A new model of a tidally disrupted star

A new semi-analytical model of a star evolving in a tidal field is proposed. The model is a generalization of the so-called 'affine' stellar model. In our model the star is composed of elliptical shells with different parameters and different orientations, depending on time and on the radial Lagrangian coordinate of the shell. The evolution equations of this model are derived from the virial relations under certain assumptions, and the integrals of motion are identified. It is shown that the evolution equations can be deduced from a variational principle. The evolution equations are solved numerically and compared quantitatively with the results of 3D numerical computations of the tidal interaction of a star with a supermassive black hole. The comparison shows very good agreement between the main ``integral'' characteristics describing the tidal interaction event in our model and in the 3D computations. Our model is effectively a one-dimensional Lagrangian model from the point of view of numerical computations, and therefore it can be evolved numerically $10^{2}-10^{3}$ times faster than the 3D approach allows. This makes our model well suited for intensive calculations covering the whole parameter space of the problem.Comment: This version is accepted for publication in ApJ. Stylistic and grammatical changes, new Appendix adde

The Gauss-Legendre Sky Pixelization for the CMB polarization (GLESP-pol). Errors due to pixelization of the CMB sky

We present developing of method of the numerical analysis of polarization in the Gauss--Legendre Sky Pixelization (GLESP) scheme for the CMB maps. This incorporation of the polarization transforms in the pixelization scheme GLESP completes the creation of our new method for the numerical analysis of CMB maps. The comparison of GLESP and HEALPix calculations is done.Comment: 23 pages, 12 figure

Continuous Symmetries of Difference Equations

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalized symmetries acting on solutions of difference equations, but leaving the lattice invariant. The other is to restrict to point symmetries, but to allow them to also transform the lattice.Comment: Review articl

Effectiveness and safety of tocilizumab in patients with systemic sclerosis : a propensity score matched controlled observational study of the EUSTAR cohort

Objectives Tocilizumab showed trends for improving skin fibrosis and prevented progression of lung fibrosis in systemic sclerosis (SSc) in randomised controlled clinical trials. We aimed to assess safety and effectiveness of tocilizumab in a real-life setting using the European Scleroderma Trial and Research (EUSTAR) database. Methods Patients with SSc fulfilling the American College of Rheumatology (ACR)/EULAR 2013 classification criteria, with baseline and follow-up visits at 12±3 months, receiving tocilizumab or standard of care as the control group, were selected. Propensity score matching was applied. Primary endpoints were the modified Rodnan skin score (mRSS) and FVC at 12±3 months compared between the groups. Secondary endpoints were the percentage of progressive/regressive patients for skin and lung at 12±3 months. Results Ninety-three patients with SSc treated with tocilizumab and 3180 patients with SSc with standard of care fulfilled the inclusion criteria. Comparison between groups did not show significant differences, but favoured tocilizumab across all predefined primary and secondary endpoints: mRSS was lower in the tocilizumab group (difference -1.0, 95% CI -3.7 to 1.8, p=0.48). Similarly, FVC % predicted was higher in the tocilizumab group (difference 1.5 (-6.1 to 9.1), p=0.70). The percentage of progressive/regressive patients favoured tocilizumab over controls. These results were robust regarding the sensitivity analyses. Safety analysis confirmed previously reported adverse event profiles. Conclusion Although this large, observational, controlled, real-life EUSTAR study did not show significant effectiveness of tocilizumab on skin and lung fibrosis, the consistency of direction of all predefined endpoints generates hypothesis for potential effectiveness in a broader SSc population

Application of New Efficient Hoveyda–Grubbs Catalysts Comprising an N→Ru Coordinate Bond in a Six-Membered Ring for the Synthesis of Natural Product-Like Cyclopenta[b]furo[2,3-c]pyrroles

The ring rearrangement metathesis (RRM) of a trans-cis diastereomer mixture of methyl 3-allyl-3a,6-epoxyisoindole-7-carboxylates derived from cheap, accessible and renewable furan-based precursors in the presence of a new class of Hoveyda–Grubbs-type catalysts, comprising an N→Ru coordinate bond in a six-membered ring, results in the difficult-to-obtain natural product-like cyclopenta[b]furo[2,3-c]pyrroles. In this process, only one diastereomer with a trans-arrangement of the 3-allyl fragment relative to the 3a,6-epoxy bridge enters into the rearrangement, while the cis-isomers polymerize almost completely under the same conditions. The tested catalysts are active in the temperature range from 60 to 120 °C at a concentration of 0.5 mol % and provide better yields of the target tricycles compared to the most popular commercially available second-generation Hoveyda–Grubbs catalyst. The diastereoselectivity of the intramolecular Diels–Alder reaction furan (IMDAF) reaction between starting 1-(furan-2-yl)but-3-en-1-amines and maleic anhydride, leading to 3a,6-epoxyisoindole-7-carboxylates, was studied as well