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Investigation of probabilistic aspects reliability of isotropic bodies with internal defects

Kvit Roman

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 3

73--84

EN

A study of the stress state and reliability of an isotropic body with the same material crack resistance and evenly distributed internal defects-cracks under the conditions of homogeneous axisymmetric loading is carried out. Defects are characterized by two independent random variables – a radius and orientation angle. The probability density distribution of the defect radius is chosen in the form of an exponential law. The probability density distribution of the defect orientation angle is chosen in the form of a law that corresponds to the material isotropy. The influence of the loading level, type of stress state and body size (number of defects) on the most probable value, the mean value and the dispersion of failure loading (strength) are investigated.

2

Probability-statistical estimation method of feed influence on the tangential cutting force under turning

Krupa V., Tymoshenko N., Kobelnyk V., Petrechko I.

Journal of Achievements in Materials and Manufacturing Engineering

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2022

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Vol. 114, nr 1

22--31

EN

Purpose: This research aims to develop the mathematical model and propose a method for estimating the feed stochasticity impact on the tangential cutting force during turning. The main reason for this research is that the existing models for determining the tangential component of the cutting force do not take into account the stochasticity of the feed rate. Design/methodology/approach: Measurements of tangential cutting force during turning on general-purpose lathes with known feed dispersion parameters were made. The mathematical model was developed, and dispersion characteristics (mean value, dispersion and mean square deviation) of the tangential cutting force component depending on the corresponding dispersion characteristics of the feed rate were obtained. The method of assessing the impact of stochasticity of the feed rate on the tangential cutting force is proposed. Findings: As the result of the carried-out investigations, it is proved that the stochasticity of the feed rate affects the dispersion of the tangential cutting force during turning. For specific conditions, the share of feed stochasticity in the dispersion of tangential cutting force component is from 40 to 60% and should be taken into account while prescribing rational cutting modes. Practical implications: The obtained results make it possible to adjust the cutting modes, particularly the amount of feed, under the conditions of real equipment to ensure certain power characteristics of the cutting process to prevent overloads during cutting. This investigation benefits to the establishment of additional factors affecting oscillations in the cutting process. Originality/value: The probabilistic-statistical approach is used in this investigation in order to prove that the stochasticity of the feed rate affects the dispersion of the tangential cutting force component.

3

Adapting the Methods for Assessing a Water Quality when Normalizing the Pollutant Discharges in Ukraine to the Regulatory Requirements of the European Union

Yurasov Sergey, Safranov Tamerlan, Chugai Angelina, Kuryanova Svetlana, Artvykh Julia

Ecological Engineering & Environmental Technology

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2022

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Vol. 23, iss. 3

167--176

EN

The article presents general positions and features of a water quality assessment according to the norms of the European Union (EU), shows their difference from the national (Ukrainian) standards. It is proposed to improve the Ukrainian standards for assessing a water quality in accordance with the EU standards. On the example of the Danube and the Dniester rivers, a chronological variability of the water quality indicators is considered, the time trends of the indicators are approximated and the parameters of their distribution laws are determined. The following dependences are established: when approximating the distribution of the indicators it is better to use the lognormal law; an indicators time trend is reflected more accurately by the exponential dependence; a lognormal distribution of a trend-normalized indicator can be formally considered as one-parameter (one of the parameters – an average value of the logarithms of the normalized series – is zero). It is shown that for the previous period of time and in the future when normalizing the discharges of pollutants together with wastewater, a water quality assessment in the control points of the water bodies will meet the requirements of the EU standards on a frequency of exceeding the maximum permissible concentrations with the security which is equal to 5 or 10% depending on the purpose of the water body (5% – for fishery facilities, 10% – for drinking and recreational water use facilities).

4

Strength statistical characteristics of the isotropic materials with disc-shaped defects

Kvit R.

Journal of Applied Mathematics and Computational Mechanics

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2018

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Vol. 17, nr 4

25--34

EN

The expressions of the probabilities density distribution of failure loading for an elastic isotropic body under the action of a homogeneous axisymmetric loading are written. The disc-shaped cracks that do not interact with each other are uniformly distributed. The correlation for finding the most probable, mean value, dispersion and variation coefficient of failure loading are obtained. The dependence of the mentioned statistical strength characteristics on the type of applied loading, number of defects (body sizes) and structure material heterogeneity are investigated.

5

Dependence of trip length frequency distribution on characteristics of route network elements

Horbachov P., Svichynskyi S.

Archives of Transport

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2014

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Vol. 30, iss. 2

21--30

EN

The up-to-date methods of the demand modelling for municipal public transport (MPT) services are not perfect and they require an objective estimation, enhancement and improvement. These refinements are to take into account the functions of population allocation in modern cities. The possibility of the definition of population allocation functions on the basis of characteristics of public transport stops allocation, the regularities of distances between adjacent stops and distances between a pair of stops are investigated.

6

Some Remarks on Rings

Obojska L., O’Hara P.

Commentationes Mathematicae

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2010

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Vol. 50, [Z] 1

35-39

EN

Algebraic structures such as Rings, Fields, Boolean Algebras (Set Theory) and σ-Fields are well known and much has been written about them. In this paper we explore some properties of rings related to the distribution law. Specifically, we shall show that for rings there exists only one distribution law. Moreover, for the ring (Zp(p-1)n+, ź), where (p, n) = 1 there exist isomorphic groups (G, +), (H, ź), G,H⊆ Zp(p-1)n of the order (p - 1). Finally, we note that every ring (Zpn,+, ź) contains subfields mod(pn).