Mathematical Methods
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Anna Wójtowicz ◽  
Krzysztof Wójtowicz

AbstractWe define a model for computing probabilities of right-nested conditionals in terms of graphs representing Markov chains. This is an extension of the model for simple conditionals from Wójtowicz and Wójtowicz (Erkenntnis, 1–35. 10.1007/s10670-019-00144-z, 2019). The model makes it possible to give a formal yet simple description of different interpretations of right-nested conditionals and to compute their probabilities in a mathematically rigorous way. In this study we focus on the problem of the probabilities of conditionals; we do not discuss questions concerning logical and metalogical issues such as setting up an axiomatic framework, inference rules, defining semantics, proving completeness, soundness etc. Our theory is motivated by the possible-worlds approach (the direct formal inspiration is the Stalnaker Bernoulli models); however, our model is generally more flexible. In the paper we focus on right-nested conditionals, discussing them in detail. The graph model makes it possible to account in a unified way for both shallow and deep interpretations of right-nested conditionals (the former being typical of Stalnaker Bernoulli spaces, the latter of McGee’s and Kaufmann’s causal Stalnaker Bernoulli models). In particular, we discuss the status of the Import-Export Principle and PCCP. We briefly discuss some methodological constraints on admissible models and analyze our model with respect to them. The study also illustrates the general problem of finding formal explications of philosophically important notions and applying mathematical methods in analyzing philosophical issues.

2021 ◽  
Francesca Bertacchini ◽  
Pietro S. Pantano ◽  
Eleonora Bilotta

Abstract Providing a product with characteristics of beauty and creative innovation is one of the aims of any contemporary industry to meet the needs of customers and satisfy their aesthetic and functional requirements. To study the production process and the realisation of creative products with aesthetically pleasing attributes, we created a smart production environment that allows the construction of simple textured polygons (triangles, squares, rhombuses and pentagons) through a software application. Birkhoff aesthetical measure, Euclidean Distance and Entropy Measure have been developed and applied to a sample of smart products, manufactured in the implemented environment, to analyse their aesthetical, creative and the order-complexity-chaos features respectively. The results provided us with measurable quantities of the sought qualities for the sample and for each distinct product, combining the metrics to visualise the creative space in two and threedimensional spaces. Further mathematical methods, such as Point Process and Density Probability Map applied on the same sample, allowed us to move from a statistical space to probabilistic landscapes, with enhanced forecasting capability on creative features for all future products. Industrial applications are expected in the production and evaluation of products from a creative point of view.

2021 ◽  
Vol 5 (4) ◽  
pp. 412
Vaulin Vladimir Ivanovich ◽  
Singeev Sergey Aleksandrovich

Background: The article presents the results of a study of ensuring fire safety in medical and preventive institutions (LPI) on the example of the central city hospital.Objectives: Research is aimed at improving the fire safety of hospital complexes and hospitals in modern conditions.Materials and Methods: The study used the methods of system analysis of scientific research and statistical data on ensuring fire safety, methods of structural analysis of the practice of ensuring fire safety of hospital complexes, mathematical methods for calculating the evacuation of people from a building and the spread of a fire in a building, methods for calculating the economic efficiency of means of support fire safety.Results and Discussion: Based on the analysis of fire statistics in healthcare facilities in Russia, it is concluded that it is advisable to improve the fire safety of hospitals and hospital complexes in modern conditions. The point of view is expressed that along with the fact that fire safety in hospitals is observed, the analysis indicates the existing problems in the practice of implementation.Conclusion: In order to increase the level of fire safety, it is possible to introduce: a modern fire alarm system; video of control systems and monitoring of safety of objects on the territory of the medical facility; installation of automatic fire extinguishing systems in fire-hazardous premises; installation of additional emergency lighting and reflectors indicating the direction of evacuation in case of fire and smoke; carrying out organizational and practical measures to ensure the safety of patients in a medical institution in an emergency situation (ES), namely, it is proposed to develop a memo of actions for patients in the hospital complex on inpatient treatment in case of an emergency with a list in the instruction log; provision of medical facilities with individual rescue equipment and provision of hospitals and hospital complexes with highrise buildings with modern evacuation means.International Journal of Human and Health Sciences Vol. 05 No. 04 October’21 Page: 412-417

