Mathematical Probability Theory Research Articles

«Theory of everything»: types of information and the theory of interpretation in «Philosophy of chance» by Stanisław Lem

The article is focused on the S. Lem’s perspective of the literary work as a product of the reader’s apprehension of the text in the culture discourse. The aim of the research is to describe the Lem’s view on the structure of the text; Lem’s encounter as a writer, a reader, and a philosopher is used to state the conditions and characteristics of the text interpretation. By the means of multiple introspection the author of “Philosophy of chance” devotes his research to the explanation of his model of the literary work as a product of the social-cultural existence. Moreover, the author’s aim is to state the characteristics of the text creation and interpretation. Therefore, the research shows a new, “cybernetic” approach to the text interpretation based on the comparison between the text structural characteristics and the rules of the mathematical theory of probability and the theory of information. The futurological view lies in the hypothesis about the text as a “self-learning program” (also known as a neuronet) which can transform due to the developing conditions of the interpretation process. As a matter of fact, S. Lem highlights two types of information: selective and structural. Both types might be identified in the text, but that depends on the reader, his encounter and expertise.

The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory

Abstract This article applies mathematical probability theory to statistical algorithms to conduct game analysis on the relevant marketing decisions of foreign trade cross-border e-commerce. We build a theoretical framework for the collaborative development of SMEs and cross-border e-commerce platforms. At the same time, build a trustworthy transaction margin mechanism for cross-border e-commerce transactions in a fuzzy market environment. The participation of the blockchain big data platform can promote the development of foreign trade cross-border e-commerce toward a more transparent and healthy partnership.

Numerical study on oxygen transport pattern in porous transport layer of proton exchange membrane electrolysis cells

A transient, two-dimensional and two-phase numerical model is established to study the nature of oxygen transport in proton exchange membrane electrolysis cells (PEMEC). Randomly generated circle fibers are used to construct a patterned porous transport layer (PTL), and the volume of fluid (VOF) method is employed to capture accurate gas-liquid interfaces. The patterns of oxygen transport and the relationship between multiple transport paths are analyzed in detail. We propose for the first time the concept of ‘isolation belt’, which is composed of a series of narrow throats, hindering the spontaneous combination of different oxygen transport paths. The influence of PTL perforation and spatially-graded fiber diameters on oxygen transport are explored. The numerical results show that perforation can probabilistically destroy the ‘isolation belt’, forming a transport path with high priority, which helps to reduce oxygen saturation. Moreover, when the porosity of PTL remains unchanged, reducing the fiber diameter in the region near the catalyst layer (CL) can significantly reduce the local oxygen saturation. The pressure variation reveals its consistency with the maximum throat width of the oxygen transport path, which indicates the law of capillary pressure. From the perspective of mathematical probability theory, a novel functional expression of the profile of oxygen saturation with respect to the structural properties of PTL is proposed to make a concise explanation of gas bubble transport in the context of PEMEC or similar gas-liquid porous flow. The highlights in this paper include: • Comprehensive spatiotemporal profile for in the process of oxygen penetration. • The concept of isolation belt for spontaneous merging of oxygen pathways. • A mathematical explanation for probability of oxygen saturation distribution. • Influence of PTL perforation and graded fiber diameters on oxygen saturation.

Failure analysis of the segment finger bar mower and force interaction of the blade segment with the plant stem

