In this paper we consider an aggregation technique introduced by Yıldıran [45] to study the convex hull of regions defined by two quadratic inequalities or by a conic quadratic and a quadratic inequality. Yıldıran [45] shows how to characterize the convex hull of open sets defined by two strict quadratic inequalities using Linear Matrix Inequalities (LMI). We show how this aggregation technique...

Quadratic programming (QP) is an optimization problem wherein one minimizes (or maximizes) a quadratic function of a finite number of decision variable subject to a finite number of linear inequality and/ or equality constraints. In this paper, a quadratic programming problem (FFQP) is considered in which all cost coefficients, constraints coefficients, and right hand side are characterized by ...

A $Gamma$-so-ring is a structure possessing a natural partial ordering, an infinitary partial addition and a ternary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a $Gamma$-so-ring. In this paper we introduce the notions of subdirect product and $(phi,rho)$-product of $Gamma$-so-rings and study $(phi,rho)$-represen...

The stability of discrete-time systems with time varying delay in the state can be analyzed by using a discrete-time extension of the classical Lyapunov-Krasovskii approach. In the networked control systems domain a similar delay stability problem is treated using a switched system transformation approach. The paper aims to establish a relation between the switched system transformation approac...

ABSTRACT: In this paper we derive guaranteed hybrid gain, sector, and disk margins for nonlinear optimal and inverse optimal hybrid regulators that minimize a nonlinear-nonquadratic hybrid performance functional. Furthermore, we develop a hybrid return difference inequality to provide connections between dissipativity and optimality of nonlinear hybrid controllers. Specifically, we show that op...

We give a necessary and sufficient condition on a radially symmetric potential V on a bounded domain Omega of (n) that makes it an admissible candidate for an improved Hardy inequality of the following type. For every element in H(1)(0)(Omega) integral(Omega) |vector differential u|2 dx - ((n - 2)/2)2 integral(Omega) |u|2/|x|2 dx > or = c integral(Omega) V(x)|u|2 dx. A characterization of the b...

We show how to use the parallelized kangaroo method for computing invariants in real quadratic function fields. Specifically, we show how to apply the kangaroo method to the infrastructure in these fields. We also show how to speed up the computation by using heuristics on the distribution of the divisor class number, and by using the relatively inexpensive baby steps in the real quadratic mode...

Let $S(\rho)$ be the von Neumann entropy of a density matrix $\rho$. Weak monotonicity asserts that $S(\rho_{AB}) - S(\rho_A) + S(\rho_{BC}) S(\rho_C)\geq 0$ for any tripartite $\rho_{ABC}$, fact is equivalent to strong subadditivity entropy. We prove an operator inequality, which, upon taking expectation value with respect state reduces weak inequality. Generalizations this inequality one invo...