Corrigenda to ``New primitive whose degree is a Mersenne exponent,' and some new primitive pentanomials

We report an error in our previous paper [#!K1!#], where we announced that we listed all the primitive trinomials over of degree 859433, but there is a bug in the sieve. We missed the primitive trinomial and its reciprocal, as pointed out by Richard Brent et al. We also report some new primitive pentanomials.

     

Test of effective cluster interactions by pion scattering

The superposition of effective interactions is studied by a cluster approach to the pion-nucleus potential with particular emphasis on the treatment of the Pauli principle between the clusters. The model is based on the formalism of Kerman, McManus, and Thaler and constructs the pion-nucleus interaction by a superposition procedure of pion-cluster interactions in the framework of the fish-bone model. The second-order contribution due to excitations of the relative motion between the clusters has been taken into account as well as true absorption. A test calculation of ^+_20 scattering with the cluster approach reproduces the gross structure of the differential elastic cross section and the total non-elastic cross section of conventional calculations quite well. Furthermore, it is confirmed that the three-body Pauli interaction is negligible also in the case of a realistic and rather complicated pion-nucleus interaction thus justifying the usual folding approach. The rotational bands contribute about 10% to the cross sections.     

New primitive whose degree is a Mersenne exponent

All primitive trinomials over with degree 859433 (which is the 33rd Mersenne exponent) are presented. They are and its reciprocal. Also two examples of primitive pentanomials over with degree 86243 (which is the 28th Mersenne exponent) are presented. The sieve used is briefly described.

     

On <Emphasis Type="Italic">g</Emphasis>-functions for Laguerre function expansions of Hermite type

We examine weighted L ^p boundedness of g-functions based on semigroups related to multi-dimensional Laguerre function expansions of Hermite type. A technique of vector-valued Calderón–Zygmund operators is used.     

The single-mode rate equations for semiconductor lasers with thermal effects

A mathematical model describing the coupling of electrical,optical and thermal effects in semiconductor lasers is introduced.Numerical and asymptotic solutions are derived, including expressionsfor key physical quantities such as the initial time delay,the frequency of spike oscillation and the temperature rise,together with its influence on the photon density, the electronconcentration and the threshold current. The consequences ofthermal effects in reducing efficiency are thus quantified.     

3-manifold Groups and Nonpositive Curvature

We prove that the fundamental group of any compact Haken manifold of zero Euler characteristic, which is neither Nil nor Sol, is nonpositvely curved on the large scale. Submitted: August 1997, Revised version: January 1998     

Shuffle-compatible total orders

Sunto We introduce the concept of shuffle- and union-compatibility of total orders on words over a finite alphabet. This works only in a graded manner respecting the length of words. We classify all such orders by even exhibiting a normal form. For union-compatibility we draw on experience gained in a generalisation of Kruskal's packing theorem, as well as in working with rigidified surjections, for shuffle compatibility we also draw on Saizeva-Trevisan's characterisation of compatible total orders on finitely generated free commutative groups.     

Die Bestimmung von Kupfer in Stahl, Ferrolegierungen, Aluminium, Chrom, Kobalt, Mangan und Nickel

Zusammenfassung In der vorliegenden Arbeit wird die Anwendbarkeit des Extraktionsverfahrens mit 2,2-Dichinolyl zur Bestimmung von Kupfer in Ferrolegierungen, Nickel, Nickeloxyd und verschiedenen Metallen untersucht. Es werden einfache Arbeitsweisen angegeben, um die einzelnen Probematerialien in Lösung zu bringen. Da nur Kupfer(I)-ionen den Komplex mit Dichinolyl bilden, ist der Reduktionsvorgang vor der Extraktion eine entscheidende Stufe im Analysengang. Die Reduktion erfolgt mit H₂SO₃ unter Zusatz von Eisen(II)-chloridlösung. Der störende Einfluß der das Kupfer begleitenden Legierungselemente ist unmerklich, selbst wenn diese Elemente in sehr großem Überschuß gegenüber dem Kupfer vorhanden sind. Die vorgeschlagene Modifikation des Verfahrens von Elwell eignet sich zur Bestimmung von 0,001 bis 2% Cu in legierten und hochlegierten Stählen, in Ferrolegierungen und in Metallen wie Aluminium, Nickel, Mangan, Chrom, Kobalt. Das Bestimmungsverfahren ist den anderen bisher in der Stahl- und Eisenmetallanalyse üblichen Methoden hinsichtlich Zeitaufwand, Einfachheit, Empfindlichkeit und auch Genauigkeit weitaus überlegen.     

3-manifolds with(out) metrics of nonpositive curvature

Oblatum 9-X-1994 & 10-IV-1995