Renovation cycle diagram

The problem of estimating the number of summands of random variables for a total normal distribution law or a sample average with a normal distribution is investigated. The Central limit theorem allows us to solve many complex applied problems using the developed mathematical apparatus of the normal probability distribution. Otherwise, we would have to operate with convolutions of distributions that are explicitly calculated in rare cases. The purpose of this paper is to theoretically estimate the number of terms of the Central limit theorem necessary for the sum or sample average to have a normal probability distribution law. The article proves two theorems and two consequences of them. The method of characteristic functions is used to prove theorems. The first theorem States the conditions under which the average sample of independent terms will have a normal distribution law with a given accuracy. The corollary of the first theorem determines the normal distribution for the sum of independent random variables under the conditions of theorem 1. The second theorem defines the normal distribution conditions for the average sample of independent random variables whose mathematical expectations fall in the same interval, and whose variances also fall in the same interval. The corollary of the second theorem determines the normal distribution for the sum of independent random variables under the conditions of theorem 2. According to the formula relations proved in theorem 1, a table of the required number of terms in the Central limit theorem is calculated to ensure the specified accuracy of approximation of the distribution of the values of the sample average to the normal distribution law. A graph of this dependence is constructed. The dependence is well approximated by a polynomial of the sixth degree. The relations and proved theorems obtained in the article are simple, from the point of view of calculations, and allow controlling the testing process for evaluating students ' knowledge. They make it possible to determine the number of experts when making collective decisions in the economy and organizational management systems, to conduct optimal selective quality control of products, to carry out the necessary number of observations and reasonable diagnostics in medicine.

Introduction. The article develops a dynamic expert system (ES) based on a model of a system for monitoring the technical condition of signal generators in telecommunication systems. In the proposed system, decision-making is based on a constant analysis of the parameters of the time-frequency parameters of signals generated by generators in infotelecommunication systems. The purpose of the work is to develop an expert system based on a model of a system for monitoring the technical condition of signal generators in infotelecommunication systems. Research results: In the course of the work, an analysis of expert systems was carried out, a dynamic expert system was selected from the real-time communication classification, the structure of the expert system was proposed, each of its elements was considered, an expert system was developed that allows predicting changes in the parameters of transmission channel generators in telecommunication systems, and the resulting expert system was tested based on two assumptions, which allows us to draw conclusions about the correctness of the development. For this purpose, the result of processing the input data is given based on two assumptions – the law of normal distribution and the uniform distribution law. On the basis of this, it can be concluded that the proposed developed version of the ES construction and the software product implementing it is working. The expert system makes it possible to analyze incoming data in the current time, as well as generate an output.

The paper analyzes the homogeneity of the stochastic structure of the samples of oil flax fibres of the Ukrainian and Polish selections. The distribution laws of fibres as mixtures of the normal and logarithmically normal distribution laws are identified. The general probability distribution law of fibre lengths of oil flax of the Ukrainian selection is a mixture of four logarithmically normal laws of distribution, and the general probability distribution law of fibre lengths of oil flax of the Polish selection is a mixture of a normal distribution law and three logarithmically normal laws of distribution. The parameters of the relevant components of the common distribution laws are found as a result of solving the problem of nonlinear optimization using the method of generalized lowering gradient that is implemented in Excel tabular processor. The adequacy of the built nonlinear models of the distribution laws is proved by estimating the value of the determination index. The comparative analysis of distribution laws of general totalities, from which the oil flax fibre samples of the Ukrainian and Polish selections are obtained, is conducted by the Kolmogorov-Smirnov statistical criterion. This criterion allows us to test and reject the hypothesis about belonging of two independent samples to the same general totality. The analysis of the general distribution laws shows that the oil flax fibres of the Ukrainian selection have a more pronounced tendency to stratification by a fibre length. Such a fibre is easily divided into factions. The oil flax fibres of the Polish selection have a larger part of short and extra-long fibres. Thus, it is clear that raw materials of the Ukrainian selection are more suitable for the production of non-woven materials of different target purposes, and the Polish selection - for the production of ropes, cords, etc. The obtained results can be used by specialists at processing enterprises for a reasonable choice of raw materials, optimization of processing modes and improving ready-made product quality.

