Bright solitons from defocusing nonlinearities

We report that defocusing cubic media with spatially inhomogeneous nonlinearity, whose strength increases rapidly enough toward the periphery, can support stable bright localized modes. Such nonlinearity landscapes give rise to a variety of stable solitons in all three dimensions, including 1D fundamental and multihump states, 2D vortex solitons with arbitrarily high topological charges, and fundamental solitons in 3D. Solitons maintain their coherence in the state of motion, oscillating in the nonlinear potential as robust quasi-particles and colliding elastically. In addition to numerically found soliton families, particular solutions are found in an exact analytical form, and accurate approximations are developed for the entire families, including moving solitons.Comment: 13 pages, 6 figures, to appear in Physical Review

An Empirical Process Central Limit Theorem for Multidimensional Dependent Data

Let $(U_n(t))_{t\in\R^d}$ be the empirical process associated to an $\R^d$-valued stationary process $(X_i)_{i\ge 0}$. We give general conditions, which only involve processes $(f(X_i))_{i\ge 0}$ for a restricted class of functions $f$, under which weak convergence of $(U_n(t))_{t\in\R^d}$ can be proved. This is particularly useful when dealing with data arising from dynamical systems or functional of Markov chains. This result improves those of [DDV09] and [DD11], where the technique was first introduced, and provides new applications.Comment: to appear in Journal of Theoretical Probabilit

Current views on the assessment of vascular wall elasticity in pregnant women with arterial hypertension

Aim of the study was to improve our understanding about a clinical and prognostic role of vascular wall elasticity in pregnant women with arterial hypertension.Цель исследования — усовершенствовать представление о клинической и прогностической роли эластичности сосудистой стенки у беременных с артериальной гипертензией

TMOKE as efficient tool for the magneto-optic analysis of ultra-thin magnetic films

Ultra-thin magnetic dielectric films are of prime importance due to their applications for nanophotonics and spintronics. Here, we propose an efficient method for the magneto-optical investigation of ultra-thin magnetic films which allows one to access their state of magnetization and magneto-optical properties. It is based on the surface-plasmon-polariton-assisted transverse magneto-optical Kerr effect (TMOKE). In our experiments, sub-100 nm-thick bismuth-substituted lutetium iron-garnet films covered with a plasmonic gold grating have been analyzed. The excitation of surface plasmon-polaritons provides resonance enhancement of TMOKE up to 0.04 and makes it easily detectable in the experiment. For films thicker than 40 nm, the TMOKE marginally depends on the film thickness. A further decrease in the film thickness diminishes TMOKE since for such thicknesses the surface plasmon-polariton field partly penetrates inside the non-magnetic substrate. Nevertheless, the TMOKE remains measurable even for few-nm-thick films, which makes this technique unique for the magneto-optical study of ultra-thin films. Particularly, the proposed method reveals that the off-diagonal components of the magnetic film permittivity tensor grow slightly with the reduction of the film thickness.Comment: 5 page

Catalytic sulfation of betulin with sulfamic acid : experiment and DFT calculation

Betulin is an important triterpenoid substance isolated from birch bark, which, together with its sulfates, exhibits important bioactive properties. We report on a newly developed method of betulin sulfation with sulfamic acid in pyridine in the presence of an Amberlyst(®)15 solid acid catalyst. It has been shown that this catalyst remains stable when being repeatedly (up to four cycles) used and ensures obtaining of sulfated betulin with a sulfur content of ~10%. The introduction of the sulfate group into the betulin molecule has been proven by Fourier-transform infrared, ultraviolet-visible, and nuclear magnetic resonance spectroscopy. The Fourier-transform infrared (FTIR) spectra contain absorption bands at 1249 and 835–841 cm(−1); in the UV spectra, the peak intensity decreases; and, in the nuclear magnetic resonance (NMR) spectra, of betulin disulfate, carbons С3 and С28 are completely shifted to the weak-field region (to 88.21 and 67.32 ppm, respectively) with respect to betulin. Using the potentiometric titration method, the product of acidity constants K(1) and K(2) of a solution of the betulin disulfate H(+) form has been found to be 3.86 × 10(–6) ± 0.004. It has been demonstrated by the thermal analysis that betulin and the betulin disulfate sodium salt are stable at temperatures of up to 240 and 220 °C, respectively. The density functional theory method has been used to obtain data on the most stable conformations, molecular electrostatic potential, frontier molecular orbitals, and mulliken atomic charges of betulin and betulin disulfate and to calculate the spectral characteristics of initial and sulfated betulin, which agree well with the experimental data

Current status of the problem of cardiovascular diseases in the Nizhny Novgorod region: possible ways to reduce mortality

The article considers the urgent problem of combating cardiovascular diseases (CVDs) in the Nizhny Novgorod region, including the high prevalence of CVDs and the timely identification of risk factors. The changes in mortality from all and individual causes was analyzed. Attention was paid to the negative impact of the coronavirus disease 2019 (COVID-19) pandemic on the health of people suffering from noncommunicable diseases. We also described the necessity to improve healthcare efficiency for CVD patients by improving the complex of managerial and preventive measures