in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.

In this study, by a non-negative homogeneous kernel k we prove some extensions of Hardy's inequalityin two and three dimensions

Let $D$ be an integral domain and $star$ a semistar operation stable and of finite type on it. We define the semistar dimension (inequality) formula and discover their relations with $star$-universally catenarian domains and $star$-stably strong S-domains. As an application, we give new characterizations of $star$-quasi-Pr"{u}fer domains and UM$t$ domains in terms of dimension inequal...

This paper addresses questions involving the sharpness of Vojta's conjecture and Vojta's inequality for algebraic points on curves over number elds. It is shown that one may choose the approximation term m S (D;?) in such a way that Vojta's inequality is sharp in Theorem 2.3. Partial results are obtained for the more diicult problem of showing that Vojta's conjecture is sharp when the approxima...

let $d$ be an integral domain and $star$ a semistar operation stable and of finite type on it. we define the semistar dimension (inequality) formula and discover their relations with $star$-universally catenarian domains and $star$-stably strong s-domains. as an application, we give new characterizations of $star$-quasi-pr"{u}fer domains and um$t$ domains in terms of dimension ine...

A framework for robustness analysis of input constrained nite receding horizon control is presented. Under the assumption of quadratic upper bounds on the nite horizon costs, we derive suucient conditions for robust stability of the standard discrete-time linear-quadratic receding horizon control formulation. This is achieved by recasting conditions for nominal and robust stability as an implic...