Mathematical Modeling
Vol. 6 (2022), Issue 4

Table of Contents

  • THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING

    • Procedure for analyzing the quality, structure and subjective rating of distorted images by the Full- Reference technique

      pg(s) 100-102

      In the present work, we study the regularities of the influence of the type of distorting algorithm on the result of evaluating the image quality by the Full-Reference method in the presence of subjective quality assessments. As an example, we used the TID2013 database with 3000 images distorted by 24 types of algorithms and subjective mean square scores (MOS) quality ratings. An image quality score based on the Weibull distribution model and the usual PSNR similarity measure is applied. It is shown that the applied distorting algorithms are classified into two types – normal, leading to results consistent with the Human Visual System, and “anomalous”, the corresponding quality estimates of which are disordered or chaotic.

    • D – optimal plans in the case of a piecewise constant function

      pg(s) 103-105

      It is known that a large number of algorithms of the Monte Carlo method and experiment planning are based on the choice of a
      certain probability distribution ρ.
      This probability distribution ρ is given on a measurable space (X, B). And a given measurable space (X, B) has a density ρ(x) = dρ/dν by
      some σ-finite measure v on (X,B).
      When choosing a probability distribution ρ, the problem of solving the problem of finding the optimal density ρ arises.
      As a result of solving the tasks, an explicit form of the Least squares Method of unknown parameters and variance was obtained. The
      criterion of D – optimality is considered.
      The D-optimal plans considered in this article are well known due to an important class of efficiency functions. To compare plans in terms of
      D-optimality, the effectiveness of an arbitrary plan relative to the optimal plan is determined.
      Thus, this article is devoted to the analysis of methods for constructing D-optimal experimental plans, where the basic object is a piecewise
      constant function.

    • Classification of Digital Images using topological signatures – A Case Study

      pg(s) 106-109

      Topological Data Analysis (TDA) is relatively new filed of Applied Mathematics that emerged rapidly last years. The main tool of Topological Data Analysis is Persistent Homology. Persistent Homology provides some topological characteristics of the datasets. In this paper we will discuss classification of digital images using their topological signatures computed with Persistent Homology. We will experiment on the Fashion-MNIST dataset. Using Topological Data Analysis, the classification was improved.

  • MATHEMATICAL MODELLING OF TECHNOLOGICAL PROCESSES AND SYSTEMS

    • A mathematical pathway to achieve sustainable design and friendly management of combined biodiesel/dairy supply chain

      pg(s) 110-113

      This study proposes a mathematical pathway to achieve sustainable design and resource-friendly management of a biodiesel supply chain produced from dairy waste scum. In the work, the features of a combined biodiesel/dairy supply chain are outlined and a set of design and management tools is developed, which is formulated in MILP terms. The optimization criterion is defined in terms of economic sustainability and environmental assessment data is applied as part of it. The purpose of the defined mathematical model is to obtain optimal operating conditions of the considered combined supply chain. A test example based on a case study from Bulgaria was considered. The results of the toolbox implementation can be used as a decision-making tool.

    • Irrigation Scheduling for Some Crops Under Arid Environment of Rosso, Mauritania

      pg(s) 114-117

      The study was performed to identify irrigation scheduling of some common crops such as seed-maize, tomato, carrot, rice, alfalfa, and tomato plants at arid Rosso province, Mauritania. In that purpose, crop water requirement, ETc, for those crops were calculated by Cropwat software computer program. In results, ETc values for Rice, Alfalfa, Carrot, Maize (grain), and Tomato crops were calculated as about 1378 mm, 1542 mm, 814 mm, 705 mm, and 956 mm respectively. The irrigation water requirements, I, for the examined crops were found as 1677 mm, 1535 mm, 811 mm, 699 mm, and 950 mm, respectively. In accordance with our findings, the following suggestions can be considered; crop pattern should be designated in accordance with current water resources; water delivery systems should be converted to modernized systems; deficit irrigation can be applied for some crops; farmers should be educated about correct water management, and there should be strong relationships between landowners and water managers.

