The fractional Schr\"{o}dinger operator and Toeplitz matrices

Confining a quantum particle in a compact subinterval of the real line with Dirichlet boundary conditions, we identify the connection of the one-dimensional fractional Schr\"odinger operator with the truncated Toeplitz matrices. We determine the asymptotic behaviour of the product of eigenvalues for the $\alpha$-stable symmetric laws by employing the Szeg\"o's strong limit theorem. The results of the present work can be applied to a recently proposed model for a particle hopping on a bounded interval in one dimension whose hopping probability is given a discrete representation of the fractional Laplacian.Comment: 10 pages, 2 figure

Spectra and Light Curves of GRB Afterglows

We performed accurate numerical calculations of angle-, time-, and frequency-dependent radiative transfer for the relativistic motion of matter in gamma-ray burst (GRB) models. Our technique for solving the transfer equation, which is based on the method of characteristics, can be applied to the motion of matter with a Lorentz factor up to 1000. The effect of synchrotron self-absorption is taken into account. We computed the spectra and light curves from electrons with a power-law energy distribution in an expanding relativistic shock and compare them with available analytic estimates. The behavior of the optical afterglows from GRB 990510 and GRB 000301c is discussed qualitatively.Comment: 8 pages, 7 figure

Largest ancient fortress of South-West Asia and the western world?:Recent fieldwork at Sasanian Qaleh Iraj at Pishva, Iran

The article presents recent works at Qale Iraj, near Varamin, Iran. My short contribution is on the Middle Persian ostraka found at the site

Spectra of Hydrogen-poor Superluminous Supernovae from the Palomar Transient Factory

Most Type I superluminous supernovae (SLSNe-I) reported to date have been identified by their high peak luminosities and spectra lacking obvious signs of hydrogen. We demonstrate that these events can be distinguished from normal-luminosity SNe (including Type Ic events) solely from their spectra over a wide range of light-curve phases. We use this distinction to select 19 SLSNe-I and four possible SLSNe-I from the Palomar Transient Factory archive (including seven previously published objects). We present 127 new spectra of these objects and combine these with 39 previously published spectra, and we use these to discuss the average spectral properties of SLSNe-I at different spectral phases. We find that Mn II most probably contributes to the ultraviolet spectral features after maximum light, and we give a detailed study of the O II features that often characterize the early-time optical spectra of SLSNe-I. We discuss the velocity distribution of O II, finding that for some SLSNe-I this can be confined to a narrow range compared to relatively large systematic velocity shifts. Mg II and Fe II favor higher velocities than O II and C II, and we briefly discuss how this may constrain power-source models. We tentatively group objects by how well they match either SN 2011ke or PTF12dam and discuss the possibility that physically distinct events may have been previously grouped together under the SLSN-I label

Glycosaminoglycans and Sialylated Glycans Sequentially Facilitate Merkel Cell Polyomavirus Infectious Entry

Merkel cell polyomavirus (MCV or MCPyV) appears to be a causal factor in the development of Merkel cell carcinoma, a rare but highly lethal form of skin cancer. Although recent reports indicate that MCV virions are commonly shed from apparently healthy human skin, the precise cellular tropism of the virus in healthy subjects remains unclear. To begin to explore this question, we set out to identify the cellular receptors or co-receptors required for the infectious entry of MCV. Although several previously studied polyomavirus species have been shown to bind to cell surface sialic acid residues associated with glycolipids or glycoproteins, we found that sialylated glycans are not required for initial attachment of MCV virions to cultured human cell lines. Instead, glycosaminoglycans (GAGs), such as heparan sulfate (HS) and chondroitin sulfate (CS), serve as initial attachment receptors during the MCV infectious entry process. Using cell lines deficient in GAG biosynthesis, we found that N-sulfated and/or 6-O-sulfated forms of HS mediate infectious entry of MCV reporter vectors, while CS appears to be dispensable. Intriguingly, although cell lines deficient in sialylated glycans readily bind MCV capsids, the cells are highly resistant to MCV reporter vector-mediated gene transduction. This suggests that sialylated glycans play a post-attachment role in the infectious entry process. Results observed using MCV reporter vectors were confirmed using a novel system for infectious propagation of native MCV virions. Taken together, the findings suggest a model in which MCV infectious entry occurs via initial cell binding mediated primarily by HS, followed by secondary interactions with a sialylated entry co-factor. The study should facilitate the development of inhibitors of MCV infection and help shed light on the infectious entry pathways and cellular tropism of the virus

Approaches to the therapy of heart failure with reduced ejection fraction. Resolution of an online meeting of the Volga Federal District experts

At an online meeting of experts held on May 14, 2021 additional research results on a sodium-glucose co-transporter-2 (SGLT2) inhibitor empagliflozin in patients with heart failure with reduced ejection fraction were considered. According to the data from the EMPEROR-Reduced international study, cardiovascular and renal effects of empagliflozin therapy in patients with and without type 2 diabetes (T2D) were analyzed. A number of proposals and recommendations was accepted regarding the further study of cardiovascular and renal effects of empagliflozin and its use in clinical practice in patients with heart failure, regardless of the T2D presence