Auxiliary Operator Research Articles

Destabilization of synchronous periodic solutions for patch models

We study the destabilization of synchronous periodic solutions for general patch-models with cross-diffusion-like couplings, where the underlying kinetic systems have stable periodic solutions bifurcating from double homoclinic loops. We first reduce the stability problem of synchronous periodic solutions for patch models into that for lower-dimensional systems, then analyze the destabilization by using the Floquet theory and solving a class of boundary value problems. After establishing the Fredholm alternative properties for an auxiliary linear operator, we give the characteristic function to determine the Floquet spectra for the reduced systems, and then the conditions for the destabilization. Finally, we apply the main results to a patch model with a two-dimensional kinetic system.

ORGANIZATION OF THE LOGISTICS PROCESS OF CARGO HANDLING

The paper establishes that the logistics process in a warehouse includes a technological process of cargo handling, which covers the totality of all main and auxiliary operations carried out in a certain sequence. The success of the rational organization of the technological process in a warehouse is closely related to the optimal selection and implementation of the warehousing system, which determines what technical means will be used for each operation. In addition, it has been found that the biggest problem that exists in a warehouse when managing the cargo handling process is the connection between material (commodity) and information (document management) flows. Therefore, in order to improve this process, the paper proposes a functional model of the logistics process of cargo handling in a warehouse that will allow for a visual demonstration of the interconnected promotion of material (goods flow) and information flows through the warehouse. In addition, in order to optimize management decision-making, analysis and monitoring of logistics costs, the paper provides an appropriate decomposition of the logistics process of cargo handling by the main groups of operations: unloading, receiving and warehousing, picking, shipping and delivery. Thus, the rational implementation of the logistics process in a warehouse is the key to the warehouseʼs profitability. Therefore, a rationally organized logistics process in a warehouse will help to achieve: rational warehouse planning when allocating work areas, which helps to reduce costs and improve the cargo handling process; efficient use of space when placing equipment, which will increase the warehouse capacity; use of universal equipment that performs various warehouse operations and significantly reduces the fleet of lifting and handling machines; minimization of intra-warehouse transportation routes in order to reduce operating costs.

Spherical Hybrid Nanoparticles for Homann Stagnation-Point Flow in Porous Media via Homotopy Analysis Method

Non-axisymmetric stagnant-point flows for flat plates in porous media containing spherical Cu-Al2O3-H2O nanoparticles are studied using the homotopy analysis method (HAM). The governing equations are transformed into three coupled non-linear ordinary differential equations through similarity transformations. A large degree of freedom is provided by HAM when selecting auxiliary linear operators. By transforming nonlinear coupled ordinary differential equations with variable coefficients into linear ordinary differential equations with constant coefficients, nonlinear coupled ordinary differential equations can be solved. Over the entire domain, these equations can be solved approximately analytically. The analysis involves a discussion of the impact of many physical parameters generated in the proposed model. The results have shown that skin friction coefficients of Cfx and Cfy increase with volume fraction of hybrid nanofluid and the coefficient of permeability increasing. For the axisymmetric case of γ = 0, when volume fraction, φ, φ1, φ2 = 0, 5%, 10%, 20%, Cfx = Cfy = 1.33634, 1.51918, 1.73905, 2.33449, it can be found that the wall shear stress values increase by 13.68%, 30.14%, and 74.69%, respectively. In response to an increase in hybrid nanofluid volume fractions, local Nusselt numbers Nux increase. Nux decrease and change clearly with the coefficient of permeability increasing in the range of γ < 0; the values of Nux are less affected in the range of γ > 0.

