INTRODUCTION An increasing number of studies are utilizing different magnetic resonance (MR) methods to quantify bone marrow fat due to its potential role in osteoporosis. Our aim is to compare the measurements of bone marrow fat among T1-weighted magnetic resonance imaging (MRI), modified Dixon method (also called fat fraction MRI (FFMRI)), and magnetic resonance spectroscopy (MRS). METHODS ...

The uniformly minimum variance unbiased (UMVU), maximum likelihood, percentile (PC), least squares (LS) and weighted least squares (WLS) estimators of the probability density function (pdf) and cumulative distribution function are derived for the generalized Rayleigh distribution. This model can be used quite effectively in modelling strength data and also modeling general lifetime data. It has...

In this paper an efficient algorithm is proposed for removal of salt & pepper noise from digital images. The proposed algorithm consists of two stages: in first stage the noisy image is processed by adaptive median filter and in the second stage the output of first stage is further processed by modified mean filter. The first stage classifies noisy pixels by comparing each pixel in the image to...

The onset of condensation of hard spheres in a gravitational field is studied using density-functional theory (DFT). We find that the local density approximation yields results identical to those obtained previously using the kinetic theory [Physica A 271, 192, (1999)], and a weighted density-functional theory gives qualitatively similar results, namely, that the temperature at which condensati...

We prove that smooth $C^\infty$ functions are dense in weighted fractional Sobolev spaces on an arbitrary open set, under some mild conditions the weight. also obtain a~similar result non-weighted defined by kernel similar to $x\mapsto |x|^{-d-sp}$. One may consider results be a~version of Meyers--Serrin theorem.