Bifurcation of special periodic solutions to delay-differential equations

Summary We consider a class of forced delay differential equations in which the delay is given by /2 and investigate the problem of finding its special periodic solutions. We first approximate these by a Rayleigh-Ritz-Galerkin sequence. Our second method introduces an averaged model thought to give a qualitative approximation to the solution behavior. The effects of cubic and quintic nonlinearities are compared.

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Zusammenfassung Wir untersuchen eine Klasse von forcierten Differentialgleichungen mit Zeitverzögerung /2 und suchen nach speziellen periodischen Lösungen. Zunächst approximieren wir Lösungen durch eine Folge von Rayleigh-Ritz-Galerkin-Näherungen. Als zweite Methode benutzen wir ein Mittelungsverfahren zur qualitativen Approximation des Lösungsverhaltens. Die Effekte von Nichtlinearitäten dritter und fünfter Ordnung werden verglichen.

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Supported in part by the DAAD/CONICYT Professor Exchange Program.

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Supported in part by CONICYT (Grant 89-576) and University of Concepción (Grant 20-12-17).

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Supported in part by DICYT at the University of Santiago (Grant 16-14).     

Funktionen mit formalem eulerprodukt

As is well known the development of Riemann's -function as an Eulerproduct allows assertions about the behaviour of the range of even in the strip {s/1/2

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Gekürzter Teil der Habilitationsschrift des Verf.     

Gruppi ortogonali di indice di Witt minimale generati da tre involuzioni

In this paper, we prove that the orthogonal groups ^–(2l+2, q) and P^–(2l+2, q), l3, q odd, are generated by three involutions.

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Dedicato a A. Wagner in occasione del suo 60° compleanno

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Lavoro eseguito nell'ambito del finanziamento del M.U.R.S.T. e dei Gruppi Nazionali del C.N.R. (G.N.S.A.G.A.).     

Regulär operierende,invariante Mengen semilinearer Abbildungen

For a vectorspace V of dimension at least 2, all subsets of L(V) are determined which are invariant under conjugation with elements of GL(V) and which act sharply transitive on V/0. Furthermore the kernel of the corresponding translation plane is described.

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Herrn Professor Dr. Helmut Karzel zum 60. Geburtstag gewidmet     

Rationale Homotopietypen

We call a CW-complex unstable, if all attaching maps vanish under suspension. For a one-connected CW-space X we construct a unstable CW-complex ¯X and a mapping ¯XX, which is a rational homotopy equivalence. As an application we imbed the rational Hurewicz-homomorphism into an exact sequence.

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Der Autor wurde von der CNRS Frankreich unterstützt.     

Zur Fortsetzbarkeit von Ordnungsfunktionen einer affinen Ebene

We show that every order function of a translation plane with kernel GF(2), GF(3) can he extended to an order function of the projective closure.

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Herrn Professor Dr. Hanfried Lenz zum 70. Geburtstag     

A new technique for rational extrapolation to the limit

Summary Two new algorithms are proposed for extrapolation to the limit. Both algorithms are based on the use of continued fractions as interpolating functions and infinity as extrapolation point. Some relationships with the algorithm, of Bulirsch and Stoer (for rational extrapolation) and the -algorithm (for defining the limit of a sequence) are given. Some examples illustrate the usefulness of the given algorithms and their convergence.

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Zusammenfassung Es werden zwei neue Extrapolationsverfahren angegeben. Die beiden Verfahren sind entwickelt aus dem Gebrauch von Kettenbrüchen als interpolierende Funktionen und unendlich als Extrapolationspunkt. Einige Beziehungen mit dem Algorithmus von Bulirsch und Stoer (zur rationalen Extrapolation) und dem -Algorithmus (zur Bestimmung des Limes einer Folge) werden gezeigt. Einige Beispiele illustrieren den Gebrauch dieser Verfahren und ihre Konvergenz.

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Parts of this paper have been presented, as second theme, for obtaining a doctoral degree in mathematics, at the University of Leuven (Belgium). The work was done while the author was an Aspirant of the N.F.W.O. (Nationaal Fonds voor Wetenschappelijk Onderzoek, Belgium).

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Now at the University of Göttingen (Germany) as an Alexander von Humboldt-Stipendiat.     

A solution procedure for the two-stage stochastic program with simple recourse

For the stochastic program with simple recourse a solution procedure is given which generates a finite sequence of linear substitutive-programs so that, finally either the initially given problem is proved to be unsolvable or an optimal solution for it is given by the optimal solution of the substitutive program.

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Zusammenfassung Für das stochastische Programm mit einfacher Kompensation wird ein Lösungsverfahren vorgeschlagen. Dieses Verfahren erzeugt eine endliche Folge linearer Ersatzprogramme derart, daß schließlich die Lösung eines dieser Ersatzprogramme als Lösung der ursprünglichen Aufgabe erkannt oder die Unlösbarkeit des gestellten Problems aufgedeckt wird.

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This research has been supported by Sonderforschungsbereich 72, University of Bonn.     

Eine charakterisierung der Permutationsgruppe PSL(2, K) über einem quadratisch abgeschlossenen Körper K der Charakteristik ≠2

This paper gives a characterization of the permutation group PSL(2, K) over a quadratic closed field of characteristic 2.

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Herrn Professor Dr. H. Salzmann zum 60. Geburtstag gewidmet.     

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.     