РОЗРАХУНКОВО-АНАЛІТИЧНЕ ПОРІВНЯННЯ ПОКАЗНИКІВ ВЛАСТИВОСТЕЙ ВАРІАНТІВ КОНСТРУКТИВНО-ТЕХНОЛОГІЧНИХ РІШЕНЬ ТРАНСВЕРСАЛЬНИХ З’ЄДНАНЬ “МЕТАЛ + КОМПОЗИТ”

The question of selection of variants for objective optimization of manufacturing preparation of production of different structural-manufacturing solutions of metal-composite articles and units with transversal connections are actualized. Several variants of structural-manufacturing solutions (SMS) of joints are considered. Three types of fastening connections are selected for analysis, i.e. with pyramidal, cylindrical and sheet-formed micro-fasteners (MF).Structural schemes of possible manufacturing processes of creation fastening micro-elements with different shapes are suggested. These schemes take into consideration influence of both main and auxiliary operations, which have to be taking into account at estimation of manufacturing process duration and energy consumption.Possibility of micro-fasteners manufacturing of aluminum, titanium alloya and stainless steels is considered at comparison of numerical parameters of manufacturing processes.Producing of micro-fasteners by means of milling with both disc and cylindrical mills, and up-to-date methods of electro-erosion treatment of materials with electrode-tool or with moving wire is analyzed as comparing parameters of different manufacturing processes.Properties of manufacturing processes of fastening elements forming are determined as actual ones. Duration of connecting elements manufacturing and required energy resources consumption are selected as exact actual parameters,Qualimetric model of manufacturing processes selection with consequent their optimization in accordance with goal functions is synthesized. Incoming, controllable and outcoming parameters of the model are determined. Approach to calculation of complex quality index of micro-fasteners manufacturing is suggested. This approach is used for calculation numerical quality indexes of different manufacturing processes. General conclusions are done.

On the algebraic approach to GUP in anisotropic space

Motivated by current searches for signals of Lorentz symmetry violation in nature and recent investigations on generalized uncertainty principle (GUP) models in anisotropic space, in this paper we identify GUP models satisfying two criteria: (i) invariance of commutators under canonical transformations, and (ii) physical independence of position and momentum on the ordering of auxiliary operators in their definitions. Compliance of these criteria is fundamental if one wishes to unambiguously describe GUP using an algebraic approach and, surprisingly, neither is trivially satisfied when GUP is assumed within anisotropic space. As a consequence, we use these criteria to place important restrictions on what or how GUP models may be approached algebraically.

Differences in perception of safety in driving environment according to shared PMD user experience through multi-criteria analysis

A shared personal mobility device (PMD) is a transportation model that rents personal transportation devices, such as bicycles and kickboards, through a sharing platform. The use of shared PMD has increased, but related complaints and traffic accidents are doubling with it every year. This study applied an analytic network process (ANP) methodology for the multi-criteria analysis. A survey including normal citizens was conducted to evaluate the importance of safety regarding shared PMD experience.The evaluation factors differ according to the experience of using the shared PMD device, although ‘driving continuity’ and ‘separation of sidewalks and roadways’ were the most important. PMD users gave greater priority to ‘removal of the road gap’, ‘traffic safety signs’, ‘dedicated parking area’ and ‘management of obstacles’ compared to non-users. On the other hand, for non-PMD users, ‘bicycle lane width’, ‘strengthening enforcement’, and ‘user safety education’ were more important. The results showed that importance differed depending on the participant's experience of using a shared PMD or the lack of it. In the case of users, factors that have a direct effect on driving were prioritised, and in the case of non-users, auxiliary operations and management, such as crackdowns and education, were prioritised.

Multi-Frequency Homotopy Analysis Method for Coupled Van der Pol-Duffing System with Time Delay

This paper mainly studied the analytical solutions of three types of Van der Pol-Duffing equations. For a system with parametric excitation frequency, we knew that the ordinary homotopy analysis method would be unable to find the analytical solution. Thus, we primarily used the multi-frequency homotopy analysis method (MFHAM). First, the MFHAM was introduced, and the solution of the system was expressed by constructing auxiliary linear operators. Then, the method was applied to three specific systems. We compared the numerical solution obtained using the Runge–Kutta method with the analytical solution to verify the correctness of the latter. Periodic solutions, with and without time delay, were also compared under the same parameters. The results demonstrated that it was both effective and correct to use the MFHAM to find analytical solutions to Van der Pol-Duffing systems, which were classical systems. By comparison, the MFHAM proved to be effective for time delay systems.

