Parametrized\bar \partial operator on pseudoconvex setsoperator on pseudoconvex sets

Sunto Si dimostra l'esistenza della soluzione per l'operatore di Cauchy-Riemann parametrizzato, nel caso continuo per varietà fortemente pseudoconvesse e nel caso differenziabile per varietà di Stein.

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Entrata in Redazione il 20 maggio 1975.

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Supported by C.N.R. research groups.     

Teaching the Independence of $\bar X$ and $S^2$

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Teaching the Independence of $\bar X$ and $S^2$

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Kostenoptimaler Vertrieb eines Konsumgutes einschließlich Standortbestimmung mit ganzzahliger linearer Optimierung

Zusammenfassung Das vorliegende Modell ist mit der Zielsetzung entwickelt worden, den Kohlensäuretransport von Produktionsquellen über mehrere Zweigniederlassungen bis letztlich zum Kunden zu optimieren. Durch Einbeziehung von Kapazitäts- und Standortfragen spielt das Fixkostenproblem und damit das Problem der Ganzzahligkeit bei einigen Variablen in diesem Modell eine entscheidende Rolle. Die Lösung des Transportproblems erfolgt mit Hilfe des IBM-Standardprogramms MPSX-MIP (revidierte Simplexmethode und Branch- and-Bound-Algorithmus).

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Summary The problem discussed has been developed with the object to minimize the transportation costs for carbon-dioxide from sources over several depots to the customers. By including questions of capacity and location problems the fix charge problem and with this the integer variables play a dominant role in the presented model. The solution of the distribution problem is received by the IBM standard program MPSX-MIP (Simplex method revised with Branch and Bound algorithm).

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Als Vortrag gehalten auf der DGOR-Tagung 1973 in Karlsruhe.     

Ein funktionalanalytischer Beweis des Satzes von Cauchy-Kowalewsky

Using functional analytic methods, in particular the fixed point theorem of Schauder-Tychonoff, a new and short proof is given for the classical Cauchy-Kowalewsky theorem on analytic partial differential equations.

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Herrn Prof. Dr. F.W. Schafke zum 60. Geburtstag gewidmet     

Sur les endomorphismes holomorphes permutables de $$\mathbb{P}^k$$

Let , be holomorphic endomorphisms of of degrees , . Assume that and that for all integers , . We then show that are critically finite. Moreover there is an orbifold such that , are coverings of . In the case we give the list of commuting pairs satisfying the above conditions. We also show that any endomorphism is approximable by endomorphisms commuting only with their iterates.

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Sur les endomorphismes holomorphes permutables de $\mathbb{P}^k$

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Received: 6 April 2001 / Published online: 17 June 2002     

Ein Beitrag zur Baire-Kategorie-Theorie

In several papers Morgan II showed, that many analogies between topological and measure spaces can be subsumed under an abstract theory of Baire category. The purpose of this paper is to prove a unified version of two classical theorems in measure theory and topology, which has applications to the theory of Cauchy's functional equation.

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Herrn Hans-Joachim Kowalsky zum 60. Geburtstag gewidmet     

Druckverteilung an Eisenbahnzügen beim Kreuzen

Summary Under the condition of a plain flow of a perfect fluid the unsteady problem of passing by of two trains with any shapes of their heads is investigated. The application of the singularity method gives a system of integral-equations which is replaced by a system of linear equations.Two special problems are solved. The passing by of two trains of equal shape one time with the same speed and the other time when one train is at rest. In this case, the fluctuations of the pressure on the surface of the train at rest are very rapid and have a high amplitude.

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Herrn Prof. Dr. K. Oswatitsch zum 60. Geburtstag gewidmet     

Die Brückner-Vostokov-Formel für das Hilbertsymbol und ihre Geltung im Fallp=2

We prove the formula of Brückner and Vostokov for the classical Hilbert symbol, following a method of Kato, which employs cristalline, cohomology theory. However, we don't presume anything exceeding classical number theory. We show that, up to a factor ±1, this formula essentially holds also in the casep=2. Using this result, we can easily prove for example the complete classical formulas for the biquadratic Hilbert symbol over the field .

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Diese Arbeit ist ein Teil der Dissertation des Autors     

Remarks on the local regularity of the\overline \partial

Summary Let Ω⊂⊂C ⁿ be a pseudo-convex domain with smooth real-analytic boundarybΩ; the local regularity in of the is then strictly related not only with the subellipticity of such problem, but also with certain geometric conditions onbΩ: ifn=2 and α is a (0,1)-form, such relations are equivalences.

