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Photoluminescence from the surface of Nafion polymer membrane upon swelling in water under irradiation by electromagnetic waves at a frequency of 100 MHz was studied. In these experiments, natural deionized (DI) water with a deuterium content of 157 ppm and deuterium-depleted water (DDW, deuterium content is 1 ppm) were explored. We have studied for the first time the effect of linearly and randomly polarized low-frequency electromagnetic radiation on the luminescence excitation. To obtain low-frequency electromagnetic radiation with random polarizations, anisotropic solid submicron-sized particles, which result in depolarization effects upon scattering of the initially linearly polarized radiation, were used. We compared two types of colloidal particles: spherically symmetric (isotropic) and elongated (anisotropic). If the radiation is linearly polarized, the intensity of luminescence from the Nafion surface decreases exponentially as the polymer is soaked, and such a behavior is observed both in natural DI water and DDW. When spherically symmetric submicron-sized particles are added to a liquid sample, the luminescence intensity also decreases exponentially upon swelling in both natural DI water and DDW. At the same time, when anisotropic submicron-sized particles are added to DI water, random jumps in the luminescence intensity appear during swelling. At the same time, the exponential decrease in the luminescence intensity is retained upon swelling in DDW. A qualitative theoretical model for the occurrence of random jumps in the luminescence intensity is presented.

Background: This article is devoted to the study of the effect of electrochemically activated water (catholyte with pH 9.3) on organic compounds of the plant matrix of brewer’s spent grain in order to extract various compounds from it. Methods: Brewer’s spent grain was obtained from barley malt at a pilot plant by mashing the malt followed by filtration and washing of the grain in water and storing it at (0 ± 2) °C in craft bags. For the organic compound quantitative determination, instrumental methods of analysis (HPLC) were used, and the results were subjected to mathematical analysis. Results: The study results showed that at atmospheric pressure, the alkaline properties of the catholyte showed better results compared to aqueous extraction with respect to β-glucan, sugars, nitrogenous and phenolic compounds, and 120 min was the best period for extraction at 50 °C. The excess pressure conditions used (0.5 ÷ 1 atm) revealed an increase in the accumulation of non-starch polysaccharide and nitrogenous compounds, while the level of sugars, furan and phenolic compounds decreased with increasing treatment duration. The waste grain extract ultrasonic treatment used revealed the effectiveness of catholyte in relation to the extraction of β-glucan and nitrogenous fractions; however, sugars and phenolic compounds did not significantly accumulate. The correlation method made it possible to reveal the regularities in the formation of furan compounds under the conditions of extraction with the catholyte: Syringic acid had the greatest effect on the formation of 5-OH-methylfurfural at atmospheric pressure and 50 °C and vanillic acid under conditions of excess pressure. Regarding furfural and 5-methylfurfural, amino acids had a direct effect at excess pressure. It was shown that the content of all furan compounds depends on amino acids with thiol groups and gallic acid; the formation of 5-hydroxymethylfurfural and 5-methylfurfural is influenced by gallic and vanillic acids; the release of furfural and 5-methylfurfural is determined by amino acids and gallic acid; excess pressure conditions promote the formation of furan compounds under the action of gallic and lilac acids. Conclusions: This study showed that a catholyte allows for efficient extraction of carbohydrate, nitrogenous and monophenolic compounds under pressure conditions, while flavonoids require a reduction in extraction time under pressure conditions.

Рассматривается круг вопросов, связанных с точным интегрированием уравнений движения механических систем в непотенциальном силовом поле (часто называемых циркуляционными). Подход к интегрированию основан на теореме Эйлера-Якоби-Ли: если $n$ - число степеней свободы, то (с учeтом сохранения фазового объeма) для точного интегрирования необходимо иметь ещe $2n-2$ первых интегралов и полей симметрий, находящихся в некоторых естественных отношениях. Указаны случаи движения в непотенциальном поле, интегрируемые с помощью разделения переменных. Обсуждаются геометрические свойства систем с ненeтеровыми полями симметрий. Указаны примеры существования неприводимых полиномиальных интегралов третьей степени по импульсам. Рассмотрена задача об условиях существования однозначных полиномиальных интегралов циркуляционных систем с двумя степенями свободы и торическим пространством положений. Показано, что в типичном случае уравнения движения вообще не допускают непостоянных полиномиальных интегралов. Библиография: 32 названия.