Analytical and numerical discussion for the quadratic integral equations

In this work, we study the existence of at least one solution of the Quadratic integral equation with Phase-lag term. Our proof depends on a suitable combination of the Darbo?s fixed point principle and the technique of measures of noncompactness. Homotopy perturbation method is presented to obtain an approximate solution of Quadratic integral equation with Phase-lag term. Convergence and error estimate of Homotopy perturbation method are obtained. Homotopy perturbation method is a powerful device for solving a wide variety of problems. It gives excellent flexibility to the expression of the solution and how the solution is explicitly obtained, and provides great freedom in choosing the base functions of the desired solution and the corresponding auxiliary linear operator of homotopy. These methods produce the solutions in terms of convergent series without needing to restrictive assumptions, to illustrate the ability and credibility of the methods, we deal with two examples that show simplicity and effectiveness.

Research on Automatic Lane Changing Method for Electric Vehicles Based on Deep Deterministic Policy Gradient Algorithm

Intelligent driving is an important feature of electric vehicles, and automatic lane-changing is an important auxiliary operation in the driving process. It involves complex data such as the external environment, vehicle status, and relationship characteristics of other vehicles. This paper proposes research on automatic lane-changing methods for electric vehicles based on a deep deterministic policy gradient algorithm aiming at the complexity of automatic lane-changing for electric vehicles. First, use the actor-critic model of deep reinforcement learning to realize the design of an automatic lane-changing algorithm. On this basis, the actor-critic model is further improved, and a deep deterministic policy gradient algorithm is proposed and applied to the automatic lane-changing strategy of electric vehicles, which improves the accuracy of automatic lane-changing and thus ensures the safety of vehicle driving.

Модернізація розкидача органічних добрив «ПРТ-10» для використання в технології механізованого компостування

The purpose of the work is to present the results of testing mock-up samples of technical devices and equipment for the «PRT-10» organic fertilizer spreader to ensure that they fulfill the functional capabilities of mechanized composting and meet the requirements of the technological regulations. Methods and materials. To form a shoulder width of 2.5-3.5 m, a modernized spreader of organic fertilizers of the «PRT-10» type with replaceable drum-milling working bodies was used. Mock-up samples of the working bodies proposed by the author were installed at the places of installation of the existing drums, the main structural difference of which is the presence of right and left spiral lines. The blade installations are directed toward each other, which ensures the movement of raw materials from the side walls to the middle of the container. At the same time, the design of the drive of the working bodies did not change. Results. One of the options for increasing the efficiency of compost production is the expansion of technological capabilities and the development of additional technical devices and equipment for the spreader of organic fertilizers «PRT-10». The design of the mechanized composting device proposed by the author is a separate replaceable module installed on the rear board at the location of two drums of the «PRT-10» serial device. The main purpose of the replaceable module is pre-grinding, mixing of components, and formation of the edge during the preparation of a multi-component mixture that accumulates in the spreader trailer in the technology of mechanized composting. The use in the construction of the «PRT-10» serial spreader of interchangeable drums with the right and left directions of blade installation provides the technological height of the formed edge up to 1.6-1.7 m. The width of the base of the edge is 2.5-3.0 m, which agrees with the basic width values captured by aerators-mixers. The productivity of the unloading tool is up to 100 t/h. A special device for moistening mixtures with a moisture content of 30-45% ensures the introduction of water up to 40-60 l/t. Calculations carried out by the author on the use of the modernized spreader of organic fertilizers «PRT-10» and the aerator-mixer «AZK-2» in the production of composts proved economic advantages in the form of a reduction in fuel consumption during 4 cycles of aeration of the mixture – by 2.5 times. Conclusions. The use of a modernized device on transport units makes it possible to reduce the number of technical means involved in auxiliary operations of mechanized composting. Compost production using the modernized «PRT-10» spreader is economically feasible in existing economic conditions up to 2.0-2.2 thousand tons per processing season. For larger volumes, it is more appropriate to use the «AZK-2» trailed aerator mixer. Key words: compost mixture, burt, modernized spreader, replaceable drum, attached device, moistening, straw layer, mixing, grinding.

