Construction Of Mathematical Model Research Articles

Retailer‐to‐Individual Customer Product Supply Strategies Under a Semireal Demand Pattern

In the consumer goods supply chain, there are three different modes of demand: real, false, and semireal. It is an interesting topic to discuss the optimal profit of enterprises according to these three demand patterns. This paper develops three mathematical models that can be used to investigate the factors that affect retailers with respect to the design of product supply strategies for individual customers under a semireal demand pattern and thereby addresses the problem of retailers’ maximum profitability. The results of the present study show that these models may effectively help retailers develop appropriate supply strategies for individual customers under a semireal demand pattern; in turn, this may help retailers improve operational performance. The main contribution of the current study lies in the construction of mathematical models of product supply strategies for the individual customer in the off‐invoice mode, the scan‐back mode, and the unsold‐item processing mode under the semireal demand pattern. The effectiveness of the models has been verified through numerical calculations. In concrete management practice, the mathematical model given in this paper can be used to effectively adjust the quantity of goods purchased, correct retail prices, and optimize sales discounts to maximize profits.

Development of control algorithms for magnetoelectric generator with axial magnetic flux and double stator based on mathematical modeling

The object of this research is electromechanical processes in a generator with an axial magnetic flux and a double stator and an additional non-contact excitation winding operating as part of autonomous electric power systems. The power of the additional excitation system is about 2 % of the generator power. The presence of an additional non-contact winding, which is powered by direct current, makes it possible to control the generator voltage by changing the excitation current. This resolves the task to stabilize the output voltage of the generator with permanent magnets when the load and shaft speed change. This paper reports the construction of a three-dimensional field axisymmetric mathematical model of the generator under study, which has made it possible to calculate and investigate its characteristics and parameters, in particular the magnitude of magnetic induction in all structural elements. The model built takes into account the influence of finite effects, magnetic scattering fields, and the radial-axial nature of the closure of the main magnetic flux and the magnetic flux of the additional excitation winding. The use of a structure with a double stator makes it possible to more efficiently utilize the usable volume of the generator and to increase its power. A mathematical model of the generator in the d-q coordinate system was built, which has made it possible to synthesize algorithms for controlling the automatic voltage stabilization system of the generator voltage under conditions of change in load and shaft speed. Control algorithms were developed on the basis of the concept of inverse dynamics problems in combination with minimizing local functionalities of instantaneous energy values, which ensures that the system is robust when changing generator parameters and that regulators are implemented in a simple way, due to the lack of differentiation operations. Based on the models built and algorithms developed, the quality of control of the generator's output voltage when the load and frequency of the generator change was investigated by modeling in the MATLAB/Simulink environment. When setting a jump in the rated load and changing the rotational speed within ±15 % of the rated value, the automatic stabilization system provides astatic voltage control at a given level of 48 V. The results can be practically used in the design of autonomous electric power systems with high energy conversion efficiency, in particular wind turbines and hydraulic units

On the Inclusion of Adaptive Potential in Species Distribution Models: Towards a Genomic-Informed Approach to Forest Management and Conservation

Ecological modeling refers to the construction and analysis of mathematical models aimed at understanding the complexity of ecological processes and at predicting how real ecosystems might evolve. It is a quickly expanding approach boosted by impressive accelerations in the availability of computational resources and environmental databases. In the light of foreseeing the effect of climate change on forest ecosystems, the branch of ecological modeling focusing on species distribution models (SDMs) has become widely used to estimate indices of habitat suitability and to forecast future tree distributions. However, SDMs are usually informed based solely on environmental data without any reference to the genetic makeup underlying responses to the environment, the possibility of exchanging variants helping to persist in situ, or the capacity to chase suitable conditions elsewhere. Among the main evolutionary processes that may complement forecasts of range shifts are local adaptation and gene flow, i.e., the occurrence of genetic variants conferring a population the optimal fitness in its own habitat and the exchange of adaptive alleles between populations. Local adaptation and gene flow could be described by indices of genetic diversity and structure, genetic load, genomic offset, and an admixture of genetic lineages. Here, we advocate for the development of a new analytical approach integrating environmental and genomic information when projecting tree distributions across space and time. To this aim, we first provide a literature review on the use of genetics when modeling intraspecific responses to the environment, and we then discuss the potential improvements and drawbacks deriving from the inclusion of genomic data into the current SDM framework. Finally, we speculate about the potential impacts of genomic-informed predictions in the context of forest conservation and provide a synthetic framework for developing future forest management strategies.

