We investigate the level density for several ensembles of positive random matrices of a Wishart-like structure, W=XX(†), where X stands for a non-Hermitian random matrix. In particular, making use of the Cauchy transform, we study the free multiplicative powers of the Marchenko-Pastur (MP) distribution, MP(⊠s), which for an integer s yield Fuss-Catalan distributions corresponding to a product o...

The explicit formulas for the sums of positive powers of the integers si unrepresentable by the triple of integers d1, d2, d3 ∈ N, gcd(d1, d2, d3) = 1, are derived.

n The Federalist, James Madison wrote that in fashioning the federal relationship "the convention must have been compelled to sacrifice theoretical propriety to the force of extraneous circumstances." These sacrifices which produced a "compound republic, partaking both of the national and federal character" were "rendered indispensable" by what Madison termed "the peculiarity of our political s...

This paper analyzes the extent to which the justices of the U.S. Supreme Court cast votes that support the positions of the president, or more generally the Executive Branch. Can presidents count on such deference from those justices they nominate or those whom are nominated by other presidents of the same party? Or, do the justices demonstrate judicial independence and impartiality such that t...

We experimentally study light localization at phase-slip waveguides and at the intersection of phase slips in a two-dimensional (2D) square photonic lattice. Such systems allow for the observation of a variety of effects, including the existence of spatially localized modes for low powers, the generation of strongly localized states in the form of discrete bulk and surface solitons, as well as ...

Dissipative engineering constitutes a framework within which quantum information processing protocols are powered by system-environment interaction rather than by unitary dynamics alone. This framework embraces noise as a resource and, consequently, offers a number of advantages compared to one based on unitary dynamics alone, e.g., that the protocols are typically independent of the initial st...

We continue the study of partially ordered generalized patterns (POGPs) considered in [9] for permutations and in [10] for words. We deal with segmented POGPs (SPOGPs). We state some general results and treat a number of patterns of length 4. We prove a result from [8] in a much simpler way and also establish a connection between SPOGPs and walks on lattice points starting from the origin and r...