APPROXIMATE CALCULATION OF SUMS I: BOUNDS FOR THE ZEROS OF GRAM POLYNOMIALS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Zeros of classical orthogonal polynomials of a discrete variable

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.

On the use of Gram matrix in observability analysis

This letter presents some notes on the use of the Gram matrix in observability analysis. This matrix is constructed considering the rows of the measurement Jacobian matrix as vectors, and it can be employed in observability analysis and restoration methods. The determination of nonredundant pseudo-measurements (normally injections pseudo-measurements) for merging observable islands into an observable (single) system is carried out analyzing the pivots of the Gram matrix. The Gram matrix can also be used to verify local redundancy, which is important in measurement system planning. Some numerical examples` are used to illustrate these features. Others features of the Gram matrix are under study.

Genomics of pyrrolnitrin biosynthetic loci: evidence for conservation and whole-operon mobility within Gram-negative bacteria

Pyrrolnitrin (PRN) is a tryptophan-derived secondary metabolite produced by a narrow range of Gram-negative bacteria. The PRN biosynthesis by rhizobacteria presumably has a key role in their life strategies and in the biocontrol of plant diseases. The biosynthetic operon that encodes the pathway that converts tryptophan to PRN is composed of four genes, prnA through D, whose diversity, genomic context and spread over bacterial genomes are poorly understood. Therefore, we launched an endeavour aimed at retrieving, by in vitro and in silico means, diverse bacteria carrying the prnABCD biosynthetic loci in their genomes. Analysis of polymorphisms of the prnD gene sequences revealed a high level of conservation between Burkholderia, Pseudomonas and Serratia spp. derived sequences. Whole-operon- and prnD-based phylogeny resulted in tree topologies that are incongruent with the taxonomic status of the evaluated strains as predicted by 16S rRNA gene phylogeny. The genomic composition of c. 20 kb DNA fragments containg the PRN operon varied in different strains. Highly conserved and distinct transposase-encoding genes surrounding the PRN biosynthetic operons of Burkholderia pseudomallei strains were found. A prnABCD-deprived genomic region in B. pseudomallei strain K96243 contained the same gene composition as, and shared high homology with, the flanking regions of the PRN operon in B. pseudomallei strains 668, 1106a and 1710b. Our results strongly suggest that the PRN biosynthetic operon is mobile. The extent, frequency and promiscuity of this mobility remain to be understood.

Antimicrobial ent-pimarane diterpenes from Viguiera arenaria against Gram-positive bacteria

The dichloromethane crude extract from the roots of Viguiera arenaria (VaDRE) has been employed in an antimicrobial screening against several bacteria responsible for human pathologies. The main diterpenes isolated from this extract, as well as two semi-synthetic pimarane derivatives, were also investigated for the pathogens that were significantly inhibited by the extract (MIC values lower than 100 mu g mL(-1)). The VaDRE extract was significantly active only against Gram-positive microorganisms. The compounds ent-pimara-8(14),15-dien-19-oic acid (PA): PA sodium salt; ent-8(14),15-pimaradien-3 beta-ol; ent-15-pimarene-8 beta,19-diol; and ent-8(14),15-pimaradien-3 beta-acetoxy displayed the highest antibacterial activities (MIC values lower than 10 mu g mL(-1) for most pathogens). In conclusion, our results suggest that pimaranes are an important class of natural products for further investigations in the search of new antibacterial agents. (c) 2009 Elsevier B.V. All rights reserved.

Friedmanniella spumicola sp nov and Friedmanniella capsulata sp nov from activated sludge foam: Gram-positive cocci that grow in aggregates of repeating groups of cocci

Two Gram-positive, non-motile, non-spore-forming, strictly aerobic, pigmented cocci, strains Ben 107(T) and Ben 108(T), growing in aggregates were isolated from activated sludge samples by micromanipulation. Both possessed the rare type A3 gamma' peptidoglycan. Major menaquinones of strain Ben 107(T) were MK-9(H-4) and MK-7(H-2), and the main cellular fatty acid was 12-methyltetradecanoic acid (ai-C-15:0). In strain Ben 108(T), MK-9(H-4), MK-9(H-2) and MK-7(H-4) were the menaquinones and again the main fatty acid was 12-methyltetradecanoic acid (ai-C-15:0). Polar lipids in both strains consisted of phosphatidyl inositol, phosphatidyl glycerol and diphosphatidyl glycerol with two other unidentified glycolipids and phospholipids also present in both. These data, together with the 16S rDNA sequence data, suggest that strain Ben 107(T) belongs to the genus Friedmanniella which presently includes a single recently described species, Friedmanniella antarctica. Although the taxonomic status of strain Ben 108(T) is far less certain, on the basis of its 16S rRNA sequence it is also adjudged to be best placed in the genus Friedmanniella, The chemotaxonomic characteristics and DNA-DNA hybridization data support the view that Ben 107(T) and Ben 108(T) are novel species of the genus Friedmanniella. Hence, it is proposed that strain Ben 107(T) (=ACM 5121(T)) is named as Friedmanniella spumicola sp. nov. and strain Ben 108(T) (=ACM 5120(T)) as Friedmanniella capsulata sp. nov.

