A Nonlinear Approximate Solution to the Damped Pendulum Derived Using the Method of Successive Approximations

An approximate analytic solution to the damped pendulum is derived using the method of successive approximations to obtain a nonlinear approximation for the system. We take the approximate solution to the undamped pendulum using the method of successive approximations and compare it to the damped pendulum solution when a linear approximation is used. By looking at these two solutions, we can make an educated guess about the form of the general, approximate solution to the nonlinear damped pendulum. By adjusting the initial guesses and the initial conditions, we derive approximate solutions in three ways. Using MATLAB, the approximate solutions are compared to the full numerical solution through the Euler-Cromer method. To determine how accurate the approximations are, the errors of the approximations are calculated relative to the full numerical Euler-Cromer solution. Each new approximation came with a significant decrease in error, with the final error being 0.0099. This resulted in an improvement to the method of successive approximations. Finally, our best approximation is compared to an available and previously published work

Closed form solution for a double quantum well using Gr\"obner basis

Analytical expressions for spectrum, eigenfunctions and dipole matrix elements of a square double quantum well (DQW) are presented for a general case when the potential in different regions of the DQW has different heights and effective masses are different. This was achieved by Gr\"obner basis algorithm which allows to disentangle the resulting coupled polynomials without explicitly solving the transcendental eigenvalue equation.Comment: 4 figures, Mathematica full calculation noteboo

Daptomycin versus vancomycin plus gentamicin for treatment of bacteraemia and endocarditis due to Staphylococcus aureus: subset analysis of patients infected with methicillin-resistant isolates

Objectives: In a prospective, randomized trial, daptomycin was non-inferior to standard therapy for Staphylococcus aureus bacteraemia and right-sided endocarditis. Since rates of infection due to methicillin-resistant S. aureus (MRSA) infection are increasing and treatment outcomes for bacteraemia caused by MRSA are generally worse than those observed with methicillin-susceptible S. aureus bacteraemia, clinical characteristics and treatment results in the trial’s pre-specified subset of patients with MRSA were analysed. Methods: Clinical characteristics and outcomes of patients receiving daptomycin were compared with those receiving vancomycin plus low-dose gentamicin. Success was defined as clinical improvement with clearance of bacteraemia among patients who completed adequate therapy, received no potentially effective non-study antibiotics and had negative blood cultures 6 weeks after end of therapy. Results: Twenty of the 45 (44.4%) daptomycin patients and 14 of the 43 (32.6%) vancomycin/gentamicin patients were successfully treated (difference 11.9%; confidence interval −8.3 to 32.1). Success rates for daptomycin versus vancomycin/gentamicin were 45% versus 27% in complicated bacteraemia, 60% versus 45% in uncomplicated bacteraemia and 50% versus 50% in right-sided MRSA endocarditis. Cure rates in patients with septic emboli and in patients who received pre-enrolment vancomycin were similar between treatment groups. However, in both treatment groups, success rates were lower in the elderly (≥75 years). Persisting or relapsing bacteraemia occurred in 27% of daptomycin and 21% of vancomycin/gentamicin patients; among these patients, MICs of ≥2 mg/L occurred in five daptomycin and four vancomycin/gentamicin patients. The clinical course of several patients may have been influenced by lack of surgical intervention. Conclusions: Daptomycin was an effective alternative to vancomycin/gentamicin for MRSA bacteraemia or right-sided endocarditis

Historic genetic structuring and paraphyly within the Great-tailed Grackle

The Great-tailed Grackle (Quiscalus mexicanus) and Boat-tailed Grackle (Q. major) are sister species that have expanded their ranges during historical times. This expansion has created an area of sympatry between these species in Texas and Louisiana, and between distinctive Great-tailed Grackle subspecies in the southwestern United States and northern Mexico. We investigated the evolutionary histories of both species using mitochondrial DNA sequence data and modern phylogenetic methods. Our results reveal genetic structure within Great-tailed, but not Boat-tailed Grackles. Great-tailed Grackles are separated into two clades, but range expansion in the north has led to secondary contact between them. Boat-tailed Grackles are monophyletic and are embedded within the Great-tailed Grackle assemblage, rendering the latter paraphyletic. These results reveal a complex phylogeographic pattern caused by recent range expansion and secondary contact of once allopatric units

IgG-index predicts neurological morbidity in patients with infectious central nervous system diseases

<p>Abstract</p> <p>Background</p> <p>Prognosis assessment of patients with infectious and neoplastic disorders of the central nervous system (CNS) may still pose a challenge. In this retrospective cross-sectional study the prognostic value of basic cerebrospinal fluid (CSF) parameters in patients with bacterial meningitis, viral meningoencephalitis and leptomeningeal metastases were evaluated.</p> <p>Methods</p> <p>White blood cell count, CSF/serum glucose ratio, protein, CSF/serum albumin quotient and Immunoglobulin indices for IgG, IgA and IgM were analyzed in 90 patients with bacterial meningitis, 117 patients with viral meningoencephalitis and 36 patients with leptomeningeal metastases in a total of 480 CSF samples.</p> <p>Results</p> <p>In the initial spinal tap, the IgG-index was the only independent predictor for unfavorable outcome (GOS < 5) in patients with infectious CNS diseases but not in patients with leptomeningeal metastases. The sensitivity and specificity of an IgG-index of 0.75 and higher for predicting unfavorable outcome was 40.9% and 80.8% in bacterial meningitis and 40% and 94.8% in viral meningoencephalitis, respectively. No significant associations between CSF parameters and outcome could be observed in follow-up CSF samples.</p> <p>Conclusion</p> <p>The present study suggests that in infectious CNS diseases an elevated IgG-Index might be an additional marker for the early identification of patients at risk for neurological morbidity.</p

The role of cranial CT in the investigation of meningitis

More patients with meningitis are undergoing CT and the number of inappropriate requests are increasing. There are few abnormal CT scans presenting a contraindication for lumbar puncture and the majority of these patients usually have clinical signs to suggest raised intracranial pressure

Increasing incidence and mortality of infective endocarditis: a population-based study through a record-linkage system

<p>Abstract</p> <p>Background</p> <p>Few population-based studies provide epidemiological data on infective endocarditis (IE). Aim of the study is to analyze incidence and outcomes of IE in the Veneto Region (North-Eastern Italy).</p> <p>Methods</p> <p>Residents with a first hospitalization for IE in 2000-2008 were extracted from discharge data and linked to mortality records to estimate 365-days survival. Etiology was retrieved in subsets of this cohort by discharge codes and by linkage to a microbiological database. Risk factors for mortality were assessed through logistic regression.</p> <p>Results</p> <p>1,863 subjects were hospitalized for IE, with a corresponding crude rate of 4.4 per 100,000 person-years, increasing from 4.1 in 2000-2002 to 4.9 in 2006-2008 (p = 0.003). Median age was 68 years; 39% of subjects were hospitalized in the three preceding months. 23% of patients underwent a cardiac valve procedure in the index admission or in the following year. Inhospital mortality was 14% (19% including hospital transfers); 90-days and 365-days mortality rose through the study years. Mortality increased with age and the Charlson comorbidity index, in subjects with previous hospitalizations for heart failure, and (in the subcohort with microbiological data) in IE due to Staphylococci (40% of IE).</p> <p>Conclusions</p> <p>The study demonstrates an increasing incidence and mortality for IE over the last decade. Analyses of electronic archives provide a region-wide picture of IE, overcoming referral biases affecting single clinic or multicentric studies, and therefore represent a first fundamental step to detect critical issues related to IE.</p