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In this paper, we investigate the movement of an inverted pendulum, the suspension point of which performs high-frequency oscillations along a line making a small angle with the vertical. We prove that under certain conditions on the function describing the oscillations of the suspension point of the pendulum, a periodic motion of the pendulum arises, and it is asymptotically stable.

Under consideration is some class of systems of nonlinear differential equations. The exponentially dichotomous linear part of the systems is assumed to have periodic coefficients. Using the author’s criterion of exponential dichotomy, we establish the conditions of existence of periodic solutions and prove stability of the solutions under small perturbations of coefficients in the linear part and nonlinear terms.

This paper is a short essay about Sergei L'vovich Sobolev (1908–1989), an outstanding mathematician of the 20th century, who made fundamental contributions to the development of the modern theory o...

We study the class of systems of differential equations defined by one class of matrix quasielliptic operators and establish solvability conditions for the systems and boundary value problems on $ {𝕉}^{n}_{+} $ in the special scales of weighted Sobolev spaces $ W^{l}_{p,\sigma} $ . We construct the integral representations of solutions and obtain estimates for the solutions.

We consider the Cauchy problem for an implicit system of linear partial differential equations. It belongs to the class of pseudohyperbolic systems. We prove the unique solvability of the Cauchy pr...

The Cauchy problem for one pseudohyperbolic system is considered. The unique solvability of this problem in Sobolev spaces is proved. Systems of this type arise in describing wave dynamics in rods.

Commercial hyper-cross-linked polystyrene (HCLPS) was shown to be a promising support for the development of heterogeneous catalysts intended for fine organic synthesis. This paper summarizes the results of multiyear studies on the creation of heterogeneous Pd-, Ptand Ru-containing catalysts based on MN100 and MN270 HCLPS. Data obtained by characterization of HCLPS and the related catalysts using various physical and physicochemical methods are reported. It was shown that commercial HCLPS can be used in the catalyst synthesis as spherical grains or as a powder. The form of HCLPS, along with the features of the metal catalyst precursor, essentially affect the distribution of Pd, Pt and Ru compounds and the sizes of metal-containing nanoparticles formed in the polymer environment. In addition, this is the first study that considers in detail the effect of catalyst treatment in flowing hydrogen at 300 °C on the surface chemical composition of the MN100 powder samples impregnated with Pd, Pt and Ru compounds.

The paper presents data on the chemical, physical and microbiological changes during storage of paste from the fruits of small-fruited apple trees processed with microwaves. After six month of storage the content of water soluble solids increased 1.02 times (from 21.50 % to 21.93 %). The sugar-acid index decreased 1.23 times (from 10.25 % to 8.35 %); the titratable acidity increased 1.13 times (from 9.92 g/dm3 to 11.21 g/dm3). The mass fraction of pectin substances decreased 2.51 times (from 2.31 % to 0.92 %) and the content of Vitamin C decreased 1.26 times (from 24.1 mg/100 g to 19.12 mg/100 g). The number of mesophilic aerobic and facultative anaerobic microorganisms did not exceed 200 colony-forming units (CFU) per gram. The number of yeasts did not exceed 260 CFU/g and the number of filamentous fungi did not exceed 620 CFU/g. No pathogenic or facultative pathogenic bacteria were found during all the period of storage.

Potatoes belong to the most important food crop, are a useful food product and a valuable raw material for food products. The quality of potato tubers depends on the fertilizer’s application and the doses of the active substance. The study about the influence of fertilizer systems (organic, organic-mineral, mineral) on the productivity and quality of potato tubers is relevant. The effect on the quality of potatoes when using fertilizer systems depends on the soil and climatic conditions of the natural cultivation zone, biological characteristics of the variety and other factors. Starch is an indicator of the quality of potato tubers. The starch content in potato tubers increases with the use of mineral fertilizers. The starch content in tubers of early-ripening potato varieties increases their marketability. During heat treatment, the size of starch grains affects the consistency of potato pulp.

In the paper, we consider systems of linear delay difference equations with periodic coefficients. We establish sufficient conditions for the asymptotic stability of the zero solution to the systems and obtain estimates of the stabilization rate of solutions at infinity. When obtaining the results we use a discrete analog of Lyapunov–Krasovskii functional.

In the present paper, we consider a class of functional difference equations with periodic coefficients. We establish criteria for asymptotic stability of the zero solution to the equations and obtain estimates characterizing the decay rates of solutions to these equations at infinity.

Ecosystems of different ranks are represented by components (climate, topography, soil, vegetation, wildlife, people). Over the course of evolution ecosystem components are interconnected with each other complexly. The study of any of them provides information about the evolution of the natural environment and material for identifying features of natural zoning, including regionality. Soil is a key component of the terrestrial ecosystem and many critical processes occur in the soil. The content of humus, its group and fractional composition allow us to draw conclusions about the genesis of paleosols. In the modern warming period – Holocene – there was a fluctuation of ecosystems on the territory of the southern Yenisei Siberia in the range: forest-tundra – forest (taiga) – steppe (forest-steppe).

Green spaces such as parks and street trees represent a key component of urban ecosystems. Planting trees and shrubs in cities provides a number of environmental, economic, social and health benefits and also preserves biodiversity in highly urbanized areas. The key problem of the ecological landscaping in Central Siberia is to select plants species resistant both to high level of pollutants and to large variations in temperature. Basing on the comparative study of growth characteristics and physiological state of plants in natural and urban ecosystems we recommend 31 plants species of 16 families for ecological landscaping. Recommended species for ecological landscaping in Central Siberia are Abies sibirica, Acer platanoide, Amorpha fruticosa, Berberis thunbergii, Berberis vulgaris, Cornus alba, Cotoneaster lucidus, Crataegus sanguine, Dasiphora spp., Forsythia spp., Juglans mandshurica, Juniperus Sabina, Larix sibirica, Philadelphus spp., Physocarpus opulifolius, Picea obovata, Picea pungens, Pinus sibirica, Pinus sylvestris, Ribes aureum, Rosa rugosa, Salix alba, Salix ledebouriana, Salix purpurea, Sorbaria sorbifolia, Sorbus aucuparia, Spiraea salicifolia, Syringa josikaea, Tamarix ramosissima, Tilia cordata, Viburnum opulus. Coniferous plants are presented with 7 species of 5 genera. Deciduous plants are presented with 24 species of 21 genera. The list of recommended plants species includes both trees and shrubs.

It investigates of metformin’s therapeutic potential and its influence on carbohydrate, lipid,cytokine metabolism in patients with essential hypertension with accompained type 2 diabetesmellitus. It shows that treatment with metformin significantly improves lipid metabolism in patientswith combined pathology. Metabolic effects of metformin lead to decreasing of body mass index,proinflammatory cytokine — interleukine-6 plasma levels in patients with essential hypertension withaccompained type 2 diabetes mellitus. Positive pharmacologic effects of metformin are connected withglycemic control, diminishing of insulin, glycated hemoglobine and insulineresistance index

1. The new pneumatic system with a measurement limit of 0–600μ provides a high accuracy with a comparatively simple scheme. 2. The distinguishing feature of the new system is the possibility of changing the normal characteristic curve of the “nozzle-gate” system and thus increase the sensitivity for small gaps. The experiments show that the best results are obtained when the value of the coefficientα is approximately equal to 2.5-3 and the value of the coefficients, 2–2.5. 3. The new pneumatic system can find wide use in active automatic checking devices with continuous measurement of the removal of allowances and observation of the course of the process, in automatic checking devices for measuring parts with large allowances, etc.