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Milewski J.,Pozna University of Technology | Banaszak G.,Adam Mickiewicz University | Lulek T.,Adam Mickiewicz University | Labuz M.,University of Rzeszow
Physica B: Condensed Matter

The exact solution of the eigenproblem of the Heisenberg Hamiltonian for the XXX model in the case of a magnetic ring with N=5 nodes is presented in a closed algebraic form. It is demonstrated that the eigenproblem itself is expressible within the extension of the prime field Q of rationals by the primitive fifth root of unity, whereas the associated Bethe parameters, i.e. pseudomomenta, phases of scattering, and spectral parameters, require some finite field extensions, such that the nonlinearity remains algebraic rather than transcendental. Classification of exact Bethe Ansatz eigenstates in terms of rigged string configurations is presented. © 2010 Elsevier B.V. All rights reserved. Source

Ulacha G.,West Pomeranian University of Technology | Stasinski R.,Pozna University of Technology
2012 Picture Coding Symposium, PCS 2012, Proceedings

In the paper optimization of lossless image coders based on Adaptive Neural Networks (AdNN) is addressed. Firstly, a detailed analysis of the influence of AdNN parameters on coder performance (average bitrate, time complexity) is done. Secondly, an improved technique denoted AdNN is proposed. Its main features are introduction of contexts, variable training window size, and post-processing by NLMS algorithm. Experiments show that indeed, the new method is better than others based on neural networks, and that it can even compete with the best existing image lossless coding algorithms. © 2012 IEEE. Source

Cempel C.,Pozna University of Technology
ICQR2MSE 2011 - Proceedings of 2011 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering

Working machine can be considered as an equivalent energy processor (EP) with internally limited energy dissipation. This means, we have limited machine lifetime and breakdown time, and the observed vibration symptoms of machine condition can be incorporated into EP model. Up to now one level of EP model have been in use, but using Singular Value Decomposition (SVD) we need two levels EP, and due to this it is possible to trace several independent faults of machine during its life. This possibility allow us to formulate concept of machine as a multilevel energy processor, and using SVD we determine the second sublevel of this multilevel EP. The present paper illustrates this way of thinking, and allows us to deepen our understanding of machine life and the wear on two levels; overall machine damage and particular functional faults as well. © 2011 IEEE. Source

Schmeidel E.,Pozna University of Technology | Zbaszyniak Z.,Pozna University of Technology
Computers and Mathematics with Applications

Using the technique of Darbo's fixed point theorem we investigate a nonlinear second order difference equation of the form Δ( rnΔ xn)= anf(xn+ 1) where x N0→R, a,r N0→R and fR→R is a continuous function. Additionally, the Sturm-Liouville difference equation is considered as a special case of the above equation. Sufficient conditions for the existence of an asymptotically periodic solution of this equation are obtained. An example illustrates the result. Next, the conditions under which this equation has no asymptotically periodic solutions are presented. © 2012 Elsevier Ltd. All rights reserved. Source

Morchao J.,Pozna University of Technology | Migda M.,Pozna University of Technology
Computers and Mathematics with Applications

We give sufficient conditions for the boundedness of all solutions of some classes of systems of difference equations with delays, by comparison of their norms with the solution of certain auxiliary scalar difference equations. © 2012 Elsevier Ltd. All rights reserved. Source

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