Интеграция бактериальных заквасочных культур с рыбным сырьем: подбор и обоснование

An important aspect of the technology of processing fish raw materials is the development of food products of various directions using modern methods of biotechnological processing. In this regard, in food biotechnology, special attention is paid to biotransformation by promising strains of bacterial starter cultures to produce food products with improved quality characteristics, and in particular with a functional orientation. The use of bacterial starter cultures in the production of fish food products can be a way to extend the shelf life due to the formation of metabolites of their vital activity (acids and bacteriocins), which are the main factor of bioconservation. At the same time, the biochemical activity of bacterial starter cultures will contribute to improving the organoleptic and structural-mechanical properties of raw materials, as well as increasing the nutritional value and synthesis of vitamins and other nutrients, and giving the final product probiotic properties. This trend is a response to the interest of the population of the Russian Federation in probiotic products, which allows to normalize the indigenous microflora of the gastrointestinal tract, thereby strengthening the human body and its immune system as a whole. In this regard, the analysis of data on the justification of the use of bacterial starter cultures for the biotransformation of fish raw materials was carried out, and the necessary strains of microorganisms were selected. The analysis of scientific and technical databases has shown the prospects of scientific developments on the use of bacterial starter cultures as protective microorganisms and the study of the influence of the conditions of cultivation and preservation of bioactivity of a living cell under the influence of physical and chemical factors during the technological process of production and subsequent storage of products, which is of particular importance for the creation of probiotic food products. The conducted research will be used in the construction of mathematical models of the process of biotransformation of fish raw materials as a basis for the development of technological processing parameters for its subsequent use in the formulations of "fast food" products containing functional components, which is justified by the accelerated rhythm of life and the desire of modern society to monitor their nutrition by eating products that support a healthy lifestyle.
 In food biotechnology, special attention is given to biotransformation of promising strains of bacterial starter cultures for the production of food products with improved quality characteristics and functional orientation. In this regard, the analysis of data on the justification of the use of commercial, potentially commercial fish types for biotransformation by bacterial starter cultures and the selection of the necessary strains of microorganisms, which will be used in the construction of mathematical models of the process of biotransformation of fish raw materials as a basis for the development of technological parameters of processing.

On the Maximum Energy Efficiency of Random Access-Based OMA and NOMA in Multirate Environment

The paradigm of the upcoming 5G and beyond is the machine type communications (MTC), where a large number of devices automatically operate wireless communications. Due to their automatic and energy-intensive operations, energy efficiency (EE) becomes very important, but there is a lack of investigation for EE of random access networks, which is the underlying platform for MTC. In this paper, we focus on the EE of random access orthogonal and non-orthogonal multiple access (OMA and NOMA) networks. We first construct mathematical models of their EE performances. Information-theoretic theories are employed to transform probabilistic decodability into deterministic form for OMA, and along with the unique features of NOMA decoding process, by pivoting around the decodability of a specific packet, we realize the modeling for NOMA. Then, based on the established models, exploiting the nature of random access networks, a complementary geometric programming approach is used for performance optimization. From our investigation, the following results are discovered: (1) NOMA has significant advantage over OMA in EE performance due to its strong data recovery; (2) to maximize the EE performance, devices with higher data rate should transmit more frequently, but with lower transmission power; (3) lower data rates have beneficial effects on EE.

