Distance between vertical asymptotes of solutions of certain nonlinear differential equations

AbstractIn [S.B. Eliason, On the distance between vertical asymptotes of solutions of a second-order differential equation, J. Math. Anal. Appl. 35 (1971) 148–156], Eliason asks the question if there are results concerning bounds for the distance between vertical asymptotes of solutions of the second-order differential equation (ry′)′−pyf(y)=0, in the case where the solution y has at least one zero between each consecutive pair of its vertical asymptotes. In this paper, we answer in the affirmative by presenting such results. We also present other related results for some other nonlinear differential equations

Effect of obesity on constant workrate exercise in hyperinflated men with COPD

<p>Abstract</p> <p>Background</p> <p>Chronic obstructive pulmonary disease (COPD) and a high body mass index (BMI) can both affect pulmonary volumes as well as exercise tolerance, but their combined effect on these outcomes is not well known. The aim of this study was to investigate the effects of increased BMI during constant workrate cycle ergometry in patients with COPD.</p> <p>Methods</p> <p>Men with COPD and hyperinflation were divided according to World Health Organization BMI classification: 84 normal BMI (NBMI), 130 overweight (OW) and 64 obese (OB). Patients underwent spirometric and lung volumes assessment and an incremental cycling exercise test. This was followed by a constant workrate exercise test (CET) at 75% of peak capacity. Inspiratory capacity and Borg dyspnea scores were measured at baseline, during and at the end of CET.</p> <p>Results and discussion</p> <p>FEV₁% predicted was not different across BMI classes. Total lung capacity and functional residual capacity were significantly lower in OB and OW compared to NBMI patients. Peak VO₂in L·min^-1was significantly higher in OB and OW patients than in NBMI patients. CET time was not different across BMI classes (p = 0.11). Changes in lung volumes and dyspnea during CET were not different between BMI categories.</p> <p>Conclusions</p> <p>OB and OW patients with COPD had a higher peak VO₂than their lean counterparts. Endurance time, dyspnea and changes in lung volumes during CET were similar between BMI categories.</p

Some New Inequalities for a Sum of Exponential Functions

Abstract In this paper, we present some new inequalities for sums of exponential functions which improve upon upper and lower estimates given in Ahmad [2004]. In some cases, a more general choice of exponential function parameters is allowed. Numerical comparisons are also made. Besides upper and lower bounds for minimum values, we present a very accurate approximation to the minimum values considered i

A weighted least-squares procedure for estimating the parameters of Altham's multiplicative generalization of the binomial distribution

A weighted least-squares procedure is proposed for estimating the two parameters of the multiplicative generalization of the binomial distribution proposed by Altham (1978). These estimators are asymptotically efficient and are offered as simpler alternatives to the maximum likelihood estimators. In some small sample cases, the proposed estimators have smaller mean squared error.Binomial distribution Maximum likelihood estimation Multivariate normal Weighted least squares