We study the problem of the existence and asymptotic stability of a stationary solution of an initial boundary value problem for the reaction–diffusion–advection equation assuming that the reaction ...and advection terms are comparable in size and have a jump along a smooth curve located inside the studied domain. The problem solution has a large gradient in a neighborhood of this curve. We prove theorems on the existence, asymptotic uniqueness, and Lyapunov asymptotic stability for such solutions using the method of upper and lower solutions. To obtain the upper and lower solutions, we use the asymptotic method of differential inequalities that consists in constructing them as modified asymptotic approximations in a small parameter of solutions of these problems. We construct the asymptotic approximation of a solution using a modified Vasil’eva method.
We prove the existence and the Lyapunov asymptotic stability of a stationary boundary layer solution of the initial–boundary value problem for a two-dimensional singularly perturbed ...reaction–diffusion–advection equation. We construct an asymptotic approximation to this solution using the boundary function method. The proofs are based on the applicability of the asymptotic method of differential inequalities.
A new mineral-organic composite by in situ immobilization of poly(4-vinylpyridine-co-styrene-co-maleic anhydride) on the silica gel surface was synthesized. According to TG-analysis, the composite ...contained 31.84 wt.% of immobilized copolymer. The highest sorption activity of a new composite was established towards micro-quantities of Cu (II) ions in neutral medium as well as towards Pb(II) and Fe(III) ions in a slightly acidic medium with the background of phthalate buffer and no sorption activity towards Cd(II) ions. The composite obtained exhibits a sorption capacity higher in 1.88, 5.00 and 3.35 times for Fe(III), Cu(II) and Pb(II) ions respectively in comparison with parent silica gel.
A number of new organo-mineral composites in different mass ratios of organic and inorganic components were obtained by adsorption on the silica gel surface of 4-vinylpyridine-styrene copolymer. The ...fact of the copolymer immobilization on the silica gel surface was confirmed by Fourier transform infrared spectroscopy (FTIR) spectroscopy and thermogravimetry combined with mass-spectrometry analysis. Thermogravimetric analysis was employed for estimation of copolymers mass content in the composite obtained. It has been established that all the synthesized composites exhibit sorption activity toward traces of Cu (II), Pb (II) and Fe (III) ions in neutral aqueous medium.
Powders of maghemite γ-Fe
2
O
3
with an average diameter of 8 nm, γ-Fe
2
O
3
/SiO
2
composites with an agglomerate diameter of about 50 nm and a size of interspersed γ-Fe
2
O
3
particles of 6 nm, and ...γ‑Fe
2
O
3
/SiO
2
/aptamer(FAS9) composites were synthesized by chemical deposition. Mössbauer spectra were measured, the static and dynamic magnetic properties of the powders were studied, and the coercive force was determined, which decreases from 14 Oe for γ-Fe
2
O
3
powders to 3 Oe for the γ-Fe
2
O
3
/SiO
2
composite. It is shown that the particle blocking temperature is close to room temperature. The increment of temperature of the powders was measured in the ferromagnetic resonance mode; the temperature of the Fe
2
O
3
/SiO
2
composite (Δ
T
≈ 16°C) turned out to be higher than that of the pure γ-Fe
2
O
3
powder (Δ
T
≈ 10°C). It has been experimentally shown that temperature increment Δ
T
is proportional to the square of the microwave field amplitude. It has been shown that the composition γ-Fe
2
O
3
/SiO
2
/aptamer FAS9 is able to effectively bind to tumor cells, and FMR hyperthermia leads to a decrease in the viability of tumor cells.
Polystyrene (PS)-diphenyloxazole (PPO) nanoparticles with attached cross-linked poly-N-isopropylacrylamide (PNIPAM) chains were obtained resulting in PS-PPO-PNIPAM hybrid nanosystems (NS). ...Fluorescence spectra of chlorin e
6
added to PS-PPO-PNIPAM hybrid NS revealed electronic excitation energy transfer (EEET) from PS matrix and encapsulated PPO to chlorin e
6
. EEET efficiency increased strongly during 1 h after chlorin e
6
addition, indicating that uptake of chlorin e
6
by PNIPAM part of hybrid NS still proceeds during this time. Heating of PS-PPO-PNIPAM-chlorin e
6
NS from 21 to 39 °C results in an enhancement of EEET efficiency; this is consistent with PNIPAM conformation transition that reduces the distance between PS-PPO donors and chlorin e
6
acceptors. Meanwhile, a relatively small part of chlorin e
6
present in the solution is bound by PNIPAM; thus, further studies in this direction are necessary.
