Properties Of Operators Research Articles

Common local spectral properties for the operator products

In their paper [Generalized Clines Formula for g-Drazin Inverse in a Ring, Filomat 35(8) (2021) 2573–2583], Chen and Abdolyousefi examined the common spectral properties of operators [Formula: see text] and [Formula: see text], subject to the following conditions: [Formula: see text] [Formula: see text] In this note, we explore the common local spectral properties of these operators. We demonstrate that [Formula: see text] and [Formula: see text] shared the single-valued extension property, the Bishop property [Formula: see text], the property [Formula: see text], the decomposition property [Formula: see text], and decomposability. Furthermore, we investigate the closedness of the analytic core and the quasinilpotent part. We also delve into the Dunford’s property [Formula: see text] and the property [Formula: see text].

Dependence of Tractor Traction Properties on Agricultural Machinery Connections

Tractor traction properties depend on many factors including engine power, operating weight and tractor weight distribution across axles, dimensions, profile, gears range and gear count in the gearbox. Moreover, the tractor technical condition plays a vital role, encompassing aspects from the fuel system affecting the engine power output, to the chassis, influencing terrain traversability, maneuverability, and soil deformation. (Research purpose) The paper addresses several research problems. To investigate the impact of the agricultural machinery connections with the tractor on the tractor traction properties, and determine the impact of agricultural machinery weight, and grip width on the main technical and economic parameters. To analyze how geometrical parameters of tractors and agricultural machinery correlate with soil reactions under the machine support wheels as well as the front and rear wheels of the tractor. To determine the influence of the design characteristics of cultivators with varying working widths on the main operational properties of the machine-tractor unit. (Materials and methods) The study involves examining the operation of the Belarus 82.1 tractor with cultivators KPS-4 and KPS-5 from different manufacturers. Various methods were employed, including calculation, calculation-construction, calculation-graphic analysis, economic-mathematical techniques, along with comparison, measurement, and description. (Results and discussion) This study identified indicators impacting the load redistribution transmitted to the tractor from mounted cultivators. Based on these indicators, alterations in soil reactions under cultivator support wheels and the tractor’s rear wheels were deduced. (Conclusions) The calculations on the effect of mounted cultivators with different working widths (different operating weight) on the redistribution of soil reactions between axles, enabled the determination of modifications in tractor traction force, machine-tractor unit productivity, and specific fuel consumption.

Approximation Properties of Parametric Kantorovich-Type Operators on Half-Bounded Intervals

The main purpose of this paper is to introduce a new family of parametric Kantorovichtype operators on the half-bounded interval. The convergence properties of these new operators are investigated. The Voronovskaja-type weak inverse theorem and the rate of uniform convergence are obtained. Furthermore, we obtain some shape preserving properties of these operators, including monotonicity, convexity, starshapeness, and semi-additivity preserving properties. Finally, some numerical illustrative examples show that these new operators have a better approximation performance than the classical ones.

О влиянии топливного биоэтанола на эксплуатационные свойства транспортных двигателей

Purpose: To comprehensively consider the effect of bioethanol as an additive to gasoline on the operational properties of transport engines from the point of view of their differences in physical and chemical properties and technologies, taking into account not only advantages, but also disadvantages. To more profoundly evaluate the volatility of gasoline-ethanol mixtures at different ethanol and water contents, and its effect on startability. Methods: Comparison of available data in normative and reference literature, also in scientific publications. Conducting an experiment using the standard method for gasoline to measure the saturated vapor pressure of gasoline-ethanol mixture of various composition. Results: From the collected data, parameters of the gasoline-ethanol mixture that are important for operation of transport engines have been identified. The need for a detailed assessment of the influence of the composition of such mixtures on the structural materials of transport engines has been identified. Data have been obtained on the volatility of mixtures in a wide temperature range, simulating real operating conditions. No significant deterioration in startability has been revealed. A visible violation of the phase stability of mixtures containing more than 7.5% water has been noted. Practical significance: The measured degree of volatility and startability of gasoline-ethanol mixtures of the various composition allows us to conclude that their level in comparison with gasoline, for mixtures with a 5% ethanol content is satisfactory, and for mixtures with 85% ethanol, is relatively satisfactory. For the first time, the parameters of the provided standard procedure are expanded, relative to the usual temperature recommended when measuring the vapor pressure, to possibly wider limits, allowing a more complete picture to be obtained.

