We prove a new extremal inequality, motivated by the vector Gaussian broadcast channel problem. As a corollary, this inequality yields a generalization of the classical vector entropy-power inequality (EPI). As another corollary, this inequality sheds insight into maximizing the differential entropy of the sum of two jointly distributed random variables.

Global inequality is a relatively recent topic. It was not until the early 1980s that the first calculations of inequality across world citizens were done.1 This is because in order to calculate global inequality, one needs to have data on (within-) national income distributions for most of the countries in the world, or at least for most of the populous and rich countries. But it is only from ...

In this paper necessary and sufficient conditions for the validity of the generalized Hardy inequality for the case −∞ < q p < 0 and 0 < p q < 1 are derived. Furthermore, some special cases are considered.

The main goal of this work is to provide quantum parametrized Hermite-Hadamard like type integral inequalities for functions whose second derivatives in absolute values follow different convexities. A new identity derived twice differentiable functions, which used as a key element our demonstrations along with several basic such as: power mean inequality, and Holder’s inequality. symmetry the s...

We apply the hypergeometric method of Thue and Siegel to prove, if a and b are positive integers, that the inequality 0 < |a − b | < 1 4 max{a, b} has at most a single solution in positive integers x and y. This essentially sharpens a classic result of LeVeque.