Szego polynomials: some relations to L-orthogonal and orthogonal polynomials

We consider the real Szego polynomials and obtain some relations to certain self inversive orthogonal L-polynomials defined on the unit circle and corresponding symmetric orthogonal polynomials on real intervals. We also consider the polynomials obtained when the coefficients in the recurrence relations satisfied by the self inversive orthogonal L-polynomials are rotated. (C) 2002 Elsevier B.V. B.V. All rights reserved.

VOICES FROM THE SOUTH: DIALOGICAL RELATIONSHIPS AND COLLABORATION IN MATHEMATICS EDUCATION

This chapter presents a collaborative experience between two neighbouring countries from South America: Argentina and Brazil. Our purpose is to share a model of international collaboration that we consider to be an alternative to the classical movement of early mathematical and scientific knowledge between East and West and between North and South. We start our chapter with a general discussion about the phenomenon of globalization considering some local examples. We characterize our collaboration exploring the tensions and difficulties we faced along our own professional development at the local as well as the international level. We describe the development of our prior collaborative work that established the foundation for our international collaboration portraying the local mathematics education communities. We refer to some balances that were created among our relationships, the expansion of our collaborative network, and how this particular collaboration allows us to contribute to the regional field and inform the international one. We discuss the way that the search for balance and symmetry, or at least a complementary asymmetry in our collaborative relationships, has led us to generate a genuine and equitable collaboration.

Magnesium levels in nutrient solution and common bean (Phaseolus vulgaris L cv Carioca) development. Evaluation of the growth relations and assimilate partitioning

The effect of magnesium levels in nutrient solution upon relation between shoot and root, leaf weight ratio and assimilate partitioning of common bean (Phaseolus vulgaris L. cv Carioca) was studied. Bean plants (3 per pot) were grown in 6 l pots containing Hoagland & Arnon n. 2 solution modified to obtain 2.4, 24.3, 48.6, 72.9 and 97.2 ppm of magnesium. The experimental design was a completely randomized factorial replicated 3 times with 5 levels of magnesium and 5 samplings wich were done forthnightly. Therefore, it may be suggested that the 48.6 ppm of magnesium level proposed by Hoagland & Amen (1950) is the best choice for the common bean, according to the conditions of this experiment. Magnesium concentrations over 48.6 ppm didn't show significant alterations of the evaluated parameters. Nutrient solution with 2.4 ppm of magnesium content provides higher efficiency to the common bean plants during almost all its cycle, except the final of the reproductive phase. These results suggest that magnesium concentration increased to 48.6 ppm, in the cycle final perhaps could increase the productivity.

BROKEN SU(8) AND HADRONIC MASS RELATIONS IN HEAVY-QUARK EFFECTIVE THEORY

Mass relations for hadrons containing a single heavy quark (charm or beauty) are studied from the viewpoint of a quark model with broken SU(8) symmetry, developed by Hendry and Lichtenberg some time ago, in comparison to that of the heavy quark effective theory. The interplay of the two approaches is explored and spectroscopic consequences derived.