On the distribution of the number of customers in the symmetric M/G/1 queue

We consider an M/G/1 queue with symmetric service discipline. The class of symmetric service disciplines contains, in particular, the preemptive last-come-first-served discipline and the processor-sharing discipline. It has been conjectured in Kella et al. [1] that the marginal distribution of the queue length at any time is identical for all symmetric disciplines if the queue starts empty. In this paper we show that this conjecture is true if service requirements have an Erlang distribution. We also show by a counterexample, involving the hyperexponential distribution, that the conjecture is generally not true. AMS Subject Classifications Primary—60K25; Secondary—90B22     

Toward phenanthridin-2-ylidene: electrophilicity versus acidity in planar-constrained C-aryl iminium salts

A phenanthridinium salt was prepared in four steps, including an intramolecular CH-arylation and a hydride abstraction reaction. Treatment with sterically demanding bases does not lead to the corresponding carbene, but rather to addition products: the planar-constrained geometry significantly enhances the electrophilicity over the acidity of C-aryl iminium salts.     

Regioselectivity in the ene-reaction of singlet oxygen with cyclic alkenes: photooxygenation of methyl-substituted 1,4-cyclohexadiene derivatives

The photooxygenation of the 1-methyl-, 2,3-dimethyl-, and 1,4-dimethylcyclohexa-1,4-dienes, which are readily available through Birch reduction, yielded the corresponding ene-products. The formed endocyclic dienes were trapped by the addition of singlet oxygen to give the corresponding bicyclic endoperoxy hydroperoxides. In the case of 1-methylcyclohexa-1,4-diene and 1,4-dimethylcyclohexa-1,4,-diene, the cis-effect determined the product distribution. Photooxygenation of 2,3-dimethylcyclohexa-1,4-dienes gave mainly exocyclic olefin, which was attributed to the lowered rotational barrier of the methyl group and increased reactivity of the methyl groups.     

A finite cutting plane method for facial disjunctive programs

This paper shows that any linear disjunctive program with a finite number of constraints can be transformed into an equivalent facial program. Based upon linear programming technique, a new, finite cutting plane method is presented for the facial programs.

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Zusammenfassung Die Arbeit zeigt, daß jedes lineare disjunktive Optimierungsproblem mit endlich vielen Restriktionen in ein äquivalentes Fazetten-Problem transformiert werden kann. Auf der Grundlage von linearer Optimierungstechnik wird für das Fazetten-Problem ein neues, endliches Schnittebenenverfahren vorgestellt.

     

Adsorbed state and vibrational excitation of N2 on Pd(110)

High-resolution vibrational electron energy loss spectroscopy, low-energy electron diffraction and Auger electron spectroscopy have been used to study the interactions of nitrogen with the Pd(110) surface. At 120 K, N₂ is chemisorbed molecularly on the Pd(110) surface, and the (2 × 1)-N₂ structure is formed. Most probably, the N₂ molecules are chemisorbed in the on-top sites of the bulk-like Pd(110) surface in the upright-linear structure. The Pd---N₂ bond energy is estimated to be ˜ 6 kcal/mol. The Pd---N₂ and N---N stretching vibrations of N₂ admolecules on Pd(110) are observed at 30 and 278 meV, respectively. The primary-energy dependence and angle dependence of their excitation cross sections agree reasonably well with the prediction of the dipole theory. The electron beam-induced effects are briefly discussed.     

Paying the Price for Sugar and Spice: Shifting the Analytical Lens in Equity Research

The analytical stance taken by equity researchers in education, the methodologies employed, and the interpretations that are drawn from data all have an enormous impact on the knowledge that is produced about sources of inequality. In the 1970s and 1980s, a great deal of interest was given to the issue of women's and girls' underachievement in mathematics. This prompted numerous different research projects that investigated the extent and nature of the differences between girls' and boys' achievement and offered reasons why such disparities occurred. This work contributed to a discourse on gender and mathematics that flowed through the media channels and into schools, homes, and the workplace. In this article, I consider some of the scholarship on gender and mathematics, critically examining the findings that were produced and the influence they had. In the process, I propose a fundamental tension in research on equity, as scholars walk a fine and precarious line between lack of concern on the one hand and essentialism on the other. I argue in this article that negotiating that tension may be the most critical role for equity researchers as we move into the future.     

Book reviews

Ohne Zusammenfassung

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Book reviews

     

Realization of an OpenMath Server for REDUCE

Various approaches and standards for transferring mathematical objects between different computer programs in multimedia environment in the framework of the OpenMath project are described. The use of these standards might revolutionize the exchange of mathematical information caused by the development of computer algebra tools and telecommunication possibilities. The standards make it possible to create databases and easily save and use mathematical objects obtained in different applications, e.g., to exchange the data obtained in different computer algebra systems and place information on the Internet. Bibliography: 9 titles.     

Pourquoi, pour qui enseigner les mathématiques? Une mise en perspective historique de l’évolution des programmes de mathématiques dans la société française au XXe siècle

Evolutions of mathematical curricula in French society have been marked by the successive answers intitutions have given to the following question since one century: Why and whom teaching mathematics? Here I present two of these, one given in 1908 and one in 1967. Each symbolises a breaking period of reforms in secondary mathematics teaching in France. We will see in the two first part of this paper that they belong to two different worlds, with social, institutional, ideological and mathematical specific features. In the third part, I’ll focus on geometry, showing the effects of the different answers concerning the public and the aims of mathematical teaching.     

Closure laws for a two-fluid two-pressure modelLois de fermeture pour un modèle à deux pressions d'écoulement diphasique

Closure laws for interfacial pressure and interfacial velocity are proposed within the frame work of two-pressure two-phase flow models. These enable us to ensure positivity of void fractions, mass fractions and internal energies when investigating field by field waves in the Riemann problem. To cite this article: F. Coquel et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 927–932.