Second Order Freeness and Fluctuations of Random Matrices: II. Unitary Random Matrices

We extend the relation between random matrices and free probability theory from the level of expectations to the level of fluctuations. We show how the concept of "second order freeness", which was introduced in Part I, allows one to understand global fluctuations of Haar distributed unitary random matrices. In particular, independence between the unitary ensemble and another ensemble goes in the large $N$ limit over into asymptotic second order freeness. Two important consequences of our general theory are: (i) we obtain a natural generalization of a theorem of Diaconis and Shahshahani to the case of several independent unitary matrices; (ii) we can show that global fluctuations in unitarily invariant multi-matrix models are not universal.Comment: 31 pages, new section on failure of universality added, typos corrected, additional explanation

Urban Pluvial Flood Risk in Romania, in the Context of Floods Directive Implementation

Romania is a flood prone country and same are her cities. Pluvial floods can occur in urban or rural areas without a direct connection with river or a water body. As part of the Floods Directive implementation, Romania has identified, in the first cycle, a number of 17 urban areas with a significant pluvial flood risk potential. For every urban area identified, flood hazard and flood risk maps have been developed. Based on this, the present paper tries to present some of the main risk receptors, that could give an insight related to the level of risk at which the urban areas are exposed. What is the quantitative risk profile of this cities, what can be done further to mitigate this risk and are there any other urban areas at risk of pluvial flooding? The present paper seeks to provide an answer at the above questions and present potential solutions for pluvial risk reduction

A science based approach to topical drug classification system (TCS).

The Biopharmaceutics Classification System (BCS) for oral immediate release solid drug products has been very successful; its implementation in drug industry and regulatory approval has shown significant progress. This has been the case primarily because BCS was developed using sound scientific judgment. Following the success of BCS, we have considered the topical drug products for similar classification system based on sound scientific principles. In USA, most of the generic topical drug products have qualitatively (Q1) and quantitatively (Q2) same excipients as the reference listed drug (RLD). The applications of in vitro release (IVR) and in vitro characterization are considered for a range of dosage forms (suspensions, creams, ointments and gels) of differing strengths. We advance a Topical Drug Classification System (TCS) based on a consideration of Q1, Q2 as well as the arrangement of matter and microstructure of topical formulations (Q3). Four distinct classes are presented for the various scenarios that may arise and depending on whether biowaiver can be granted or not

Measures for Improving the Aquatic Biodiversity on the Lower Sector of Bega Veche River

For surface water bodies, the main environmental objectives set out in the Water Framework Directive are aimed at achieving the good ecological status, respectively the good potential for heavily modified and artificial water bodies. The Banat River Basin Management Plan 2016-2021 identified several significant pressures at watercourses level, such as Bega Veche, which lead to the failure to achieve these objectives. This paper presents the proposed green measures which have a beneficial role from a biological and ecological point of view, which involve natural water retention measures and renaturation of water streams banks, including measures to improve the retention capacity at catchment level

On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density

We are concerned with the long time behaviour of solutions to the fractional porous medium equation with a variable spatial density. We prove that if the density decays slowly at infinity, then the solution approaches the Barenblatt-type solution of a proper singular fractional problem. If, on the contrary, the density decays rapidly at infinity, we show that the minimal solution multiplied by a suitable power of the time variable converges to the minimal solution of a certain fractional sublinear elliptic equation.Comment: To appear in DCDS-

A Practical Guide to Multi-Objective Reinforcement Learning and Planning

Real-world decision-making tasks are generally complex, requiring trade-offs between multiple, often conflicting, objectives. Despite this, the majority of research in reinforcement learning and decision-theoretic planning either assumes only a single objective, or that multiple objectives can be adequately handled via a simple linear combination. Such approaches may oversimplify the underlying problem and hence produce suboptimal results. This paper serves as a guide to the application of multi-objective methods to difficult problems, and is aimed at researchers who are already familiar with single-objective reinforcement learning and planning methods who wish to adopt a multi-objective perspective on their research, as well as practitioners who encounter multi-objective decision problems in practice. It identifies the factors that may influence the nature of the desired solution, and illustrates by example how these influence the design of multi-objective decision-making systems for complex problems

Perturbed nonlocal fourth order equations of Kirchhoff type with Navier boundary conditions

Abstract We investigate the existence of multiple solutions for perturbed nonlocal fourth-order equations of Kirchhoff type under Navier boundary conditions. We give some new criteria for guaranteeing that the perturbed fourth-order equations of Kirchhoff type have at least three weak solutions by using a variational method and some critical point theorems due to Ricceri. We extend and improve some recent results. Finally, by presenting two examples, we ensure the applicability of our results

Noble gas and carbon isotope systematics at the seemingly inactive Ciomadul volcano (Eastern‐Central Europe, Romania): evidence for volcanic degassing

Ciomadul is the youngest volcano in the Carpathian-Pannonian Region, Eastern-Central Europe, which last erupted 30 ka. This volcano is considered to be inactive, however, combined evidence from petrologic and magnetotelluric data, as well as seismic tomography studies suggest the existence of a subvolcanic crystal mush with variable melt content. The volcanic area is characterized by high CO2 gas output rate, with a minimum of 8.7 × 103 t yr-1. We investigated 31 gas emissions at Ciomadul to constrain the origin of the volatiles. The δ13C-CO2 and 3He/4He compositions suggest the outgassing of a significant component of mantle-derived fluids. The He isotope signature in the outgassing fluids (up to 3.10 Ra) is lower than the values in the peridotite xenoliths of the nearby alkaline basalt volcanic field (R/Ra 5.95Ra±0.01) which are representative of a continental lithospheric mantle and significantly lower than MORB values. Considering the chemical characteristics of the Ciomadul dacite, including trace element and Sr- Nd and O isotope compositions, an upper crustal contamination is less probable, whereas the primary magmas could have been derived from an enriched mantle source. The low He isotopic ratios could indicate a strongly metasomatized mantle lithosphere. This could be due to infiltration of subduction-related fluids and postmetasomatic ingrowth of radiogenic He. The metasomatic fluids are inferred to have contained subducted carbonate material resulting in a heavier carbon isotope composition (13C is in the range of -1.4 to -4.6 ‰) and an increase of CO2/3He ratio. Our study shows the magmatic contribution to the emitted gases