To study the long-term effect of enhanced external counterpulsation (EECP) therapy on exercise tolerance, quality of life (QoL), and indicators of the structural and functional state of the ...cardiovascular system in patients with stable ischemic heart disease (IHD) complicated by chronic heart failure (CHF).
This open randomized EXCEL study included 120 patients with verified IHD complicated by NYHA II-III functional class CHF with reduced or mid-range left ventricular (LV) ejection fraction. Patients were randomized into group 1 (n=40), optimal drug therapy (ODT) and EECP (35 hours, 2 courses per year); group 2 (n=40), ODT and EECP (35 hours, 1 course per year); and group 3 (control; n=40), ODT and placebo counterpulsation (35 h, 1 course per year). All patients underwent a 6-minute walk test (6MWT), evaluation of clinical status, QoL with the MLHFQ and SF-36 questionnaires, structural and functional state of large blood vessels and microvasculature, measurement of brain natriuretic peptide precursor (NT-proBNP), and echocardiography at baseline and after 12 months.
In groups 1 and 2 after 12 months, the 6MWT distance increased statistically significantly (44.5 and 24.9%, respectively) and the following indexes improved: QoL (SF-36, MLHFQ), the condition of large blood vessels (phase shift, radial augmentation index, central aortic systolic pressure (CASP)) and microvasculature (occlusion index, percentage of perfused capillaries, percentage of capillary recovery), and the LV systolic function (from 40.6±7.5 to 47.5±10.2% and from 41.3± 6.8 to 43.9±10.3%, respectively). The proportion of patients with a >20% increase in the 6MWT at 12 months was 97.5, 72.5, and 7.7%, respectively. A statistically significant decrease in NT-proBNP was observed in all groups. In group 3, the incidence of hospitalizations for CHF and the risk of the composite endpoint were significantly higher.
For the 12-month study period, the effects of EECP in patients with IHD complicated by CHF included improvements in exercise tolerance, QoL, vascular and cardiac functional parameters, and a decrease in the incidence of adverse outcomes.
Copolymer of 4-vinylpyridine with styrene was in situ immobilized on silica gel surface via the heterogeneous radical polymerization. Anchorage of the copolymer on the surface layer was confirmed by ...IR spectroscopy. The quantity of copolymer on the silica gel surface was evaluated as 25.73 wt.% by TG and DSC-MS analysis. “Islet” location of polymer layer on the silica surface was confirmed by the scanning electron microscopy. A high adsorption activity of silica gel with immobilized copolymer towards microquantitatives of Cu(II), Cd(II), Pb(II), Fe(III), and Ni(II) ions in steady state conditions as well as of Ni(II) ions in dynamic regime was found.
Ecotoxicity of dust was assessed for different functional zones in three Moscow districts. Ecotoxicity was estimated by the reaction of higher plants using a new approach to the implementation of ...biotesting method and by changes in the biomass and respiration of microorganisms in residential and transport zones as compared to recreational zones. The proposed method of assessing urban dust toxicity upon modeling dust transfer to soil-like substrates allowed us to solve the main methodological problem, i.e., the choice of control. By the example of perennial ryegrass (
Lollium perenne
L.), it was found out that annual volume of dust deposition upon a high load within a one-meter zone from the road surface does not manifest toxicity, whereas a three-year volume suppresses plants up to 27% relative to the control. No significant differences were found between the phytotoxicity of dust in different functional zones; and phytotoxicity did not correlate with any of the studied properties of dust (organic carbon content (C
org
), pH, electrical conductivity, moisture capacity, particle-size composition). Basal respiration and carbon content in microbial biomass (C
mic
) of dust were maximal in the recreational zones of the city (3.1–7.2 μg C–CO
2
g
–1
h
–1
and 314–435 μg g
–1
, respectively) decreasing by 27–71% in residential and by 76–81% in the transport zones. Significant correlations of basal respiration and C
mic
with C
org
were observed (
r
S
= 0.57 and 0.61, respectively,
p
< 0.05,
n
= 49). High values of microbial metabolic quotient
q
CO
2
of dust and a small share of C
mic
in C
org
indicate unfavorable conditions for microorganisms.
A singularly perturbed boundary value problem for a second-order quasilinear ordinary differential equation is studied. We consider a new class of problems in which the nonlinearities experience ...discontinuities, which leads to the appearance of sharp transition layers in a neighborhood of the points of discontinuity. The existence of solutions is proved, and their asymptotic expansion with an internal transition layer is constructed.
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