Rational Conditions Research Articles

COMMON FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS IN COMPLETE METRIC SPACES

IJungck and Rhoades [13] introduced the notion of coincidentally commuting (weakly compatible) mappings, which is weaker than compatibility. Many interesting, fixed point theorems for weakly compatible maps satisfying contractive type conditions have been obtained by various authors. Goyal [5,6] prove some common fixed point theorems for six mappings involving rational contractive conditions by using notions of compatibility, weak compatibility and commutativity, in complete metric spaces. In this paper, we prove a common fixed point theorem for three pairs of weakly compatible mappings in complete metric spaces satisfying a rational inequality without any continuity requirement which generalize several previously known results due to Imdad and Ali [7], Goyal [5], Imdad-Khan [8], JeongRhoades [9] and others.

Бесконтактная оценка промеров головы молочных коров

A system for non-contact assessment of animals using three-dimensional cameras will facilitate the grading process. To develop a system for non-contact exterior assessment of animals using automatic video cameras, it is necessary to justify the rational design and operating conditions of the system. Based on digital vision, the authors determined the necessary parameters of the system using three measurements of the head: head length, forehead length and maximum forehead width. 15 adult animals of the zebu-type black-motley breed with a height of 1300 to 1500 mm were studied. To ensure coverage of the cow’s head in any position, three cameras were used: two located above the animal at a height of 2 m from the floor (the minimum distance from the camera to the head was 500 to 800 mm) and one in front of the animal at a distance of at least 2 m from the head and at a height 1.3 to 1.5 m from the floor. The signal from the identification antenna of the signal from the RFID tag of the animal initiated the acquisition of a three-dimensional image at a speed of 5 to 10 frames/s. Based on the measurements, the system automatically determines the broad-headed and big-headed indices. As a result of the study, the authors determined rational parameters for the location of cameras. The efficiency of shooting and accurate measurement of head measurements is ensured when the cow’s head is tilted relative to the camera at an angle of 45° and when the upper camera is located at a level of 2 m from the floor. When the head is tilted 65° and above, shooting is provided with the front camera located at a distance of at least 2 m from the head and at a height of 1.3 to 1.5 m from the floor. In their subsequent research, the authors plan to justify the rational design and operational-technological parameters of the model.

A determination of rational parameters for drying plant extracts of wild and cultivated plants with antioxidant properties

The article focuses on the drying of callus extracts of Ocimum basilicum and Eleutherococcus senticosus by pseudo-boiling bed method. During the study, rational conditions for the drying process were determined: temperature 90 ℃, aspiration 100 ± 0.8 m3/h and solution feed rate of 8 ± 0.3ml/min. It was possible to increase the antioxidant activity of the extract under the given conditions. The study of fluidized bed drying of the extract of callus cultures of basil (Ocimum basilicum) and Eleutherococcus senticosus (Eleutherococcus senticosus) allows to obtain extracts with higher concentration of biologically active substances. The results of the article can be useful for agro-, bio- and food industries.

Preperiodic points with local rationality conditions in the quadratic unicritical family

Preperiodic points with local rationality conditions in the quadratic unicritical family

Improving the technology of waxes obtaining from oil and fat waste

The object of the research is the extraction of waxes from the waste of the oil and fat industry – spent perlite. As a result of oil winterization, a significant amount of spent filter powders is formed, the disposal of which poses a danger to the environment. At the same time, winterization waste contains a significant amount of oil and wax, which are important components of many types of products. Oil and wax extraction involves the use of volatile, fire-hazardous solvents. An urgent task is to develop new safe and effective technologies for obtaining oils and waxes from winterization waste. The technology of extracting waxes from spent perlite, obtained as a result of winterization of sunflower oil, which involves treatment of perlite with sodium chloride solution, was investigated. Perlite was used according to SOU 15.4-37-210:2004 (CAS Number 93763-70-3) with indicators: mass fraction of fat – 20.1 %, peroxide value – 19.5 ½ O mmol/kg, acid value – 3.5 mg KOH/g. The temperature of mass settling after treatment with sodium chloride is 20 °C, the duration – 10 hours. The following rational conditions for perlite processing using sodium chloride were determined: the concentration of dry sodium chloride (by weight of perlite) – 35.0 %, the duration of mass boiling – 30 minutes. Under these conditions, the experimental value of the saponification value of the obtained wax was 120.5 mg KOH/g. Wax quality indicators: melting point 71.5 °C, acid value 1.6 mg KOH/g, mass fraction of moisture 0.63 %. The obtained results make it possible to obtain high-quality waxes from the waste of the oil and fat industry using a safe and affordable substance (sodium chloride). This will make it possible to avoid the need for waste disposal and increase the profitability of oil and fat enterprises due to obtaining valuable products from production waste

