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1
Content available remote 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
Content available 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
Content available remote The adaptation of the cross validation aproach for RBF-based collocation methods
Krowiak A., Podgórski J.
Technical Transactions
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2017
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Vol. 7(114)
147--156
EN
The paper shows the adaptation of the cross validation approach, known from interpolation problems, for estimating the value of a shape parameter for radial basis functions. The latter are involved in two collocation techniques used on an unstructured grid to find approximate solution of differential equations. To obtain accurate results, the shape parameter should be chosen as a result of a trade-off between accuracy and conditioning of the system. The cross validation approach called "leave one out" takes these aspects into consideration. The numerical examples that summarize the investigations show the usefulness of the approach.
PL
W artykule pokazano adaptację algorytmu krzyżowego sprawdzania, znanego z zagadnień statystyki i interpolacji, do wyznaczenia wartości współczynnika kształtu w radialnych funkcjach bazowych. Funkcje te użyto w dwóch typach technik kolokacyjnych stosowanych na nieregularnej siatce do przybliżonego rozwiązywania równań różniczkowych. Aby otrzymać rezultaty o odpowiedniej dokładności, współczynnik kształtu powinien być dobrany na bazie kompromisu pomiędzy dokładnością a uwarunkowaniem układu równań. Przedstawiony algorytm, zwany "leave one out", bierze te aspekty pod uwagę. Podsumowaniem artykułu są numeryczne testy, które pokazują użyteczność tego podejścia.
4
Content available remote 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.
5
Content available 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.
6
Content available On the maximum likelihood estimator in the generalized beta regression model
Rydlewski J. P., Mielczarek D.
Opuscula Mathematica
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2012
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Vol. 32, no. 4
761-774
EN
The subject of this article is to present the beta – regression model, where we assume that one parameter in the model is described as a combination of algebraically independent continuous functions. The proposed beta model is useful when the dependent variable is continuous and restricted to the bounded interval. The parameters are obtained by maximum likelihood estimation. We prove that estimators are consistent and asymptotically normal.
7
Content available remote 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.
8
Content available A note on the maximum likelihood estimator in the gamma regression model
Rydlewski J. P.
Opuscula Mathematica
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2009
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Vol. 29, no. 3
305-312
EN
This paper considers a nonlinear regression model, in which the dependent variable has the gamma distribution. A model is considered in which the shape parameter of the random variable is the sum of continuous and algebraically independent functions. The paper proves that there is exactly one maximum likelihood estimator for the gamma regression model.
9
Content available remote Neuronowa analiza zagadnień symulacji częstości drgań własnych i identyfikacji parametrów geometrycznych łuków płaskich
Kłos M.
Zeszyty Naukowe Politechniki Rzeszowskiej. Budownictwo i Inżynieria Środowiska
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2007
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z. 45 {243}
103-112
PL
Zaproponowano zastosowanie sztucznych sieci neuronowych do symulacji częstości drgań własnych i identyfikacji parametrów geometrycznych łuku (rozpiętości, wyniosłości i wysokości przekroju poprzecznego). Zbiór danych wygenerowano za pomocą programu MES. W zagadnieniu odwrotnym wektor wejściowy składał się z sześciu pierwszych częstości własnych. Stwierdzono prawidłowość nieco niższej dokładności aproksymacji neuronowej w problemie odwrotnym oraz korzystny wpływ regularyzacji bayesowskiej na zmniejszenie liczby parametrów sieci w porównaniu z sieciami projektowanymi bez regularyzacji.
EN
This paper presents the possibility of application of Artificial Neural Networks in the simulation of eigenfrequencies and identification of shape parameters of arches (span, arch height and cross-section thickness). For the numerical simulation the models were updated by ANNs with input vectors consisting of shape parameters of arches. In the inverse problem the input vector is composed of the first six eigenfrequencies. The multilayer feed-forward networks and bayesian regularization were applied.
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