A low-temperature technology was developed for producing a nanocomposite based on poly (lactic-co-glycolic acid) and zinc oxide nanoparticles (ZnO-NPs), synthesized by laser ablation. Nanocomposites were created containing 0.001, 0.01, and 0.1% of zinc oxide nanoparticles with rod-like morphology and a size of 40–70 nm. The surface of the films from the obtained nanomaterial was uniform, without significant defects. Clustering of ZnO-NPs in the PLGA matrix was noted, which increased with an increase in the concentration of the dopant in the polymer. The resulting nanomaterial was capable of generating reactive oxygen species (ROS), such as hydrogen peroxide and hydroxyl radicals. The rate of ROS generation increased with an increase in the concentration of the dopant. It was shown that the synthesized nanocomposite promotes the formation of long-lived reactive protein species, and is also the reason for the appearance of a key biomarker of oxidative stress, 8-oxoguanine, in DNA. The intensity of the process increased with an increase in the concentration of nanoparticles in the matrix. It was found that the nanocomposite exhibits significant bacteriostatic properties, the severity of which depends on the concentration of nanoparticles. In particular, on the surface of the PLGA–ZnO-NPs composite film containing 0.001% nanoparticles, the number of bacterial cells was 50% lower than that of pure PLGA. The surface of the composite is non-toxic to eukaryotic cells and does not interfere with their adhesion, growth, and division. Due to its low cytotoxicity and bacteriostatic properties, this nanocomposite can be used as coatings for packaging in the food industry, additives for textiles, and also as a material for biomedicine.

The long-term cooperation between the Rogante Engineering Office (REO) and the Petersburg Nuclear Physics Institute (PNPI) of the National Research Centre “Kurchatov Institute” in the field of neut...

Abstract We consider the Koopman operator generated by an invertible transformation of a space with a finite countably additive measure. If the square of this transformation is ergodic, then the orthogonal Koopman operator is a symplectic transformation on the real Hilbert space of square summable functions with zero mean. An infinite set of quadratic invariants of the Koopman operator is specified, which are pairwise in involution with respect to the corresponding symplectic structure. For transformations with a discrete spectrum and a Lebesgue spectrum, these quadratic invariants are functionally independent and form a complete involutive set, which suggests that the Koopman transform is completely integrable.

This paper addresses the problem of stability of equilibria of mechanical systems in nonpotential force fields. In the linear approximation, any nonpotential force is uniquely represented as the sum of a potential force and a circulatory force. The instability of equilibrium is established for the nonlinear problem in the case when the linearized system has a pair of zero eigenvalues. The mechanism of stability loss is due to the appearance of two asymptotic trajectories, one that enters an equilibrium point and one that exits it. A similar result takes place when additional gyroscopic forces and viscous friction forces are taken into account. Asymptotic solutions can be obtained in the form of series in inverse powers of time whose coefficients are polynomials in logarithms of time.

The work reports a number of results on the dynamics of swelling and inferred nanostructure of the ion-exchange polymer membrane Nafion in different aqueous solutions. The techniques used were photoluminescent and Fourier transform IR (FTIR) spectroscopy. The centers of photoluminescence were identified as the sulfonic groups localized at the ends of the perfluorovinyl ether (Teflon) groups that form the backbone of Nafion. Changes in deuterium content of water induced unexpected results revealed in the process of polymer swelling. In these experiments, deionized (DI) water (deuterium content 157 ppm) and deuterium depleted water (DDW) with deuterium content 3 PPM, were investigated. The strong hydration of sulfonic groups involves a competition between ortho- and para-magnetic forms of a water molecule. Deuterium, as it seems, adsorbs competitively on the sulfonic groups and thus can change the geometry of the sulfate bonds. With photoluminescent spectroscopy experiments, this is reflected in the unwinding of the polymer fibers into the bulk of the adjoining water on swelling. The unwound fibers do not tear off from the polymer substrate. They form a vastly extended “brush” type structure normal to the membrane surface. This may have implications for specificity of ion transport in biology, where the ubiquitous glycocalyx of cells and tissues invariably involves highly sulfated polymers such asheparan and chondroitin sulfate.

