable by the Cartan involution. Reciprocally any closed convex cone of the positive Weyl chamber whose interior is non empty and which is stable by the opposition involution can be obtained this way.?We relate this limit cone and the limit set of to the set of open semigroups of G which meet .?We also prove similar results over any local fields.

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Propriétés Asymptotiques des Groupes Linéaires

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Submitted: January 1996     

The life and work of Sophie Germain

We discuss the life of Sophie Germain, her struggle to educate herself and to win acceptance within the French mathematical community, and her contributions to number theory and to the theory of elasticity.

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Received: 23 January 2003, Accepted: 25 March 2003, Corespondence to: Gareth Jones     

Systèmes de racines sur un anneau commutatif totalement ordonné

A theory of root systems over a totally ordered commutative ring is developed. This theory includes, in particular, the usual finite root systems and the Kac-Moody real root systems. It is adapted to the construction of twisted Kac-Moody groups.

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Dédié à Jacques Tits à l'occasion de son soixantième anniversaire     

Aerodynamische Kräfte auf schlanke Rotationskörper

Summary Comparison between measurements of the normal force of fiveslender bodies of revolution with different base areas in supersonic flow and the simple airshiphull theory ofMunk or the more accurate linearised theory ofpotential flow show considerable discrepancy not only at large, but also at small angles of attack.To get better agreement with the experimental results, it is shown to be more important to estimate theeffects of viscosity than to consider higher orders of potential flow theory.

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Vorgetragen am Astronautischen Kongress 1953 in Zürich, zufolge Abwesenheit des Verfassers durch HerrnB. Chaix, Institut für Aerodynamik der ETH.     

A Metric Space with Transfinite Asymptotic Dimension 2ω + 1*

The authors construct a metric space whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both 2ω + 1, where ω is the smallest infinite ordinal number. Therefore, an example of a metric space with asymptotic property C is obtained.     

Rami globali e parametrizzazione

Summary In this paper, using the theory of henselian rings and in particular the notion of henselian and strict henselian couples, we study the behaviour of analytic branches of an affine algebraic variety at a point x, when x varies along a singular subvariety; moreover we construct an algebraic and canonical procedure, which parametrises the branches.

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Lavoro eseguito nell'ambito della sez. 3 del G.N.S.A.G.A. del C.N.R. e con il supporto finanziario del Ministero della Pubblica Istruzione.     

Su alcune algebre caratteristiche nella teoria dei getti

Summary N. Teleman’s definition of ? characteristic algebra of a Lie algebra extension ? is applied to two classical exact sequences of the theory of the jets, which are of interest in the theory of higher order connections. In the first case, the resulting characteristic algebras are shown to coincide with the ordinary characteristic algebras of the bundles (with connected structure group) of higher order frames on a manifold, and not to depend on the order of the jets. For the second case, the characteristic algebras are proved to be alwaysℝ.

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Entrata in Redazione il 17 marzo 1976.

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Lavoro eseguito nell’ambito del Gruppo di Ricerca del C.N.R. ? Strutture algebriche e geometriche ?.     

Stabilità asintotica in media per moti fluidi viscosi in domini esterni

Summary In this paper we prove some asymptotic stability results for Navier-Stokes fluid filling an exterior domain. In particular, we show that if the Reynolds number associated to the basic flow is sufficiently small, then the energy of perturbations tends to zero as t,provided only that the energy is finite at t=0.This result also solves, as a special case, a problem pointed out by J. Leray in [25].

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Lavoro eseguito sotto gli auspici del G.N.F.M. (C.N.R.).     

Sulla propagazione ondosa in un sistema viscoelastico lineare in presenza di forze di massa

Riassunto Si studia la propagazione ondosa che si determina in un sistema viscoelastico lineare sotto l'azione di assegnate forze di massa e per effetto di prefissate condizioni al contorno. Mediante l'analisi asintotica di una particolare serie di Neumann che interviene nella soluzione, si dimostrapoi l'esistenza di una regione di ?strato limite? pert→∞, in corrispondenza di tempi di rilassamento molto ?piccoli?.

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Summary We study the wave propagation which takes place in a linear-viscoelastic model under the action of prefixed mass forces and of boundary data. The solution of this problem is expressed by means of a particular Neumaun's series. The asymptotic analysis of it shows the existence of a boundary-layer region fort→∞ when very ?small? characteristic relaxation times occur.

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

Dualità per alcune classi di moduliE-compatti

Summary Starting from a topological module E over a commutative discrete ring A, the category C(E) of E-compact modules is defined as the class of all A-modules topologically isomorphic to closed submodules of direct product of copies of E. Under suitable assumptions it is shown that C(E) is dual of the category of abstract A-modules M for whichHom _A(M, E) separates points of M. The duality theory so obtained contains as particular cases Pontryagin's duality between discrete and compact abelian groups and Macdonald's duality between lineary discrete and linearly compact modules over a complete local ring. There are also some applications to the theory of linearly compact modules over noetherian rings.