Modern livestock development trends in the agricultural production structure include the use of feed mixers and distribution equipment. However, a stream of malfunctions and failures is reported for mixer-feeders due to factors that are specific to agricultural enterprises in Ukraine, which reduce the operational reliability of feed mixers and distributors. The study aims to evaluate the quantitative indicators of the in-service reliability of mixer-feeders and develop methods to improve them. The reliability test plan [NMT] was used, which implies a certain number of research objects (N), objects undergoing repair in case of performance loss (M), and tests terminated when the operating time (T) is reached. Initial information was collected and processed, and empirical data on the time between failures of KUHN PROFILE 12.2 DS and PROFILE 14.2 DS mixer-feeders in Ukraine were analysed. The analysis established that the faulty condition of mixers-feeders in the initial operation period is caused by the second complexity group failures. Failures related to the loss of the grinding and mixing mechanism, which limits the average time between failures of the feed mixture and distribution equipment, were identified among the second complexity malfunction group. A statistical analysis of the mixer-feeder failure occurrence was carried out. The failure probability of the grinding-mixing mechanism of the feed mixer was determined to be within the normal distribution law. The main parameters of the given theoretical distribution law were determined by calculation results. The calculations determined that the average time between failures is 3152.0 motor-hours; the standard deviation is 902.6 motor-hours; and the coefficient of variation is 0.40. An average time between failures of the study objects was proved to be consistent with the normal distribution law following Kolmogorov’s agreement criterion. Calculations determined that the average reliability index value, according to the normal distribution law, is within the confidence intervals: 1964.2 motor-hours – lower confidence limit; 4339.8 motor-hours – upper confidence limit. The obtained results may be used to improve the mixer-feeder operational reliability

This article presents a comparison of modular construction technology with traditional construction based on the results of the survey. The aim of the survey was to find out experts opinion about modular construction, the innovative way of building and its advantages and disadvantages compared to traditional building method. The results of the survey showed that modular construction has more pros than cons compared with the traditional construction method and is more economical and saves more time and materials. The most important criteria that demonstrates the clear advantage of modular construction technology is the duration of construction, the quality of work performed, and the safety of work. DOI: http://dx.doi.org/10.5755/j01.sace.23.2.21579

The article deals with matters concerned with the problem of determining the statistical characteristics of variable parameters (the variation range and distribution law) in analyzing the uncertainty and sensitivity of calculation results to uncertainty in input data. A comparative analysis of modern approaches to uncertainty in input data is presented. The need to develop an alternative method for estimating the uncertainty of model parameters used in thermal–hydraulic computer codes, in particular, in the closing correlations of the loop thermal hydraulics block, is shown. Such a method shall feature the minimal degree of subjectivism and must be based on objective quantitative assessment criteria. The method includes three sequential stages: selecting experimental data satisfying the specified criteria, identifying the key closing correlation using a sensitivity analysis, and carrying out case calculations followed by statistical processing of the results. By using the method, one can estimate the uncertainty range of a variable parameter and establish its distribution law in the above-mentioned range provided that the experimental information is sufficiently representative. Practical application of the method is demonstrated taking as an example the problem of estimating the uncertainty of a parameter appearing in the model describing transition to post-burnout heat transfer that is used in the thermal–hydraulic computer code KORSAR. The performed study revealed the need to narrow the previously established uncertainty range of this parameter and to replace the uniform distribution law in the above-mentioned range by the Gaussian distribution law. The proposed method can be applied to different thermal–hydraulic computer codes. In some cases, application of the method can make it possible to achieve a smaller degree of conservatism in the expert estimates of uncertainties pertinent to the model parameters used in computer codes.

The article presents the results of an evaluation of universities’ role in shaping cities and impact on their socio-economic and spatial development. Using the examples of Lund and Cambridge as university cities, it examines the positive and negative aspects of studentification. Universities exert a multifaceted influence on city development manifested in economic dynamics, demographic shifts, spatial changes, and community cohesion issues. The specifics of contemporary social, economic, and spatial aspects of "studentification" are highlighted through the case studies of Lund and Cambridge. Concentration of students, constituting nearly a third of residents, emerges as the primary outcome of university influence, affecting population dynamics, shaping age structure, and mitigating population aging. Universities’ pivotal role lies in knowledge production and high-quality personnel training, fostering innovative economic sectors within cities. Assessing universities’ spatial impact on city development, GIS-generated heat maps illustrate the distribution of bicycle infrastructure and service areas in urban spaces. The correlation between bicycle parking, entertainment venues, eateries, and other service facilities concentration with university infrastructure and main student accommodation places is evident. Challenges in city development encompass seasonal load on the city environment and infrastructure, the "city and mantle" phenomenon fostering conflicts between residents and students over urban planning, new housing construction, and use of public spaces, alongside issues of gentrification and spatial segregation. Conducting a SWOT analysis of Lund and Cambridge as university cities, this article outlines their development strategies.