Scientific observations on the quality and reliability of combine harvesters have shown that of all the delays of equipment, 32...35% of the total operating time, technical failures account for 17.4...19.8%. Most of the failures were observed with the failure of combine parts, mechanical transmissions, hydraulic systems, etc. Quantitative analysis of harvester failures has shown that most failures occur in the operation of the cutting device, namely the finger bar mower. The working hypothesis is that it is possible to increase the reliability of the cutting device of harvesting machines in ordinary operating conditions and in the event of sudden failures by applying a coating on the blade segment, without significantly changing its geometric parameters, and performing notches that ensure both a decrease in the mass of the segment and its destruction without plastic deformation when foreign objects enter the cutting zone. The main problem of the reliability of segments of cutting device, harvesting equipment, is the cutting edge of the blade, which wears out and deforms during operation. From the above, it follows that the purpose of the study is to improve the reliability of segment finger bar mower machines by improving the mechanical properties of segments, these investigations are relevant and of practical interest. The study includes the use of mathematical probability and reliability theory, analysis, and a systematic approach to provide an analytical description of the operation of a cutting device segment. The consequence of this scientific investigation is an analysis of failures and malfunctions of the machinery, presented graphically, a diagram of how a plant stem segment is cut and the forces acting on the stem and the segment during the cutting process are depicted. These materials have scientific and informative content that would be of interest to engineers and scientists in the process of research and production of cutting device segments

Метод Монте-Карло для оценки устойчивости функционирования объекта информатизации в условиях массированных компьютерных атак

Methods of mathematical statistics and probability theory are deeply studied and can be successfully used as a means of assessing the stability of the functioning of informatization objects (OI) in the normal conditions of its application. The standard conditions allow us to obtain representative descriptive statistics, evaluate the corresponding probabilistic characteristics and apply the methods of probability theory. Ensuring the reliability of the functioning 
 of OI in normal conditions is provided by effective operational cover. However, for massive computer attacks (MCA), the dynamics of OI behavior and the development of the situation are unpredictable, and the events themselves are rare, which does not allow the above methods to be correctly applied. The significance and novelty of the study lies in the positive assessment of the applicability of the Monte Carlo method for assessing the survivability of the restored OI, which is subject to MCA and has temporary redundancy (recoverability). Assessing OI survivability is considered from the point of view of the need to implement a methodology for ensuring the risks of information security associated with MCA. The statement of the problem, the modeling algorithm, and solution examples are given, on the basis 
 of which it is possible to recommend the Monte Carlo method for solving the set problem. The enlarged stages of the statistical modeling procedure are given, the solution of the actual problem of assessing OI stability for MCA conditions is described. The obtained partial conclusions may be of interest for planning further scientific research in the direction of improving the processes of decision making to ensure the sustainability of the functioning of OI in conditions of targeted aggressive influences. A case of statistical modeling is given, taking into account possible scenarios for applying MCA and interpreting the simulation results

Dempster-Shafer Theory of Belief Functions: A Language for Managing Uncertainties in the Real-World Problems

The main purpose of this article is to introduce the Dempster-Shafer (DS) Theory of Belief Functions. The DS Theory is founded on the mathematical theory of probability and is a broader framework than the probability theory. It reduces to probability theoryunder a special condition. In addition, the article illustrates problems in representing pure positive, pure negative evidence, and ambiguity under probability theory and shows how this problem is resolved under DS Theory. Next, the article describes and illustrates Dempster’s rule of combination to combine two or more items of evidence. Also, the article introduces Evidential Reasoning approach and its applications to various disciplines such as accounting, auditing, information systems, and information quality. Examples are provided where DS Theory is being used for developing AI and Expert systems within the business disciplines and outside of the business disciplines.

РАЗРАБОТКА ИНФОРМАЦИОННОЙ МОДЕЛИ, ПРЕДУПРЕЖДАЮЩЕЙ ВОДИТЕЛЯ О ДВИЖЕНИИ ПО ОПАСНОМУ УЧАСТКУ УДС

The analysis of the statistics of road accidents on one of the sections of the road network adjacent to the core of the urban agglomeration was carried out, and the percentage ratio of the type of transport used and the number of vehicles in the family was determined using a sociological survey. According to the results of the documentary study, it was determined that Tuesday and Sunday are the most dangerous days of the week with the largest number of road accidents, as well as the most common and frequently occurring types of accidents are collisions and hitting pedestrians. On the basis of mathematical statistics and theory of probability, the correlation dependence between the proposed time ranges is established. The information model has been developed that allows warning the driver about driving on a dangerous section of the road network and using the proposed methods to improve road safety.