    • Optimization of Cooling Performance of Horizontal Commercial Refrigerator Prototype with Mathematical Modeling

      pg(s) 118-120

      In recent years, the problem of food safety and traceability has been one of the difficulties faced by restaurant and hotel businesses. Food spoilage can occur at any stage of the food chain; most of all food spoilage is due to improper storage conditions in refrigerators. Increasing attention to food quality and safety requires the development of sensitive and reliable analysis methods as well as innovative technologies for maintaining freshness and food quality. Freshness is a factor that has both health qualities and features that affect customer satisfaction and business profitability. Within the scope of this study, simulation studies were carried out to improve the cooling performance with mathematical modeling on a horizontal commercial refrigerator (operating temperature: -2/+8°C) prototype. Along with the original design, evaluations were made with mathematical modeling according to many different variables (temperature, airflow distribution, etc.) that affect the cooling performance, and R&D gains were achieved in developing the prototype according to the most suitable working conditions.

    • Planning and analysis of materials handling processes in production company using modelling and simulations

      pg(s) 121-126

      In this paper is presented the method of planning and analysis of the materials handling line in one production company. The method consists of design, simulations, and analysis with the support of Arena simulation software. The design of the line is accomplished using modular modelling with interconnected modules and blocks, and simulations will be carried out to view the flow of boxes with materials and the functionality of main units and processes. The modelled line contains all the necessary units of the input processes, production and output processes, warehouses, materials handling vehicles, and the process flow of packages. Analysis will investigate key performance parameters and evaluate the functionality of the line. Production and logistics companies are implementing various software to plan and design their materials handling line, internal transports and production processes prior to the implementation and development of their plant. This enables them to plan the work, determine influential parameters and identify problems in the functionality. Results will be given in the graphical and tabular forms, which will represent the analysis of performance parameters and line efficiency.

  • MATHEMATICAL MODELLING OF SOCIO-ECONOMIC PROCESSES AND SYSTEMS

    • Schedule process modelling of a “wood processing SME” based on IEC/EN 62264 standard

      pg(s) 127-130

      The purpose of the research is to present a solution to production planning optimization problems, in cases of short-term customer orders and variable production load. The main reasons for the emergence of the task are the introduction of SMEs to unregulated electricity market and the increasing price of electricity due to the imposition of additional components in the formation of the price.The lack of traditional market and the small number of regular customers of SMEs make it difficult to forecast electricity consumption, and therefor impractical to request electricity for long-term periods of time. A possible solution related to the implementation of operational management systems, which, through the introduction of standard models, will enable the implementation of optimization algorithms for production planning.

    • Assessing the impact of intellectual capital on economic growth

      pg(s) 131-133

      The article explains the elements that have the largest share in intellectual capital and explains the possibility of quantitative assessment of the specific weight of these elements in intellectual capital. Here on the example of the Republic of Azerbaijan on the basis of statistical data the value of works and services on intellectual capital in Azerbaijan is analyzed, as well as the dynamics of added value created at the expense of intellectual capital. In the article, the impact of added value created by intellectual capital on economic growth in Azerbaijan has been evaluated in the software package Eviews-12.

  • MATHEMATICAL MODELLING OF MEDICAL-BIOLOGICAL PROCESSES AND SYSTEMS

    • Hemorheological models applied to data analysis in groups of healthy individuals and in patients with type 2 diabetes mellitus

      pg(s) 134-136

      The study aims to analyze the experimental haemorheological data with mathematical models and to analyze the interrelationship between the rheological parameters of the blood and blood rheology determinants. The study aims to develop this experimental basis of prognostic mathematical and hemorheological models for the interrelationship between the set of parameters. Two known models are used to describe the non-Newtonian rheological properties of blood – the shear stresses – shear rate dependences. The parameters of the simplest models – the power law and the Herschel-Bulkley law were used to analyse the differences between the hemorheological characteristics of blood from healthy individuals and a group of patients with diabetes mellitus type 2 (T2DM). The experimental data are statistically processed using the Mann-Whitney U-test for intergroup comparison of independent variables, as well as t-test. The Statistica program was used for statistical processing.