The results of integrity of narrowband and wideband lumped element circulators design methodology to the computer aided design system of microwave devices AWR Microwave Office are presented in the article. The calculation method of narrow band circulators circuits which consist of serious and shunt tuning capacities is investigated. The simple and visual method of wideband ferrite isolators optimize design based on circulation impedance calculation is described here. The results of design of the ultra wideband circulator with shunt capacity, serious resonant matching circuit and serious resonant circuit between common terminal and ground are considered. The new theoretical results of calculation of two schematics of wideband high power circulators with serious tuning capacity are presented. The first schematic is formed with matching resonant network being connected in serious at each terminal. It is shown that double hump characteristic is realized. The second schematic is formed with serious resonant network connected between common terminal and the ground. It is shown that four-order Tchebycheff characteristic is realized.

We consider nonautonomous linear systems of differential equations admitting a time-dependent first integral that is a quadratic form. The duality between mutually adjoint linear systems with quadratic integrals is established. Conditions for the spectrum of such linear systems to be symmetric about zero are indicated. We prove that a linear system is stable if and only if it admits a first integral that is a positive definite quadratic form. For linear systems with a quadratic integral, invariant measures whose densities are positive functions of time are studied. An explicit form of a series of quadratic integrals is specified if one of them is known. It is shown that the degree of instability of a regular linear system (the number, counting multiplicities, of positive points in the spectrum) is at most the maximum of the indices of inertia of a reducible quadratic integral.

Abstract Linear systems of differential equations with an invariant in the form of a positive definite quadratic form in a real Hilbert space are considered. It is assumed that the system has a simple spectrum and the eigenvectors form a complete orthonormal system. Under these assumptions, the linear system can be represented in the form of the Schrödinger equation by introducing a suitable complex structure. As an example, we present such a representation for the Maxwell equations without currents. In view of these observations, the dynamics defined by some linear partial differential equations can be treated in terms of the basic principles and methods of quantum mechanics.

In this paper the results of experimental studies of the combustion of a round microjet of hydrogen in a ring subsonic coaxial air jet are presented. It is shown that the combustion scenario for a subsonic hydrogen jet outflow is associated with the presence of a “bottleneck flame region” and nozzle heating, but the initial spherical shape of the flame region is transformed into a cylindrical one. It was found that the combustion of a round microjet of hydrogen in a satellite ring coaxial air jet at a supersonic outflow velocity is accompanied by the presence of supersonic cells.

Linear evolution equations of mathematical physics admitting an invariant in the form of a positive quadratic form are considered. In particular, this includes the string vibration equation, the Liouville kinetic equation, the Maxwell system of equations and the Schrodinger equation. Conditions for the existence of an invariant Gaussian measure are indicated, which makes it possible to apply well-known results of ergodic theory (Poincare’s recurrence theorem, Birkhoff–Khinchin ergodic theorem, etc.). We discuss the Hamiltonian property of such systems and conditions for their complete integrability. The ergodic properties of Kronecker flows on infinite-dimensional tori are studied. A general theorem on the averaging of quadratic forms is established.

The results of experimental investigations of the features of diffusion combustion during the interaction of a round supersonic microjet of air in the center and a coaxial (coflowing ring) jet of hydrogen. Such combustion is accompanied by a number of new phenomena: the formation of a cone-shaped flame near the nozzle сutoff, the locking of the combustion region in this cone, the presence of small-scale supersonic cells in the resulting flow, and the formation of laminar sections and their turbulization.

The properties of the Gibbs ensembles of Hamiltonian systems describing the motion along geodesics on a compact configuration manifold are discussed. We introduce weakly ergodic systems for which the time average of functions on the configuration space is constant almost everywhere. Usual ergodic systems are, of course, weakly ergodic, but the converse is not true. A range of questions concerning the equalization of the density and the temperature of a Gibbs ensemble as time increases indefinitely are considered. In addition, the weak ergodicity of a billiard in a rectangular parallelepiped with a partition wall is established.

