We generalize the Gebelein inequality for Gaussian random vectors in R^d.

Udowodniono prawa wielkich liczb dla funkcjonałów gaussowskichkorzystając z nierówności Gebeleina.

In this paper, we estimate aversion to rank inequality (ATRI) underlying selected Italian income inequality indices, I, notably the Pietra index, the Bonferroni index and the “new” Zenga index. We measure ATRI by the parameter v of the generalised Gini index G(v). ATRI is distinct from aversion to income inequality, as measured by parameter ε of Atkinson’s index A(ε). We propose eliciting v from the equation I = GE(v). As, in general,...

Design optimization of passive microwave components is an intricate process, especially if the primary objective is a reduction of the physical size of the structure. The latter has become an important design consideration for a growing number of modern applications (mobile communications, wearable/implantable devices, internet of things), where miniaturization is imperative due to a limited space allocated for the electronic circuitry....

We derive a simple lower bound on the geometric measure of entanglement for mixed quantum states in the case of a general multipartite system. The main ingredient of the presented derivation is the triangle inequality applied to the root infidelity distance in the space of density matrices. The obtained bound leads to entanglement criteria with a straightforward interpretation. The proposed criteria provide an experimentally accessible,...