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Nekrasov matrices, as a subclass of H-matrices, exhibit unique functionalities and hold significant importance in diverse fields. These matrices are characterized by their distinctive structure, which endows them with numerous remarkable properties. This paper extends the study of Nekrasov matrices by introducing a new subclass of H-matrices, termed DN-matrices, and explores their properties, particularly focusing on the Schur complement.

In this paper, we consider two-dimensional multi-term time-space fractional diffusion-wave equations. We develop an alternating direction implicit (ADI) spectral method based on Legendre spectral approximation in space and finite difference discretization in time. We also prove the numerical stability and convergence of the developed scheme and that the error is O(τ²+N^γ-r), where Ν,τ,γ,r are the polynomial degree, time step size, Riesz derivative order and the regularity of the exact solution, respectively.

A continuous-discrete stochastic model describing the dynamics of a spatially heterogeneous population is presented. The individuals of the population are located in a system consisting of two interconnected compartments. The individuals move between the compartments along unidirectional pipes. The duration of individual motion along the pipes is specified by constants or functions depending on time. The individuals located in the second compartment can contact one of the reproduction centers located in this compartment. As a result of contact with a reproduction center, an individual begins the process of fission. The reproduction of the individuals arising due to fission occurs until the number of descendants exceeds a threshold level, otherwise the reproduction of individuals ends. The population formed after the completion of fission contains descendant individuals that are not subject to fission and leave the system over time. The assumptions of the model are formulated, a probabilistic formalization of the model and an algorithm of numerical modeling based on the Monte Carlo method are given. The results of a computational experiment to simulate the dynamics of the population depending on the parameters of the model are presented.

For an isotropic random field a simple computer-efficient grid model is developed which provides sufficiently high accuracy of solutions to stochastic transport problems for small correlation lengths. Results of test estimation of the time asymptotics of mean particle flux in a random multiplying medium are presented.

In this paper, we explore a double-step method for solving nonlinear equations containing a differentiable and non-differentiable operator. Our approach is built upon a combination of three different methods. We have analyzed the local convergence of the suggested method, considering both Lipschitz and L-average conditions & established the superquadratic (≈ 2.414) order of convergence. Finally we have pictured numerical results in comparison with several existing methods.

The content of total ash, ascorbic acid, tannins was determined in the leaves and flowers of Hemerocallis species: H. citrina, H. fulva, H. lilio-asphodelus, H. middendorffii, H. minor, cultivated under the conditions of the forest-steppe zone of the Novosibirsk Region. Biochemical parameters were determined during the flowering period in 2022. It has been found that the concentration of tannins, ascorbic acid, total ash in the leaves is 1.3-1.5 times higher than in the flowers. The leaves are distinguished by the highest content of ascorbic acid (11.43-16.35 mg/100 g). The specificity of the content of these substances in plants depending on the species, vegetative and generative organs during the flowering period is noted.

The paper presents the results of creating a new oil-displacing composition based on the ternary system of deep eutectic solvents (DES) “pentaerythritol - urea - choline chloride” with surfactants, and the results of laboratory tests of its effect on the filtration characteristics of the heterogeneous formation of the Usinskoye field with heavy and high-viscosity oil. As a result of studying the physicochemical characteristics and phase equilibrium of the ternary DES system, a new oil-displacing composition of prolonged action was created, based on the ternary DES system “pentaerythritol - urea - choline chloride” and surfactant, applicable for various geological and physical conditions of fields, in particular in the Arctic zone of the Russian Federation. The effectiveness of the composition was assessed for sections of the field at the early and late stages of development. It has been established that the use of the composition based on DES and surfactants leads to the equalisation of filtration flows with an increase in formation coverage, restoration of the initial permeability and, as a consequence, to a significant increase in the oil displacement coefficient at both low and high temperatures.

Maintaining a stable content of phenylpropanoids (rosavins: rosavin, rosarin, rosin, and cinnamic alcohol) and phenylethanoids (salidroside and tyrosol) in line with pharmacopoeial standards remains a critical challenge for scaling up the cultivation of Rhodiola rosea L. to meet global demand. One possible cause of low compound levels is the inadequacy of current standardisation methods for raw materials and preparations of Rhodiola rosea. This study aimed to identify the optimal drying temperature for raw materials from even-aged clonal plants of Rhodiola rosea cv. ‘Mattmark’. Results showed that higher drying temperatures reduced phenylethanoid levels, with room-temperature drying is optimal. In contrast, the maximal concentrations of rosavins, mainly rosavin, were detected at increased temperature (80 °C). Analysis of the relative distribution of phenylpropanoids revealed that higher drying temperature causes an increase in the proportion of rosavin and a decrease in cinnamic alcohol content, while rosarin and rosin levels remained stable. It has been shown that rosavin is the dominant phenylpropanoid independently of temperature. Thus, drying rhizomes at 80 °C enhanced rosavin content by 20 % but significantly (by a factor of 1.5-2) reduced total phenylethanoids. Therefore, drying at room temperature is recommended to maximise the total phenylethanoid and phenylpropanoid content in the raw material.

The elements of D. I. Mendeleev’s Periodic System (Mendeleev’s Table) have the relative atomic weight calculated as the average value of the atomic weights of several isotopes. The number of these isotopes is quite large; however, there is a lack of convenient and accessible systematisation for practical work. This article proposes a method and a device for such systematisation.

Antimicrobial resistance (AMR) constitutes one of the foremost threats to global public health in the XXI century: according to the data of the World Health Organization for 2025, one of the six laboratory-confirmed bacterial infections exhibits resistance to standard antibiotic therapy, with annual resistance rates increasing by 5-15 % across more than 40 % of pathogen-antibiotic combinations. Amid the declining efficacy of single-target antibiotics, the development of multitarget hybrid antibacterial agents - single molecules incorporating two or more pharmacophoric moieties capable of simultaneously engaging distinct bacterial targets - has gained critical relevance. This review systematically outlines the principal strategies for designing such hybrids: linked, fused, and merged pharmacophores. It also addresses key pharmacokinetic and toxicological considerations, limitations inherent to conventional combination therapy, and the advantages conferred by hybrid molecules, including a unified pharmacokinetic profile, elimination of chemical incompatibilities between components, and simplified dosing regimens. Particular emphasis is placed on the mechanisms of action of hybrid compounds. Several reviewed hybrids demonstrate low minimum inhibitory concentrations, reduced frequencies of spontaneous resistance emergence, and favourable fractional inhibitory concentration indices (FIC ≤ 0.5), underscoring the therapeutic potential of this approach. Some examples of compounds are highlighted for their potent activity against diverse resistant bacterial strains and biofilms. A number of hybrid compounds have successfully advanced through clinical trials (TNP-2092, TNP-2198, cefilavancin, DNV-3837).