Modeling the influence of startup ecosystem components: Entrepreneurial aspect

Defining the basis for the development of a country’s start-up ecosystems as the basis for activating entrepreneurship is an urgent task of restoring the country’s economy. The purpose of this study is to identify ways to improve the country’s start-up ecosystem based on the construction of economic and mathematical models for activating business activities. The research methodology is based on statistical research methods, namely dynamics analysis; to assess the strength of the influence of each component of the start-up ecosystem on the change in position in the rating, regression correlation analysis was chosen, which allows identifying the strength of the influence of factors on the final indicator. The components of the start-up ecosystem were investigated, which means an interactive and interdependent set of institutions whose activities create an environment for the qualitative and quantitative growth of start-ups as subjects of innovative entrepreneurship development. The use of statistical analysis methods for the data of the countries, which were grouped into 5 clusters, allowed determining the absolute changes in the values of the Global Start-up Ecosystem Index rating indicators from Start-up Blink: rating change, quantitative component, qualitative component, business environment, general summary. Based on regression-correlation analysis, economicmathematical models were built, which describe the influence of the components of the country’s ecosystem on the change in the rating positions in the section of four clusters, demonstrating: a strong connection between the factors and the result (Clusters 2, 4). Weak connection for the countries of Clusters 3, 5, which indicates the dependence of the development of start-up ecosystems on other factors that are not considered in their description and which affect the development of start-ups and entrepreneurship in the countries of Clusters 3, 5. The practical value of this paper is that the results of the study can serve as the basis for the local and state authorities to form strategies to develop start-up ecosystems at the national and regional level

SIMULATION OF THE PROCESS DYNAMICS OF ALUMINA CALCINATION IN ROTATING DRUM FURNACES

The issues of modeling processes occurred in drum-type rotary kilns in steady-state (static) modes are considered in details in the literature, unlike the processes occurred in dynamic conditions (transient modes). However, management and optimization of technological regimes require gaining information about the dynamics of those processes. The goal of the study is analysis of the process of alumina calcination. The quality indicators of the process have a significant impact on the process of aluminum electrolysis. Calcination of aluminum hydroxide is a final stage in all technologies of alumina production. We present the results of theoretical construction of mathematical models of the dynamics of heat and mass transfer processes upon heat treatment of the initial aluminum hydroxide. Three types of models are constructed under different initial conditions which describe the main regularities of the process with different degree of accuracy. Proceeding from the data of the theoretical study a methodology has been developed for experimental study of the dynamics of the process along the main control channels: "hydrate loading - flue gas temperature," "natural gas consumption - temperature in the calcination zone," and "natural gas consumption - flue gas temperature." Transfer functions and differential equations of the process were thus obtained for the studied channels. The revealed good agreement between the structures of theoretical and experimental models made it possible to formulate recommendations for the construction of a process control system for alumina calcination. The temperature in the calcination zone affects the fuel (gas) consumption and determines the quality of the resulting alumina. The flue gas temperature must be maintained at the desired level using a two-circuit system which stabilizes the aluminum hydroxide charge with correction for the flue gas temperature. The temperature in the lower head of the furnace is an integral indicator of the interaction of two flows: the flow of burning gas and the counter-moving flow of the material. This temperature in the steady state operation of the furnace is a control parameter associated with the quality of the resulting alumina. When managing gas consumption, it is also necessary to maintain an optimal fuel-air ratio to ensure complete fuel combustion with maximum efficiency.

A Reliable Way to Deal with the Coupled Fractional Korteweg-De Vries Equations within the Caputo Operator

The development of numeric-analytic solutions and the construction of fractional order mathematical models for practical issues are of the highest concern in a variety of physics, applied mathematics, and engineering applications. The nonlinear Kersten–Krasil’shchik-coupled Korteweg–de Vries-modified Korteweg–de Vries (KdV-mKdV) system is treated analytically in this paper using a unique method, known as the Laplace residual power series (LRPS) approach to find some approximate solutions. The RPS methodology and the Laplace transform operator are combined in the LRPS method. We provide a detailed introduction to the proposed method for dealing with fractional Kersten–Krasil’shchik-linked KdV-mKdV models. When compared to exact solutions, the approach provides analytical solutions with good accuracy. We demonstrate the effectiveness of the current strategy compared to alternative methods for solving nonlinear equations using an illustrative example. The LRPS technique’s results show and highlight that the method may be used for a variety of time-fractional models of physical processes with simplicity and computing effectiveness.

