Generalised ‘join the shortest queue’ policies for the dynamic routing of jobs to multi-class queues

Jobs or customers arrive and require service that may be provided at one of several different stations. The associated routing problems concern how customers may be assigned to stations in an optimal manner. Much of the classical literature concerns a single class of customers seeking service from a collection of homogeneous stations. We argue that many contemporary application areas call for the analysis of routing problems in which many classes of customer seek service provided at a collection of diverse stations. This paper is the first to consider routing policies in such complex environments which take appropriate account of the degree of congestion at each service station. A simple and intuitive class of policies emerges from a policy improvement approach. In a numerical study, the policies were close to optimal in all cases.     

Dedekind’s and Frege’s views on logic

A contextual and comparative analysis shows that Dedekind and Frege do not understand the terms “logic” and “arithmetic” in the same way. More specifically the meaning and the scope of the corresponding concepts are essentially different for them. Consequently Dedekind and Frege have different conceptions of the relationship between arithmetic and logic.     

Complements to ‘The Bruhat order on symmetric varieties’

We give several complements to the paper The Bruhat order on symmetric varieties. Our main result shows that the partial order on the set of twisted involutions in the Weyl groupW, which was introduced in the earlier paper, agrees with the partial order on induced by the usual Bruhat order onW.R. W. Richardson died on 15 June. 1993.     

A supplement to ‘A note on invariant measure semigroups’

A unified definition of measure semigroup is given and it is shown how the types of invariance for the measure are formulated and what effect they have on the embeddability of an Abelian semigroup in a group. The online version of the original article can be found under doi:.     

A note on ‘on antipodal graphs’

A lemma stated in our earlier paper has been corrected without affecting the major content of that paper. An independent proof for the succeeding lemma in that paper has also been produced. It is be noted that given a graph G, the antipodal graph A(G) is uniquely defined, but given A(G), there exist more than one graph H such that A(H) = A(G).     

Cryptanalytic results on ‘Dual CRT’ and ‘Common Prime’ RSA

In this paper we study weaknesses of two variants of RSA: Dual RSA and Common Prime RSA. Several schemes under the framework of Dual RSA have been proposed by Sun et al. (IEEE Trans Inf Theory 53(8):2922–2933, 2007). We here concentrate on the Dual CRT-RSA scheme and present certain range of parameters where it is insecure. As a corollary of our work, we prove that the Dual Generalized Rebalanced-RSA (Scheme III of Sun et al.) can be efficiently broken for a significant region where the scheme has been claimed to be secure. Next we consider the Common Prime RSA as proposed by Wiener (IEEE Trans. Inf. Theory 36:553–558, 1990). We present new range of parameters in Common Prime RSA where it is not secure. We use lattice based techniques for the attacks.     

Electrstatic force on an ‘almost sinusoidal’ surface due to a line charge

The electrostatic force on an almost sinusoidal surface due to a line charge situated symmetrically above a crest is calculated. This force is then compared to the force on a perfectly smooth sheet.

---

Résumé Nous obtenons la force électrostatique sur la surface sinusoidale quand une ligne de charge est située au-dessus d'une crête. La comparison de cette force avec la force sur le plan lisse est effectuée.

     

Teachers’ views on creativity in mathematics education: an international survey

The survey described in this paper was developed in order to gain an understanding of culturally-based aspects of creativity associated with secondary school mathematics across six participating countries. All participating countries acknowledge the importance of creativity in mathematics, yet the data show that they take very different approaches to teaching creatively and enhancing students’ creativity. Approximately 1,100 teachers from six countries (Cyprus, India, Israel, Latvia, Mexico, and Romania) participated in a 100-item questionnaire addressing teachers’ conceptions about: (1) Who is a creative student in mathematics, (2) Who is a creative mathematics teacher, (3) In what way is creativity in mathematics related to culture, and (4) Who is a creative person. We present responses to each conception focusing on differences between teachers from different countries. We also analyze relationships among teachers’ conceptions of creativity and their experience, and educational level. Based on factor analysis of the collected data we discuss relevant relationships among different components of teachers’ conceptions of creativity as they emerge in countries with different cultures.     

Some comments on Wolfe's ‘away step’

We give a detailed proof, under slightly weaker conditions on the objective function, that a modified Frank-Wolfe algorithm based on Wolfe's away step strategy can achieve geometric convergence, provided a strict complementarity assumption holds.Research supported by FCAC (Québec) and NSERC (Canada).