International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

Action potential propagation in cardiac tissue by using cable equations is studied. The work discusses a one-dimensional model of continuously coupled myocytes. Electrical behavior in cardiac tissue is averaged over many cells. Therefore, the transmembrane potential behavior for a single cell is studied. Using the monodomain model, in the absence of current at the beginning and end of the cable (cell), the initial-boundary problem is posed and solved analytically. The problem is solved by the method of separation of variables. Numerical modeling of transmembrane potential propagation is implemented. Transmembrane isopotential contours and graphs corresponding to the obtained numerical results are presented.

This study explores the role of grandparents in the education of their grandchildren within an overlapping generations model. We introduce an endogenously determined time allocation, where grandparents decide how much time to dedicate to their grandchildren’s education based on a trade-off between leisure and educational contributions. The model shows that grandparental involvement in education influences the intergenerational transmission of human capital, with the potential for long-term effects on economic outcomes. By combining theoretical analysis and simulations, we highlight the dynamic relationship between grandparental education, human capital development, and the generational transmission process.

Mathematical Optimization or Mathematical Programming is a set of theoretical and applied methods originating from applied mathematics to computer science, used to find the optimal value, given some predefined criterion for optimality and based on some input parameters. More precisely, it concerns finding the input parameters of a function (called the objective function) which maximize/minimize its output. Mathematical Optimization is widely used for various quantitative or computational problems that arise everywhere in science and engineering, ranging from statistics and applied math to aerospace engineering and finance. In the following paper, we demonstrate the use of two classical optimization algorithms – Gradient Descent and Lagrangian Multipliers method – in model development in finance and trading. The specific stochastic process on which the trading model is based is called the Ornstein-Uhlenbeck (O-U) process and the point of the use of these two optimization approaches is
to find the parameters that minimize the log likelihood function of this process. This fits the O-U process to the historical data and in the context of finance and trading, maximizes our profits and helps us hedge against losses

The study of sleep is crucial for understanding various physiological and neurological processes, yet research on different sleep phases often comes with high costs and requires specialized equipment. To address these challenges, we developed a portable and relatively inexpensive oculograph, which enables more accessible sleep studies. A critical technical aspect of using the device is the necessity for mathematical transformations to interpret the signals generated by eye movements, which are often complex and prone to noise. We implemented several mathematical procedures for noise reduction, signal filtering, and the extraction of key signal features. To assess the accuracy of the oculograph, we conducted 10 daytime experiments with predefined protocols involving specific eye movements. The results indicate that the oculograph successfully measures eye movements with high precision, which was further validated through comparison with graphical signal representations. Moreover, we performed tests for nighttime use of the device, and validation of REM sleep signals is planned using a camera to record the subject during sleep. These promising outcomes suggest significant potential for the oculograph to help sleep research by offering a more affordable and mobile solution, suitable for both laboratory and home environments. The mathematical procedures and signal processing techniques presented here are tailored to the needs of psychological and medical sleep studies. Additionally, practical applications of the oculograph for targeted sleep research, including tracking eye movements during various sleep stages, are proposed.

Financial data or insurance claim data often exhibit skewness to the right and extreme values, so that classical right skewed distributions like Exponential, Gamma, Weibull or Lognormal fail to capture their behavior. However, built from different distributions on distinct contiguous intervals, two-component spliced (or composite) models often provide a better fit on the right tail, especially since the right tail distribution is considered to be of heavy-tailed type (usually Pareto). In this work, we introduce two bivariate composite distributions defined from a bivariate type I Pareto distribution for values larger than some thresholds, and a bivariate distribution less heavy-tailed on the complementary domain. We present some properties of the new distributions and discuss an estimation method, illustrated on a real data set from insurance.

The new platforms coming out on the social media space are faced from the beginning with a fierce contest. The competition for user attention is hard and the main players (Facebook, TikTok, Instagram, Reddit) have a huge advantage. To overcome these problems many of the newly lunched platform are making use of gamification strategy to keep the user engaged. The gamification strategy usually provides the user with a form of digital reputation but on some platform, it can be even a form of digital currency which can be exchanged for benefits or real products. To validate the user actions there is not always an automatic process, and the platforms are relaying on the community to cross-validate the authenticity and the value of the respective actions. The validation of the user actions can be automated but not always. When the validation cannot be automated, and the task requires human intervention the process is in his most part outsourced to the community and only a small number of the validation will be done by platform operators. The validation done by the platform operators will give credits to the users whose actions were validated. After certain amount of credit is given to a user, he became trusted, and his action can validate the actions of other users. The trusted user will act almost as a platform operator by validating other users’ actions. In this paper we simulate and analyse how the trust can be propagated into different social networks configuration. We start by defining a mathematical framework for modelling the users and the actions. After we introduce two different algorithms for propagating the trust in the community and finally for each configuration, we simulate the propagation of the trust and discuss the results.

In order to obtain the methods of assessing the quality of the functioning of the motor transport company, it is necessary to develop a methodology for quantitative evaluation of this quality. This methodology should be based on mathematical models of the quality of operations of the motor transport firm.
For purposeful formation of quality, the paper proposes an adequate method of analysis of this quality. At the same time, a method of evaluating the quality of the functioning of the automobile enterprise, evaluating the quality of the decisions taken to improve this property, and forecasting the expected quality of the functioning have been developed.

In the following article are presented the technical characteristics of real living space. A temperature model for this particular space was developed based on various experimental data, such as (external and internal) temperature, humidity, atmospheric pressure and energy consumption over seven years – 2016-2022.

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.

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.

In this paper we consider the task of estimating the volume of recreational fish catch yield in a water body. We design mathematical models for the tasks varying in complexity and generality and demonstrate how they can be solved using Bayesian approach. A Markov Chain Monte Carlo (MCMC)-based Bayesian approach is widely used as a solution for stochastic models. To solve the simplest case of a proposed model we have used the PyMC library. The proposed models were later used to estimate the recreational fishing capacity of the water bodies in Qazaqstan.

An important task of analyzing the behavior of individuals in society, in a large crowd of people is the development of mathematical models of behavior. The complexity lies in the heterogeneous nature of individuals, in the diversity of their behavioral characteristics, interests, and features of social behavior. Here the possibility of mathematical modeling of crowd behavior is considered and a mathematical model is proposed.