The Barankin bound is generalized to the vector case in the mean square error sense. Necessary and sufficient conditions are obtained to achieve the lower bound. To obtain the result, a simple finite dimensional real vector valued generalization of the Riesz representation theorem for Hilbert spaces is given. The bound has the form of a linear matrix inequality where the covariances of any unbi...

OBJECTIVE The aim of this study was to examine the impact that national income and income inequality in high and low income countries have on the relationship between dental caries and sugar consumption. METHODS An ecological study design was used in this study of 73 countries. The mean decayed, missing, or filled permanent teeth (DMFT) for 12-year-old children were obtained from the WHO Oral...

The prime purpose of this paper is to provide a refinement Jensen’s inequality in connection with positive finite sequence. We deal the for particular cases and point out relation between new result earlier results inequality. As results, we obtain refinements quasi-arithmetic power mean inequalities. Finally, several are obtained information theory help main results.

background: despite significant reduction in global disease prevalence, leprosy still has a high rate of disability while its determinants are unfair and many of them are amendable. the objective of this study was to measure inequality of disability in leprosy in iran. methods: this was a cross‑sectional study (2006‑2007) on all living people affected by leprosy registered in w. azerbaijan prov...