Designing a voltage control system of the magnetoelectric generator with magnetic flux shunting for electric power systems

The object of research in this work is a three-phase magnetoelectric generator with magnetic flux shunting based on industrial induction electric motors. The presence of a magnetic shunt makes it possible to control the voltage of the generator by changing the excitation current in the non-contact electrical winding of the magnetic shunt, which is powered by direct current. Thus, the problem of stabilization of the output voltage of the generator with permanent magnets is solved when the speed of rotation and load change. This paper reports the construction of a three-dimensional field mathematical model of the generator, which allows for electromagnetic calculations of the generator with specified parameters, taking into consideration the influence of final effects, magnetic scattering fields, as well as their radial-axial nature. The results of the calculation of the electromagnetic field are the initial parameters for building a simulation model in the MATLAB-Simulink environment. A simulation model of a magnetoelectric generator with magnetic flux shunting under conditions of changing rotational speed and load has been constructed in the MATLAB-Simulink environment. On the basis of the built models, the performance characteristics of a magnetoelectric generator with magnetic flux shunting were established, which show the limits of control of the output voltage. Adjusting characteristics were determined at zero and rated shunt current for different types of load. The adjusting characteristics of the generator are presented at the rated voltage of the generator for different types of load and with an increase to 150 % of the rated value. The study's results show the high efficiency of the voltage control system of a magnetoelectric generator with a magnetic shunt at different speeds of rotation and load

Functional Scheme of the Biomachine System

A functional scheme for biomachine systems is proposed, similar to the typical scheme of a functional system of a behavioral act according to P.K. Anokhin. Such schemes are a certain necessary step towards the formalization and construction of mathematical models for systems, as well as specific practical systems. In the theory of biomachine systems, the proposed functional scheme plays the same role and serves as an easy-to-perceive informal description of the functioning of a biomachine system.

Incorporating Mitochondrial Gene Expression Changes Within a Testable Mathematical Model for Alzheimer's Disease: Stress Response Modulation Predicts Potential Therapeutic Targets.

Alzheimer's disease is a specific form of dementia characterized by the aggregation of amyloid-β plaques and tau tangles. New research has found that the formation of these aggregates occurs after dysregulation of cellular respiration and the production of radical oxygen species. Proteomic data shows that these changes are also related to unique gene expression patterns. This study is designed to incorporate both proteomic and gene expression data into a testable mathematical model for AD. Manipulation of this new model allows the identification of potential therapeutic targets for AD. We investigate the impact of these findings on new therapeutic targets via metabolic flux analysis of sirtuin stress response pathways while also highlighting the importance of metabolic enzyme activity in maintaining proper respiratory activity. Our results indicate that protective changes in SIRT1 and AMPK expression are potential avenues for therapeutics. Combining our mitochondrial gene expression analyses with available protein data allowed the construction of a new mathematical model for AD that provides a useful approach to test the efficacy of potential AD therapeutic targets.

A Reliable Technique for Solving Fractional Partial Differential Equation

The development of numeric-analytic solutions and the construction of fractional-order mathematical models for practical issues are of the greatest importance in a variety of applied mathematics, physics, and engineering problems. The Laplace residual-power-series method (LRPSM), a new and dependable technique for resolving fractional partial differential equations, is introduced in this study. The residual-power-series method (RPSM), a well-known technique, and the Laplace transform (LT) are elegantly combined in the suggested technique. This innovative approach computes the fractional derivative in the Caputo sense. The proposed method for handling fractional partial differential equations is provided in detail, along with its implementation. The novel approach yields a series solution to fractional partial differential equations. To validate the simplicity, effectiveness, and viability of the suggested technique, the provided model is tested and simulated. A numerical and graphical description of the effects of the fractional order γ on approximating the solutions is provided. Comparative results show that the suggested method approximates more precisely than current methods such as the natural homotopy perturbation method. The study showed that the aforementioned method is straightforward, trustworthy, and suitable for analysing non-linear engineering and physical issues.