Сравнение энергетической эффективности грузовых электровозов переменного тока с коллекторным и асинхронным тяговым приводом

Electric locomotives with asynchronous traction drive are operated on the Russian road network in passenger and freight traffic. The advantage of such a drive is a large specific power. At first glance, electricity consumption of an electric locomotive with asynchronous traction drive should be less than that of an electric locomotive with a collector traction drive. The same is declared by manufacturers of traction rolling stock [1, 2]. But the answer to the question which electric locomotive is more economical in freight traffic: with a collector or asynchronous traction drive? - is far from being unambiguous [3, 4, 5]. In order to determine which electric locomotives have the best energy efficiency regarding the traction drive, a comparison of electric energy costs for traction of freight trains by electric locomotives of the VL80S series with collector traction drive, operated in two- and three-section versions, and a promising two-section electric locomotive of the 2ES7 series with asynchronous traction drive was performed. The energy efficiency assessment was carried out using methods based on elements of mathematical statistics and probability theory, including estimation of the distribution parameters of the studied quantities, statistical hypothesis testing and variance analysis. This article presents the main results of the research carried out at the testing area of the Gorky Railway during the pilot operation of the 2ES7 series electric locomotive on the Druzhinino - Vekovka section.

ENERGY EFFICIENT SOLUTIONS IN INFRASTRUCTURE PROJECTS OF SORTING COMPLEXES OF RAILWAY STATIONS

Purpose. Improving approaches and methods of calculation and design of energy-efficient sorting slides of railway stations, taking into account the mechanization of their braking positions based on the use of modern car moderators, including energy efficient structures. Methodology. The research was performed using the methods of the theory of bitter calculations in combination with the tools of mathematical statistics and probability theory. The assessment of the possible economic effect was carried out taking into account the technical and economic calculations on the criterion of the given savings of annual costs. Results. An estimate of the predicted value of the speed of the very good runner at the entrance to the brake positions when calculating their needs. An adaptive approach to the calculation of the required power of the 1st and 2nd brake positions on the descent part of the sorting slides is proposed. The condition of technological reliability and "survivability" of the system of control of speeds of movement of couplings at rolling down from a sorting hill is checked taking into account action of probabilistic factors. The economic effect of reducing the need for car decelerators for the braking positions of the slides, as well as energy efficiency of sorting complexes. Practical value. The obtained important scientific and practical results to substantiate the reduction of energy consumption and increase the energy efficiency of sorting stations can be used to develop new projects and to survey the parameters of existing sorting complexes, including non-mechanized slides.

Reliability and maintainability of scraper conveyor used in coal mining in the Jiu Valley

Purpose.The aim of the study is to determine and analyse causes of faults in the operation of TR-7A scraper conveyor and to estimate the required time for their remediation and select the methods of their prevention and elimination. Methods. The characteristic of a system, such as the scraper conveyor, intended to fulfil its specified function in time and operation conditions, can be studied, theoretically, by determining its operational reliability. This implies the existence of a framework that incorporates several interconnected components of technical, operational, commercial and management nature. The quantitative expression of reliability was based on elements of mathematical probability theory and statistics (exponential distribution law), failure and repair mechanism not being subject to certain laws. Findings. The following TR-7A subassemblies, if defective, could have been the cause of a failure: chains, hydraulic couplings, chain lifters, drive, return drums, some electrical equipment. After 28 months of monitoring the TR-7A operation, we have established the number of failures (defects) ni, the operating time between failures ti, frequency of failures fc, time to repair tri, weight repair time pr, mean time between failures (MTBF), mean time to repair (MTR). Originality.Data collection and processing involves the adoption of specific procedures to allow the correct highlighting of the causes and frequency of failures. The accomplishment of this approach allowed finding the solutions for increasing reliability of some subassemblies of TR-7A conveyor (i.e., those subjected to abrasive wear). Practical implications.One solution was to use materials with compositional and functional gradient in the case of worn surfaces of some subassemblies. It was successfully applied for the chain lifters where a significant increase in the mean time between failures was obtained. The field of application of these materials can be extended to the metal subassemblies of machines and equipment with abrasion wear that occurs both in underground mines and in quarries.