Rate of approximation of blending type modified univariate and bivariate λ-Schurer-Kantorovich operators

In this work, we investigate some approximation properties of blending type univariate and bivariate Schurer-Kantorovich operators based on shape parameter λ ∈ [−1, 1]. We evaluate some moment estimates and obtain several direct theorems. Next, we construct the bivariate version of proposed operators and compute rate of approximation with the partial and complete modulus of continuity. Moreover, we present certain graphical and numerical results for univariate and bivariate versions of these operators.

Influence of biocides on the operational properties of lubricant compositions

O organization of the production of lubricants, the creation of motor oils for various brands of locomotive, stationary, industrial, large-load self-loading ship diesels used in Republic, researched of highly effective additives and additive packages, is possible with the development of new lubricant compositions. For this purpose, investigation of multifunctional additives and additive packages in base oils according to the latest requirements has the great importance. Additives included in additive compositions in optimal concentration meet the requirements for a number of quality indicators of oils. The component added to these compositions – the biocide – may have a negative effect on the mentioned operating properties. Therefore, the main physico-chemical and operating properties of new bio-sustainable lubricants should be checked and the options recommended for application should be scientifically and practically justified. It is known, that the basic operational properties of lubricating oils are their oxidation, corrosion, corrosion and washing properties. As a result of the research conducted in the field of creating bio-sustainable additive compositions for various purpose lubricants on the basis of multifunctional additives and additive packages, it was determined that using organic compounds of different composition (α-phenyl-β-nitroethene biocide in the amount of 0.25 %) as a biocide can increase their service life possible. The specified properties of bio-sustainable oil samples created by adding biocide are determined by the relevant GOST. Our goal is to study the effect of biocide added to the oil composition.

PRODUCTION OF DRILLING FLUIDS BASED ON COTTON SOAPSTOCKS

For effective oil production, this is necessary to ensure high-quality drilling, opening of reservoirs. Many tasks that-arise during drilling are solved with the-help of-process fluids. The purpose of the work is to create new drilling fluids based on secondary resources, surfactants. The composition of-a new drilling mud for drilling wells is proposed. Methods. One of-the main indicators of hydrophobic emulsion solutions is filtrate output. The operational properties of the filtrate-release of hydrophobic emulsion solutions differ slightly from other indicators. When filtering hydrophobic emulsion solutions in a porous-medium, the kinetic factor associated with the-rate of formation of the filtration crust becomes of great importance. Results and discussion. The instantaneous filtrate output of-systems of hydrophobic emulsion solutions stabilized by surfactants is reduced due to the rapid formation of a bound filtration crust by means of-fast interactions, therefore, it’s strengthened by slow interaction bonds. This formation of charge-transfer complexes, electronic donor-acceptor, long-lived free stable radicals, hydrogen, covalent bonding carried out with an induction period at a close distance, determines a decrease in-the filtration yield of the solution. Conclusion. Cotton soapstocks are valuable additives in the composition of drilling fluids-to improve their operational properties. According to the limit values of the parameters, the-reagents are arranged in the following-series according to-filtrate: fatty acid salts > emultal > soapstock > tar distillation of fatty-acids. At the same time, the parameters of the hydrophobic emulsion solution are always, except for GJC and FFA, where after the limit value of their quantities, the filtrate output increases, improves with-the concentrations of-reagents.