The change of load of the transformer substation TS 10 / 0,4 kV in the mode of maximum and minimum load is measured.It is noted that the process is nonstationary at the daily interval.Hourly intervals of time are highlighted on the daily graph of electrical load, the study of the law of distribution is conducted, and the normal law of distribution is confirmed by Pearson's criterion.The stationarity test was performed on parametric tests, namely the verification of the Fisher's Fisher's constant variance and the mathematical expectation of the Student's t-test and the correlation function.The values of numerical characteristics were obtained at the stationary areas and a probabilistic mathematical model of the TS 10 / 0.4 kV load was constructed.

Warning and prevention of natural emergencies is based on the analysis and forecasting of threats of emergency situations in the state. At the same time, the forecasting of natural emergencies should be aimed at regulating natural safety in the country, assessing the threats of emergencies and their prevention. Prevention of natural emergencies of various natures, minimization of their consequences is a component of creating safe conditions for the individual and society as a whole, an integral part of the state policy of national security of the country. Ensuring safety in emergency situations requires reliable functioning of the emergency response system adequate to the level and nature of threats. The effectiveness of planning and implementing measures to prevent natural emergencies is determined by the quality of forecasting the threats of their occurrence Since the processes of occurrence of natural emergencies are of a random nature, knowledge of the law of distribution of the random variable “number of emergencies” in the state on the basis of statistical data acquires importance. The article presents the results of checking the compliance of statistical data on natural emergencies in the state with the normal distribution law. Based on the processing and analysis of monitoring data for natural emergencies, a hypothesis was put forward about the normal law of distribution of the random variable the «number of natural emergencies» in the state in accordance with the available information. Pearson’s goodness-of-fit test was chosen to test the proposed hypotheses. An assessment was made in accordance with the chosen criterion of the hypothesis about the agreement of the sample distribution with the law of normal distribution. Asa result of the research, it was found that the hypothesis put forward does not contradict the statistical data of monitoring natural emergencies over a certain period of time. The parameters of the established distribution law were evaluated.

The limit measurement errors in the geodesy are determining for the normal distribution law, But the errors, exceeding the limits are throw aside and accidental errors are obey the cut law. Cut laws are not study enough. The article is leading the results of calculate the probabilities hit accidental measurements errors for intervals σ, 2σ, 2,5σ, 3σ for cut normal and cut logical distribution laws. The analysis was accomplished.The probabilities of the cut normal and normal laws is different immaterial. 0,043 - maximum of the different. The normal law replace to the cut normal law is not recommending. Probabilities of the cut law may to use, when it is allowing to avoid the repetition of the field measurements.

In order to counter contemporary threats to the security of contemporary societies radical experimentation into new ways of living is needed. Taking inspiration from the global phenomenon of informal cities and their unique relationship with waste materials and spaces, this thesis proposes alternative ways of approaching community development in Affluent World cities. It envisions a development paradigm that incorporates user control in the design and construction of housing and other community infrastructure, encouraging the scavenging of materials and the re-appropriation of underused land. In line with the successful development practices now being carried out in informal settlements around the world, this bottom-up approach to development has surprising and encouraging implications for the practice of architecture and the quality of the built environment. Far from a dystopian view of society, this thesis presents an approach to building resilience into cities in a manner that does not shy away from the most pressing problems of today.

This chapter focuses on the contemporary evolution of regional differences in the development of the country. Scientific studies of regions have demonstrated the wide scope and depth of problems related to the regional aspects of a country's development. The introduction of a planned economy and a new regional development policy followed. The regional differentiation in farming can be illustrated by figures relating to the value of total production. The considerable decline in investment from 1979 onward suggests that there have been no major changes in regional differences in subsequent years. The crisis had multiple consequences, but it also meant pressure on investment outlays, limited availability of areas for construction, lower volume and quality of food, deterioration of the situation in forestry. The basic disparities were in housing construction and technical and social infrastructure. These disparities were more acutely felt in the regions that were urbanizing at a faster pace or that had conurbations.

