This paper establishes continuous and discrete two-sided estimates for a class of quasilinear parabolic convection–diffusion–reaction equations with unbounded nonlinearities and reaction coefficients of arbitrary sign. For nonpositive reaction coefficients, rigorous continuous two-sided bounds are derived for classical solutions, together with an a priori estimate in the strong C-norm. These results extend, in a structurally coherent manner, the corresponding theory available for linear parabolic problems. For reaction coefficients of arbitrary sign, second-order unconditionally monotone schemes are constructed. By applying the Ladyzhenskaya transformation u = ve^λt, alternative discrete two-sided estimates are derived for the numerical solution and shown to be fully consistent with their continuous counterparts. Finally, convergence of the developed schemes is rigorously proved in the L₂-norm.

The paper is devoted to the development of probabilistic and statistical analysis of non-homogeneous high-order Markov chains for cases in which the matrix of one-step transition probabilities is time-varying. Models for deterministically non-homogeneous and stochastically non-homogeneous high-order Markov chains are constructed. Probabilistic properties of these models are analyzed and some approaches to statistical estimation of the model parameters are proposed.

An expression for the gradient force acting in a Gaussian beam of optical radiation on a transparent dielectric microsphere is derived within the Rayleigh–Gans approximation, which imposes a constraint on the phase shift of the wave as it passes through the microsphere. The approximation of an undamped beam is assumed. The inhomogeneity of the incident radiation within the microsphere is taken into account. The resulting expression for the gradient force in the Rayleigh–Gans approximation reduces to the known expressions for the gradient force in the Rayleigh approximation. The expression for the gradient force is radially symmetric, regardless of the direction of light wave polarization in the beam cross section. It is shown that for particles satisfying the Rayleigh–Gans approximation, the gradient force acting in the transverse direction of the beam is smaller than the gradient force calculated in the Rayleigh approximation. This difference increases with increasing particle size.

A correction factor for the Rayleigh–Gans theory is computed as a function of twice the square of the ratio of the microsphere radius to the light beam radius. It is shown that even for a microsphere radius of 3.5 wavelengths, the gradient force in the Rayleigh–Gans approximation is half that in the Rayleigh approximation.

The results of an experimental study of ghost vibrational resonance in an optoelectronic spiking neuron based on a vertical-cavity surface-emitting laser and a single-photon avalanche photodiode are presented. It is shown that passing a signal representing the sum of harmonics of a fundamental frequency absent from the signal through the optoelectronic spiking neuron, with the addition of a high-frequency signal of appropriate amplitude, leads to the appearance of ghost frequencies in the spiking neuron’s response. These results can be used in artificial spiking neural networks for processing complex signals.

Bacteriophages of phytopathogenic bacteria of the genera Pseudomonas, Dickeya, and Xanthomonas, which are the causative agents of vegetable crops diseases, have been isolated and characterized. Based on the results of molecular genetic analysis of the isolated phages, their identification has been carried out, and their suitability and safety for use in plant protection have been established. It has been shown that biologics based on bacteriophage consortia are highly effective against phytopathogenic bacteria (50–69 %), while those based on a combination of bacteriophages and antagonistic bacteria exhibit broad-spectrum activity and can be used to control a wide range of bacterial and fungal pathogens.

This paper presents study results on the polymorphism of Atroviolacea (ATV) Solanum lycopersicum gene orthologs in pepper (genus Capsicum) and eggplant (S. melongena), as well as the developments in molecular markers associated with anthocyanin accumulation in various parts of these crops, whose fruits, along with tomatoes, constitute important vegetable products for functional nutrition. Based on sequencing of homologous genes (ETC3-1 and ETC3-2 MYB-like transcription factor (TF) ETC3 in pepper, and SmeATV MYB-like TF in eggplant) in accessions with varying levels of anthocyanin accumulation in vegetative organs and fruits, alleles leading to the synthesis of nonfunctional amino acid sequences have been identified; these are associated with increased anthocyanin accumulation in pepper and with enhanced repression of anthocyanin synthesis in eggplant. Molecular markers targeting these alleles of the homologous genes have been deve- loped, enabling the discrimination of breeding material according to anthocyanin accumulation in fruits and vegetative organs, have been developed.

