Harnack and pointwise estimates for degenerate or singular parabolic equations

In this paper we give both an historical and technical overview of the theory of Harnack inequalities for nonlinear parabolic equations in divergence form. We start reviewing the elliptic case with some of its variants and geometrical consequences. The linear parabolic Harnack inequality of Moser is discussed extensively, together with its link to two-sided kernel estimates and to the Li-Yau differential Harnack inequality. Then we overview the more recent developements of the theory for nonlinear degenerate/singular equations, highlighting the differences with the quadratic case and introducing the so-called intrinsic Harnack inequalities. Finally, we provide complete proofs of the Harnack inequalities in some paramount case to introduce the reader to the expansion of positivity method.Comment: Survey paper, 50 pages, 5 figures. Comments welcom

Tuning the Re/Os Clock: Stellar-Neutron Cross Sections

The neutron-capture cross sections of 186,187Os have been recently measured at the CERN neutron time-of-flight facility n_TOF for an improved evaluation of the Re/Os cosmo-chronometer. This experimental information was complemented by nuclear model calculations for obtaining the proper astrophysical reaction rates at s-process temperatures. The calculated results and their implications for the determination of the time-duration of nucleosynthesis during galactic chemical evolution is discusse

Transcriptional alteration of gene biomarkers in hemocytes of wild ostrea edulis with molecular evidence of infections with bonamia spp. And/or marteilia refringens parasites

The European flat Ostrea edulis is highly susceptible to intracellular parasitic infections, particularly bonamiosis and marteiliosis. The defensive response of oyster to both bonamiosis and marteiliosis is typically mediated by hemocytes, which play a pivotal role in immune system homeostasis. In the present study, we first used a DNA-based tool in order to rapidly and specifically detect the presence of parasites in oysters from natural banks in the middle Adriatic Sea. In a second step, we used qRT-PCR to analyze the mRNA levels of a set of genes (i.e., superoxide dismutase (SOD), glutathione S-transferase (GST), metallothionein (MT), heat shock protein (HSP) 70 and 90, inhibitor of apoptosis (IAP), fas ligand (FAS), galectin (GAL) and extracellular superoxide dismutase (Ec-SOD)) expressed by hemocytes of flat oysters infected by the parasites, present singularly or in combination, compared to hemocytes from non-infected specimens. The results indicate that the presence of parasite DNA may be associated to a general upregulation of host genes related to apoptosis, detoxification and oxidative stress protection, with the exception of Ec-SOD, whose trend to a downregulation might reflect a mechanism for parasite escape before internalization

Correlation functions of disorder operators in massive ghost theories

The two-dimensional ghost systems with negative integral central charge received much attention in the last years for their role in a number of applications and in connection with logarithmic conformal field theory. We consider the free massive bosonic and fermionic ghost systems and concentrate on the non-trivial sectors containing the disorder operators. A unified analysis of the correlation functions of such operators can be performed for ghosts and ordinary complex bosons and fermions. It turns out that these correlators depend only on the statistics although the scaling dimensions of the disorder operators change when going from the ordinary to the ghost case. As known from the study of the ordinary case, the bosonic and fermionic correlation functions are the inverse of each other and are exactly expressible through the solution of a non-linear differential equation.Comment: 8 pages, late

Hidden Florence Analytics Reports 2017-18

This is the final version.The article associated with this dataset is available in ORE at http://hdl.handle.net/10871/128865This report looks at the data available for the app Hidden Florence for the period between 8th January 2017 and 31st January 2018. The report is divided into three main sections: Section 1 is an historical overview of metrics related to the type of audience of the app from April 2015 to January 2018. Data here are gathered only from two platforms, iTunes and Google Play. Within Section 1, there is also a subsection (1.3) dedicated to the analysis of the sessions and their geography for data collected from iTunes Analytics. Section 2 looks at the data available on the platform Google Analytics. It is organised as a comparative analysis between data extrapolated from the previous report (Report 2015-17) and the current data available for the period from 8th January 2017 – 31st January 2018. Here data are investigated accordingly to the category of type of audience of the app. Section 3 looks at the data available for users’ behaviours for the period that goes from 8th January 2017 to the 31st January 2018. Here, a recurrent distinction of the data is between users accessing the app in Florence and users engaging with it elsewhere.Arts and Humanities Research Council (AHRC)University of Exeter (IIB

Stability of Tin- versus Lead-Halide Perovskites: Ab Initio Molecular Dynamics Simulations of Perovskite/Water Interfaces

Tin-halide perovskites (THPs) have emerged as promising lead-free perovskites for photovoltaics and photocatalysis applications but still fall short in terms of stability and efficiency with respect to their lead-based counterpart. A detailed understanding of the degradation mechanism of THPs in a water environment is missing. This Letter presents ab initio molecular dynamics (AIMD) simulations to unravel atomistic details of THP/water interfaces comparing methylammonium tin iodide, MASnI3, with the lead-based MAPbI3. Our results reveal facile solvation of surface tin-iodine bonds in MASnI3, while MAPbI3remains more robust to degradation despite a larger amount of adsorbed water molecules. Additional AIMD simulations on dimethylammonium tin bromide, DMASnBr3, investigate the origins of their unprecedented water stability. Our results indicate the presence of amorphous surface layers of hydrated zero-dimensional SnBr3complexes which may protect the inner structure from degradation and explain their success as photocatalysts. We believe that the atomistic details of the mechanisms affecting THP (in-)stability may inspire new strategies to stabilize THPs