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An analytical technique for solving general linear integral equations of the second kind and its application in analysis of flash lamp control circuit

100%

Hetmaniok E. , Słota D. , Trawiński T. , Wituła R.

tom Vol. 62, nr 3

413--421

In this paper an application of the homotopy perturbation method for solving the general linear integral equations of the second kind is discussed. It is shown that under proper assumptions the considered equation possesses a unique solution and the series obtained in the homotopy perturbation method is convergent. The error of approximate solution, received by taking only the partial sum of the series, is also estimated. Moreover, there is presented an example of applying the method for approximate solution of an equation which has a practical application for charge calculation in supply circuit of the flash lamps used in cameras.

Variance and variation reduction technique in the quasi-Monte Carlo global illumination algorithm

63%

Kozankiewicz P.

tom Vol. 9, No. 1/2

289-296

The accuracy of the Monte Carlo and quasi-Monte Carlo algoriths depends on variance and variation in the sense of Hardy-Krause of the integral. This paper contains an error estimation of the quasi-Monte Carlo algorithm for some discontinuous functions that appear in radiosity and global illumination computation. Also an algorith that transforms the integral to reduce variance and variation is presented. It takes advantage of the BRDF properties and it can be used with diffuse and non-diffuse environments.

Overview and error interpretation of estimating fractal parameters of pore space based on computer image analysis

51%

Figiel M. , Figiel M.

Zeszyty Naukowe Instytutu Gospodarki Surowcami Mineralnymi Polskiej Akademii Nauk

2018