Zum Integrationsproblem sphärischer Hüllkurvenpaare

Since H.R. MüLLER [1] it is well known that spherical envelope pairs X,X to a given roll sliding number are solutions of two conjugate Riccati differential equations. For two special cases an integral is known [1,3]. By use of the fundamental differential equations of the polodes [2] we show the existence of two classes of integrable curves X,X.

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Herrn Professor Dr. H.R. Müller zum 65. Geburtstag gewidmet     

Über fastgeordnete affine Ebenen

An example of an affine plane is constructed, which cannot be ordered, but can be embedded in an ordered projective plane. There is no such an example, if the affine plane is a translation plane with kernel GF(2).

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Herrn Rafael Artzy zum 75. Geburtstag gewidmet     

Zur Erzeugung von kinematischen RÄumen aus einbettbaren Berührstrukturen

In [4] it was shown, that exactly those algebras (A,K) belong to chain geometries embeddable in projektive spaces which are kinematic, that means x² Kx + K for all x A. Those algebras were studied by KARZEL for describing certain incidence groups namely the kinematic spaces. It will be shown how to construct the kinematic space from the embedded chain geometry.

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Herrn Professor Dr. W. Burau zum 70. Geburtstag gewidmet     

Rechtseiträume

Rectangular spaces are defined to be incidence spaces on which an equivalence relation is defined on the linesB and a congruence relation is defined on the point pairsP ² which is compatible with the relation and the incidence structure. Every rectangular space which contains a line with only a finite number of points is a euclidean space. In any regtangular space of characteristic 2 there exists a unique reflection on each line. Thus, as in the case of rectangular planes, rectangular spaces of arbitrary dimension and of characteristic 2 can be characterized in terms of commutative kinematic spaces with involutory automorphisms.Our main result is the theorem which states that any rectangular space of characteristic 2 can be embedded into a euclidean space of equal dimension. From this embedding property we conclude that every rectangular space of characteristic 2 can be described as a subgeometry of a vector space supplied with a quadratic form. Finally we present examples of rectangular spaces of arbitrary dimension which are not euclidean spaces.

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Herrn Prof. H. Karzel und Herrn Prof. H. Wähling in Dank gewidmet

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Diese Arbeit ist in einer anderen Form in meiner Habilitationsschrift Zur Theorie der Rechtseiträume unter besonderer Berücksichtigung des ebenen Falles (Technische Universität München 1987) enthalten.     

über die Desintegration von abstrakten Massen

Summary Under the condition that a lifting exists, the existence of the disintegration of abstract positive bounded measures is established. Basic properties of this disintegration as well as the special case of bounded Radon measures are studied.

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Die vorliegende Arbeit wurde wÄhrend einer Förderung durch die Alexander von Humboldt Stiftung abgefa\t.     

Zur Charakterisierung der Lorentz-Transformationen

A bijection of the n-dimensional space-time that leaves invariant one pseudo-euclidean distance >0 is an (inhomogeneous) Lorentz transformation. Beside this result a new proof of a theorem of BPORCHERS and HPEGERFELDT concerning case =0 is given.

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Herrn WERNER BURAU zum 70. Geburtstag gewidmet.     

Über die endliche Lösbarkeit des Plateau-Problems in Riemannschen Mannigfaltigkeiten

We prove finiteness results of Plateau's problem for boundary curves in a normal chart of radius R < /2 in an analytic Riemannian manifold. It is shown that for analytic there exist only finitely many minimal surfaces of the type of the disc bounded by , which represent an absolute minimum of area, and if boundary branch points are excluded, there exist only finitely many relative minima in the normal chart. If lies on the boundary of a strict convex manifold, there cannot exist any boundary branch points.

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Die vorliegende Arbeit entstand als Dissertation am Mathematischen] Institut der Universität Saarbrücken.

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Herrn Prof. Dr. F. Tomi möchte ich für die Bereitstellung des Themas und für seine Betreuung sehr herzlich danken.     

Statistische Entscheidungsprobleme mit nichtkompaktem Aktionenraum

It is shown that in the general statistical decision problem [3], [4] where the loss function is lower semicontinuous and maximal at infinity the set of statistical decision functions can be topologized such that it is compact and that the risk function is lower semicontinuous.

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Diese Note entstand während eines Aufenthalts an der Westfälischen Wilhelms-universität Münster     

Bordismus verzweigter Überlagerungen von Niedrigdimensionalen Sphären

The concept of bordism between branched coverings is a generalization of the concept of regular homotopy between such maps as given in [3].The main result of this article states that for n=2,3 any two branched coverings of the n-sphere with a finite and equal number of sheets are bordant.

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Diese Arbeit entstand während eines Aufenthaltes des Autors am Sonderforschungsbereich Theoretische Mathematik der Universität Bonn.     

Zur UnverfÄlschtheit des Pitman-Tests auf positive stochastische AbhÄngigkeit

Summary Let be the class of all two dimensional continuous distributions with positive (negative) likelihood ratio dependence. It is shown that the Pitman permutation test for testing independence against positive likelihood ratio dependence at level is unbiased and of level for . Furthermore, it is optimal against the class of normal distributions with positive correlation coefficient .

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Herr Dr. G. Nölle ist am 20. 7. 1968 verstorben.

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Herrn Professor Dr.H. Witting, Munster, danken wir flür RatschlÄge und Hinweise bei der Fertigsteliung dieser Arbeit.