Smooth dynamical systems on closed manifolds with invariant measure are considered. The evolution of the density of a nonstationary invariant measure is described by the well-known Liouville equation. For ergodic dynamical systems, the Liouville equation is expressed in Hamiltonian form. An infinite collection of quadratic invariants that are pairwise in involution with respect to the Poisson bracket generated by the Hamiltonian structure is indicated.

The experimental research results on diffusion combustion of a round hydrogen microjet flowing from a slit micronozzle at subsonic and supersonic speeds are presented. For the first time, four scenarios of diffusion combustion of a round hydrogen microjet have been identified, including supersonic combustion in the presence of supersonic cells both in air and in hydrogen. It has been found that flame stabilization for a subsonic microjet velocity of hydrogen is associated with the presence of a “bottleneck flame region” leading to the nozzle choking phenomenon, and flame stabilization for a supersonic microjet flow is associated with the presence of supersonic cells. A hysteresis of the diffusion combustion process of a plane microjet of hydrogen is found depending on the method of ignition of the microjet (near or far from the nozzle exit) and the direction of change in the rate of its outflow (growth or decrease).

The results of experimental investigations into the effect of distributed suction through a finely perforated permeable section on the spatial development of disturbances at the nonlinear stage of their evolution in the boundary layer of a straight wing are presented. It is shown that distributed suction makes possible reducing the intensity of both natural pulsations of the boundary-layer velocity and artificial ones generated by an external acoustic field at the fundamental frequency and its harmonics by two orders of magnitude. Affecting significantly the average flow, suction rules out the turbulent state of the boundary layer below the impact area and shifts the flow separation keeping it in the laminar state.

The results of experimental investigations of the effect of distributed suction through a perforated section of a symmetric wing profile on the spatial development of disturbances in the boundary layer are presented. It is shown that this method of control makes it possible to reduce by ten times the intensity of natural pulsations of the boundary-layer velocity, while the disturbance intensity decreases by about 20 times, when an acoustic field is applied at the subharmonic frequency of the fundamental wave. The suction also significantly affects the mean flow up to eliminating the separation of the boundary layer near the trailing edge of the wing instead of contributing only a decrease in the intensity of high-frequency pulsations for natural and forced disturbances.

Background: The present article considers the influence of malt with various adjuncts on beer organic compounds and taste profile composition, with more attention paid to the phenol complex change. The topic under consideration is relevant since it studies the interactions of phenolic compounds with other biomolecules, and expands the understanding of the adjuncts organic compounds contribution and their joint effect on beer quality. Methods: Samples of beer were analyzed at a pilot brewery using barley and wheat malts, barley, rice, corn and wheat, and then fermented. The beer samples were assessed by industry-accepted methods and using instrumental analysis methods (high-performance liquid chromatography methods—HPLC). The obtained statistical data were processed by the Statistics program (Microsoft Corporation, Redmond, WA, USA, 2006). Results: The study showed that at the stage of hopped wort organic compounds structure formation, there is a clear correlation between the content of organic compounds and dry substances, including phenolic compounds (quercetin, catechins), as well as isomerized hop bitter resines. It is shown that the riboflavin content increases in all adjunct wort samples, and mostly with the use of rice—up to 4.33 mg/L, which is 9.4 times higher than the vitamin levels in malt wort. The melanoidin content in the samples was in the range of 125–225 mg/L and its levels in the wort with additives exceeded the malt wort. Changes in β-glucan and nitrogen with thiol groups during fermentation occurred with different dynamics and depending on the adjunct’s proteome. The greatest decrease in non-starch polysaccharide content was observed in wheat beer and nitrogen with thiol groups content—in all other beer samples. The change in iso-α-humulone in all samples at the beginning of fermentation correlated with a decrease in original extract, and in the finished beer there was no correlation. The behavior of catechins, quercetin, and iso-α-humulone has been shown to correlate with nitrogen with thiol groups during fermentation. A strong correlation was shown between the change in iso-α-humulone and catechins, as well as riboflavin and quercetin. It was established that various phenolic compounds were involved in the formation of taste, structure, and antioxidant properties of beer in accordance with the structure of various grains, depending on the structure of its proteome. Conclusions: The obtained experimental and mathematical dependences make it possible to expand the understanding of intermolecular interactions of beer organic compounds and take a step toward predicting the quality of beer at the stage of using adjuncts.