Development and implementation of grade 62PP steel production with special requirements for non‑metallic inclusions content

OJSC “BSW – Management Company of Holding “BMC” produces high‑quality steel used in the automotive, railway, and oil and gas industries. The production of these steel grades involves controlling a range of quality parameters for both continuous cast and hot‑rolled steel billets to ensure the required mechanical, technological, and operational properties of the finished products. The steelmaking process aims to obtain high‑quality steel with the desired microstructure – low levels of harmful impurities and non‑metallic inclusions (hereinafter referred to as NV). This article describes the work and results obtained in the development of the technology for producing hot‑rolled grade 62PP steel, using the example of low‑hardenability carbon steel intended for the production of springs used in vehicle suspension.

INFLUENCE OF PLASTICIZING AND AIR-ENTRAINING ADMIXTURES ON CONCRETE PROPERTIES

In the modern construction industry of Kazakhstan, to ensure the needs of the market, there is an urgent essential to improve the quality of concrete and expand its functional purpose. To a large extent, this is achieved by designing concrete as composite materials with different structures, quantities and nature of components. The multicomponent composition makes it possible to effectively manage the structure formation processes of the concrete cementing matrix and obtain concretes with the required properties. This article presented the effect of plasticizing and air-entraining admixtures on the properties of heavy concrete. The compositions of concrete mixture with plasticizing and air-entraining admixtures were selected. The results of study of plasticizing and air-entraining admixtures effect on average density, workability, compressive strength of concrete samples are presented. The effectiveness of introduction of a complex admixtures was evaluated in order to further improve operational properties of concrete. The plasticizing effect makes it possible to increase workability of concrete mortar while by reducing water-cement ratio from 0,5 to 0,38. Due to this, density and strength of concrete increased while improving operational characteristics. The combined effect of plasticizing and air-entraining admixtures had a positive effect on mobility of concrete mortar and its strength of concrete samples. The significant strength of 47,2 MPa was achieved with the combined introduction of a plasticizing and air-entraining admixtures in the amount of 1,2% and 0,5% of the cement weight, thereby increasing the strength of concrete samples by 32% compared to the control sample.

Strong unique continuation property for fourth order Baouendi-Grushin type subelliptic operators with strongly singular potential

In this paper, we prove the strong unique continuation property for the following fourth order degenerate elliptic equationΔX2u=Vu, where ΔX=Δx+|x|2αΔy (0<α≤1), with x∈Rm,y∈Rn, denotes the Baouendi-Grushin type subelliptic operators, and the potential V satisfies the strongly singular growth assumption |V|≤c0ρ4, whereρ=(|x|2(α+1)+(α+1)2|y|2)12(α+1) is the gauge norm. The main argument is to introduce an Almgren's type frequency function for the solutions, and show its monotonicity to obtain a doubling estimate based on setting up some refined Hardy-Rellich type inequalities on the gauge balls with boundary terms.

Application of a Three-Level Elastoviscoplastic Model for Describing Complex Loading Processes

It is known that the meso- and microstructures of metals determine the physical, mechanical and operational properties of their final products. Scientific and technological progress of recent decades has given impetus to the elaboration and use of models capable of describing the evolving structure of materials. The most promising are multilevel models that include internal variables and are based on physical theories of elastoplasticity (elastoviscoplasticity). This paper presents the structure and basic relationships of a three-level (macro-, meso-1 and meso-2 levels) elastoviscoplastic model. The developed model operates on such internal variables as dislocation densities on slip systems, barriers on split dislocations and sources of edge dislocations. The model describes the mechanisms of production, annihilation, formation of barriers and sources of dislocations. The law of hardening directly takes into account the densities of dislocations and barriers. The mechanism of inelastic deformation is the gliding of edge dislocations along slip systems. Special emphasis is placed on the influence of split dislocations (prone to forming hard Lomer–Cottrell and Hirth barriers) on the deformation of the material. The model is used to describe the behavior of an elastoviscoplastic polycrystalline aggregate with an FCC lattice. Geometric nonlinearity is taken into account by utilizing decomposition of the crystallite motion into quasi-rigid and deformation components. For this purpose, a rigid moving coordinate system for the crystal lattice is introduced. Examples of the application of the model for analyzing the simple and complex deformation mechanisms of materials with different stacking fault energies and, consequently, with different tendencies toward the decomposition of dislocations and barrier formation are given.