The performed study is the result of collecting statistical data on failures of port transshipment and floating cranes. It is found that many accidents of components and parts of crane mechanisms can be associated with an erroneous determination of design loads. In order to increase the strength reliability, numerous field tests were carried out in river and sea ports under various modes of transshipment for different types of cargo. Tests have shown that operational loads are random in nature, and their laws of distribution over time of individual crane mechanisms can be approximated by truncated normal Gauss laws, accounting for which at the stage of new design developments, as shown by the practice of performing strength fatigue calculations, is not possible. In the article, in order to use the obtained laws at the design stage, it is proposed to replace the representation of operational loads with initial moments that are common to the entire crane mechanism, and transfer individual characteristics consideration such as stress concentration coefficients, fatigue curve parameters, operating time or test base, to subsequent stages of machine components development. For practical testing of the operational loads representation by the normal Gauss laws, a critical analysis of their initial moments, which makes it possible to identify inconsistencies in the representations of variable loads proposed for strength calculation, is given. For the corrected truncated normal load distribution law, the initial moments, the value of the order of which corresponds to the formulas structure used in calculating fatigue resistance at variable load amplitudes (in particular, under alternating loading modes), are determined. The presentation of corrected normal distribution laws with initial moments complements the normative documents used in practice when performing strength calculations under variable loading conditions, significantly simplifies calculations and makes it possible to take it into account at the stage of new design developments in accordance with the formulas established in the current normative documents.

In the last few decades, South Tangerang City has transformed into a supporting city for Jakarta. It has become a popular choice for professionals working in Jakarta who are looking for a more affordable and environmentally friendly residential option. The private sector has been a dominant actor in the housing construction in South Tangerang. The private sector constructs the vast majority of new housing, which is aimed at middle and upper-income households. The massive development of the private sector in many townships such as Bintaro, Alam Sutera, and BSD City has resulted in South Tangerang having good infrastructure of international standard. However, the private sector's massive land ownership causes significant problems for South Tangerang's city development. The study investigates the phenomenon through in-depth interviews with housing stakeholders, including local governments, private developers, and academics in South Tangerang. Land prices in Indonesia have caused affordability issues in South Tangerang. The study investigates how and at what cost this model of private-sector-led development affects housing provision in South Tangerang. This private-sector-led development may have contributed to the problem of rising land prices, making affordable housing difficult to build. Since 2013, no subsidized housing has been built in the South Tangerang area by a private developer because the land price makes it unfeasible. Besides, local government intervention is also limited because the cost of acquiring land for infrastructure and housing development has become expensive. It raised the question of whether this development model, which has made the private sector the sole determinant of housing prices, can be sustained in the future.

The article presents research on the evaluation and selection of the sprayers for surface application of liquid mineral fertilizers to the soil based on the criterion of minimizing the power to disperse a unit of their volume and the quality of their distribution over the underlying surface. The expediency of using a combined hydro-pneumatic-mechanical sprayer has been established, which combines simplicity and reliability of the technological process execution inherent in the pneumatic method of dispersion, low power costs for this process (no more than 4 kW/t), as well as the possibility of using compressed air for pneumatic-mechanical spraying. The prospects of using rotating petal and plate-type sprayers for surface application of liquid mineral fertilizers, ensuring uneven distribution not exceeding 8%, expressed by the variation coefficient, have been substantiated. It has been determined that, regardless of the type of the atomizer, at a given speed (1700 min –1 ), the zone of stable distribution of the sprayed liquid (spray pattern width) is determined by the value of 2.2 m. The obtained characteristics of the quality of the distribution of the working fluid in the spray pattern allow concluding that as the pressure in the system increases, the flow rate of the working fluid increases, but the pattern of its deposition on the collecting surface follows the law of normal distribution. It has been established that the diameter of the sprayer and the pressure in the system exert the maximum influence on the quality indicator of the distribution of the working fluid, while the values of these factors are at a minimum level. Since the values of the coefficients for X 1 (the normalized value of the liquid pressure in the system) and X 2 (the normalized value of the nozzle hole diameter) are negative, their increase leads to a decrease in the uneven distribution of the working liquid on the underlying surface. In this case, the minimum value of unevenness – 3.6% – is achieved when the values of all factors are at the maximum level.