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Riassunto Se Ω⊂⊂C ⁿ è un dominio pseudo-convesso con frontierabΩ definita da una funzione analitica reale e ?liscia?, la regolarità locale delle soluzioni in del αè in stretta relazione non solo con la subellitticità di tale problema ma anche con certe condizioni geometriche sulla struttura dibΩ: sen=2 ed α è una (0,1)-forma, tali relazioni sono delle equivalenze.

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

Anwendungen des Quotienten-Differenzen-Algorithmus

Summary The present paper gives several applications of the quotient-difference (=QD)-algorithm [see ZAMP5, 233 (1954)]. These include the summation of infinite series with the aid of continued fractions and the solution of algebraic equations. For the latter, a slight modification of the QD-algorithm is developed in § 5.

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Institut für angewandte Mathematik der ETH.     

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.     

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.     

Lokal endliche Andre-Systeme

Lüneburg's generalization of a construction ofAndre is used to describe all countable, locally finite André-systems and the locally finite André-nearfields. The last section gives a characterization of those countable, locally finite André-planes which have locally finite groups of affine projectivites.

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Herrn Professor Dr. Walter Benz zum 60. Geburtstag     

Zur Stabilität der Strömung in einem horizontalen Rohr bei ungleichmässig erwärmter Wand

Summary The linear fluid motion in a horizontal pipe heated from below is considered, when the temperature field outside the pipe is linear. By the method of small perturbations it is shown that the fluid motion becomes unstable for a critical value of the Rayleigh number, i.e., there is an additional convective motion, the streamlines of which are concentric curves in the plane of a cross-section of the pipe.

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Die Untersuchung wurde vom Wirtschaftsministerium des Landes Baden-Württemberg gefördert.     

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.     

Multi-objective integer programming: A general approach for generating all non-dominated solutions

In this paper we develop a general approach to generate all non-dominated solutions of the multi-objective integer programming (MOIP) Problem. Our approach, which is based on the identification of objective efficiency ranges, is an improvement over classical ε-constraint method. Objective efficiency ranges are identified by solving simpler MOIP problems with fewer objectives. We first provide the classical ε-constraint method on the bi-objective integer programming problem for the sake of completeness and comment on its efficiency. Then present our method on tri-objective integer programming problem and then extend it to the general MOIP problem with k objectives. A numerical example considering tri-objective assignment problem is also provided.     

Zu einem Satz von Skolem über lineare Unabhängigkeit von Werten gewisser Thetareihen

We consider arithmetic properties of the solution of a functional equation f(qx)=xf(x)+1, where q0 is a rational number satisfying certain conditions. A linear independence measure is obtained for the values of f and its derivatives at rational points, both in the archimedian and p-adic case. The proof uses a refinement of the method followed by skolem in the corresponding qualitative considerations.

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Diese Arbeit entstand während der erste Autor Stipendiat der Alexander von Humboldt-Stiftung war.     

Über eine Klasse von Brezelknoten

The paper gives a classification of pretzel knots (p,qq,rr) with one even cross number. The Alexander polynomial is computed in general and it is proved that its degree is always twice the genus of the knot. The classification does not include amphicheirality.

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Mit 3 Abbildungen

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Diese Resultate sind in meiner Dissertation Die Längskreisinvariante und Brezelknoten, Frankfurt a. M. 1978, enthalten.     

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 ?.     

Sull'omotopia uniforme

Summary Following in the classical theory's footsteps, it is possible to construct a ? rational homotopy theory ?. To this purpose, we take all the uniform maps f: I _Q ⁿ →S (where I_Q is the closed unit interval of the rational line equipped with the standard metric uniformity) as paths of a uniform space S. This brings us to the definition of the rational homotopy groups Q_n(S, U_Q, x) and enables us to consider the related exact sequences. All these objects are uniform invariants. The main problem which arises now is to find a suitable space S* in order that its classical homotopy groups Π_n(S*,x) are isomorphic to the classical ones of S. We are able to reach an answer to this question if S is a metrizable uniform space. Since considering the completion Ŝ of S serves no useful purpose (as it is shown by a simple example), we prove that the required space is the ? rational path completion ? S* of S, with S⊆S*⊆Ŝ. We finally recall that the rational uniform homotopy is a special case of regular homotopy, which has been defined and widely investigated in[1].

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Entrata in Redazione il 5 gennaio 1978.

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Lavoro svolto nell'ambito del gruppo GNSAGA del CNR.