Six topics on inscribable polytopes

Inscribability of polytopes is a classic subject but also a lively research area nowadays. We illustrate this with a selection of well-known results and recent developments on six particular topics related to inscribable polytopes. Along the way we collect a list of (new and old) open questions.Comment: 11 page

Magnetic structure in a U(Ru_0.92Rh_0.08)₂Si₂ single crystal studied by neutron diffraction in static magnetic fields up to 24 T

We report the high-field induced magnetic phase in single crystal of U(Ru0.92Rh0.08)2Si2. Our neutron study combined with high-field magnetization, shows that the magnetic phase above the first metamagnetic transition at Hc1 = 21.6 T has an uncompensated commensurate antiferromagnetic structure with propagation vector Q2 = ( 2/3 0 0) possessing two single-Q domains. U moments of 1.45 (9) muB directed along the c axis are arranged in an up-up-down sequence propagating along the a axis, in agreement with bulk measurements. The U magnetic form factor at high fields is consistent with both the U3+ and U4+ type. The low field short-range order that emerges from the pure URu2Si2 due to Rh-doping is initially strengthened by the field but disappears in the field-induced phase. The tetragonal symmetry is preserved across the transition but the a axis lattice parameter increases already at low fields. Our results are in agreement with itinerant electron model with 5f states forming bands pinned in the vicinity of the Fermi surface that is significantly reconstructed by the applied magnetic field.Comment: 5 pages, 4 figures, accepted as Rapid Communication, Physical Review B (2017

Noncollinear magnetic structure in U2Pd2In at high magnetic fields

We report an unexpected magnetic field driven magnetic structure in the 5f electron Shastry Sutherland system U2Pd2In. This phase develops at low temperatures from a noncollinear antiferromagnetic ground state above the critical field of 25.8 T applied along the a axis. All U moments have a net magnetic moment in the direction of the applied field, described by a ferromagnetic propagation vector qF 000 and an antiferromagnetic component described by a propagation vector qAF 0 0.3012 due to a modulation in the direction perpendicular to the applied field. We conclude that this surprising noncollinear magnetic structure is due to a competition between the single ion anisotropy trying to keep moments, similar to the ground state, along the [110] type directions, Dzyaloshinskii Moryia interaction forcing them to be perpendicular to each other and application of the external magnetic field attempting to align them along the field directio

Aerosol and its radiative effects during the aeroradcity 2018 Moscow experiment

During the AeroRadCity-2018 spring aerosol experiment at the Moscow State University Meteorological Observatory the aerosol properties of the atmosphere and radiative aerosol effects were analyzed using a wide complex of measurements and model COSMO-ART simulations over Moscow domain. The program of measurements consisted of columnar aerosol AERONET retrievals, surface PM10, black carbon (BC) and aerosol gas precursors mass concentrations, as well as radiative measurements under various meteorological conditions. We obtained a positive statistically significant dependence of total and fine aerosol optical depth (AOD) mode (R2 ~0.4) with PM concentrations. This dependence has revealed a pronounced bifurcation point around PM10=0.04 mgm-3. The modelled BC concentration is in agreement with the observations and has a pronounced correlation with PM, but not with the AODs. The analysis of radiative effects of aerosol has revealed up to 30% loss for UV irradiance and 15% - for shortwave irradiance at high AOD in Moscow. Much intensive radiation attenuation is observed in the afternoon when remote pollution sources may affect solar fluxes at elevated boundary layer conditions. Negative (cooling) radiative forcing effect at the top of the atmosphere from -18 Wm-2 to -4 Wm-2 has been evaluated. Mean difference in visible AOD between urban and background conditions in Moscow and Zvenigorod was about 0.01 according to measurements and model simulations, while in some days the difference may increase up to 0.05. The generation of urban aerosol was shown to be more favorable in conditions with low intensity of pollutant dispersion, when mean deltaAOD550 was doubled from 0.01 to 0.02