Construction of a mathematical model for approximating the sphere by strips of unfolding surfaces

Approximating non-expandable surfaces by compartments of expandable ones makes it possible to simplify the process of obtaining the required shape without loss of operational properties. There is a known approximation of a sphere using the example of a ball when its surface can consist of polygons. However, this list does not exhaust the possible options for approximating the sphere. Its approximation by truncated cones tangent to parallels or by congruent cylindrical petals tangent to meridians is known. Any line on the surface of a sphere is a line of curvature. This means that the common line of contact of the expanded surface with the sphere will be a line of curvature for the expanded surface as well (rectilinear generatrices of the expanded surface will cross this line at a right angle). When building a sweep of such a surface, the line of contact will be transformed but the rectilinear generatrices will remain perpendicular to it, which simplifies the construction of the sweep. The approximation of the sphere by congruent strips, the number of which can be different, starting from one, is considered. A necessary condition for such an approximation is a common line of contact of adjacent strips. To this end, the line of contact on the sphere or the guide curve must have an appropriate shape. Such a curve is taken as a slope line (a curve whose tangents form a constant angle of inclination to the horizontal plane). The study results are the parametric equations of the strip touching the sphere and its corresponding equations on the sweep. The construction of the strip on the sweep is explained by the invariance of the geodesic curvature of the guide curve when the strip is bent until it aligns with the plane. This explains the difference between the proposed approach and conventional methods of sphere approximation. Approximating the sphere by strips of unfolding surfaces has a practical application in architecture with spherical elements, as well as in religious buildings with domes in the form of a part of the sphere

Robust calculus for biotransformation in wastewater generalised across thousands of chemicals and conditions

Environmental context Decades of research tried to understand the inherent complexity of biodegradation of contaminants. We describe calculus of biodegradation driven by bioavailability, redox, geometry and acclimation (adaptation) of microbiota. We tested predictions for thousands of contaminants across wastewater treatment plants, explaining up to 70% of the variance in observations. This competes with more intensive methods, and enables more efficient monitoring, experimentation and data interpretation. Rationale Release of harmful contaminants of emerging concern (CECs) in the environment prompts possible adverse toxicological effects. Increasing population, water use and process wastewater generation require more efficient removal of contaminants that allows for effluent discharge within environmental regulatory limits. Wastewater treatment plants (WWTPs) can remove hazardous contaminants, limiting unwanted release. Fine-tuning WWTP settings to fit the location, time, season, wastewater type, etc. may enhance removals to reduce CEC concentrations and toxic pressures. Methodology For this purpose, we need robust tools to calculate removal efficiencies. We studied influences of operational settings and CEC properties on their removal in WWTPs. For this purpose, we parameterised thermochemical properties of CECs: for their (1) speciation and acidification, (2) (re/im)mobilisation due to (de)sorption into solid/water, (3) redox-mediated biotransformation and (4) acclimation of biomass so to utilise metabolic pathways for biotransformation. By combining these parameters, we developed an energy-based framework for calculating biotransformation rates. Results We evaluated our calculus using removal efficiency (%) data for 373 measurements of 60 CECs in 14 different Dutch WWTPs and an additional 667 CECs in 49 WWTPs across the world. Our prediction precision, R2 ≈ 0.65 (P &lt; 10−5), captures influences of wastewater characteristics (multiple measurements for each WWTP). It is higher than R2-values of modelling approaches currently available. Our model explains CEC removal with appreciative certainty. We identified outliers during evaluation. These outliers were attributed mostly to back-transformation and uncertainty in long-term background concentrations of contaminants, causing consequent acclimation of microbial consortia. Discussion Biodegradability and CEC-degrading biomass can be estimated from concentration and environmental residence time. Our framework and underlying parametrisations have a mechanistic basis, utilising simple WWTP operational information (CEC concentration, temperature, suspended solids concentration, oxygen demand, etc.). Thereby, our work has wide potential for implementation. Our approach can supplement current fate assessment for CECs for improved environmental risk assessments. We conclude by discussing the potential for removal enhancement.