Argumentation-induced rational issue polarisation

Computational models have shown how polarisation can rise among deliberating agents as they approximate epistemic rationality. This paper provides further support for the thesis that polarisation can rise under condition of epistemic rationality, but it does not depend on limitations that extant models rely on, such as memory restrictions or biased evaluation of other agents’ testimony. Instead, deliberation is modelled through agents’ purposeful introduction of arguments and their rational reactions to introductions of others. This process induces polarisation dynamics on its own. A second result is that the effect size of polarisation dynamics correlates with particular types of argumentative behaviour. Polarisation effects can be soothed when agents take into account the opinions of others as premises, and they are amplified as agents fortify their own beliefs. These results underpin the relevance of argumentation as a factor in social-epistemic processes and indicate that rising issue polarisation is not a reliable indicator of epistemic shortcomings.

АВТОМАТИЗИРОВАННАЯ ТЕХНОЛОГИЧЕСКАЯ УСТАНОВКА ДЛЯ ПРОВЕДЕНИЯ ПРОЦЕССА ВАКУУМНОГО НАСЫЩЕНИЯ ПАРАМИ ПРЯНО-КОПТИЛЬНЫХ АРОМАТИЗАТОРОВ ЭКСТРУДИРОВАННЫХ МЯСОРАСТИТЕЛЬНЫХ ПРОДУКТОВ

The article describes the design and principle of operation of an automated technological installation for car-rying out the process of vacuum saturation with vapors of spicy and smoky flavors of extruded meat and vege-table products for functional purposes. A method for controlling the process under study is proposed. The method has the following advantages: helps to increase the productivity of the equipment by ensuring the co-ordinated operation of the steam generator and the smoking chamber; It provides a reduction in specific en-ergy costs by maintaining the most rational conditions for the process. A mathematical model of the process has been developed that can be used to create smoking installations, as well as a method for controlling the technological modes of the process of saturation with spicy-smoky flavors of extruded meat and vegetable products for functional purposes. An equation is obtained that allows us to determine the value of specific en-ergy consumption per 1 kg of finished products within the selected intervals of variation of input factors. The results of the solved optimization problem made it possible to identify a rational range of changes in input factors according to the three investigated criteria for the functioning of the smoker. As suboptimal intervals for changing parameters, the following should be taken: the pressure created by the vacuum pump in the pipeline, 31-35 kPa; the rate of vapor supply of spicy and smoky flavors to the smoking chamber, 0.65-0.8 m/s; the temperature in the smoking chamber, 38-42 °C.

Cooperation maintenance in dynamic discrete-time multicriteria games with application to bioresource management problem

We consider a dynamic, discrete-time, game model where the players use a common resource and seek to optimize different criteria. The center (referee) shares the resource available for exploitation between the competitors. To construct a multicriteria Nash equilibrium the bargaining solution is adopted. To obtain a multicriteria cooperative equilibrium, a modified bargaining scheme that guarantees the fulfillment of individual rationality conditions is applied. Two approaches to maintain cooperative behavior, namely, the cooperative incentive equilibrium and the time-consistent payoff distribution procedure, are considered. Moreover, the cooperative incentive equilibrium is constructed under the assumption that the center punishes players for deviations. A dynamic bi-criteria bioresource management problem is investigated to illustrate the solution concepts proposed.

Kant’s Rationalist Account of Hope

Abstract Few fates seem worse than living without cause for hope. Yet what is it to have a cause for hope? And how is it related to having hope? Although these questions have received relatively little philosophical attention, I argue that Kant advances a rationalist account of hope that addresses them. My central thesis has two parts. First, hope is a rational attitude for Kant; certain rational conditions are needed to differentiate hope from other desiderative attitudes (such as mere wishing or fantasizing). Second, these rational conditions involve causal inferences made by the hoping agent. To hope, an agent must make certain inferences about the cause of her desire and the cause of her belief that the object of her desire is possible. In short, to hope requires an agent to take herself to have a cause for hope.