A discrete Laplace-Beltrami operator for simplicial surfaces

We define a discrete Laplace-Beltrami operator for simplicial surfaces. It depends only on the intrinsic geometry of the surface and its edge weights are positive. Our Laplace operator is similar to the well known finite-elements Laplacian (the so called ``cotan formula'') except that it is based on the intrinsic Delaunay triangulation of the simplicial surface. This leads to new definitions of discrete harmonic functions, discrete mean curvature, and discrete minimal surfaces. The definition of the discrete Laplace-Beltrami operator depends on the existence and uniqueness of Delaunay tessellations in piecewise flat surfaces. While the existence is known, we prove the uniqueness. Using Rippa's Theorem we show that, as claimed, Musin's harmonic index provides an optimality criterion for Delaunay triangulations, and this can be used to prove that the edge flipping algorithm terminates also in the setting of piecewise flat surfaces.Comment: 18 pages, 6 vector graphics figures. v2: Section 2 on Delaunay triangulations of piecewise flat surfaces revised and expanded. References added. Some minor changes, typos corrected. v3: fixed inaccuracies in discussion of flip algorithm, corrected attributions, added references, some minor revision to improve expositio

Safety and Effectiveness of Pharmacologic Conversion of Atrial Fibrillation and Flutter: Results of Multicenter Trial. Part II: Assessment of Safety

Aim. We aimed to assess safety and effectiveness of class III antiarrhythmic drug Refralon for conversion of atrial fibrillation (AFib) and flutter (AFl) in post-registration trial and to compare data of primary center (National medical research center in cardiology) with data of other hospitals.Material and Methods. We performed retrospective cohort study in 727 patients (451 enrolled in primary center and 276 enrolled in other hospitals) admitted between June 24, 2014 and June 24, 2019. Refralon was administered for conversion of AFib and AFl in intense care units in escalating doses (10-30 micrograms/kg) intravenously.Results. Conversion of AFib and AFl into sinus rhythm was achieved in 53,6% after administration of 10 mcg/kg dose, in 73% after administration of 20 mcg/kg dose and in 91,6% after administration of Refralon in dose up to 30 mcg/kg. No mortality and no major adverse cardiac events registered in our study. Asystole >3.0 sec observed in 5% (35 of 727) of patients): in 5% (24 of 451) of patients enrolled in primary center and in 4% (11 of 276) of patients enrolled in other hospitals; 95% confidence interval (CI) [-0.09; 0.113]. Asystole> 5.0 s observed in 1.7% of patients who further required non-urgent implantation of a permanent pacemaker due to manifestations of sinus node dysfunction. Cardiac conduction disturbances (exclusively sinus bradycardia) were registered in 7% (53 of 727) patients: in 8% (37 of 451) of patients enrolled in primary center and in 6% (17 of 276) of patients enrolled in other hospitals; 95% CI: [-0.1; 0.15]. Only 0.14% of patients had symptomatic sinus bradycardia that resolved after atropine injection. Ventricular arrhythmias (exclusively Torsade de pointes tachycardia in excessive QT interval prolongation) were registered in 1.7% (12 of 727) patients: in 2% (9 of 451) of patients in primary center and in 1% (3 of 276) of patients of other hospitals; 95% CI: [-0.06; 0.08]. QTc interval prolongation to values >500 ms documented in 19% (138 of 727) of patients: in 21% (95 of 451) of patients in primary center and in 16% (43 of 276) of patients in other hospitals; 95% CI: [-0.13; 0.24].Conclusion: In post-registration multicenter trial Refralon demonstrated good safety profile in conversion of AFib and AFl. Potential risk of TdP tachycardia mandates precautions with the use of the drug. In other hospitals Refralon did not demonstrate lower safety than in primary medical center

The Schläfli formula and Einstein manifolds

The celebrated formula of Schlafli relates the variation of the dihedral angles of a smooth family of polyhedra in a space form and the variation of volume. We give a smooth analogue of this classical formula -- our result relates the variation of the volume bounded by a hypersurface moving in a general Einstein manifold and the integral of the variation of the mean curvature. The argument is direct, and the classical polyhedral result (as well as results for Lorenzian space forms) is an easy corollary. We extend it to variations of the metric in a Riemannian Einstein manifold with boundary. We apply our results to give some rigidity results for Ricci-flat manifolds with umbilic boundaries. R'esum'e La c'el`ebre formule de Schlafli relie la variation des angles di`edres d'une famille lisse de poly`edres dans un espace `a courbure constante et la variation du volume. On donne un analogue r'egulier de cette formule classique -- notre resultat relie la variation du volume born'e par une ..