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Lipowa, Poland

Piotrowski E.W.,University of Biaystok | Sladkowski J.,University of Silesia | Syska J.,University of Silesia
Physica A: Statistical Mechanics and its Applications | Year: 2010

Two of the present authors have put forward a projective geometry based model of rational trading that implies a model for subjective demand/supply profiles if one considers closing of a position as a random process. We would like to present the analysis of a subjectivity in such trading models. In our model, the trader gets the maximal profit intensity when the probability of transaction is ∼0.5853. We also present a comparison with the model based on the Maximum of Entropy Principle. To the best of our knowledge, this is one of the first analyses that show a concrete situation in which trader profit optimal value is in the class of price-negotiating algorithms (strategies) resulting in non-monotonic demand (supply) curves of the Rest of the World (a collective opponent). Our model suggests that there might be a new class of rational trader strategies that (almost) neglects the supplydemand profile of the market. This class emerges when one tries to minimize the information that strategies reveal. © 2010 Elsevier B.V. All rights reserved. Source

Bezubik A.,University of Biaystok | Hrivnak J.,Czech Technical University | Pota S.,Czech Technical University
Journal of Physics: Conference Series | Year: 2013

The symmetric and antisymmetric exponential functions of two variables, based on the permutation group S2, are considered. Explicit formulas for the corresponding families of the orthogonal polynomials are derived and the properties of these orthogonal polynomials, such as their generating functions, continuous and discrete orthogonality, are presented. A connection of these polynomials with characteristic polynomials of some particular matrices is shown. © Published under licence by IOP Publishing Ltd. Source

Naumowicz A.,University of Biaystok
International Journal of Computer Mathematics | Year: 2010

In this paper, we report on the results of a case study aimed at selecting a prospective CA system to be used by the Mizar proof-checking system for performing computations of Grobner bases in Mizar's module responsible for equality calculus. A rudimentary interface has been implemented for each of considered CA systems, and tested in order to assess its feasibility in connection with the Mizar proof checker. Source

Trzesniewski T.,Jagiellonian University | Czerny B.,Copernicus Astronomical Center | Karas V.,Czech Republic Astronomical Institute | Pechaccek T.,Czech Republic Astronomical Institute | And 3 more authors.
Astronomy and Astrophysics | Year: 2011

Aims. We study the variability mechanism of active galactic nuclei (AGN) within the framework of the flare model. We examine the case of Seyfert/LINER galaxy NGC 4258, which is observed at high inclination angle and exhibits rapid fluctuations in its X-ray light curve. Methods. We construct a model light curve based on the assumption of magnetic flares localized in the equatorial plane and orbiting with Keplerian speed at each given radius. We calculate the level of variability as a function of the inclination of an observer, taking into account all effects of general relativity near a rotating supermassive black hole. Results. The variability level is a monotonic function of the source inclination. It rises more rapidly for larger values of the black hole spin (Kerr parameter a) and for steeper emissivity (index β of the radial profile). We compare the expected level of variability for the viewing angle 81.6 deg, as inferred for NGC 4258, with the case of moderate viewing angles of about 30 deg, which are typical of Seyfert type-1 galaxies. Conclusions. Highly inclined sources such as this one are particularly suitable to test the flare model because the orbital motion, Doppler boosting, and light bending are all expected to have maximum effect when the accretion disk is seen almost edge-on. The model is consistent with the NGC 4258 variability, where the obscuring material is thought to be localized mainly toward the equatorial plane rather than forming a geometrically thick torus. Once the intrinsic timescales of the flare duration are determined with higher precision, this kind of highly inclined objects with a precisely known mass of the black hole can be used to set independent constraints on the spin parameter. © 2011 ESO. Source

Gieniusz R.,University of Biaystok | Ulrichs H.,University of Munster | Bessonov V.D.,University of Biaystok | Bessonov V.D.,RAS Institute of Metal Physics | And 3 more authors.
Applied Physics Letters | Year: 2013

Single antidot as a passive point excitation source has been implemented to create caustic spin-wave beams in yttrium iron garnet film. Diffraction of surface magnetostatic spin waves from such antidot is investigated experimentally and theoretically. Our experimental results from Brillouin light scattering spectroscopy indicate that the diffraction beams, which manifest as reflection, extinction, and semicaustic lines, are tunable by the frequency and direction of the incident wave. Numerical calculations are in good agreement with the experimental findings and explain the directions of caustic beams caused by the diffraction. © 2013 American Institute of Physics. Source

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