In this paper the failure of Hardy’s nonlocality proof for the class of maximally entangled states is considered. A detailed analysis shows that the incompatibility of the Hardy equations for this class of states physically originates from the fact that the existence of quantum perfect correlations for the three pairs of two-valued observables (D11,D21), (D11,D22), and (D12,D21) [in the sense o...

Schrödinger equations with Hardy-type singular potentials have been the object of a quite large interest in the recent literature, see e.g. [1, 7, 8, 12, 15, 18, 20, 25, 26, 28]. The singularity of inverse square potentials V (x) ∼ λ|x|−2 is critical both from the mathematical and the physical point of view. As it does not belong to the Kato’s class, it cannot be regarded as a lower order pertu...

Let μ1 and μ2 be positive σ-finite measures on Ω1 and Ω2 respectively, k : Ω1 × Ω2 → R be a non-negative function, and K(x) = ∫ Ω2 k(x, y) dμ2(y), x ∈ Ω1. We state and prove a new class of refined general Hardy-type inequalities related to the weighted Lebesgue spaces L and L, where 0 < p ≤ q < ∞ or −∞ < q ≤ p < 0, convex functions and the integral operators Ak of the form Akf(x) = 1 K(x) ∫ Ω2 ...

Two new species, Sarcophaga (Sarcosolomonia) collessi sp.nov. and Sarcophaga (Sarcorohdendorfia) clavus sp.nov., both collected in Queensland, Australia, are described, and the following four new synonymies are proposed: Sarcophaga horti Blackith and Blackith, 1988 syn.nov. of Sarcophaga bancroftorum Johnston and Tiegs, 1921; Sarcophaga fergusonina Hardy, 1940 syn.nov. of Sarcophaga assimilis M...