Solutions rationnelles de certaines équations fonctionnelles

Dans cet article, nous démontrons essentiellement les deux résultats suivants, qui montrent que les solutions séries formelles à coefficients dans de certaines équations fonctionnelles sont rationnelles. Soient tout d'abords un entier naturel non nul, eta _i ,b _i ,(i = 1, , s), 2s nombres complexes, lesa _i étant non nuls. On définit l'ensembleA comme étant l'intersection des parties de , contenant l'origine et stables par toutes les applicationsg _i (x) = a _i x + b _i . On a alors le résultat suivant: Théorème 1.Soient f, R ₁, ,R _s s + 1 fractions rationnelles de (x), régulières à l'origine, et a_i, b_i (i = 1,, s), 2s éléments de . On suppose que les a_i sont non nuls et de module strictement inférieur à un pour tout i = 1,, s. Soit y(x) un élément de [[x]], vérifiant l'équation fonctionnelle

Some remarks on derivations in Banach algebras and related results

Summary In the first section of this paper we consider some functional equations which are closely connected to derivations (i.e. additive mappings with the propertyD(ab) = aD(b) + D(a)b) on Banach algebras. IfD is a derivation on some algebraA, then the equationD(a) = – aD(a ^–1 )a holds for all invertible elementsa A. It seems natural to ask whether this functional equation characterizes derivations among all additive mappings. It is too much to expect an affirmative answer to this question in arbitrary algebras, since it may happen that even in normed algebras the group of all invertible elements contains only scalar multiples of the identity. We try to answer the question above in Banach algebras, since in Banach algebras invertible elements exist in abundance. In the second section of the paper we prove some results concerning representability of quadratic forms by bilinear forms.     

On an application of Hall's representatives theorem to a finite geometry problem

It is well-known thatn points not belonging to a hyperplane determine at leastn hyperplanes. The possible configurations of hyperplanes in the case when the number of hyperplanes is equal ton are known, too. In this paper we obtain these results by means of Hall's representatives theorem. The setting is that of a finite geometry.     

A proof of Freud's conjecture for exponential weights

LetW (x) be a function nonnegative inR, positive on a set of positive measure, and such that all power moments ofW ²(x) are finite. Let {p _n (W ²;x)} ₀ denote the sequence of orthonormal polynomials with respect to the weightW ²(x), and let {A _n } ₁ and {B _n } ₁ denote the coefficients in the recurrence relation

Normal subgroups and elementary theories of lattice-ordered groups

We show that any lattice-ordered group (l-group) G can be l-embedded into continuously many l-groups H _i which are pairwise elementarily inequivalent both as groups and as lattices with constant e. Our groups H _i can be distinguished by group-theoretical first-order properties which are induced by lattice-theoretically nice properties of their normal subgroup lattices. Moreover, they can be taken to be 2-transitive automorphism groups A(S _i ) of infinite linearly ordered sets (S _i , ) such that each group A(S _i ) has only inner automorphisms. We also show that any countable l-group G can be l-embedded into a countable l-group H whose normal subgroup lattice is isomorphic to the lattice of all ideals of the countable dense Boolean algebra B.     

~(19)F-NMR法测定聚醚多元醇中伯羟基的相对含量

<正> 聚醚多元醇是聚氨酯材料的主要原料之一.多元醇中伯羟基含量的多少对反应活性有着直接的影响,因此,准确地测定伯羟基含量已成为许多研究者关心的课题,并已报道了不少测定方法,其中主要包括化学动力学方法、~1H-核磁共振(NMR)法和~(19)F-NMR法,~1H-NMR法系利用不同的酰化剂,将聚醚多元醇酰化后测其酰化物的~1H-NMR谱,从伯、仲羟基相应的酯基氢的积分比例来计算伯羟基的相对含量,但由于体系中存在其它含氢基因,且是大量的,使测量困难或应用受到限制.~(19)F-NMR法测伯羟     

Metrological role of neutron activation analysis. IB. Inherent characteristics of relative INAA as a primary ratio method of measurement

This is the second part of a paper which deals with the advantages and disadvantages of relative instrumental neutron activation analysis concerning traceability and uncertainty, and the current scope and possible future extensions of neutron activation analysis as a primary ratio method. The first part of this paper has been published in this Journal [1]. Received: 19 March 2001 Accepted: 2 October 2001     

On the existence of MOLS with equal-sized holes

We consider a pair of MOLS (mutually orthogonal Latin squares) having holes, corresponding to missing sub-MOLS, which are disjoint and spanning It is shown that a pair of MOLS withn holes of sizeh exist forh 2 if and only ifn 4 For SOLS (self-orthogonal Latin squares) with holes, we have the same result, with two possible exceptions SOLS with 7 or 13 holes of size 6     

Some asymptotic results useful in enumeration problems

Suppose one is given two related generating functionsa(x) = a _n x ⁿ andb(x) = b _n x ⁿ , often it is of interest to determine the limiting behaviour of the quantitiesa _n /b _n We survey some earlier results of this nature and give some new ones