Searching for a Tide Table for Business

The article investigates the methods and conceptions of statistical inference used in business forecasting in the United States and in Europe in the 1920s. After presenting the methods and arguments used by the members of the Harvard Committee on Economic Research in the first years after its establishment in 1919, the article explores the far-reaching changes in method and conviction from 1922 on. The members’ realization that the future evolved differently than predicted prompted them to give up their hope for mechanical means of forecasting and to revoke their calls for the employment of the mathematical theory of probability in economics. Instead, they established an extensive correspondence with economic and political decision-makers that allowed them to base their forecasts on “inside information.” Subsequently, the article traces European attempts to adopt the Harvard Index of General Business Conditions in the early 1920s. Impressed by the seemingly mechanical working of the Harvard index, European economists and statisticians sought to establish similar indices for their countries. However, numerous revisions of the Harvard index in the mid-1920s cast doubt on the universality of the index and the existence of stable patterns and led European researchers to pursue different paths of investigation. The article complicates the larger history of statistical inference in economics in two meaningful ways. First, it argues that statistical inference with probability was not the long-sought solution for the problem of objectivity but a long-contested, and repeatedly discarded, approach. Second, it shows that these contestations were often triggered by deviations between forecasts and the conditions actually observed and by this means argues for the importance of the historical context in the history of economics.

Analysis of the reliability of the plates of complex shapes for the cams of automatic half-hose machines by the criterion of fatigue strength

The purpose of the work is to develop the algorithm for calculation of the probability of failure-free operation of flexible plates of complex shapes for the cams, using the criterion of fatigue strength, to make decisions on minimization of their sizes with the subsequent evaluation of the implemented measures. The studies are performed on the example of a plate for the cam, the configuration of which provides both beam and double console deformations at the same time. The comprehensive approach is presented, which includes dynamic analysis of the needle impact on the cam surface, computer simulation of geometric parameters of the plate by the finite element method (FEM) according to the condition of strength, and classical principles of mathematical statistics and Theory of Probability. The finite-element model with a volumetric 8-node element is used, which allows, with ease of calculations, to obtain the results with a high accuracy when determining the stress-deformed state of the study object. The computer simulation is performed using Code_Aster software with free access. Also, in the calculation of reliability, the random nature of the multifactorial influence on the value of the plate fatigue limit and the loading variations of the cam are considered. When determining the equivalent forces, taking into account the cyclical operation of the machine, the forces that affect the cams during the production of one product are taken as a loading. The numbers of cycles corresponding to these loadings are calculated by the formulas, which are made as a result of the analysis of trajectories of needles motion concerning the cams when knitting different sections of the product. When calculating equivalent stresses, only stresses that influence the accumulation of fatigue failures are used, that is, the values greater than the half of the detail fatigue limit.The proposed computational approach can be used to generate the cams with flexible work plates of different configurations, including under the equal stress condition.

The Maxim of Probabilism, with special regard to Reichenbach

It is shown that by realizing the isomorphism features of the frequency and geometric interpretations of probability, Reichenbach comes very close to the idea of identifying mathematical probability theory with measure theory in his 1949 work on foundations of probability. Some general features of Reichenbach’s axiomatization of probability theory are pointed out as likely obstacles that prevented him making this conceptual move. The role of isomorphisms of Kolmogorovian probability measure spaces is specified in what we call the “Maxim of Probabilism”, which states that a necessary condition for a concept to be probabilistic is its invariance with respect to measure-theoretic isomorphisms. The functioning of the Maxim of Probabilism is illustrated by the example of conditioning via conditional expectations.