2021 ◽  
Vol 16 (1(21)) ◽  
pp. 93-99
Maka Lomtadze

The article focuses on the application of mathematical methods in economics, in particular discussing economic problems that are easily solved using derivatives. The purpose of the article is to show students the way and opportunity to use mathematical methods to solve economic problems. To this end, the article discusses and analyzes several economic tasks in detail, which will be interesting and easy for students to master. I considered the derivative of a function as the rate of change and introduced the definition: The instantaneous rate of change of the function f with respect to x at a point is called the derivative if it exists. With the help of this definition I have discussed and explained Task 1: Suppose that the increase in production of a certain product over a period of time is described by a function And population growth is described by the following function: Where is the number of years from the initial period, then the production of these products per capita is given by the function: Find the growth rate of product production. By solving this task I came to the conclusion that after a year the production of products per capita increases. In the following tasks I used the method of finding the extremum values of a function using a derivative, namely I equated the first-order derivative to 0, found the critical points, and with the help of the second-order derivative I determined the extremes of the function. I discussed task 2: For the production of X volume of products, the firm plans a cost that is calculated by the formulan . For what volume of production will the average cost be the smallest? Find the numerical value of this small expense. Solving this problem, I came to the conclusion that the given function of the average cost takes on the least value when the output volume is a unit , and this value is equal to: which is the marginal cost when producing the volume output. I discussed Task 3: How many products should be sold in order for a firm to profit maximally if the derivative cost function is known: And return function: Here I came to the conclusion: if 600 units of the product are sold, then the firm's profit will be maximum and it will be numerically equal At the end of the article I discussed such a task 4 of applied optimization. What is the minimum amount of material needed to make a 2 liter cylindrical jar? Where I came to the conclusion: the smallest amount of material will be spent to get a cylindrical vessel if we take the height 2 times the radius of the base.

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4270
Gianpiero Colangelo ◽  
Gianluigi Spirto ◽  
Marco Milanese ◽  
Arturo de Risi

In the last years, a change in the power generation paradigm has been promoted by the increasing use of renewable energy sources combined with the need to reduce CO2 emissions. Small and distributed power generators are preferred to the classical centralized and sizeable ones. Accordingly, this fact led to a new way to think and design distributions grids. One of the challenges is to handle bidirectional power flow at the distribution substations transformer from and to the national transportation grid. The aim of this paper is to review and analyze the different mathematical methods to design the architecture of a distribution grid and the state of the art of the technologies used to produce and eventually store or convert, in different energy carriers, electricity produced by renewable energy sources, coping with the aleatory of these sources.

Daria Ivashchenko ◽  
Oleksandr Kutsenko

Today, the urgent problem facing humanity is the problem of fighting epidemics and pandemics. One of the ways to solve this problem is the use of mathematical methods for predicting the pandemic process and assessing the impact of measures taken by health authorities to reduce the rate of development of the disease. Based on the analysis of a variety of information sources, the article considers the most effective approach to mathematical and computer modeling of the development of the epidemic on the basis of individually oriented and multi-agent approaches. The analysis of the problem of modeling the development of epidemics on the basis of a multi-agent approach, as well as the possibilities of predicting the course of the epidemiological process is carried out. An example of the structure of a multicomponent simulation model based on the generally accepted verbal model of the spread of viral diseases is given. As an example, the methodology of simulation agent-based modeling using the Any Logic software product of distribution processes 2019-nCoV is considered. The obtained averaged indicators confirmed the main hourly average periods of infection, which were obtained by purely statistical methods. Based on the analysis of published works, the possibilities of managing the development of the epidemic by influencing these factors have been investigated. A relatively simple method of mathematical modeling and forecasting of the epidemic situation has been proposed. It is shown that a timely and adequate forecast is a prerequisite for planning the structure, scale, timing of the necessary measures aimed at preventing epidemics and outbreaks of disease, as well as reducing and eliminating their negative consequences. Keywords: agent simulation, epidemic, math modeling, pandemic, prognostication, simulation.

