Zur Bestimmung des optimalen Standortes eines Einkaufszentrums

Zusammenfassung Zur Bestimmung des optimalen Standortes eines (überregionalen) Einkaufszentrums kann ein Modell konstruiert werden, das dem Ansatz zur Bestimmung des mechanischen Schwerpunktes einer mit Massen bewichteten Fläche ähnlich ist. Eine Besonderheit ist die einzubauende Entfernungsfunktion. Es werden das Modell und zu berücksichtigende Grundgegebenheiten diskutiert, es wird auf rechentechnische Probleme hingewiesen, es wird ein Anwendungsfall erwähnt und es werden Beispiele konstruiert.

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Summary A model is constructed to determine the optimum geographical position of a shopping-center. This model is similar to the statement for fixing the center of gravity of a weighted area. A special property is the consideration of a function of distance. The facts and the model are discussed and computational problems, examples and the application to a case are mentioned.

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Vorgel. v.:H. Albach     

Regelflächen im vierdimensionalen affinen Raum

In this paper we develop a theory of ruled surfaces of the four dimensional real affine space. An invariant moving frame is constructed using the halfinvariant methods of G. BOL whereby we get some geometric results. Furthermore a complete system of affine invariants is given and finally we consider ruled W-surfaces.

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Die vorliegende Arbeit enthält Teile der Dissertation des Verfassers (Universität Freiburg i. Br. 1977).     

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     

Kreisflächen im zweifach isotropen Raum

In this paper we consider cyclic surfaces in an isotropic space of degree two, i.e. a three dimensional real affine space with the metric ds²=dx². The local differential geometry of the first and second order of there surfaces is developed. An invariant moving frame is constructed by means of which some interesting questions of the extensive theory are solved.

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Herrn Professor Dr. WERNER BURAU zum 70. Geburtstag     

Zur Theorie der bedingten Tests

Summary The construction of a most powerful similar test with Neyman structure for composite hypotheses is frequently accomplished by the solution of a class of auxiliary problems asking for the determination of most powerful tests for simple hypotheses on the regions of constancy of a sufficient statistic. In detail, this class of so-called conditional tests has to be constructed so as to yield a test composed by them. This method due to Neyman is among others used by Fraser [3], Kendall-Stuart [6], Lehmann [7], Lehmann-Scheffé [8], Witting [11]. The present paper investigates the suppositions on which this construction is possible and the form of the tests obtained hereby. In particular, it is shown that these tests are easy to determine in the case of dominated hypotheses.

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Gekürzte Fassung einer von der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Münster i. Westf. angenommenen Dissertation.

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Der Autor ist am 20. 7. 1968 verstorben.

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Herrn Professor Dr. H. Witting, Münster, danke ich für zahlreiche Anregungen bei der Fertigstellung dieser Arbeit.     

Bemerkungen zum Problem der nichtkonvexen Programmierung

Zusammenfassung Jeder nichtkonvexen wird eine konvexe Optimierungsaufgabe zugeordnet, deren globale Lösung auch die der ursprünglich gegebenen Aufgabe ist. An drei Beispielen wird dann gezeigt, wie man in gewissen Fällen das Problem der Konstruktion dieser äquivalenten Aufgabe lösen kann.

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Summary To each nonconvex optimization problem is associated a convex one whose global solution is the same as that of the original problem. By means of three examples it is shown how in certain cases this equivalent problem can be constructed.

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Vorgel. V.:H. P. Künzi.     

Zur Charakterisierung einer Klasse von Hyperbelstrukturen

A characterisation of those (B^*G)-Geometries (in the sense of Benz) is given, which can be constructed with the help of nearfields F, char F 2, in which the multiplicative group F^*(·) has a subgroup A with index [F^*:A]=2.

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Werner Burau zum 70. Geburtstag gewidmet     

Feldtheorie in der Variationsrechnung Mehrfacher Integrale

The theory of geodesic fields of VAGNER [12] and LIESEN [10] evidently yields the best results in comparison with the field theories of the LEPAGEan bundle. We try to elucidate the theory form a FINSLER-geometric point of view and to make it better applicable. A regularity condition analogous to the HADAMARD sufficient Legendre-condition is deduced, which is less restrictive than the conditions of the original CARATHEODORY and de DONDER-WEYL field theories. Local geodesic fields are constructed. We give a sufficient Legendre-and Weierstraß-condition and finally discuss the scope of field theory.

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Herrn Professor Dr. Dr. Otto Volk zum 80. Geburtstag am 13. Juli 1972 gewidmet     

Zur Bestimmung des günstigsten Standortes einer Betriebsfiliale

Zusammenfassung Am Beispiel des Warenhausproblems wird auf der Basis der linearen Planungsrechnung und der Spieltheorie ein mathematisches Modell konstruiert, das allgemeineren Problemen der Energie- und Warenversorgung als Grundlage dienen kann. In einem ersten Teil werden die zur Rechnung notwendigen Formeln hergeleitet und Hinweise auf Änderungsmöglichkeiten gegeben. In einem zweiten Teil wird dann das Warenhausproblem mit vorgegebenen Zahlen durchgerechnet. Die Lösungen werden auf ihre wirtschaftliche Bedeutung hin untersucht.

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Summary On example of the warehouse problem a mathematical model will be constructed basing on the theory of linear programming and theory of games, which can be used basically for more general problems of energy- or ware-supply. In the first part the formulas necessary for programming will be written and possibilities for change will be given. In the second part the warehouse problem will be counted over with predetermined numbers. The results will be tested on its economical importance.

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Vorgel. v.: W. Knödel     

Partial regularity for the solutions to nonlinear parabolic systems

Sunto Si estendono a sistemi non lineari di tipo parabolico alcuni risultati di regolarità parziale delle soluzioni di sistemi ellittici.

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Entrata in Redazione il 19 settembre 1972.

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Research supported in part by a C.N.R. fellowship at the University of Paris.

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Research partially supported by NSF Grant GP 16115.     

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 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.     

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.     

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.     

Probabilistic aspects of the relationships between the discrete kinetic theory and lattice model

A general procedure for the construction of a spatial lattice model related with a general discrete velocity model is derived. Explicit relations for the 6, 8 and 14 discrete models are stated.

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Riassunto Si ricava, nell'ambito della teoria cinetica discreta, un procedimento generale per la costruzione di un modello al lattice spaziale. Si stabiliscono relazioni esplicite per i modelli a 6, 8 e 14 velocità.

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This work is partially supported by C.N.R.-G.N.F.M. project PS IPPMI of C.N.R.-G.N.F.M. and by the Minister for the Scientific Research.     

Flow in networks with amplification and coupling

Summary The network model presented in an earlier paper [1] is generalized by introducing amplification in arcs and coupling between arcs. The appropriate modifications of the earlier results are stated and the usefulness of the new model is illustrated by examples.

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Zusammenfassung Das in einer früheren Arbeit [1] angegebene Netzwerkmodell wird durch Einführung von Verstärkern in Leitungszweigen und Kopplung von Leitungszweigen verallgemeinert. Die entsprechenden Verallgemeinerungen der früheren Ergebnisse werden besprochen, und die Nützlichkeit des neuen Modells wird durch Beispiele illustriert.

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Vorgel. v.:J. Nitsche.     

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.     

Sul campo elettromagnetico di un dipolo in presenza di un plasma non lineare

Summary Given a magnetic dipole with frequency ω located in a spherical cavity centre surrounded by a non linear plasma, the electromagnetic field inside and outside the cavity is studied by a successive approximation method.

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

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Entrata in Redazione il 23 giugno 1972.     

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.     

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.