TİBBİ İNFORMASİYA SİSTEMLƏRİNDƏ İSTİFADƏ OLUNAN RİYAZİ APARAT

Biosystem of the human body is viewed as a whole. First of all adequate mathematical machine selection and class of biosystems needs to be assigned for creation of mathematical model of biological system. Biosystem has two types of appoach. One of them is supposed to be a simple approach, the other is likely to be very complex – indexed approach. Different biosystems with determination properties are usually described by differential and integral equations, linear and nonlinear algebra. In some cases, algebraic polynoms with timed argument are used for presenting determined biosystem dynamics. Adequate mathematical modeling machine, probability theory, Markov and random processes theory and the laws are applied for the description of likely characterized biosystems. Key words: biosystem, biocybernetic issues, differential and integral equations, mathematical model, Markov chains, Bayes method, artifical neural networks

ФАЛЬСИФИЦИРУЕМОСТЬ НАУЧНЫХ ТЕОРИЙ И ПРОБЛЕМА ДЮГЕМА. (АНАЛИТИЧЕСКИЙ ОБЗОР)

The criterion of falsifiability is the cornerstone of the methodological doctrine of K. Popper. According to Popper, a theory is falsifiable and, therefore, scientific if there is at least one statement describing some phenomena in the world with which the prediction derived from this theory is incompatible. If falsified, the theory must be rejected. However, P. Duhem showed that scientific theories are tested experimentally only in conjunction with a number of auxiliary assumptions, the truth of which is implicitly assumed by the experimenter. At the same time, the result of the experiment, which contradicts the predictions of the system «theory and auxiliary assumptions», does not in itself say which component of this system is false. Identifying faulty components is what constitutes the Duhem problem. A promising way to solution of this problem may be associated with the application of Bayes' theorem and the methods of mathematical probability theory and statistics.

Statistical Characteristics of Flow Field through Open and Semi-Closed Bileaflet Mechanical Heart Valve

The formation of thrombi on the streamlined surface of the bileaflet mechanical heart valves is one of the main disadvantages of such valves. Thrombi block the valve leaflets and disrupt the cardiovascular system. Diagnosis of thrombosis of the bileaflet mechanical heart valves is relevant and requires the creation of effective diagnostic tools. Hydroacoustic registration of the heart noise is one of the methods for diagnosing the operation of a mechanical heart valve. The purpose of the research is to determine the statistical characteristics of the vortex and jet flow through the open and semi-closed bileaflet mechanical heart valve, to identify hydroacoustic differences and diagnostic signs to determine the operating conditions of the valve. Experimental studies were conducted in laboratory conditions on a model of the left atrium and left ventricle of the heart between which there was the bileaflet mechanical heart valve. Hydrodynamic noise was recorded by miniature pressure sensors, which were located downstream of the valve. The vortex and jet flow behind the prosthetic heart valve were non-linear, random processes and were analyzed using the methods of mathematical statistics and probability theory. The integral and spectral characteristics of the pressure field were obtained and the differences in the noise levels and their spectral components near the central and side jets for the open and semi-closed mitral valve were established. It was shown that hydroacoustic measurements could be an effective basis for developing diagnostic equipment for monitoring the bileaflet mechanical heart valve operation. Doi: 10.28991/SciMedJ-2020-0204-1 Full Text: PDF

Fractional order of Legendre-type matrix polynomials

Recently, special functions of fractional order calculus have had many applications in various areas of mathematical analysis, physics, probability theory, optimization theory, graph theory, control systems, earth sciences, and engineering. Very recently, Zayed et al. (Mathematics 8:136, 2020) introduced the shifted Legendre-type matrix polynomials of arbitrary fractional orders and their various applications utilizing Rodrigues matrix formulas. In this line of research, we use the fractional order of Rodrigues formula to provide further investigation on such Legendre polynomials from a different point of view. Some properties, such as hypergeometric representations, continuation properties, recurrence relations, and differential equations, are derived. Moreover, Laplace’s first integral form and orthogonality are obtained.