The challenge of multidrug resistance: The treatment of gram-negative rod infections

Infections caused by multidrug-resistant gram-negative bacteria are an increasing problem worldwide. Treatment of these microorganisms is a challenge because resistance limits dramatically therapeutic options. In this review, we discuss data of in vitro susceptibility and clinical studies of possible agents for the management of these infections. Currently, published data are limited, and there are no randomized clinical trials involving the treatment of infections caused by multidrug-resistant gram-negative rods. For imipenem-resistant Acinetobacter spp., most studied options are polymyxins and sulbactam. No newer antimicrobials active against Pseudomonas aeruginosa are available or under investigation. Tigecycline presents a broad spectrum of activity in vitro but has been studied mainly as treatment of community-acquired infections, as has ertapenem. They are potential options against extended-spectrum P-lactamase-producing Enterobacteriaceae, and tigecycline may be useful in treating Acinetobacter infections.

Strong Grobner bases for polynomials over a principal ideal ring

Grobner bases have been generalised to polynomials over a commutative ring A in several ways. Here we focus on strong Grobner bases, also known as D-bases. Several authors have shown that strong Grobner bases can be effectively constructed over a principal ideal domain. We show that this extends to any principal ideal ring. We characterise Grobner bases and strong Grobner bases when A is a principal ideal ring. We also give algorithms for computing Grobner bases and strong Grobner bases which generalise known algorithms to principal ideal rings. In particular, we give an algorithm for computing a strong Grobner basis over a finite-chain ring, for example a Galois ring.

Subspace wavepacket evolution with Newton polynomials

Time-dependent wavepacket evolution techniques demand the action of the propagator, exp(-iHt/(h)over-bar), on a suitable initial wavepacket. When a complex absorbing potential is added to the Hamiltonian for combating unwanted reflection effects, polynomial expansions of the propagator are selected on their ability to cope with non-Hermiticity. An efficient subspace implementation of the Newton polynomial expansion scheme that requires fewer dense matrix-vector multiplications than its grid-based counterpart has been devised. Performance improvements are illustrated with some benchmark one and two-dimensional examples. (C) 2001 Elsevier Science B.V. All rights reserved.

Post-antibiotic growth suppression of linezolid against Gram-positive bacteria

The in vitro post-antibiotic effects (PAEs) of eight different concentrations of linezolid against Gram-positive cocci were investigated and the results analysed using the sigmoid E-max model for mathematically modelling the PAE. Mean maximal linezolid PAEs against strains of Staphylococcus aureus, Staphylococcus epidermidis, Enterococcus faecalis, Enterococcus faecium and Streptococcus pneumoniae were 2.2, 1.8, 2.8, 2.0 and 3.0 h, respectively. Resistance to methicillin (for the staphylococci), vancomycin (for the enterococci) and penicillin (for the pneumococci) had no effect on the duration of the PAE. Results of PAE testing support twice-daily dosing of linezolid in humans.

On the permutation behaviour of Dickson polynomials of the second kind

The known permutation behaviour of the Dickson polynomials of the second kind in characteristic 3 is expanded and simplified. (C) 2002 Elsevier Science (USA).

The compositional inverse of a class of permutation polynomials over a finite field

A new class of bilinear permutation polynomials was recently identified. In this note we determine the class of permutation polynomials which represents the functional inverse of the bilinear class.

The use of 16s rDNA restriction fragment length polymorphism analysis for the identification of non-fermenting gram negative bacilli in a cystic fibrosis microbiology referral service

The utility of 16s rDNA restriction fragment length polymorphism (RFLP) analysis for the partial genomovar differentiation of Burkholderia cepacia complex bacterium is well documented. We compared the 16s rDNA RFLP signatures for a number of non-fermenting gram negative bacilli (NF GNB) LMG control strains and clinical isolates pertaining to the genera Burkholderia, Pseudomonas, Achromobacter (Alcaligenes), Ralstonia, Stenotrophomonas and Pandoraea. A collection of 24 control strain (LMG) and 25 clinical isolates were included in the study. Using conventional PCR, a 1.2 kbp 16s rDNA fragment was generated for each organism. Following restriction digestion and electrophoresis, each clinical isolate RFLP signature was compared to those of the control strain panel. Nineteen different RFLP signatures were detected from the 28 control strains included in the study. TwentyoneyTwenty- five of the clinical isolates could be classified by RFLP analysis into a single genus and species when compared to the patterns produced by the control strain panel. Four clinical B. pseudomallei isolates produced RFLP signatures which were indistinguishable from B. cepacia genomovars I, III and VIII. The identity of these four isolates were confirmed using B. pseudomallei specific PCR. 16s rDNA RFLP analysis can be a useful identification strategy when applied to NF GNB, particularly for those which exhibit colistin sulfate resistance. The use of this molecular based methodology has proved very useful in the setting of a CF referral laboratory particularly when utilised in conjunction with B. cepacia complex and genomovar specific PCR techniques. Species specific PCR or sequence analysis should be considered for selected isolates; especially where discrepancies between epidemiology, phenotypic and genotypic characteristics occur.

The genetics of glycosylation in Gram-negative bacteria

In recent years there has been a dramatic increase in reports of glycosylation of proteins in various Gram-negative systems including Neisseria meningitidis, Neisseria gonorrhoeae, Campylobacter jejuni, Pseudomonas aeruginosa, Escherichia coli, Caulobacter crescentus, Aeromonas caviae and Helicobacter pylori. Although this growing list contains many important pathogens (reviewed by Benz and Schmidt [Mol. Microbiol. 45 (2002) 267-276]) and the glycosylations are found on proteins important in pathogenesis such as pili, adhesins and flagella the precise role(s) of the glycosylation of these proteins remains to be determined. Furthermore, the details of the glycosylation biosynthetic process have not been determined in any of these systems. The definition of the precise role of glycosylation and the mechanism of biosynthesis will be facilitated by a detailed understanding of the genes involved. (C) 2002 Federation of European Microbiological Societies. Published by Elsevier Science B.V. All rights reserved.