We derive bounds on the variance of a random variable in terms of its arithmetic and harmonic means. Both discrete and continuous cases are considered, and an operator version is obtained. Some refinements of the Kantorovich inequality are obtained. Bounds for the largest and smallest eigenvalues of a positive definite matrix are also obtained.

Automobile manufacturers specify in their requirements the characteristics of the microgeometry of metal plate quality. These quality criteria are a necessary condition for realization of supply of metal plates to the manufacturers. Each manufacturer has its own specifications. For example the Ford company requires that the roughness average on both sides of the metal plate be within the range ...

by using generalized salagean differential operator a newclass of univalent holomorphic functions with fixed finitely manycoefficients is defined. coefficient estimates, extreme points,arithmetic mean, and weighted mean properties are investigated.

Purpose: The recent development of enamel-colored translucent zirconia makes it a viable material to produce crowns. However, achieve sufficient surface roughness for bonding, alumina particle abrasion must be employed. In this study, the effects on and sample pretreatment bond strength between composite resin core were investigated compared optimize treatment conditions.Methods: Zirconia speci...

‎we obtain the asymptotic expansion of the sequence with general term $frac{a_n}{g_n}$‎, ‎where $a_n$ and $g_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎also‎, ‎we obtain some explicit bounds concerning $g_n$ and $frac{a_n}{g_n}$.