Интенсификация процесса очистки сточных вод для ее вторичного использования на пищевых предприятиях

To date, the issues of resource conservation are of increasing concern to mankind, in this regard, the issues of the secondary use of raw materials and auxiliary materials are becoming promising. On average, food enterprises use about 50 m3 of water per se, this water in addition to the main technological process is used for auxiliary operations. The article considered standard methods of wastewater treatment from pollution and modern ways to improve the quality of treatment.

Mathematical model to assess energy consumption using water inflow-drainage system of iron-ore mines in terms of a stochastic process

Purpose is to develop a unified mathematical model to assess energy efficiency of a water inflow-drainage process as the real variant of stochastic method for water pumping from underground workings of iron-ore mines. Methods. The research process was based upon the methods of probability theory as well as stochastic modelling methods. The stochastic function integration has been reduced to summation of its ordinates and further transition to a proper boundary. Findings. A mathematical model of a water inflow-drainage system as a stochastic process has been developed in terms of input parameters of a standard operating iron-ore mine. The abovementioned has made it possible to assess realistically, substantiate, and obtain possibilities for a specific production facility as well as for generalization of the results involving determination of stochastic characteristics of drainage process. Originality. For the first time, a mathematical model of drainage from underground levels of iron-ore mines has been developed as a stochastic process. The process characteristics have been identified relying upon randomness of a water pumping technique. In contrast to the available settings, the new model parameters characterize their dispersion. Possibility to obtain complete characteristics of energy consumption has been obtained: for drainage; for water accumulation volume in underground water collectors; for water pumping from the specified mine depths over the specific period as random processes. A number of drainage features have been analyzed and differentiated being determined with the help of nor-mal law of water accumulation velocity in the underground water collectors in iron-ore mines. Practical implications. In terms of operating iron-ore mine, a generalized drainage mathematical model has been developed as a stochastic process using statistical data concerning water accumulation velocity in the underground water collectors. It has been proved that if the ordinates of water accumulation velocity in the underground water collectors obey the normal distribution law then it is expedient to characterize drainage as a stochastic process. The developed methods, studying drain-age as a stochastic process, help expand the research boundaries involving other auxiliary operations performed during underground mining of iron ore raw materials.

Application of erosion dimensional treatment methods for creation transversal fasteners in “metal-composite” joints

At design of high-loaded units of engineering objects, especially such as articles of aero-space engineering, the problem of creation of reliable joints between metal and composite articles having predefined strength and ability to fulfill given functions appears. Development and grounding of selection of structural-manufacturing solutions of “metal-composite” joints with transversal fastening elements is selected as the objective of studying. As the object for studying possible structural-manufacturing solutions of “metal-composite” joints that use transversal fastening elements which are embedded to composite and attached to metal article or produced on its surface. Three types of fastening micro-elements are considered, i.e. pyramidal monolithic, cylindrical and sheet-formed, also different technologies of fastening elements production are considered too. Mass of typical flat article with micro-pins at given load-carrying ability of “metal-composite joint” was esti-mated for above-mentioned types of micro-fasteners. Such quantitative indexes of manufacturability as labor-intensity and energy consumption of fastening elements production were considered as results of studies. Approach to comparison methods of fastening elements manufacturing is suggested. This approach is based on analysis of correspondent numerical specific indexes of labor-intensity and energy consumption. These indexes are com-pared for micro-pins which are assumed to be produced of aluminum, titanium alloys and stainless steels. Distinctive feature of suggested model of analysis is taking into consideration both main and auxiliary techno-logical operations, which influence significantly on manufacturing labor-intensity and duration. Process of classical milling with cylindrical and disc mills is compared with up-to-date methods of electro-erosion cutting with wire. Recommendations for selection shape, type and arrangement scheme of micro-fasteners on article surface and exact manufacturing process of micro-pins production at given material are formulated as conclusions.

