Comparison Methods for Solving Non-Linear Sturm-Liouville Eigenvalues Problems
SYMMETRY-BASEL
Authors: Al-Khaled, Kamel; Hazaimeh, Ashwaq
Abstract
In this paper, we present a comparative study between Sinc-Galerkin method and a modified version of the variational iteration method (VIM) to solve non-linear Sturm-Liouville eigenvalue problem. In the Sinc method, the problem under consideration was converted from a non-linear differential equation to a non-linear system of equations, that we were able to solve it via the use of some iterative techniques, like Newton's method. The other method under consideration is the VIM, where the VIM has been modified through the use of the Laplace transform, and another effective modification has also been made to the VIM by replacing the non-linear term in the integral equation resulting from the use of the well-known VIM with the Adomian's polynomials. In order to explain the advantages of each method over the other, several issues have been studied, including one that has an application in the field of spectral theory. The results in solutions to these problems, which were included in tables, showed that the improved VIM is better than the Sinc method, while the Sinc method addresses some advantages over the VIM when dealing with singular problems.
Antimicrobial resistance patterns and genotypic diversity between clinical and water systems isolates of Pseudomonas aeruginosa in Cali, Colombia
TROPICAL BIOMEDICINE
Authors: Chavez, M.; Cabezas, A. F.; Ferauds, M.; Castillo, J. E.; Caicedo, L. D.
Abstract
Pseudomonas aeruginosa is considered an opportunistic pathogen, causing a wide variety of infections in compromised hosts, also frequently develops multi-resistance to antibiotics and can colonize various habitats, including water systems. The main aim of this study was to investigate antibiotics susceptibility pattern, genotypic diversity and detection of resistence genes in P. aeruginosa isolates from clinical and aquatic environment sources. Of the 220 P. aeruginosa isolates examined, 48 were clinical isolates and 172 isolates from wastewater and freshwater. Susceptibility to eight antimicrobial agents was carried out by disk diffusion method. Clinical and environmental isolates were screened for the presence of the genes encoding bla(KPC-2), bla(CTX-M-9), bla(PER-1), bla(OXA-10), bla(IMP-1), bla(VIM-2) and bla(ampC) by polymerase chain reaction (PCR). Isolates were examined with PCR-SSCP analysis of partial DNAr 16S sequence. Isolates were mainly resistant to cefoxitin. Multidrug-resistant P. aeruginosa (MDRPA) strains were found in 70% and 90.3% of the clinical and environmental isolates, respectively. The prevalence rates of a-lactamase genes were recorded (bla(KPC-2) 41.3%, bla(VIM-2) 36.8%, bla(IMP-1) 13.6%, bla(CTX-M-9) 10.9% and bla(ampC) 10.5%,). The PCR-SSCP analysis showed three conformational patterns. All clinical isolates and most environmental isolates were grouped into a single cluster. In this study, we found that P. aeruginosa strains recovered from city water systems must be considered potential reservoir for ESBL genes, especially blaKPC-2 and blaVIM-2.