Abstract In this paper, we improve some numerical radius inequalities for Hilbert space operators under suitable condition. We also compare our results with known results. As application of result, obtain an operator inequality.

This paper deals with the threshold radius that warrants the use of single restraining rail for transit and railroads. Different railways use different threshold radius from 91m to 365m to provide restraining rail. These threshold figures are probably experience driven choices. The need for restraining rail may be related to a so-called derailment alarm coefficient of 1.2 sustained over 2m leng...