Combined Homotopy and Galerkin Stability Analysis of Mathieu-Like Equations

We propose a homotopy analysis method in combination with Galerkin projections to obtain transition curves of Mathieu-like equations. While constructing homotopy, we think of convergence-control parameter as a function of embedding parameter and call it a convergence-control function. Homotopy analysis provides a relation between the parameters of the Mathieu equation that also includes free parameters arising from the convergence-control function. We generate extra nonlinear algebraic equations using Galerkin projections and solve numerically for arriving at transition curves. We demonstrate the usefulness of our method in the case of three distinct versions of linear Mathieu equations by carefully choosing nonlinear and auxiliary operators. Since homotopy analysis does not demand smallness of any of the parameters, our approach has a distinct advantage over perturbation methods in determining transition curves covering a large region of the parameter space. The method is applicable to a wide variety of parametrically excited oscillators.

DESIGN FEATURES OF MODERN FOREIGN AGRICULTURAL TRACTORS

Analysis of the state and trends in the development of agricultural machines and the technical means that serve them shows that there is a constant process of creating more productive and economical equipment. This is primarily ensured by increasing unit capacity, increasing working and transport speeds, reducing time losses for auxiliary operations, reducing maintenance costs to a minimum; ensuring minimal impact on soil and plants; increasing reliability and wear resistance, as well as an increase in versatility and the appearance of special tractors for specific work; expansion of production of wheeled tractors with four driving wheels, wider use of hydraulic systems, electronics, automation, new materials, creation of comfortable working conditions and ease of management; ensuring labor safety. The main type of tractor in the most widespread range of capacities remains the wheeled one of the traditional layout scheme, the improvement of which is carried out taking into account the latest achievements of science and technology. There is a further update of articulated tractors with all driving wheels of the same size, with leading manufacturers experimenting with the installation of triangular track drives instead of wheels, which significantly increases their traction qualities. Characteristic features of tractors of the new generation are their universality and block-modular structure. So, depending on the market, different engines from well-known companies and unified transmissions are installed on one model of European tractors. Therefore, in this market, there is a tendency for manufacturers to cooperate with the aim of further increasing versatility, reliability, and simplifying operation: increasing the interval for changing engine oil to 500 hours, transmission oil to 2,000 hours, hydraulic oil to 1,000 hours. Cooperation also contributes to the expansion of opportunities for competition in the markets of different countries. The new generation of powerful wheeled tractors with a classic and system layout provides high efficiency mainly in technological operations with medium traction forces in combined, tillage and sowing units, which are equipped with implements with active working bodies, with front and rear GDP, as well as in transport operations.

Enhanced Ships Operation using Integrated Automation Systems

Global shipping for becoming sustainable will have to organize the ships and each field of shipping industry, in accordance efficient management and operation principles. This will require the adoption of new techniques and the transformation of companies, their ships, systems, and management practices. A modern automation and control system is a fully integrated system covering many aspects of the ship operation. Whether for cargo, passenger or special-purpose ships, Integrated Automation Systems meets every requirement in shipping and offers decisive advantages over the entire "life" of a ship. The adaptation can suit perfectly to the special requirements in shipping and creates the prerequisites for maximum economy, reliability, and safety on board. Integrated Automation includes the propulsion plant operation, power management operation on the auxiliary engines, auxiliary machinery operation, cargo loading and unloading operation, navigation and administration of maintenance and purchasing of spares. The study focuses on implementation of IAS and its contribution in ship's performance and safety. The proposed model incorporates different failure rates for the different sensors of the Integrated Automation system as well as repair actions that need to be performed. The system can experience various levels of deterioration and when a failure occurs, a repair procedure is carried out and the system is restored to its initial fully operational state. A numerical example based on the empirical data is used to illustrate the proposed model.&#x0D; &#x0D; Received: 23 September 2022 / Accepted: 28 November 2022 / Published: 20 December 2022

ASYMPTOTIC ANALYSIS ABOUT THE PERIODOGRAM OF A GENERAL CLASS OF TIME SERIES MODELS WITH SPECTRAL SUPPORTSON LINES NOT PARALLEL TO THE MAIN DIAGONAL

The aim of this paper is to make inference about a general class of time series models including fractional Brownian motion. The spectral of these processes is supported on lines not parallel to the diagonal [Formula: see text], [Formula: see text], [Formula: see text], in spectral square [Formula: see text], and this class includes stationary, cyclostationary, almost cyclostationary time series and specially fractional Brownian motions. First, the periodogram of these processes is defined and auxiliary operator is applied to explore the distribution of the periodogram. Then the asymptotical estimation for the spectral density function is proposed and asymptotical Wishart function is found. Finally, the validity of the theoretical results is studied using simulated data sets.