Металознавчі аспекти дисперсійного нітридного зміцнення високовуглецевих сталей Повідомлення 1. Вплив параметрів аустенізуючого нагріву та відпуску на фазовий перерозподіл азоту та ванадію в сталях

Systemic fundamental research for several decades at the FTIMS of the National Academy of Sciences of Ukraine and the accumulated experience of industrial application have shown that the technology of dispersion nitride hardening, which is based on the alloying of steels with nitrogen and vanadium, is a method of significantly improving the entire complex of physical, mechanical and operational properties of cast and deformed carbon, low-alloy and alloy steels of various functional purposes. The most significant advantage of the steels developed at the FTIMS of the National Academy of Sciences of Ukraine is a simultaneous significant increase in their static and cyclic strength, fracture toughness, thermal strength and heat resistance, wear resistance, annealing, weldability, reduction or complete elimination of the tendency to natural, deformation and warm embrittlement. Medium- and high-carbon pre-eutectoid and eutectoid steels of high strength and wear resistance are widely used in various fields of mechanical engineering. However, they are most widely used for railway wheels and rails. The reliability and operational resource of wheels and rails, which are in extremely harsh operating conditions, mainly determine the technical and economic performance indicators of railway transport. At the same time, existing relatively cheap non-alloyed and low-alloyed medium- and high-carbon wheel and rail steels no longer meet the modern requirements of increased speeds and load capacity of rolling stock. Keywords: carbon steels, dispersion nitride hardening, austenization, tempering, phase redistribution of nitrogen and vanadium.

Development of an algorithm for controlling the suspension of a heavy-duty vehicle using the technology of systems embedding

BACKGROUND: The article is devoted to the development of an algorithm for controlling the suspension of a heavy-duty vehicle. The paper presents a suspension control system for a heavy-duty vehicle. The relevance is linked to the fact that by 2025, industry cooperation between representatives of the high-tech industry and scientists in the field of developing intelligent vehicle control systems is planned within the Autonet ecosystem. The control systems of modernized units with a high degree of electrification and digitalization are of the greatest interest to Russian automakers. This paper describes the results of a study of the active suspension of a heavy-duty vehicle from the side of control theory.&#x0D; AIM: Development of an algorithm for controlling the suspension of a heavy-duty vehicle. A technical requirement for the monotony of the transition process was formed, since this is the main indicator of improvement of the operational properties of a vehicle, which becomes obvious especially clearly in the smoothness of the suspension.&#x0D; METHODS: In the study, the fundamentals of the theory of automatic control, the theory of linear algebra, the concept of the state space, as well as methods of systems embedding based on modern achievements of algebra were used. Computer simulation was carried out in the environment of the MATLAB/Scilab/SimInTech kind.&#x0D; RESULTS: A mathematical and computer model of a half of a four-point suspension of a heavy-duty vehicle has been developed. The paper presents a suspension control system for a heavy-duty vehicle. The control algorithm is developed using the systems nesting technology. The properties of the synthesized control system more than doubled the quality of the system compared to the characteristics of the control object.&#x0D; CONCLUSION: The practical value lies in the ability of using the results of the study in the production and testing of adaptive suspension of a heavy-duty vehicle.

The Role of Carbides in Forming the Steels Structure and Properties under Pulsed Laser Irradiation

