Development of the payment cards market in Poland in comparison with other European Union countries

The aim of this article is to identify and project trends in the development of the non-cash payment market in Poland in terms of the payment cards use. The study was carried out on the basis of data from the European Central Bank (ECB) for EU countries for the years 2000—2014. The space-time analogy method was used. In Poland, the dynamics of payments by card at POS terminals (in commercial outlets) is higher than the EU average. However, in terms of such measures as the number of payment cards per capita as well as the number of POS terminals and ATMs per 1 million inhabitants, the gap between Poland and the EU average is over 10 years. In Poland, market was similar to 20 EU countries and will maintain development trends at least until 2020.

ON THE DESIGN OF ADAPTIVE-BANDWIDTH ALL-DIGITAL PHASE-LOCKED LOOPS

The second-order adaptive-bandwidth all-digital phase-locked loop (ADB-ADPLL) is designed and analyzed by using a new design procedure. Based on a discrete-time analogy of a continuous-time PLL (CTPLL) with the z-transform, the design criterion of the ADB-ADPLL is derived and a design procedure is developed. Following the design criterion, the ADB-ADPLL can adapt its system parameters to balance the loop noise bandwidth and lock-in time. According to the design criterion, the ratio of the loop bandwidth to the reference input frequency can be maintained as a constant if the sampling frequency is a fixed multiplier of the input frequency. An example is given to illustrate the design procedure and simulation results are presented to validate the adaptive characteristics with respect to the phase noise and varying bands of input frequency.

Dissipation of intense vortices

In this article, we extend the space-time analogy shared by viscous vortices to generalize the dissipation of intense vortices Vatistas and Aboelkassem (Am. Inst. Aeronaut. Astronaut. J. 44, 912 (2006)). The main objective is to layout a mathematical algorithm that can be used to transform vortices into their dissipative phase or into a steady-state counterpart via a similarity transformation to Navier–Stokes equations. The method is applied to examine the time decay of eddies that belong to the Oseen-like concentrated type of viscous vortices. The steady-state Burgers’ vortex model was used to validate the transformation approach. This analysis shows that, upon variable transformation, Burgers’ vortex model has changed into the Oseen–Lamb class of decaying vortices. The approach is simple, general, and applicable to all kinds of viscous incompressible vortices like those of Sullivan, Rott, Bellamy-Knights, Vatistas, and Scully.

SNAP-BACK REPELLERS AND CHAOTIC TRAVELING WAVES IN ONE-DIMENSIONAL CELLULAR NEURAL NETWORKS

In 1998, Chen et al. [1998] found an error in Marotto's paper [1978]. It was pointed out by them that the existence of an expanding fixed point z of a map F in Br( z ), the ball of radius r with center at z does not necessarily imply that F is expanding in Br( z ). Subsequent efforts (see e.g. [Chen et al., 1998; Lin et al., 2002; Li & Chen, 2003]) in fixing the problems have some discrepancies since they only give conditions for which F is expanding "locally". In this paper, we give sufficient conditions so that F is "globally" expanding. This, in turn, gives more satisfying definitions of a snap-back repeller. We then use those results to show the existence of chaotic backward traveling waves in a discrete time analogy of one-dimensional Cellular Neural Networks (CNNs). Some computer evidence of chaotic traveling waves is also given.