Multilateral Inversion of A r , C r , and D r Basic Hypergeometric Series

In [Electron. J. Combin. 10 (2003), #R10], the author presented a new basic hypergeometric matrix inverse with applications to bilateral basic hypergeometric series. This matrix inversion result was directly extracted from an instance of Bailey’s very-well-poised ₆ψ₆ summation theorem, and involves two infinite matrices which are not lower-triangular. The present paper features three different multivariable generalizations of the above result. These are extracted from Gustafson’s A _r and C _r extensions and from the author’s recent A _r extension of Bailey’s ₆ψ₆ summation formula. By combining these new multidimensional matrix inverses with A _r and D _r extensions of Jackson’s ₈ϕ₇ summation theorem three balanced verywell- poised ₈ψ₈ summation theorems associated to the root systems A _r and C _r are derived.     

BestL 1-approximations of classesW 1 r by Splines fromW 1 r

We obtain the exact values of the bestL ₁-approximations of the classesW ₁ ^r of periodic functions by periodic polynomial splines of degreer and defect 1 with equidistant knots that belong to the classW ₁ ^r .Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1410–1413, October, 1994.     

Recognition by the Set of Element Orders of Symmetric Groups of Degree r and r+1 for Prime r

We prove that the symmetric group S _r of prime degree r17 is recognizable by its element order set. A test for recognizability is obtained for the symmetric group S _r+1 with r17 prime.     

On the number of (r,r+1)‐ factors in an (r,r+1)‐factorization of a simple graph

For integers d≥0, s≥0, a (d, d+s)‐graph is a graph in which the degrees of all the vertices lie in the set {d, d+1, …, d+s}. For an integer r≥0, an (r, r+1)‐factor of a graph G is a spanning (r, r+1)‐subgraph of G. An (r, r+1)‐factorization of a graph G is the expression of G as the edge‐disjoint union of (r, r+1)‐factors. For integers r, s≥0, t≥1, let f(r, s, t) be the smallest integer such that, for each integer d≥f(r, s, t), each simple (d, d+s) ‐graph has an (r, r+1) ‐factorization with x (r, r+1) ‐factors for at least t different values of x. In this note we evaluate f(r, s, t). © 2009 Wiley Periodicals, Inc. J Graph Theory 60: 257‐268, 2009     

(r n−1 ,r) Hjelmslev-Ebenen des Typsn

Ohne ZusammenfassungHerrn Günter Pickert zum 60. Geburtstag gewidmetDer Autor dankt der Stiftung Volkswagenwerk für die Unterstützung während der Abfassung dieser Arbeit     

Détermination de la réactivité d'un réacteur fortement réfléchi

Sans résuméSubside N^o 4353 du Fonds national suisse de la recherche scientifique.     

Demi-groupes réguliers

Résumé Ce travail comprend quatre parties pouvant étre lues indépendamment:I) Représentations complètes d'un demi-groupe par des transformations partielles sur ensemble.II) Translations partielles. Représentation canonique d'un demi-groupe régulier. Problèmes de structure (Produits sous-directs de demi-groupes complètement 0-simples).III) Congruences sur les demi groupes réguliers.IV) Demi-groupes complètement 0-simples.     

On the r.e. predecessors of d.r.e. degrees

Let d be a Turing degree containing differences of recursively enumerable sets (d.r.e.sets) and R[d] be the class of less than d r.e. degrees in whichd is relatively enumerable (r.e.). A.H.Lachlan proved that for any non-recursive d.r.e. d R[d] is not empty. We show that the r.e. degree defined by Lachlan for a d.r.e.set d is just the minimum degree in which D is r.e. Then we study for a given d.r.e. degree d class R[d] and show that there exists a d.r.e.d such that R d] has a minimum element 0. The most striking result of the paper is the existence of d.r.e. degrees for which R[d] consists of one element. Finally we prove that for some d.r.e. d R[d] can be the interval [a,b] for some r.e. degrees a,b, a b d. Received: 17 January 1996     

Retractions régulieres

Sans résumé     

On projective spaces PG(r, q) with r ≥ 4

In this paper a characterization of PG(r, q), r ≥ 4, in terms of planar spaces is given. Domenico Olanda: This research was carried out within the activity of INdAM-GNSAGA and supported by the Italian Ministry M.I.U.R.     