2021 ◽  
Boris Dzeboev ◽  
Anastasia Odintsova ◽  
Alena Rybkina

Abstract. The main objective of this study is to apply Discrete Mathematical Analysis (DMA) to the development of the methodology of cyclostratigraphy. This aim is supported by exploring the magnetic properties of rocks, the lithology of sediments and obtained geochronological reference definitions. The analysis was based on measurements of the variability of the magnetic susceptibility of rocks, which reflects climate variations. Astronomical cycles are global; this makes it possible to carry out a correlation analysis over a large area and on different facial types of sediments, considering their lithology and other sedimentary features. The introduction of modern methods of mathematical processing of geological data is one of the prospective areas for investigation and development in geoscience. Astronomical cycles can be revealed from measurements of scalar magnetic parameters of rocks (magnetic susceptibility as presented by the authors). Specific software developed by the authors allows the processing of measurement data and assessment of the presence of stable oscillation cycles based on the obtained measurement base. The present study attempts to apply mathematical methods to magnetic data using the existing PAST program, which allows spectral analysis of primary data with the construction of Lomb-Scargle and REDFIT periodograms. We interpret the spectral analysis data based on paleomagnetic determinations, considering the available dates for the boundaries of direct and reverse polarity chrons on a general stratigraphic scale.

А.Н. Яшкова ◽  
А.В. Морозова

В данной статье рассматриваются вопросы развития ценностной сферы у обучающихся разной занятости в период профессионального обучения. Актуальность изучения ценностной сферы учащихся позволяет уточнить современный ценностный уровень и тенденции развития социальных ориентаций, установок молодого поколения, а также пути сопровождения их профессионального становления. Предметом исследования стали особенности ценностных ориентаций молодежи разной занятости на этапе получения профессионального образования. В ходе изучения указанного предмета использовались теоретический анализ психолого-педагогической литературы, констатирующий эксперимент, диагностические методики, а также математические методы обработки эмпирических данных. В итоге выявлены различия в смысложизненных ориентациях обучающейся и работающей молодежи в период студенчества, что позволяет говорить о доминировании более важных и широких социальных ценностей у работающей молодежи, в то время как у только обучающихся более выраженными стали ценности, направленные на удовлетворение собственных потребностей и достижение личных целей. Полученная информация может быть использована в работе кураторов академических групп, практических психологов для осуществления психологического сопровождения социализации молодежи. This article examines the problem of value orientations of working and learning youth during the period of vocational training. The relevance of studying the value sphere of students makes it possible to clarify the current value level and development trends of social orientations, attitudes of the younger generation, as well as ways of accompanying their professional development. The subject of the research is the peculiarities of the value orientations of young people of different employment at the stage of obtaining vocational education. In the course of studying this subject, a theoretical analysis of psychological and pedagogical literature, ascertaining an experiment, diagnostic techniques, as well as mathematical methods of processing empirical data were used. As a result, differences were revealed in the life-meaning orientations of learning and working youth, which allows us to speak about the dominance of more important and broader social values among working youth, while only students have more pronounced values aimed at satisfying their own needs and achieving personal goals. The information obtained can be used in the work of curators of academic groups, practical psychologists for the implementation of psychological support for the socialization of youth.

Sri Purwaningsih

Aims: The purpose of this study was to determine the effect of financial ratios and corporate governance on the dependent variable, namely financial distress. Financial distress is measured using the Altman Zscore approach in 1995. Study Design: The design used in this research is causal research. Place and Duration of Study: The object of this research is companies in the retail sector listed on the Indonesia Stock Exchange in 2017-2019. The research sample was 22 samples using the purposive sampling method. So the total data was 66 companies. Methodology: The analytical method used is quantitative, namely the approach to data processing through statistical or mathematical methods collected from secondary data. It is hoped that the conclusions obtained in a study will be more measurable and comprehensive. Results: The results obtained that the financial ratios proxied through the current ratio and debt-equity ratio influence predicting the bankruptcy of the company, while the Total Assets Turn Over variable, good corporate governance variables such as the number of independent commissioners and the frequency of audit committee meetings are not able to provide an influence in predicting corporate bankruptcy.

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