Limb ischemia is a severe form of damage to skeletal muscle tissue, which leads to decreased viability and dysfunction. Mitochondrial damage plays a key role in the development of skeletal muscle ischemia. Mitochondrial transplantation as a new effective therapeutic strategy for replacing defective mitochondria is expected to increase the viability and improve the functional state of damaged skeletal muscles. An analysis of changes in the levels of a number of biochemical parameters in the blood serum of Wistar rats with experimental ischemia of the hind limbs and during the correction of these pathologies using a suspension of mitochondria was carried out. Serum levels of creatinine, alanine aminotransferase, total creatine kinase, interleukin-6 and interleukin-10 were significantly increased during experimental hind limb ischemia in rats. Correction of damage in ischemic muscles using injections of a suspension of mitochondria had protective and reparative effects in damaged tissues, which caused changes in the biochemical parameters of blood serum towards normalization. Thus, peripheral ischemia is accompanied by hyperenzymemia and increased creatine kinase activity, while local administration of a mitochondrial suspension to site of injury produces pronounced cytoprotective and immunomodulatory effect.

Cell therapy of chronic pancreatitis complications is a relevant strategy in regenerative medicine. However, the lack of research on the antifibrogenic effects of multipotent mesenchymal stromal cells (MMSCs) and the limited number of clinical trials leave many open questions regarding the mechanisms by which they regulate fibrogenesis. This article analyzes the dynamics of synthesis of extracellular matrix components (α smooth muscle actin and fibronectin) and of the principal activator of pancreatic stellate cells (transforming growth factor β) in the serum of patients with chronic pancreatitis after cell therapy based on biomedical cell product of allogeneic MMSCs administration. It has been shown that MMSCs were capable of suppressing the profibrogenic components production for 1 year in patients with chronic pancreatitis, both after intraoperative parapancreatic and after intravenous administration of biomedical cell product.

The formation of impurity sub-band states in selenium-hyperdoped silicon after pulsed laser annealing was investigated. Si samples were implanted with Se⁺ ions in single- and multi-energy regimes with dopant concentrations of 0.4– 2.2 at. %, followed by pulsed laser annealing at energy densities of 0.55–2.5 J/cm². Depth profiles of the dopant concentration, the degree of crystallinity, and the fraction of Se atoms occupying substitutional lattice sites were determined by Rutherford backscattering spectrometry in channeling mode. The formation of sub-band states was confirmed by scanning tunneling spectroscopy. The absorption spectra show a pronounced broad sub-band absorption band with a maximum at ~0.45–0.55 eV and a width of ~0.5 eV. It was found that the sub-band absorption intensity increases with the concentration of substitutional Se atoms, although this dependence is nonlinear. The optimal structural parameters (maximum crystallinity and substitutional Se fraction) are achieved after pulsed laser annealing at 1.5–2.5 J/cm²; however, the sub-band absorption intensity varies nonmonotonically and does not strictly correlate with these structural characteristics. These findings are relevant for the design of optoelectronic devices based on hyperdoped silicon with controllable sub-band absorption characteristics.

Experimental studies of pressure stratification in a vertical swirling water flow under the action of gravity were conducted. The aim of the experiment was to clarify the mechanism of pressure formation in shear flows of a viscous compressible fluid. Within the framework of existing concepts of the development of thermal and hydrodynamic processes based on the Navier–Stokes equations, there are no differences in pressure formation under the action of external mass forces in a moving and stationary medium. However, within the framework of concept of the phonon mechanism of momentum transfer, the effect of body forces differs in a moving and stationary liquid. In this case, pressure and density in a shear flow under gravity would increase more rapidly with increasing depth than in a stationary aquatic environment. This paper provides a theoretical justification for the experiment and describes the layout of the experimental setup and methodology. The results of the study confirmed the phonon mechanism of pressure formation under gravity in an intense water vortex with a vertical axis of rotation.