We establish an elementary lower estimate for the norm of the Kerzman-Stein operator for a smooth, bounded domain. The estimate involves the boundary length and logarithmic capacity. The estimate is tested on model domains for which the norm is known explicitly. It is shown that the estimate is sharp for an annulus and a strip, and is asymptotically sharp for an ellipse and a wedge.

The present paper reports on the experimental and theoretical investigations on the lower explosion limits of single dusts, gases as well of two phase mixtures such as gas/dust, vapor/dust, spray/vapor and vapor/gas. The materials used were corn starch, lycopodium, toner and high density polyethylene as dusts, methane and hydrogen as combustible (perfect) gases and acetone and isopropanol as sp...

In the paper, we analyze the L norm error estimate of lower order finite element methods for the fourth order problem. We prove that the best error estimate in the L norm of the finite element solution is of second order, which can not be improved generally. The main ingredients are the saturation condition established for these elements and an identity for the error in the energy norm of the f...

Copyright q 2010 Zisheng Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We extend the classical Bishop-Gromov volume comparison from constant Ricci curvature lower bound to radially symmetric Ricci curvature lower bound...

INTRODUCTION For survival data the coefficient of determination cannot be used to describe how good a model fits to the data. Therefore, several measures of explained variation for survival data have been proposed in recent years. METHODS We analyse an existing measure of explained variation with regard to minimisation aspects and demonstrate that these are not fulfilled for the measure. RE...

CONTEXT Ongoing efforts to improve the quality of reporting for randomized controlled trials (RCTs) include the Consolidated Standards of Reporting Trials (CONSORT) statement. We examined the frequency of explicit reporting of the number needed to treat (NNT) and the absolute risk reduction (ARR) in RCTs. METHODS Five frequently cited journals were investigated: Annals of Internal Medicine, B...

Informed participation in population based screening programmes requires an explicit sharing of information about risks and benefits. However, many factors influence perceptions of risk and the value of risk reduction promised through screening. Campaigns that selectively quote incidence to “frighten” women into undergoing mammography have been criticised. Perceived risk, not objective risk, ex...