Introduction. At present, in scientific publications, there is no unambiguous understanding and reasoned metal physical justification of the role of the carbide phase of irradiated materials in forming the required structure and achieving a given degree of hardening of surface layers of steels during pulsed laser treatment, especially in the zone of laser hardening from a solid (austenitic) state. The solution to this issue is of great importance, since it allows us to reasonably and purposefully design the required structure of surface layers of products of various functional purposes with high performance properties. The complexity and insufficiently detailed study of the process of structure formation in the surface layers of steels under extreme thermal effects of pulsed laser radiation required a series of metal physical experiments to study the fine structure of steels after high-speed high-temperature hardening. The aim of this article was to obtain, quantify and critically analyze the array of results of metal physical studies and to assess the degree of influence of the carbide phase on the formation of structure and properties of surface layers of steels in the process of pulsed laser hardening in different modes, that is, with and without melting the surface of the samples. Materials and Methods. In the work, carbon and alloyed tool steels were subjected to surface laser irradiation at a Kvant 16 installation. The radiation power density was 70–200 MW/m2. Optical, scanning probe and electron microscopy were used in conducting metal physical studies, as well as methods of diffractometric, spectral and durometric analysis of steels before and after laser treatment. Results. It was shown that laser treatment of steels with a radiation power density of 130–200 MW/m2 led to a local change in the chemical composition in the laser-fused areas of the spot, partial or complete dissolution of carbides present in the irradiated metal and an increase in the amount of residual austenite in the fused areas up to 40–60 %. It was found that on P6M5 steel, the maximum possible hardness of the irradiated zones was achieved by dissolving 30 % of carbides, on 9XC, HVG steels — 60–70 %. It was shown that under pulsed laser irradiation with q=70–125 MW/m2, that is, without melting the steel surface, "white zones" formed around carbide inclusions under the influence of thermo-deformation stresses at the boundaries of the "carbide – steel matrix" composition. They had irretrievability, dispersion of the structure and increased hardness (10–12 GPa). It was determined that the maximum hardness of laser-hardened metal in the zones of laser hardening from a solid state was achieved if the "white zones" occupied 40 % of the irradiated area of steel. It was found that the dispersion of carbides in this case was 0.5–1.5 microns. Discussion and Conclusion. The results of the conducted studies indicate that in order to obtain the best combination of hardness and viscosity of the irradiated zones during laser treatment with melting of the surface of steels of different chemical composition, it is necessary to dissolve different amounts of carbides. The dispersed structure of laser-fused steel zones, along with a sufficiently high content of residual austenite, predetermine the possibility of improving the operational characteristics of irradiated materials, especially under conditions of external shock loads. The analysis of the conducted metal physical studies irradiated without melting the surface of steels allows us to conclude that in order to obtain a high degree of hardening, it is necessary and expedient to ensure the presence of a certain volume of dispersed carbides in the structure of the irradiated steel. The structural composition of "white zones" formed during laser treatment without melting the steel surface contributes to obtaining a unique level of operational properties. The results of the performed studies contribute to the theory of steel structure formation under conditions of extreme heat exposure and allow for a rational choice of modes of surface laser processing of products and their operability.

The Shifted Wave Equation on Non-flat Harmonic Manifolds

We solve the shifted wave equation ∂2∂t2φ(x,t)=(Δx+ρ2)φ(x,t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\frac{\\partial ^2}{\\partial t^2}\\varphi (x,t)=(\\Delta _x+\\rho ^2)\\varphi (x,t) \\end{aligned}$$\\end{document}on a non-compact simply connected harmonic manifold with mean curvature of the horospheres 2ρ>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2\\rho >0$$\\end{document}. We give an explicit representation of the solution as the inverse dual Abel transform of the spherical means of their initial conditions using the local injectivity of the Abel transform and symmetry properties of the spherical mean value operator. Furthermore, we investigate the shifted wave equation using the Fourier transform on harmonic manifolds of rank one. Additionally, we obtain a result analogous to the classical Paley–Wiener theorem and use it to show an asymptotic Huygens principle as well as asymptotic equidistribution of the energy of a solution of the shifted wave equation under assumptions on the Harish–Chandra type c\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{c}$$\\end{document}-function.