Bioengineering research on sesame anti-alimentary factors inactivation for confectionery industry

The object of research. The process of inactivation of inhibitors of proteolytic enzymes of sesame seeds for use in the confectionery industry.
 Investigated problem. The use of sesame seeds in the confectionery industry is very popular, as it adds a unique taste and texture to products. However, inhibitors of seed proteolytic enzymes can limit the absorption of nutrients such as proteins. This can be a problem in terms of nutritional value and efficient use of sesame seeds in the food industry. Inactivation of inhibitors of proteolytic enzymes in sesame seeds will contribute to the stability and uniformity of the quality of raw materials, which is an important aspect in the confectionery industry. This allows enterprises to ensure high sustainable quality of products containing sesame seeds and competitive advantages of such products.
 The main scientific results. The features of the inactivation of anti-alimentary factors of sesame were studied, namely the influence of the initial humidity and the time of treatment with ultra high frequency (UHF) radiation on the inactivation degree of inhibitors of proteolytic enzymes of the seeds. Rational conditions for pre-treatment of sesame seeds for inactivation of anti-alimentary factors were established: moisture to 10–13 %, treatment time with UHF radiation 220–240 s. The peculiarities of the use of crushed sesame seeds with an inactivated anti-alimentary complex in the technology of high-nutrition chocolate pastes were studied. Organoleptic evaluation of test samples with different content of sesame seeds was carried out, during which the products were evaluated according to their appearance, uniformity, plasticity, color, taste and aroma. The effect of the content of crushed sesame seeds with an inactivated anti-alimentary complex on the consumer properties of chocolate pastes was determined.
 The area of practical use of research results. Taking into account the results of the research can contribute not only to the improvement of technological processes in confectionery production, but also to the development of new products that meet the modern requirements of consumers.
 Innovative technological product. As a result of research, an innovative food product was created, which is an innovative approach to the use of sesame seeds in the technology of chocolate pastes with increased nutritional value.
 Scope of the innovative technological product. The developed innovative technological product can be implemented in food technology. In particular, the use of sesame seeds with an inactivated anti-alimentary complex in the production of chocolate pastes should become an additional advantage for manufacturers in the market, especially in the context of increased demand for health food products.

A Contract-Theory-Based Incentive Mechanism for UAV-Enabled VR-Based Services in 5G and Beyond

The proliferation of novel infotainment services such as Virtual Reality(VR)-based services has fundamentally changed the existing mobile networks. These bandwidth-hungry services expanded at a tremendously rapid pace, thus, generating a burden of data traffic in the mobile networks. To cope with this issue, one can use Multi-access Edge Computing (MEC) to bring the resource to the edge. By doing so, we can release the burden of the core network by taking the communication, computation, and caching resources nearby the end-users (UEs). Nevertheless, due to the vast adoption of VR-enabled devices, MEC resources might be insufficient in peak times or dense settings. To overcome these challenges, we propose a system model where the service provider (SP) might rent Unmanned Area Vehicles (UAVs) from UAV service providers (USPs) to serve as micro-based stations (UBSs) that expand the service area and improve the spectrum efficiency. In which, UAV can pre-cached certain sets of VR-based contents and serve UEs via air-to-ground (A2G) communication. Furthermore, future intelligent devices are capable of 5G and B5G communication interfaces, and thus, they can communicate with UAVs via A2G links. By doing so, we can significantly reduce a considerable amount of data traffic in mobile networks. In order to successfully enable such kinds of services, an attractive incentive mechanism is required. Therefore, we propose a contract theory-based incentive mechanism for UAV-assisted MEC in VR-based infotainment services, in which the MEC offers an amount reward to a UAV for serving as a UBS in a specific location for certain time slots. We then derive an optimal contract-based scheme with individual rationality and incentive compatibility conditions. The numerical findings show that our proposed approach outperforms the Linear Pricing (LP) technique and is close to the optimal solution in terms of social welfare. Additionally, our proposed scheme significantly enhanced the fairness of utility for UAVs in asymmetric information problems.

