On the zeros of polynomials: an extension of the Enestrom-Kakeya theorem

This paper presents an extension of the Enestrom-Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown (K, L) methods. The generalization relates to relaxing one of the inequalities on the coefficients of the polynomial. Two results concerning the zeros of polynomials will be proved, one of them providing a partial answer to a conjecture by Meneguette (1994)[6]. (C) 2011 Elsevier Inc. All rights reserved.

Generators of supersymmetric polynomials in positive characteristic

In Kantor and Trishin (1997) [3], Kantor and Trishin described the algebra of polynomial invariants of the adjoint representation of the Lie superalgebra gl(m vertical bar n) and a related algebra A, of what they called pseudosymmetric polynomials over an algebraically closed field K of characteristic zero. The algebra A(s) was investigated earlier by Stembridge (1985) who in [9] called the elements of A(s) supersymmetric polynomials and determined generators of A(s). The case of positive characteristic p of the ground field K has been recently investigated by La Scala and Zubkov (in press) in [6]. We extend their work and give a complete description of generators of polynomial invariants of the adjoint action of the general linear supergroup GL(m vertical bar n) and generators of A(s).

The uncertain consequences of transferring bacterial strains between laboratories - rpoS instability as an example

Abstract Background Microbiological studies frequently involve exchanges of strains between laboratories and/or stock centers. The integrity of exchanged strains is vital for archival reasons and to ensure reproducible experimental results. For at least 50 years, one of the most common means of shipping bacteria was by inoculating bacterial samples in agar stabs. Long-term cultures in stabs exhibit genetic instabilities and one common instability is in rpoS. The sigma factor RpoS accumulates in response to several stresses and in the stationary phase. One consequence of RpoS accumulation is the competition with the vegetative sigma factor σ70. Under nutrient limiting conditions mutations in rpoS or in genes that regulate its expression tend to accumulate. Here, we investigate whether short-term storage and mailing of cultures in stabs results in genetic heterogeneity. Results We found that samples of the E. coli K-12 strain MC4100TF exchanged on three separate occasions by mail between our laboratories became heterogeneous. Reconstruction studies indicated that LB-stabs exhibited mutations previously found in GASP studies in stationary phase LB broth. At least 40% of reconstructed stocks and an equivalent proportion of actually mailed stock contained these mutations. Mutants with low RpoS levels emerged within 7 days of incubation in the stabs. Sequence analysis of ten of these segregants revealed that they harboured each of three different rpoS mutations. These mutants displayed the classical phenotypes of bacteria lacking rpoS. The genetic stability of MC4100TF was also tested in filter disks embedded in glycerol. Under these conditions, GASP mutants emerge only after a 3-week period. We also confirm that the intrinsic high RpoS level in MC4100TF is mainly due to the presence of an IS1 insertion in rssB. Conclusions Given that many E. coli strains contain high RpoS levels similar to MC4100TF, the integrity of such strains during transfers and storage is questionable. Variations in important collections may be due to storage-transfer related issues. These results raise important questions on the integrity of bacterial archives and transferred strains, explain variation like in the ECOR collection between laboratories and indicate a need for the development of better methods of strain transfer.