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Entrata in Redazione il 10 aprile 1976.

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Lavoro eseguito nell'ambito dell'attività dei gruppi di ricerca matematici del C.N.R.     

Sulla stabilità di un fluido politropico, viscoso e pesante in un contenitore limitato da pareti perfette conduttrici di calore

Sunto In questa Nota, si affronta il problema del comportamento asintotico nel tempo di perturbazioni alla quiete per il sistema di equazioni per un fluido comprimibile, viscoso e politropico. Ammesso che esista una soluzione regolare globale, si dimostra, sotto l’ipotesi che il gradiente della temperatura assegnata al bordo sia piccolo, che la differenza tra la soluzione corrispondente a dati iniziali arbitrari e la quiete decade a zero pert che tende ad infinito nella normal diL ².

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We consider the equation system for a compressible viscous polytropic fluid in a regualar bounded domain and we study the asymptotic behavior as time goes to infinity of perturbations with respect to the basic rest state. Under the assumption of the smallness of the gradient of the given temperature on the boundary, we prove the exponential decay of theL ²-norm of the difference between the solution corresponding to arbitrary initial data and the rest state.

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The second author thanks the 60% contract MURST, also she acknowledges the GNFM of italian CNR-INDAM for financial supports.     

Limiting equations in asymptotic stability problems for nonautonomous differential equations

Summary By limiting equations, we prove some asymptotic stability theorems for the origin ofR ⁿ with respect to the solutions of a differential equation , also when the functionf is not defined forx=0. Further we examine similar problems concerning the asymptotic stability of a setM ofR ⁿ that can be unbounded.

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Riassunto Mediante le equazioni limiti, si dimostrano alcuni teoremi di stabilità asintotica per l'origine diR ⁿ rispetto alle soluzioni di un'equazione differenziale , anche quando la funzionef non è definita perx=0. Vengono inoltre esaminati analoghi problemi relativi alla stabilità asintotica di un insiemeM diR ⁿ anche non limitato.

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Work performed under the auspices of the Italian Council of Research (G.N.F.M. del C.N.R.).     

Nondistorsion des horosphères dans des immeubles euclidiens et dans des espaces symétriques

We give a necessary and sufficient condition for a horosphere to be undistorted in an Euclidean building and in a symmetric space. We are using the geometry of Euclidean buildings and the asymptotic cone. As a consequence, a geometric proof of the Lubotzky-Mozes-Raghunathan theorem for -rank one lattices is given.

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Nondistorsion des horosphères dans des immeubles euclidiens et dans des espaces symétriques

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Submitted: September 1996, final version: March 1997     

The Painlevé III equation and the Iwasawa decomposition

For the third Painlevé equation an explicit isomorphism between the monodromy data and the data of the approach of Dorfmeister-Pedit-Wu, based on the Iwasawa decomposition of the loop groups, is established. As an application, this provides a simple algebraic way to calculate the monodromy data in terms of the Cauchy data at zero.

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Partially supported by the Sonderforschungsbereich 288

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Partially supported by the National Science Foundation (DMS-9315964)

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This article was processed by the author using the LAT_EX style filecljour1 from Springer-Verlag.     

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.     

Die metrische Theorie der linearen Komplexbündel von Typ 1 des einfach isotropen RaumesJ 3 (1)

According toK. Strubecker ([18]–[21]) a three dimensional real affine space with the metricds ²=dx ²+dy ² is called a simply isotropic spaceJ ₃ ⁽¹⁾ . InJ ₃ ⁽¹⁾ exist 41 types of bundles of linear line complexes. In this paper we study the metric theory of a bundle of type 1. Especially we investigate the congruence of axis, we give some isotropic and affine results and we study the complementary bundle.

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Herrn em. o. Prof. Dr. W. Wunderlich zum 75. Geburtstag gewidmet

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Im folgenden beziehen wir uns stets auf die Bezeichnungen und Resultate aus [15].     

Irrfahrten aufF 2

LetF ₂ be the free group with two generatorsa, b andP be a probability measure onF ₂ with support {a, a ^–1,b, b ^–1}. The asymptotic behavior forn of the convolution powersP ⁿ (e) at the identitye is found.

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Herrn Prof. Dr. E. Hlawka zum 60. Geburtstag gewidmet     

Zur Konstruktion Rationaler Kurven und Flächen auf Quadriken

The paper presents a powerful construction of rational curves and surfaces on quadric surfaces. These curves and surfaces are considered as solutions of certain diophantic equations in polynomial rings. A representation formula from number theory gives rise to a generalization of stereographic projection. The paper discusses the properties of this map. Some connections to advanced geometry and to the foundations of geometry are outlined.

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Herrn Professor Dr. Oswald Giering zum 60. Geburtstag gewidmet