Background: The article considers the phenolic hop compounds’ effect on the quality indicators of finished beer. The topic under consideration is relevant since it touches on the beer matrix colloidal stability when compounds with potential destabilizing activity are introduced into it from the outside. Methods: The industrial beer samples’ quality was assessed by industry-accepted methods and using instrumental analysis methods (high-performance liquid chromatography methods—HPLC). The obtained statistical data were processed by the Statistics program (Microsoft Corporation, Redmond, WA, USA, 2006). Results: The study made it possible to make assumptions about the functional dependence of the iso-α-bitter resins and isoxanthohumol content in beer samples. Mathematical analysis indicate interactions between protein molecules and different malted grain and hop compounds are involved in beer structure, in contrast to dry hopped beer, where iso-a-bitter resins, protein, and coloring compounds were significant, with a lower coefficient of determination. The main role of rutin in the descriptor hop bitterness has been established in kettle beer hopping technology, and catechin in dry beer hopping technology, respectively. The important role of soluble nitrogen and β-glucan dextrins in the perception of sensory descriptors of various technologies’ beers, as well as phenolic compounds in relation to the formation of bitterness and astringency of beer of classical technology and cold hopping, has been shown. Conclusions: The obtained mathematical relationships allow predicting the resulting beer quality and also make it possible to create the desired flavor profiles.

Microbial antibiotic resistance is an important global world health problem. Recently, an interest in nanoparticles (NPs) of silver oxides as compounds with antibacterial potential has significantly increased. From a practical point of view, composites of silver oxide NPs and biocompatible material are of interest. A borosiloxane (BS) can be used as one such material. A composite material combining BS and silver oxide NPs has been synthesized. Composites containing BS have adjustable viscoelastic properties. The silver oxide NPs synthesized by laser ablation have a size of ~65 nm (half-width 60 nm) and an elemental composition of Ag2O. The synthesized material exhibits strong bacteriostatic properties against E. coli at a concentration of nanoparticles of silver oxide more than 0.01%. The bacteriostatic effect depends on the silver oxide NPs concentration in the matrix. The BS/silver oxide NPs have no cytotoxic effect on a eukaryotic cell culture when the concentration of nanoparticles of silver oxide is less than 0.1%. The use of the resulting composite based on BS and silver oxide NPs as a reusable dry disinfectant is due to its low toxicity and bacteriostatic activity and its characteristics are not inferior to the medical alloy nitinol.

The stability of linear mechanical systems in nonpotential force fields is studied. Under the presence of circulatory forces, the system is nonconservative, yet it can always be presented in a Hamiltonian form. A point where the potential energy has its maximum is an unstable equilibrium, regardless of the presence of circulatory forces.

В работе изучаются линейные системы дифференциальных уравнений в гильбертовом пространстве, которые допускают первый интеграл в виде положительно определeнной квадратичной формы. Основное внимание уделено трeм взаимосвязанным вопросам: существованию других квадратичных интегралов, свойству гамильтоновости линейной системы, а также еe полной интегрируемости. Для невырожденных линейных систем в конечномерном пространстве на все эти вопросы известны практически исчерпывающие ответы. Результаты общего характера применяются к линейным эволюционным уравнениям математической физики: волновому уравнению, уравнению Лиувилля, уравнениям Максвелла и Шрeдингера. Библиография: 60 названий.

Рассматриваются гладкие динамические системы на замкнутых многообразиях с инвариантной мерой. Эволюция плотности нестационарной инвариантной меры описывается известным уравнением Лиувилля. Для эргодических динамических систем уравнение Лиувилля представлено в гамильтоновом виде. Указан бесконечный набор квадратичных инвариантов, которые находятся попарно в инволюции относительно скобки Пуассона, порожденной указанной гамильтоновой структурой. Библиография: 11 названий.