Rare-Earth Scandium Borate Fluoride with a Deep-Ultraviolet Cutoff Edge.

Through reasonable selections of raw materials and experimental methods, a new rare-earth borate fluoride K11Sc5(B5O10)4F6 is synthesized successfully by the high-temperature solution method in a closed system, which is the first noncentrosymmetric scandium borate fluoride. It crystallizes in the Fdd2 space group of the orthorhombic crystal system and features an extremely complicated structure constructed by the fundamental building blocks [B5O10] units, Sc-based, and K-based polyhedra. To our knowledge, K11Sc5(B5O10)4F6 is the only rare-earth borate that contains two kinds of [B5O10] groups and crystallizes in the Fdd2 space group, enriching the structural chemistry of rare-earth borates and rare-earth borate fluorides. Additionally, it is discussed in detail how F can significantly improve performance by modifying the modules in a comparison of structures. Discussion on rational synthetic conditions is instructive for obtaining rare-earth borate fluorides. Furthermore, a short cutoff edge (<190 nm) is experimentally confirmed, indicating the potential application of K11Sc5(B5O10)4F6 in ultraviolet/deep-ultraviolet regions.

Some common fixed point theorem of rational contractive mappings in dislocated metric spaces

Abstract We improve the rational contractive condition and prove the common fixed point in the dislocated metric spaces. In addition, the new generalized rational contraction has existence of a common solution for a system of integral equations.

Pyrocarbon Coating on Granular Al2O3 for HTGR-Type Power Reactor

Fourth-generation nuclear power systems are based on high-temperature gas-cooled reactors, in which the pebble fuel is the primary energy carrier. In this regard, applying protective pyrocarbon coatings on granulated fuel is an essential problem in ensuring the reliability of nuclear power plants. The article’s main idea is to research rational technological parameters of forming a pyrocarbon protective coating on the granules of a nuclear fuel model. For this purpose, granulated Al2O3 with the protective pyrocarbone coating was applied as a fuel model. The article’s aim is to study the effect of thermophysical parameters on applying a protective pyrocarbon coating on granulated Al2O3. During the experimental studies, thermal imaging of the pyrolysis process was used. The scientific novelty of the work is the equilibrium curves for the systems Al2O3:CH4, Al2O3:CH4:N2, and Al2O3:CH4:Ar. Their analysis allowed for evaluating rational thermochemical parameters of the pyrolysis process. As a result, rational thermophysical parameters of coating granulated Al2O3 with a pyrocarbon layer were evaluated, and the practical possibility of applying the pyrocarbon coating to granulated Al2O3 in the electrothermal fluidized bed was experimentally proven. It was shown that nitrogen does not significantly affect the target reaction product under a temperature of less than 1500 K. Also, the rational conditions for the pyrocarbon coating at a pressure of 0.1 MPa were realized at a temperature of 900–1500 K and using argon. Moreover, pyrocarbon was precipitated from hydrocarbon at 1073–1273 K. Overall, the need to add an inert gas for reducing the carbon black formation was proven to prevent a reduction of natural gas efficiency.

Combinatorial Auction of Used Cars Considering Pro-Environment Attribute: A Social Welfare Perspective

Air pollution is becoming more and more serious as the number of vehicles increases. To address such problems, many cities have implemented many measures, including the circular economy mode, in which used cars with low carbon emission are becoming important in the sustainable transportation and carbon abatement. Considering multi-attribute demand, this study designed combinatorial auction mechanism for the bidders of automobile enterprises on an online used-car platform to achieve social welfare maximization. Two kinds of attributes were considered, namely, price attribute and non-price attributes; the latter particularly included the pro-environment attribute based on an analysis of complementarity and substitutability. Moreover, the mechanism was proved to satisfy individual rational condition and incentive compatibility condition. Numerical application showed that preference for the pro-environment attribute can better realize social welfare and respond to national energy conservation and emission reduction targets. As a result, from the social welfare perspective, the multi-attribute combinatorial auction can provide a reference for more fair and effective allocation of used cars to bidders and can promote both buyer’s utility and seller’s income.