Combined processing of metal surfaces in agriculture with concentrated energy flows

Modern agritech technologies are complexes of technological operations for managing the production processes of agricultural crops in agrocenoses in order to achieve the planned yield and product quality while ensuring environmental safety and certain economic efficiency. An analysis of the development of agroengineering technologies for the impact of concentrated and highly concentrated energy flows on the surface of materials shows that progress in the use of flame, induction, laser, plasma and other types of energy flows has reached its limit. The technological impasse in agriculture well illustrates the axiom that it is impossible to create universal methods and tools capable of providing exponential development over significant periods of time. Quantitative and qualitative limitations in the use of each individual technology in agriculture stimulate the search for new agricultural solutions. A multiple increase in productivity, the acquisition of competitive advantages, a significant improvement in the quality of the treated surface and obtaining unique, in many respects, properties of materials in agriculture can be achieved due to the synergistic effect when using hybrid technologies. Their efficiency is ensured by saving processing time without loss of quality. The reduction of time costs occurs due to a significant reduction in the number of auxiliary operations or their complete elimination.

Self-adjusting filling control system forself-grinding drum mills

Purpose of work isan improvement of the controlling efficiency for the processes of self-grinding ores in drum mills by using adaptive settings for the perimeters of the control part of the system. Methodology. For the self-grinding process, the degree of filling of the mill drum is a critical technological variable, i.e. this parameter not only has a direct impact on the efficiency of the grinding unit in terms of the newly formed finished product, but also determines the trouble-free operation of the mill.It is known from the referenced literature that during thedecay time of the autocorrelation function for the processes of original ore’s main characteristics change is on the order of several hours or more. At the same time, the inertia of the crushed aggregate is measured in tens of minutes. Under such conditions, one should assume that quasi-stationarity and the rational use of the control system for a wide scope of self-grinding take place. Research results. Using the method of auxiliary operators, the law for setting the parameters of the main circuit of the self-adjusting system was generated, and the block diagrams of the adaptive control system for filling ore self-grinding mills were determined. The transient processes in the control system are calculated, which proves the expediency and effectiveness of the proposed approach. Scientific novelty. A new approach is proposed using an adaptive control system to regulate the degree of filling of autogenous ores mills, based on the use of the method of auxiliary operators. Practical significance. While calculating the tuning processes in the control system for the filling degree of the mill, it was found that even with a simultaneous abrupt change in the object’s parameters K0,T1,T2to the maximum value, the adaptive system completes tuning the parameters of the controllerC1, C2, C3 for a time of about 230 ÷ 270 minutes, which indicates the practical feasibility and effectiveness of this approach to control the filling level of ore self-grinding mills.

Simulation of improved pure P‐wave equation in transversely isotropic media with a horizontal symmetry axis

AbstractCharacterizing the expressions of seismic waves in elastic anisotropic media depends on multiparameters. To reduce the complexity, decomposing the P‐mode wave from elastic seismic data is an effective way to describe the considerably accurate kinematics with fewer parameters. The acoustic approximation for transversely isotropic media is widely used to obtain P‐mode wave by setting the axial S‐wave phase velocity to zero. However, the separated pure P‐wave of this approach is coupled with undesired S‐wave in anisotropic media called S‐wave artefacts. To eliminate the S‐wave artefacts in acoustic waves for anisotropic media, we set the vertical S‐wave phase velocity as a function related to propagation directions. Then, we derive a pure P‐wave equation in transversely isotropic media with a horizontal symmetry axis by introducing the expression of vertical S‐wave phase velocity. The differential form of new expression for pure P‐wave is reduced to second‐order by inserting the expression of S‐wave phase velocity as an auxiliary operator. The results of numerical simulation examples by finite difference illustrate the stability and accuracy of the derived pure P‐wave equation.