MATHEMATICAL MODEL FOR DECISION MAKING SYSTEM BASED ON THREE-SEGMENTED LINEAR REGRESSION

Context. The problem of approximation of empirical data in the decision-making system in safety management.. The object of the study was to verify the adequate coefficients of the mathematical model for data approximation using information technology.
 Objective. The goal of the work is the creation adequate math-ematical model using information technology on the bases analyze different approaches for approximating empirical data an that can be used to predict the current state of the operator in the flight safety system..
 Method. A comparative analysis of the description of the transformation of information indicators with a non-standard structure. The following models of transformation of information indicators with similar visual representation are selected for comparison: parabolas of the second and third order, single regression and regression with jumps. It is proposed to use new approaches for approximation, based on the use of the criterion proposed by Kuzmin and the Heaviside function. The adequacy of the approximation was checked using these criteria, which allowed to choose an adequate mathematical model to describe the transformation of information indicators. The stages of obtaining a mathematical model were as follows: determining the minimum sum of squares of deviations for all information indicators simultaneously; use of the Heaviside function; optimization of the abscissa axis in certain areas; use of the linearity test. The obtained mathematical model adequately describes the process of transformation of information indicators, which will allow the process of forecasting changes in medical and biological indicators of operators in the performance of professional duties in aviation, as one of the methods of determining the human factor in a proactive approach in flight safety.
 Results. The results of the study can be used during the construction of mathematical models to describe empirical data of this kind.
 Conclusions. Experimental studies have suggested recommending the use of three-segment linear regression with jumps as an adequate mathematical model that can be used to formalize the description of empirical data with non-standard structure and can be used in practice to build models for predicting operator dysfunction as one of the causes of adverse events in aviation.
 Prospects for further research may be the creation of a multiparameter mathematical model that will predict the violation of the functional state of the operator by informative parameters, as well as experimental study of proposed mathematical approaches for a wide range of practical problems of different nature and dimension.

Construction and Application of Mathematical Model of Stable Fracture Development Zone of Roof

The fractured zone in the overlying strata of a coal mine goaf is vital for effective gas drainage. The development height of the fractured zone is lied on the “saddle type” theory and calculated by empirical formula, while the horizontal range is dependent on the caving theory of the “O” circle. However, the height of the fracture zone obtained using the above method is usually too large, and only the horizontal boundary of the fracture zone is defined. Besides, the fracture development degree in different regions is not described. To accurately determine the stable development area of the fractured zone and locate the gas migration channel as well as gas enrichment horizon, in this paper, a geometric and mathematical model for gas extraction in the fractured zone is established based on common high-level drilling. Then, a method of investigating the parameters of the directional high-level drilling in the roof is proposed, and a solving means is provided. Taking Wanfeng Coal Mine as an engineering background, the reasonable parameters of the common high-level drilling were investigated, and the effect was verified using the directional high-level drilling in the roof of an adjacent working face. The results show that the stable extraction volumes of the two directional drilling holes is 1~1.8 m3/min and 0.6~1 m3/min, respectively, which exceeds the optimal extraction volumes of the ordinary drilling holes. The new method of determining the stable development area of the fractured zone is significant for improving the gas drainage effect of the high-level drill holes in the roof.

Fostering students' modelling and problem-solving skills through Operations Research, digital technologies and collaborative learning

Operations Research (OR) is a branch of applied mathematics that deals with optimization problems arising from different real contexts. The solving process of its problems is based on the construction and resolution of mathematical models, showing the possible connections between mathematics and the real world. Nevertheless, OR is not typically included in most curricula of higher secondary schools (i.e. Grades 9–12), but it is usually presented mainly at university level. To show how OR could be significant for these school students' education, the authors of this paper developed an educational project consisting of three teaching units. In this paper, we share the result of the teaching experiment related to the first unit, addressed to Grade 10. Qualitative and quantitative analyses show how it is appropriate to include OR and its typology of problems in regular school mathematics lectures. Second, these data also show how modelling and problem-solving skills, developed working with OR, can be fostered by implementing a collaborative way of working, also by making use of digital technologies. Last but not least, we demonstrate the positive impact such activities have on students' appreciation of OR.

