Sub-Rayleigh imaging via N-photon detection

The Rayleigh diffraction bound sets the minimum separation for two point objects to be distinguishable in a conventional imaging system. We demonstrate sub-Rayleigh resolution by scanning a focused beam--in an arbitrary, object-covering pattern that is unknown to the imager--and using N-photon photodetection implemented with a single-photon avalanche detector array. Experiments show resolution improvement by a factor ～(N-N(max))(?) beyond the Rayleigh bound, where N(max) is the maximum average detected photon number in the image, in good agreement with theory.     

GaN/LiNbO3 (0 0 0 1) interface formation calculated from first-principles

The stable adsorption sites for both Ga and N ions on the ideal and on the reconstructed LiNbO₃ (0 0 0 1) surface are determined by means of first-principle total energy calculations. A single N layer is found to be more strongly bound to the substrate than a single Ga layer. The adsorption of a GaN monolayer on the polar substrate within different orientations is then modeled. On the basis of our results, we propose a microscopic model for the GaN/LiNbO₃ interface. The GaN and LiNbO₃ (0 0 0 1) planes are parallel, but rotated by 30° each other, with in-plane epitaxial relationship [1 0 0]_GaN‖ [1 1  0]_LiNbO3. In this way the (0 0 0 1) plane lattice mismatch between GaN and LiNbO₃ is minimal and equal to 6.9% of the GaN lattice constant. The adsorbed GaN and the underlying LiNbO₃ substrate have parallel c-axes.     

Existence of infinitely many stationary solutions of the L2-subcritical and critical NLSE on compact metric graphs

We investigate the existence of stationary solutions for the nonlinear Schrödinger equation on compact metric graphs. In the $L^2$-subcritical setting, we prove the existence of an infinite number of such solutions, for every value of the mass. In the critical regime, the existence of infinitely many solutions is established if the mass is lower than a threshold value, while global minimizers of the NLS energy exist if and only if the mass is lower or equal to the threshold. Moreover, the relation between this threshold and the topology of the graph is characterized. The investigation is based on variational techniques and some new versions of Gagliardo–Nirenberg inequalities.     

Personal income tax reforms: A genetic algorithm approach

Given a settled reduction in the present level of tax revenue, and by exploring a very large combinatorial space of tax structures, in this paper we employ a genetic algorithm in order to determine the ‘best’ structure of a real world personal income tax that allows for the maximisation of the redistributive effect of the tax, while preventing all taxpayers being worse off than with the present tax structure. We take Italy as a case study.     

Cosmology with Gravitational Waves: A Review

Standard sirens have been the central paradigm in gravitational-wave cosmology so far. From the gravitational wave signature of compact star binaries, it is possible to measure the luminosity distance of the source directly, and if additional information on the source redshift is provided, a measurement of the cosmological expansion can be performed. This review article discusses several methodologies that have been proposed to use gravitational waves for cosmological studies. Methods that use only gravitational-wave signals and methods that use gravitational waves in conjunction with additional observations such as electromagnetic counterparts and galaxy catalogs will be discussed. The review also discusses the most recent results on gravitational-wave cosmology, starting from the binary neutron star merger GW170817 and its electromagnetic counterpart and finishing with the population of binary black holes, observed with the third Gravitational-wave Transient Catalog GWTC–3.     

Parallel decomposition methods for linearly constrained problems subject to simple bound with application to the SVMs training

We consider the convex quadratic linearly constrained problem with bounded variables and with huge and dense Hessian matrix that arises in many applications such as the training problem of bias support vector machines. We propose a decomposition algorithmic scheme suitable to parallel implementations and we prove global convergence under suitable conditions. Focusing on support vector machines training, we outline how these assumptions can be satisfied in practice and we suggest various specific implementations. Extensions of the theoretical results to general linearly constrained problem are provided. We included numerical results on support vector machines with the aim of showing the viability and the effectiveness of the proposed scheme.     

Effective algebraic degeneracy

We show that for every smooth projective hypersurface X⊂ℙ ⁿ⁺¹ of degree d and of arbitrary dimension n ≥2, if X is generic, then there exists a proper algebraic subvariety Y ⊊ X such that every nonconstant entire holomorphic curve f :ℂ→X has image f(ℂ) which lies in Y, as soon as its degree satisfies the effective lower bound d\geqslant 2ⁿ⁵d\geqslant 2^{n^{5}} .     

Critical points of solutions of degenerate elliptic equations in the plane

We study the minimizer u of a convex functional in the plane which is not Gâteaux-differentiable. Namely, we show that the set of critical points of any C ¹-smooth minimizer can not have isolated points. Also, by means of some appropriate approximating scheme and viscosity solutions, we determine an Euler–Lagrange equation that u must satisfy. By applying the same approximating scheme, we can pair u with a function v which may be regarded as the stream function of u in a suitable generalized sense.     

Condensed-phase relaxation of multilevel quantum systems. II. Comparison of path integral calculations and second-order relaxation theory for a nondegenerate three-level system

An exactly solvable model of multisite condensed-phase vibrational relaxation was studied in Paper I (Peter, S.; Evans, D. G.; Coalson, R. D. J. Phys. Chem. B 2006, 110, 18758.), where it was shown that long-time steady-state site populations of a degenerate N-level system are not equal (hence, they are non-Boltzmann) and depend on the initial preparation of the system and the number of sites that it comprises. Here we consider a generalization of the model to the case of a nondegenerate three-level system coupled to a high-dimensional bath: such a model system has direct relevance to a large class of donor-bridge-acceptor electron transfer processes. Because the quantum dynamics of this system cannot be computed analytically, we compare numerically exact path integral calculations to the predictions of second-order time-local relaxation theory. For modest system-bath coupling strengths, the two sets of results are in excellent agreement. They show that non-Boltzmann long-time steady-state site populations are obtained when the level splitting is small but nonzero, whereas at larger values of the system bias (asymmetry) these populations become Boltzmann distributed.     

Ruthenium(II) complexes containing tetrazolate group: electrochemiluminescence in solution and solid state

In this work, we report the results about the solution and solid-state phosphorescence emission properties of six Ru(II) complexes containing various 5-substituted tetrazolate ligands. The photo- and electrochemiluminescence spectra of all compounds revealed a red shifted emission with respect to the Ru(bpy)(3)(2+). Significant changes to the light emission energy and to the efficiency and sensitivity to oxygen were also determined by varying the nature of the substituent ring of the tetrazolate ligand. Light-emitting solid devices with active layers containing solid films of the same complexes were prepared, and preliminary studies of their electroinduced emission properties were performed. The electrochemiluminescence (ECL) emission intensity of two of the six complexes was of the same order of magnitude as the reference Ru(bpy)(3)(2+).