From refined estimates for spherical harmonics to a sharp multiplier theorem on the Grushin sphere

We prove a sharp multiplier theorem of Mihlin-H\"ormander type for the Grushin operator on the unit sphere in $\mathbb{R}^3$, and a corresponding boundedness result for the associated Bochner-Riesz means. The proof hinges on precise pointwise bounds for spherical harmonics.Comment: 32 page

Computationally-Effective Optimal Excitation Matching for the Synthesis of Large Monopulse Arrays

Antenna arrays able to generate two different patterns are widely used in tracking radar systems [1]. Optimal (in the Dolph�]Chebyshev sense) sum [2] and difference patterns [3] can be generated by using two independent feed networks. Unfortunately, such a situation generally turns out to be impracticable because of its costs, the occupied physical space, the circuit complexity, and electromagnetic interferences. Thus, starting from the optimal sum pattern a sub�]optimal solution for the difference pattern is usually synthesized by means of the sub�]array technique. The array elements are grouped in sub�]arrays properly weighted for matching the constrains of the difference beam. Finding the best elements grouping and the sub�]array weights is a complex and challenging research topic, especially when dealing with large arrays. As far as linear arrays are concerned, McNamara proposed in [4] an analytical method for determining the �gbest compromise�h difference pattern. Unfortunately, when the ratio between the elements of the array and sub�]arrays increases, such a technique exhibits several limitations mainly due to the ill�]conditioning of the problem and the computational costs due to exhaustive evaluations. A non�]negligible saving might be achieved by applying optimization algorithms (see for instance [5] and [6]) aimed at minimizing a suitable cost function. Notwithstanding, optimization�]based approaches still appear computationally expensive when dealing with large arrays because of wide dimension of solution space to be sampled. In order to properly deal with these computational issues, this contribution presents an innovative approach based on an optimal excitation matching procedure. By exploiting the relationship between independently�]optimal sum and difference patterns, the dimension of the solution space is considerably reduced and efficiently sampled by taking into account the presence of array elements more suitable to change sub�]array membership. In the following, the proposed technique is described pointing out, through a representative case, its potentialities and effectiveness in dealing with large arrays. This is the author's version of the final version available at IEEE

An innovative approach based on a tree-searching algorithm for the optimal matching of independently optimum sum and difference excitations

An innovative approach for the optimal matching of independently optimum sum and difference patterns through sub-arrayed monopulse linear arrays is presented. By exploiting the relationship between the independently optimal sum and difference excitations, the set of possible solutions is considerably reduced and the synthesis problem is recast as the search of the best solution in a non-complete binary tree. Towards this end, a fast resolution algorithm that exploits the presence of elements more suitable to charge sub-array membership is presented. The results of a set of numerical experiments are reported in order to validate the proposed approach pointing out its effectiveness also in comparison with state-of-the-art optimal matching techniques. (c) 2008 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works

An Empirical Investigation on the Efficiency, Capacity Ownership of Italian Airports

In this paper we study the efficiency of Italian airports applying a DEA model to 34 airports. We find that large airports are more efficient than domestic and regional ones, i.e. small airports have spare capacity since they are more distant from the frontier than large airports. The Tobit regression on the estimated DEA scores shows that efficiency is positively related with the hub premium and with privatisation. Hence we suggest that privatisation incentives to invest in large airports (close to saturation) and development plans to improve the small airports may form the benchmarks of Italian short-run air transportation policy.

The impact of airport competition on technical efficiency: A Stochastic Frontier Analysis applied to Italian airports

We investigate how the intensity of competition among airports affects their technical efficiency by computing airports’ markets on the basis of a potential demand approach. We find that the intensity of competition has a negative impact on airports’ efficiency in Italy during the 2005–2008 period. This implies that airports belonging to a local air transportation system where competition is strong exploit their inputs less intensively than do airports with local monopoly power. Furthermore, we find that public airports are more efficient than private and mixed ones. Since public airports take into account the positive externalities created by air transportation in the local economy, they are more willing to subsidize airlines in developing the airports’ connections. Hence, policy makers should provide incentives to implement airports’ specialization in local systems where competition is strong. Moreover, when regulating airport charges, they should take into account the impact of the above externalities.Airport efficiency; stochastic distance function; airport competition

Experimental Realization of Polarization Qutrits from Non-Maximally Entangled States

Based on a recent proposal [Phys. Rev. A 71, 062337 (2005)], we have experimentally realized two photon polarization qutrits by using non-maximally entangled states and linear optical transformations. By this technique high fidelity mutually unbiased qutrits are generated at a high brilliance level.Comment: RevTex, 8 pages, 6 figure

Hyperentanglement witness

A new criterium to detect the entanglement present in a {\it hyperentangled state}, based on the evaluation of an entanglement witness, is presented. We show how some witnesses recently introduced for graph states, measured by only two local settings, can be used in this case. We also define a new witness $W_3$ that improves the resistance to noise by increasing the number of local measurements.Comment: 6 pages, 2 figures, RevTex. v2: new title, minor changes in the explanation of the witness for hyperentangled states, more comments in the conclusions sectio

Realization and characterization of a 2-photon 4-qubit linear cluster state

We report on the experimental realization of a 4-qubit linear cluster state via two photons entangled both in polarization and linear momentum. This state was investigated by performing tomographic measurements and by evaluating an entanglement witness. By use of this state we carried out a novel nonlocality proof, the so-called ``stronger two observer all versus nothing'' test of quantum nonlocality.Comment: 4 pages, 4 figure

Hyperentanglement of two photons in three degrees of freedom

A 6-qubit hyperentangled state has been realized by entangling two photons in three degrees of freedom. These correspond to the polarization, the longitudinal momentum and the indistinguishable emission produced by a 2-crystal system operating with Type I phase matching in the spontaneous parametric down conversion regime. The state has been characterized by a chained interferometric apparatus and its complete entangled nature has been tested by a novel witness criterium specifically introduced for hyperentangled states. The experiment represents the first realization of a genuine hyperentangled state with the maximum entanglement between the two particles allowed in the given Hilbert space.Comment: 4 pages, 2 figures, Revtex