Чисельне моделювання нестаціонарної течії в гідравлічній системі за каві-туючою шайбою

This paper addresses the construction of an efficient mathematical model to be used in the numerical simulation of unsteady liquid flows in hydraulic systems with cavitating restrictors. Existing approaches to cavitation simulation are based either on accounting for a two-phase flow structure or on representing a cavitating flow as a homogeneous medium of variable density. In the latter case, the pressure and the density are related via the barotropic equation of liquid–vapor mixture state. The goal of this work is to verify the applicability of a cavitation model based on the barotropic equation of liquid–vapor mixture state to the numerical simulation of an unsteady flow in a hydraulic system with a cavitating ring plate. The method employed is a numerical flow simulation in the axisymmetric approximation using the complete averaged Navier–Stokes equations. It is shown that the use of the barotropic equation of liquid–vapor mixture state provides a satisfactory agreement between the computed results and the experimental data available in the literature. In agreement are the peak-to-valley values of the oscillating pressure on the pipe wall immediately downstream of the cavitating ring plate and the presence of a pronounced periodic component in the pressure vs. time relationship. It is shown that the parameters of the unsteady flow downstream of the cavitating ring plate vary when going from the ring plate to the cavity collapse location: the peak-to-valley value of the oscillating pressure on the pipe wall increases and so does the contribution of high-frequency periodic components to the pressure vs. time relationship. It seems desirable that the turbulence model employed be refined further to correctly simulate cavitation oscillations generated by periodically detached cavitation in Venturi tubes, which are used in various cavitation pulse plants.

HOMOGENEOUS PLANS OF MULTI-FACTORY EXPERIMENTS ON QUASI-RANDOM R-ROBERTS SEQUENCES FOR SURROGATE MODELING IN A VORTEX STYLE STRUCTUROSCOPY

Context. The article is devoted to the creation of multifactorial experimental plans based on quasi-random recursive Roberts Rsequences. The object of the research is the process of creating computer-aided experimental design plans. The aim of the article is to create multifactorial, namely six- and seven-factor, uniform plans of experiments with low discrepancies, study of their projection properties and demonstrate their use on the example of surrogate modeling in eddy current structuroscopy.
 Method. An iterative method of unit hypercube even filling with reference points was used for constructing multidimensional experimental plans. It provides acceptable indicators of homogeneity and is realized on the basis of quasi-random nonparametric additive recursive Roberts R-sequences using irrational numbers, which, in turn, are obtained on the basis of the generalized Fibonacci sequence. The criterion for plans perfection is the assessment of homogeneity in terms of differences invariant with respect to the rotation of coordinates and re-marking and ordering of factors and which quantitatively characterize the deviation of the generated distribution from the ideal uniform.
 Results. Six- and seven-factor computer uniform experimental plans have been created for cataloging, which are characterized by low discrepancies and sufficiently high-quality projection properties. The tendency, which had been previously proved in the authors' research, for preserving these experimental plans characteristics in multidimensional factor spaces, which is observed with increasing number of plan points, has been confirmed. The evaluation of the quality of the created experimental plans is carried out both by visual analysis of the scattering matrix of all two-dimensional projections and by quantitative indicators of heterogeneity of the set of vectors that form the plan, namely centered and cyclic discrepancies.
 The example of the initial stage of creating a surrogate model to solve the problem of identifying profiles of electrophysical parameters in eddy current structuroscopy shows certain features of the application for created plans, in particular the transition from the plan for a unit hypercube to the plan in real factor space in the form of a hyperparallelepiped, which does not significantly affect its characteristics of homogeneity of the distribution of points.
 Conclusions. For the first time, the problem of creating six- and seven-factor uniform plans of experiments with low rates of centered and cyclic discrepancies based on R-sequences of Roberts was solved. The projection properties of the created experimental plans for different number of points were investigated. The method of constructing multidimensional computer plans of experiments taking into account the peculiarities of eddy current structuroscopy was improved. The use of six-dimensional experimental plans on the example of surrogate modeling in eddy current structuroscopy was demonstrated. The results of the study can be used in the construction of surrogate mathematical models of physical processes by any known methods of approximation.

