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Iterations of homographic functions and recurrence equations involving a homographic function

100%

Górowski J. , Łomnicki A.

2015

tom 7

27-33

The formulas for the m-th iterate $(m \in N)$ of an arbitrary homographicfunction H are determined and the necessary and sufficient conditions for a solution ofthe equation $y_{m+1} = H(y_m)$, $m \in N$ to be an infinite n-periodic sequence are given. Based on the results from this paper one can easily determine some particular solutionsof the Babbage functional equation.

Interferential polychromatic filters based on the quasi-periodic one-dimensional generalized multilayer Thue - Morse structures

75%

Bouazzi Y. , Kanzari M.

Optica Applicata

2009

tom Vol. 39, nr 3

489-498

In this paper, a new type of optical filter using photonic band gap materials has been proposed. The optical filter was obtained by a combination of periodic H(LH)J and generalized Thue - Morse (GTM) quasi-periodic one-dimensional multilayer. We show that the whole structure H(LH)J[TM]PH(LH)J, where P is the repetition number of the GTM stack, has an interesting application as a polychromatic filter. However, the effect of the repetition number for producing an improved polychromatic filter is presented. So, switches like (on-on-off-off-on-on-…) have been found.

Okresowe badania emisji spalin samochodów osobowych z silnikami ZI

75%

Merkisz J. , Lijewski P. , Dobrzyński M. , Rymaniak Ł. , Ziółkowski A.

Combustion Engines

2013

tom R. 52, nr 3

740--744

W artykule przedstawiono wyniki badań emisji samochodów o dopuszczalnej masie całkowitej do 3,5 tony z silnikami ZI przeprowadzonych podczas badań okresowych dopuszczających pojazdy do ruchu. Zaprezentowane dane dotyczące stężeń związków szkodliwych spalin pozyskane zostały w czasie kontroli wybranej grupy pojazdów na Stacji Kontroli Pojazdów. Pomiary wykonywane były przy pomocy wieloskładnikowego analizatora spalin dla silników ZI firmy ATAL. Uzyskane wartości pozwoliły na opracowanie zależności dla silników spalinowych w trakcie stałych warunków pracy wynikających z konieczności zachowania procedury pomiarowej w czasie trwania okresowego badania technicznego.

The paper present the results of emission tests from cars with a maximum weight of up to 3.5 ton. of gasoline engines made during periodic inspection allowing vehicles to move. The presented data on the concentrations of harmful gases were collected during the inspection of a select group of vehicles in the Vehicle Inspection Station. The measurements were performed using a multi-gas analyzer for SI engines ATAL company. The values obtained allowed to develop according to internal combustion engines during regular working conditions resulting from the need to preserve the measurement procedure during the periodic technical inspection.

On different kinds of solutions to simplified modified form of a Camassa-Holm equation

51%

Gündoğdu H. , Gözükızıl Ö. F.

Journal of Applied Mathematics and Computational Mechanics

2019

tom Vol. 18, nr 2

31--40

In this research, our purpose is to investigate some types of solutions to a simplified modified form of the Camassa-Holm equation. The Jacobi elliptic function expansion method is applied to this equation. Then, a lot of travelling wave solutions are obtained. The derived solutions are in the form of Jacobi elliptic functions, hyperbolic functions, and trigonometric functions. Graphics of solutions are drawn in order to determine the types of the solutions. Furthermore, different kinds of solutions such as the singular kink wave solution, the kink wave solution, and the periodic solution are achieved.