Das WASP-III Computerprogramm für optimale Ausbauplanung für Elektrizitätskraftwerke

Zusammenfassung Das WASP-III Modell ermöglicht die Ermittlung des optimalen Ausbauplanes für Elektrizitätsversorgungsunternehmen (EVU) über eine Zeitspanne bis zu 30 Jahren, unter Berücksichtigung von Einschränkungen seitens der Planung. Das Optimum wird definiert durch das Minimum der abgewerteten Gesamtkosten. Das Modell verwendet Wahrscheinlichkeitsberechnungen der Produktionskosten des Systems — der Kosten der nicht zur Verfügung gestellten Energie, und — der Zuverlässigkeit, und die Methode der Dynamischen Optimierung zum Vergleich der Kosten von zur Wahl stehenden Systemausbauplänen.Dazu berücksichtigt das Modell: die Spitzenlasten und Lastkurven aller Perioden der Studiendauer; das bestehende System; vorbestimmte In- und Außerdienststellungen von Kraftwerksblökken; vorgesehene Kraftwerksblöcke für den Ausbauplan; mögliche Kombinationen von Jahresausbauplänen über die Studiendauer unter Berücksichtigung von Randbedingungen; die Lastordnung der Kraftwerksblöcke; die Resultate vorhergehender Simulationen; Investitionskosten; Kosten nicht gelieferter Energie; Wirtschaftlichkeitsparameter und Grenzwerte der Zuverlässigkeit des Systems.Das besprochene Modell ist die dritte Fassung von WASP mit den aus Tabelle 2.2 ersichtlichen Unterschieden zur zweiten Fassung.

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The WASP-III model is used for the evaluation of the optimum electric generation expansion planning over a period up to 30 years with consideration of constraints on planning. The optimum is defined by the minimum of the discounted total costs. The model uses probability calculations for the system production cost, the energy not served cost and the reliability of the system. Dynamic optimization is used for the comparison of costs of the various possible system expansion plans.With regard to this the model considers: the peak loads and load duration curves of all periods of the study; the fixed system; the committed additions and retirements of units; the variable system for expansion; possible configurations for yearly expansion with respect to imposed constraints; the loading order of units; results of previous simulations; investment costs, costs of energy not served; economic parameters and maximum permitted values of loss of load probability.This model is the third version of WASP with differences to the second version as shown in table 2.2.

     

Le réseauL 2 d'un système holonome régulier

Sans résumé     

On quasi-orthogonal polynomials of order r

The sequences of quasi-orthogonal polynomials of order r are defined for non-quasi-definite moment functionals. Properties concerning the existence of such sequences, and relations between a quasi-orthogonal polynomial of order r and a set of orthogonal polynomials are proved. Two determinantal expressions of quasi-orthogonal polynomials of order r are given. At last it is proved that three consecutive polynomials of a sequence of quasi-orthogonal polynomials of order r satisfy a three term recurrence relation.     

Recognition of Alternating Groups of Degrees r+1 and r+2 for Prime r and the Group of Degree 16 by Their Element Order Sets

It is proved that a finite group whose element order set is the same as that of an alternating group A _n of degree n=r+1 or r+2 for prime r>5 or n=16 is isomorphic to A _n .     

On monomialk-Buchsbaum curves inP r

This paper is deveted to the study of projective monomialk-Buchsbaum curves C. First, using the theory of affine semigroup rings, we give a criterion forC to bek-Buchsbaum. Then we give some lower and upper bounds for the numberk _c such thatC is strictlyk _c-Buchsbaum. For some classes of monomial curves we can computek _C explicity.     

Regularity of (0,1, …,r−2, r)* interpolation on the unit circle

The object of this paper is to show regularity of (0,1, …, r−2, r)^* interpolation on the set obtained by projecting vertically the zeros of (1−x²)p _n ^(λ) (x) (λ≥1/2) onto the unit circle, where P _n ^(λ) (x) stands for the nth ultraspherical polynomial.     

Les réseaux Riemanniens

Sans résumé     

Algèbres de Lie résolubles réelles algébriquement rigides

Résumé.  We present all real solvable algebraically rigid Lie algebras of dimension lower or equal than eight. We point out the differences that distinguish the real and complex classification of solvable rigid Lie algebras.