Surface treatment of inorganic modifier for improving carbonation resistance of geopolymers

Geopolymer (GP) is a low-carbon binder with the potential to replace Portland cement in reinforced concrete, however, the risk of corrosion to reinforced steel bars due to its low carbonation resistance must be addressed. This study proposed the use of an inorganic surface modifier, sodium aluminate solution (AN), to improve the carbonation resistance of GP. The effects of AN surface treatment on carbonation depths were investigated for GP mortars using fly ash (FA), ground granulated blast furnace slag (BFS), or their blend as active fillers. Rational AN surface treatment conditions and microstructural changes of treated GPs were also discussed. The obtained results show that AN surface treatment can significantly reduce carbonation rates of FA/BFS blend-based GP, and largely delay the onset of neutralization of heat-cured GP through the reduction of cracks and the formation of Na-gmelinite and gismondine, which refine the surface layer of GP. The surface modification using 40 wt%-AN solution reduced carbonation rate coefficient by about 70% for the FA/BFS blend-based GP cured at 80 ℃, and by above 30% for that cured at 20℃. The larger the FA blending ratio or the smaller the liquid-active filler ratio, the greater the improvement in carbonation resistance of FA/BFS blend-based GPs, caused by the AN surface modification. For the ambient-cured GP, repeated surface treatment is preferred, while for the heat-cured GP, once treatment is enough, and seal curing after the AN surface treatment is recommended regardless of the curing method.

RATIONAL CONDITIONS OF PRODUCING THE ACTIVATED CARBON WITH WELL-DEVELOPED NANOPOROUS STRUCTURE FOR THE TREATMENT OF NATURAL AND WASTE WATERS

Rational conditions for the activation of coal of a high stage of metamorphism (anthracite) have been determined, which allow the development of a nanoporous structure. Obtained activate carbon with nanoporous structure can be use for the treatment of natural and waste waters have been carried out. The structurally sorptive characteristics and granulometric size composition of obtained samples were determined. It was established that in order to obtain a sorbent with specified properties, it is necessary to introduce oxygen into the reacting mixture at the second stage of anthracite activation and control the activation time. The activation in the first stage was carried out with steam at a temperature of 750–800 °C, and in the second stage – with steam in the presence of air oxygen at 280–300 °C. The rational content of oxygen in the activating mixture is in the range of 2.7–4.4 %, while the specific surface area of activated carbon increases, which corresponds to nano-sized pores and, accordingly, the volume of the adsorption space of coal. The process led to the development of mesoporosity ~ 0.2–0.3 cm3/g, after which the microporous sample of activated carbon was impregnated with a surfactant solution. Thus, the rational conditions of activation are the duration of the process of 1.5 hours in the presence of 4.4 % oxygen in the activating mixture. It is shown that the largest values of the total specific surface area and the specific surface area of mesopores are achieved when using ionic surfactants with alkyl chain length n = 10–16 as modifiers. In particular, the use of sodium dodecyl sulfate СН3(СН2)11SO3Na as a modifier allows to obtain the largest value of the total surface Stot 1030 m2/g and the surface of mesopores Smе 334 m2/g. It was established that the activation of modified samples of activated carbon leads to a decrease in the size of granules.The content of fractions with a size of 1.0–2.0 mm and 0.5–1.0 mm is 80–85 %, which are rational for use for water purification from organic compounds.

Building a model of the impact grinding mechanism in a tumbling mill based on data visualization

A mathematical model was built based on data visualization for the impact grinding mechanism in a tumbling mill, which is mainly implemented during coarse grinding. The determination of impulse interaction parameters is problematic due to the difficulty of modeling and the complexity of hardware analysis of the behavior of intramill loading. Conceptually, it was envisaged to identify the relative dynamic parameters of the impact action as components of the model, which are criteria for the similarity of the loading movement and the grinding process. Impact power was taken as an analog of grinding performance. The initial characteristic of the impact was considered to be the averaged vertical component of the speed of loading movement in the flight zone at the boundary of contact with the shear layer. The formalization of the model revealed the effect on the performance of the mass fraction of the flight zone and the reversibility of loading. The method of numerical modeling was applied, based on experimental visualization of the behavior of granular loading in the cross section of a rotating chamber. The influence of the rotation speed on the performance at a chamber filling degree of 0.45 and a relative particle size of a milling load of 0.0104 was estimated by experimental simulation. The maximum productivity value was found at the relative speed of rotation ψω=1–1.05. A rational condition for impact grinding at ψω=0.75–0.9 has been established. The test proved the effectiveness of using visualization to evaluate dynamic loading interaction analogs. Verification of modeling results was implemented by comparison with the data of the technical standard. The use of similarity criteria unifies approaches to modeling different mechanisms of destruction. The model built makes it possible to predict the rational parameters of the grinding processes by impact, crushing, and abrasion