Solution and dynamics analysis of fractal-fractional multi-scroll Chen chaotic system based on Adomain decomposition method

In recent years, newly proposed fractal-fractional calculus operators have been used to predict the chaotic behavior of some attractors, and the new operators can capture self-similarity in the studied chaotic attractors. The results of varying with fractal order and fractional order are interesting, however, the dynamics are barely analyzed in these studies, and the law of fractal order and fractional order on the system is not clear. In this paper, the fractal-fractional differential operators with inverse operator property are redefined in the Caputo sense, and a new numerical scheme is proposed based on the sixth-order Adomain decomposition method. Then the dynamics of the new multi-scroll Chen chaotic system and its three degradation modes are analyzed completely in the fractal-fractional sense. The influence of the change of fractal order and fractional order on the chaotic system is revealed. Finally, a new physical phenomenon of the fractal-fractional chaotic system is captured by observing the coexistence of multi-scroll and two-scroll chaotic attractors of the new system through a wood-grain-like attractor basin, as well as transient chaos, chaotic jumps, and complex state transition behaviors. It is shown that fractal-fractional multi-scroll Chen system has complex and specific dynamical behaviors.

PERFORMANCE PROPERTIES OF MARINE FUEL DERIVED FROM SECONDARY POLYMER RAW MATERIALS

The article substantiates the need to determine the operational properties of shipping fuel obtained from secondary polyolefin (HDPE and PP) raw materials by catalytic pyrolysis. It is proposed to evaluate the operational properties of fuel for shipping – marine gasoil (MGO) by the value of the cetane index (CI, unit), H:C ratio, working heat of combustion (Q, MJ/kg). In view of the scheme of catalytic pyrolysis of polymeric raw materials proposed by us, which consists of two stages (I stage - the course of reactions on a mixture (1:1) of zeolitecontaining catalysts Zn-H-ZSM-5/Fe-H-ZSM-5; II stage – the course of reactions on the NiH-ZSM-5 catalyst), it is necessary to determine after each stage of the process the quality indicators of the reaction products (fractions with boiling points of -360(380) °С) given above. Also, additionally, we determined the quality indicators for the fractions obtained on the H-ZSM-5 industrial catalyst. The proposed research program, on the one hand, allows to determine the efficiency of the pyrolysis process with the selected catalysts in comparison with industrial technology, on the other hand, it will allow to adjust the process in the direction of obtaining a final product of a quality level that meets the requirements for MGO presented in ISO 8217:2017. The conducted studies showed that by the value of CI (48-50 units) and ν 40 (2,8–3,1 mm²/s) the fractions with boiling points of 180–360(380) °С, which were obtained by pyrolysis of polymer raw materials according to the two-stage technology proposed by us (on Zn-H-ZSM-catalysts 5/Fe-H-ZSM-5, Ni-H-ZSM-5) can be attributed to the brands of distillate marine fuels DMA, DFA, DMZ, DFZ (ISO 8217:2017). These fractions are also characterized by a high Н:C ratio (for HDPE – 1.62; for PP – 1.64) and working heat of combustion (for HDPE – 44.0 MJ/kg; for PP – 44.3 MJ/kg), which makes it possible to use them as fuels for shipping.

The three way Dirac operator and dynamical Turing and Dirac induced patterns on nodes and links

Topological signals are dynamical variables not only defined on nodes but also on links of a network that are gaining significant attention in non-linear dynamics and topology and have important applications in brain dynamics. Here we show that topological signals on nodes and links of a network can generate dynamical patterns when coupled together. In particular, dynamical patterns require at least three topological signals, here taken to be two node signals and one link signal. In order to couple these signals, we formulate the 3-way topological Dirac operator that generalizes previous definitions of the 2-way and 4-way topological Dirac operators. We characterize the spectral properties of the 3-way Dirac operator and we investigate the dynamical properties of the resulting Turing and Dirac induced patterns. Here we emphasize the distinct dynamical properties of the Dirac induced patterns which involve topological signals only coupled by the 3-way topological Dirac operator in absence of the Hodge–Laplacian coupling. While the observed Turing patterns generalize the Turing patterns typically investigated on networks, the Dirac induced patterns have no equivalence within the framework of node based Turing patterns. These results open new scenarios in the study of Turing patterns with possible application to neuroscience and more generally to the study of emergent patterns in complex systems.