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1

Approximation of conic sections by weighted Lupaş post-quantum Bézier curves

Khan Asif, Iliyas Mohammad, Khan Khalid, Mursaleen Mohammad

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

328--342

EN

This paper deals with weighted Lupaş post-quantum Bernstein blending functions and Bézier curves constructed with the help of bases via (p,q) -integers. These blending functions form normalized totally positive bases. Due to the rational nature of weighted Lupaş post-quantum Bézier curves and positive weights, they help in investigating from geometric point of view. Their degree elevation properties and de Casteljau algorithm have been studied. It has been shown that quadratic weighted Lupaş post-quantum Bézier curves can represent conic sections in two-dimensional plane. Graphical analysis has been presented to discuss geometric interpretation of weight and conic section representation by weighted Lupaş post-quantum Bézier curves. This new generalized weighted Lupaş post-quantum Bézier curve provides better approximation and flexibility to a particular control point as well as control polygon due to extra parameter p and q in comparison to classical rational Bézier curves, Lupaş q -Bézier curves and weighted Lupaş q -Bézier curves.

2

Quantitative assessment of working conditions in the workplace

Cherniak Olena, Trishch Roman, Kim Nataliia, Ratajczak Sabina

Engineering Management in Production and Services

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2020

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Vol. 12, no. 2

99--106

EN

Indicators, different in terms of nature and grading scales, are used to recognise hazardous and harmful factors that affect human health. However, no single methodology is available for their assessment, and the variety of qualimetric assessment methods requires in-depth research, in part on optimality and efficiency. Therefore, this work aimed to conduct several scientific studies to obtain the results of the assessment in unified units of measurement, which would provide a generalised indicator of harmful factors at the workplace. The article proposes to use dependencies to assess indicators of harmful factors, considering the maximum, minimum, and optimal values as well as the shape parameter, the change of which produces various assessments in a dimensionless scale. A hierarchy analysis method was used to obtain reliable values with a small number of experts and determine the form parameter. These efforts resulted in the value of the overall index for harmful factors, which serves as grounds for decisions regarding further improvements in working conditions. The developed methodology was used to assess the safety of working conditions at a machine-building enterprise, and the results are presented in the article.

3

Application of an RBF blending interpolation method to problems with shocks

Harris M., Kassab A., Divo E.

Computer Assisted Methods in Engineering and Science

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2015

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Vol. 22, no. 3

229--241

EN

Radial basis functions (RBF) have become an area of research in recent years, especially in the use of solving partial differential equations (PDE). Radial basis functions have an impressive capability in interpolating scattered data, even for data with discontinuities. Although, for infinitely smooth radial basis functions such as the multi-quadrics and inverse multi-quadrics, the shape parameter must be chosen properly to obtain accurate approximations while avoiding ill-conditioning of the interpolating matrices. The optimum shape parameter can vary depending on the field, such as in locations of sharp gradients or shocks. Typically, the shape parameter is chosen to maintain a high conditioning number for the interpolation matrix, rendering the RBF smooth [1–10]. However, this strategy fails for a problem with a shock or sharp discontinuity. Instead, in such cases the conditioning number must be kept small. The focus of this work is then to demonstrate the use of RBF interpolation in the approximation of sharp gradients or shocks by use of a RBF blending interpolation approach. This RBF blending interpolation approach is used to maintain the optimum shape parameter depending on the field. The approach is able to sense gradients or shocks in the field and adjust the shape parameter accordingly to keep excellent accuracy. Presented in this work, is an explanation of the RBF blending interpolation methodology and testing of the RBF blending interpolation approach by solving the Burger’s equation using the virtual finite difference method.

4

Zastosowanie radialnych funkcji bazowych w interpolacji danych rozproszonych. Cz. 2

Borkowska D.

TTS Technika Transportu Szynowego

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2013

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R. 20, nr 10

2169--2174, CD

PL

Praca poświęcona jest zagadnieniu interpolacji rozproszonych danych przez radialne funkcje bazowe (RBF). W tej części artykułu, dla wybranej RBF, zaprezentowano metody wyboru parametru kształtu oraz przebadano jego wpływ na jakość interpolacji. Przedstawiona symulacja numeryczna potwierdza zależność dokładności interpolacji od parametru kształtu.

EN

The paper is devoted to the problem of radial basis function (RBF) interpolation from scattered data. In this part of the article the methods of choosing the shape parameter are presented and the impact which the shape parameter has on the error of interpolation is analyzed. A numerical experiment confirms that the shape parameter has great impact on the accuracy of the RBF interpolation.

5

A two-layered blood flow model of Bingham type non-Newtonian fluid

Das K., Jana S.

International Journal of Applied Mechanics and Engineering

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2012

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Vol. 17, no. 1

17-26

EN

In the present paper, a two layered blood flow model through a cylindrical tube of a Bingham type non-Newtonian fluid is considered. The relative coefficients of viscosity for peripheral and core layer are determined and their nature is shown graphically for different values of the maximum hematocrit, shape parameter, etc.

6

Ocena możliwości analitycznego opisu hydrogramu wezbrania

Dąbkowski S. L., Bodalski J.

Przegląd Naukowy Inżynieria i Kształtowanie Środowiska

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2008

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Vol. 17, No. 4

5--18

PL

Matematyczny opis kształtu hydrogramu wezbrania jest pożądany w analizach i w projektach wielu budowli i urządzeń wodnych, gdyż w połączeniu ze znajomością maksymalnego przepływu w czasie wezbrania umożliwia dokładniejsze scharakteryzowanie przebiegu wezbrania w czasie, objętości fali i innych jej parametrów. Adekwatność matematycznego opisu analizuje się w przedstawionej pracy rozpatrując równania w postaci bezwymiarowej podane w pracach Baptista i Michela (1990), McEnroe (1992), Strupczewskiego (1964) oraz typowy hydrogram SCS. Analizie poddano m.in. wpływ wartości parametrów równań na możliwość „dopasowania” opisu do hydrogramu rzeczywistego tak pod względem kształtu jak i wartości uzyskiwanych wielkości. Ocenę stopnia zgodności hydrogramu „opisanego” z rzeczywistym przeprowadzono stosując trzy miary zaproponowane w pracy Sarmy i in. (1973). Analizę przeprowadzono dla 8 hydrogramów pojedynczych ze zlewni o różnym charakterze.

EN

A mathematical description of flood hydrograph is desirable in analyses and designs of many hydraulic structures because together with the maximum flow in time of tense flow it enables to determine more exactly, the volume of flood and it other parameters. The adequacy of the mathematical description is analyzed in the presented work considering equations in dimensionless equation given in the work of Baptist and Michel (1990), McEnroe (1992), Strupczewski (1964) as well as a typical hydrograph SCS. In the analysis the influence of a value of equation parameters on the possibility of “adaptation” of the description to the real hydrograph both in shape and the value of calculated values. The compatibility assessment of the calculated hydrograph with the real one was conducted applying three measures proposed in the work of Sarmy at al. (1973). The analysis was conducted for 8 individual hydrographs from drainage areas of a different character.