Data on the vertical distribution of dissolved methane in Baikal water column are analyzed. The zone of open lake now shows an increase in the concentrations of dissolved methane compared with 2002–2004. The possible causes of this phenomena are considered. Methane concentration in the aerobic water column of Baikal decreases from the surface toward the bottom. The active layer of the lake, as well as that in the ocean, contains a peak of methane concentration. In the main, deep part of the water column, methane concentration is lower than that equilibrium with the atmosphere because of the activity of aerobic methanotrophic microflora. The standard procedure of the static headspace analysis for determining methane is supplemented by measuring the pressure in a closed system. The concentrations of methane determined by methods of vacuum extraction and static headspace analysis are compared.

We discuss the relationship between the singular points of an autonomous system of differential equations and the critical points of its first integrals. Applying the well-known Splitting Lemma, we introduce local coordinates in which the first integral takes a “canonical” form. These coordinates make it possible to introduce a quasihomogeneous structure in some neighbourhood of any singular point and so to prove general theorems on the existence of asymptotic trajectories which go into or out of that singular point. We consider quasihomogeneous truncations of the original system of differential equations and show that if the singular point is isolated, the quasihomogeneous system is Hamiltonian. For a general mechanical system with two degrees of freedom, we prove a theorem on the instability of an equilibrium when it is neither a local minimum nor a local maximum of the potential energy. Bibliography: 21 titles.

Обсуждаются связи между особыми точками автономных систем дифференциальных уравнений и критическими точками их первых интегралов. С помощью известной леммы о расщеплении вводятся локальные координаты, в которых первый интеграл имеет "канонический" вид. Эти координаты позволяют ввести в окрестности особой точки квазиоднородную структуру и доказать общие теоремы о наличии асимптотических траекторий, входящих в особую точку или выходящих из нее. Исследованы квазиоднородные укорочения исходной системы дифференциальных уравнений. Показано, что при условии изолированности особой точки квазиоднородная система будет гамильтоновой. Установлена теорема о неустойчивости равновесий общих механических систем с двумя степенями свободы, когда потенциальная энергия в положении равновесия не имеет ни максимума, ни минимума. Библиография: 21 название.

Известные уравнения эволюции соленоидального векторного поля с вмороженными в сплошную среду интегральными кривыми представлены в инвариантном виде в четырехмерном пространстве-времени. Введена фундаментальная $1$-форма ($4$-потенциал), и рассмотрена задача о вариации действия (интеграл от $4$-потенциала по гладким кривым). Описаны экстремали действия в классе кривых с закрепленными концами и законы сохранения, порожденные группами симметрий. В предположении ортогональности электрического и магнитного полей уравнения Максвелла представлены в виде уравнений эволюции соленоидального векторного поля. Роль поля скоростей играет поле нормированных векторов Пойнтинга.

Рассмотрено обобщение уравнений Максвелла на псевдоримановом многообразии $M$ произвольной размерности при наличии электрических и магнитных зарядов. Доказано, что если группы когомологий $H^2(M)$ и $H^3(M)$ тривиальны, то решение этих уравнений сводится к решению уравнения Д'Аламбера-Ходжа.

In this paper, we presented the results of experimental studies of the diffusion combustion of a plain hydrogen microjet flowing from a slit micronozzle at subsonic and supersonic speeds. For the first time, four scenarios of diffusion combustion of a plain hydrogen microjet including supersonic combustion in the presence of supersonic cells in both air and hydrogen are presented. The stabilization of the subsonic combustion of a hydrogen microjet was established to be due to the presence of a «bottleneck flame region» while the stabilization of the supersonic combustion of a microjet was found to be associated with the presence of supersonic cells. The observed hyster­esis of diffusion combustion of a plain hydrogen microjet depends on both the method of igniting the microjet (near or far from the nozzle exit) and the direction of change in the rate of its outflow (growth or reduction).