In this short note, we present a refinement of the logarithmic-geometric mean inequality. As an application of our result, we obtain an operator inequality associated with geometric and logarithmic means.

Epidemiological studies have reported process-specific elevated prevalence of beryllium sensitization (BeS) and chronic beryllium disease (CBD) among workers. However, exposure-response relationships have been inconsistent, possibly due to incomplete characterization of many biologically relevant aspects of exposure, including particle size. In 1999, two surveys were conducted 3-5 months apart ...

It is well-known that for Hilbert space linear operators 0 ≤ A and 0 ≤ C, inequality C ≤ A does not imply C ≤ A. We introduce a strong order relation 0 ≤ B≪ A, which guarantees that C ≤ BAB for all 0 ≤ C ≤ B, and that C ≤ A when B commutes with A. Connections of this approach with the arithmetic-geometric mean inequality of Bhatia–Kittaneh as well as the Kantorovich constant of A are mentioned.

T his article describes an important improvement in the calculation of the Consumer Price Index (CPI). The Bureau of Labor Statistics plans to use a new geometric mean formula for calculating most of the basic components of the Consumer Price Index for all Urban Consumers (CPI-U) and the Consumer Price Index for Urban Wage Earners and Clerical Workers (CPI-W). This change will become effective ...

Academics and practitioners usually optimize portfolios on the basis of mean and variance. They set the goal of maximizing risk-adjusted returns measured by the Sharpe ratio and thus determine their optimal exposures to the assets considered. However, there is an alternative criterion that has an equally plausible underlying idea; geometric mean maximization aims to maximize the growth of the c...