Probability Modals and Infinite Domains

Recent years have witnessed a proliferation of attempts to apply the mathematical theory of probability to the semantics of natural language probability talk. These sorts of “probabilistic” semantics are often motivated by their ability to explain intuitions about inferences involving “likely” and “probably”—intuitions that Angelika Kratzer’s canonical semantics fails to accommodate through a semantics based solely on an ordering of worlds and a qualitative ranking of propositions. However, recent work by Wesley Holliday and Thomas Icard has been widely thought to undercut this motivation: they present a world-ordering semantics that yields essentially the same logic as probabilistic semantics. In this paper, I argue that the challenge remains: defenders of world-ordering semantics have yet to offer a plausible semantics that captures the logic of comparative likelihood. Holliday & Icard’s semantics yields an adequate logic only if models are restricted to Noetherian pre-orders. But I argue that the Noetherian restriction faces problems in cases involving infinitely large domains of epistemic possibilities. As a result, probabilistic semantics remains the better explanation of the data.

Study on Emitted Radiations from Filament Bulb of Different Power

The research work is carried out to find spectrum of wavelength of the emitted radiations from filament bulb. Both temperature and wavelength measurement are based on theoretical model. The temperature finding formula for tungsten filament is obtained by using blackbody radiation approach. The peak wavelength of the emitted radiation is obtained 1.461 μm and 1.125 μm for 6 and 500 watt bulb respectively by using Wein’s displacement law which depends upon temperature of the filament. The wavelength obtained by using Wein’s displacement law, is just an index, which helps to investigate, “how the radiation energy density is distributed” so as to give rise to an electromagnetic spectrum. The results obtained from the applied methodologies show that the accuracy of a model is quite good. Some mathematical techniques and probability theory are used to verify the work. The work is followed by both classical and quantum analysis to justify the results. Temperature only is not the key factor that deserves power of the bulb. The value of resistance plays a vital role in fixing power of the bulb. At least one factor is important in the calibration of the power of the bulb, “either temperature or surface area” of the filament.

Моделирование температурного поля в массиве кучи измельченной древесины

Storage of the crushed wood materials at the wood processing enterprises is carried out in the open air in formed heaps of various sizes and shapes. The disadvantage of such storage is uncontrolled self-heating of chips to critical temperatures driven by thermophiles. The payload mass of wood gets lost, its quality significantly degrades, and a risk of flame development appears without proper control. In order to prevent negative consequences, it is necessary to reject the excess heat energy from the massif of crushed wood material into the environment. Heat rejection will allow to establish control over thermal processes and operate with temperature fields inside a heap. Production engineering measures can be carried out with the use of heat pipes. This method is effective and environmentally friendly; and does not require the involvement of commercial energy consumption. Basic studies of the processes occurring in the heap massif of crushed wood were carried out for solution substantiation. The research purpose is to identify mathematical regularities describing the influence of the key factors on the processes of self-heating of crushed wood stored as the cone-formed heaps in the open air conditions. Methods of mathematical simulation, probability theory and mathematical statistics with the use of computational software systems were used as a part of the study. As a result, a system of equations those simulate the processes of self-heating of crushed wood and allow to predict the temperature field inside a heap to a given time interval is obtained, which will allow developing methods of industrial chips safe storage.For citation: Desnev A.N., Prokof’ev G.F., Tyurikov V.Yu. Simulation of the Temperature Field in the Crushed Wood Heap Massif. Lesnoy Zhurnal [Russian Forestry Journal], 2019, no. 6, pp. 213–223. DOI: 10.17238/issn0536-1036.2019.6.213