Improving the technology of the synthesis of fatty acid monoglycerides using the glycerolysis reaction

The object of research is the process of fat glycerolysis in order to obtain fatty acid monoglycerides. Monoglycerides are an important component of chemical, pharmaceutical, cosmetic, and food industry products. These substances are used as emulsifiers, structure formers, complex formers, etc. The industrial production of monoglycerides involves the use of complex technologies, as well as dangerous and unstable catalysts. An urgent task is to develop new catalysts and improve technologies for monoglycerides obtaining. The technology for the synthesis of monoglycerides by the glycerolysis method, which involves the reaction of vegetable hydrogenated fat with glycerol, was studied. Potassium glyceroxide was used as a catalyst, which is effective and safe in terms of production and use. Hydrogenated unrefined fat according to DSTU 5040 (CAS Number 68334-28-1) was used. The fat has non-standard parameters: the melting point is 51 °C, the mass fraction of moisture and volatile substances is 0.3 %, the acid value is 3.2 mg KOH/g, the peroxide value is 7.6 ½ O mmol/kg. The process duration was 90 minutes, the glycerol concentration was 50 %. Rational conditions for glycerolysis were determined: catalyst concentration (1.5 %) and temperature (140 °C). Under these conditions, the product ensured the stability of the “water – sunflower oil” emulsion of 96.8 %, the concentration of monoglycerides in the system was 0.1 %. Product parameters: mass fraction of monoglycerides – 72.5 %, free glycerol – 1.5 %, acid value – 1.7 mg KOH/g. The research results make it possible to improve the glycerolysis process using a new catalyst and obtain monoglycerides with high emulsifying ability. This will increase the profitability of the enterprise and increase the volume of production of high-quality monoglycerides for various industries

THE INFLUENCE OF EXTERNAL FACTORS ON THE ACCURACY AND RELIABILITY OF THE DETERMINATION OF ULTRA-LOW POWER ELECTRIC FIELDS

The article presents the results of an experimental study of the influence of temperature, relative humidity of the surrounding environment, as well as the coefficient of electromechanical action on the process of determining ultra-low power electric fields. The analysis of the obtained results made it possible to establish the most rational conditions for determining the force (electrical tension) and energy (distribution of surface charge and electric capacity) parameters of such fields with higher accuracy and reliability. The paper proposes an experimental experiment to establish the accuracy and reliability of power and energy parameters for determining electric fields under conditions of changes in climatic factors and the electromechanical coefficient, the implementation of which took place on a measuring stand developed with the participation of the authors. The main element of such a measuring stand is an automatic device for determining, collecting and processing information on the distribution of power and energy parameters of the electric field under the sensitive element of the measuring transducer. The results obtained as a result of the experimental research made it possible to establish that the coefficient of electromechanical influence has a decisive influence on the accuracy of measuring electric fields of ultra-low power. It is shown that an increase in the coefficient of electromechanical influence from 38 pN/V (silicon &lt;111&gt;) to 190 pN/V (PZT-8 piezoelectric ceramics) leads to an increase in the relative error of electric field determination by 4.7%. It was established that reducing the temperature to 20 °C while maintaining the relative humidity from 38 % to 74 % leads to a decrease in the relative error by 1.5-2.2 %. At the same time, a decrease in temperature with a simultaneous decrease in relative humidity leads to an increase in the reliability of the determination of electric fields (so, the probability of error-free measurement of power and energy parameters of electric fields increases by 18 %). A comparison of the results obtained by the proposed method with the results obtained by atomic force microscopy method (in the mode of measuring the leakage currents from the working areas of the investigated surfaces) was carried out, which showed a strong positive correlation between these results, which confirms the objectivity of the proposed method and the adequacy of the obtained results. The conclusions and analyzed data obtained in the article based on the results of experimental studies can be used to create a system of automatic error correction and instability determination of power and energy parameters of ultra-low power electric fields, taking into account limiting external influences.