Two inequalities for weighted sums of powers are established. Applications to Jacobian elliptic functions and Legendre’s elliptic integrals of the first kind are presented. Some known and new inequalities for circular and hyperbolic functions are obtained. Applications to certain iterative means including Gauss’ arithmetic-geometric mean and Schwab-Borchardt mean are included. Mathematics subje...

Abstract We observe that every quadrature of numerical integration together with a strictly increasing and continuous function generates mean then we study this family means. characterize the functions which generate weighted arithmetic means in way show how to obtain comparison type theorems for generated by different quadratures.

It is usually difficult to characterize the alternative hypothesis precisely in a log-likelihood ratio (LLR)-based speaker verification system. In a previous work, we proposed using a weighted arithmetic combination (WAC) or a weighted geometric combination (WGC) of the likelihoods of the background models instead of heuristic combinations, such as the arithmetic mean and the geometric mean, to...