Modeling the number of COVID-19 cases in St. Petersburg in the period 2020–2022

Intoduction. The construction of mathematical models of changes in the total and daily amounts of the coronavirus of the population of St. Petersburg in various segments and the period from 2020 to 2022. The need for research is dictated by the presence of a dysfunctional situation in the city, as well as the need to develop a methodological apparatus for short-term operational assessment of changes and forecasting of key indicators of the spread of coronavirus.
 Purpose. To assess the change in the total and daily indicators of coronavirus disease in the population of St. Petersburg in the periods May-August 2020 and 2021 and to carry out a short-term forecast.
 Methods. The solution of the problem was carried out by modeling and performing short-term prediction of the folding situation of coronavirus in St. Petersburg by the total (integral) and daily (differential) number of diseases in the region. Modelling is based on statistics that are generated through monitoring by coordinating councils to combat the spread of COVID-19 in regions and in the country.
 Results. An approach and mathematical apparatus for modeling and forecasting the dynamics of regional key indicators of the spread of the pandemic in the regions of Russia are proposed.
 Practical relevance. The proposed solution to the problem will enable the administration and health authorities to receive scientific information for evaluating and adjusting their work to create normal economic and social living conditions for residents of Russian regions.

Mathematical Model of an Antenna-Waveguide Path with Separation of Signals by Frequency–Polarization

Introduction. The creation of antenna-waveguide paths of multi-band mirror antennas (AWP MMA) is a significant task in the development of antenna-feeder devices for satellite communication systems (SSS). This task involves the construction of an adequate mathematical model of AWP MMA both without and with the implementation of an auto-tracking function built using the "frequency separation – polarization separation" method. However, the existing mathematical models have been developed only for specific AWP MMA types, thus making them unsuitable for the development of new AWP MMA. The model proposed in this paper can be used for an arbitrary number of combined frequency ranges and types of polarization.Aim. Development of a mathematical model of the AWP MMA of SSS both without and with the implementation of an auto-tracking function built using the "frequency separation – polarization separation" method.Materials and methods. The mathematical model under consideration assumes a description of the AWP MMA using block matrices. Each of these matrices describes the complex amplitudes of signals arising in each of the AWP MMA devices. This, in turn, makes it possible to analyze the influence of the parameters of each device on the characteristics of the AWP MMA of SSS as a whole with an arbitrary number of combined frequency ranges and types of polarization.Results. Two options for the construction of AWP MMA of SSS are proposed. The first option can be used in communication system antennas with software support, while the second option is applicable when a monopulse tracking method is implemented. To construct an AWP MMA model, it is proposed to use a matrix description of the characteristics of AWP MMA devices. This allows the structure of the considered AWP MMA to be varied within a wide range.Conclusion. The developed mathematical model makes it possible to describe the characteristics of each of the devices in the AWP MMA system using a certain multipole. The proposed model provides ample opportunities for controlling, at the stages of development, production and debugging, not only the characteristics of each device in the AWP MMA, but also the transmission coefficient and polarization isolation in each frequency range of the entire AWP MMA. The presented dependencies can be used to assess the relationship between parameter tolerances and the limits of changes in the characteristics of the motor vehicle.

System analysis of mathematical models of placement of transport and logistics facilities of different levels

Introduction. The formation of an overarching network of nodal freight multimodal transport and logistics centres in the Russian Federation and organisation of high-speed freight traffic on schedule on its basis requires the development of science-based proposals for the creation or modernisation of the corresponding regional transport and logistics infrastructure. One of the most important tasks in the implementation of this project in the context of limited investment resources is the correct justification of the number and choice of locations for the transport and logistics centres of the overarching network in the Russian Federation, as well as the locations of transport and logistics centres in the constituent entities of the Russian Federation.Materials and methods. This article provides an evaluation analysis of the classical methods for finding optimal centres on a plane and some construction of mathematical quantitative models for the optimal placement of transport and logistics facilities.Results. According to the evaluation analysis, the authors have drafted a scientifically based concept of a systematic approach to the issues of rational design and placement of elements of transport and logistics infrastructure, in particular, the overarching network of nodal freight multimodal transport and logistics centres, as part of a new highly efficient transport and logistics infrastructure of the Russian Federation and its international transport corridors.Discussion and conclusion. The obtained results of the study can be used for scientifically based decision-making in investment projects related to the development of transport and logistics infrastructure at both regional and federal levels: substantiation of locations and technological capacities of transport and logistics infrastructure facilities; determining the need for the development of objects of the regional transport and logistics infrastructure, while eliminating their bottlenecks; implementation of a phased set of measures to modernise the existing terminal and logistics complex.