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Search results for: FREDHOLM MAP
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Analysis of dynamics of a map-based neuron model via Lorenz maps
PublicationModeling nerve cells can facilitate formulating hypotheses about their real behavior and improve understanding of their functioning. In this paper, we study a discrete neuron model introduced by Courbage et al. [Chaos 17, 043109 (2007)], where the originally piecewise linear function defining voltage dynamics is replaced by a cubic polynomial, with an additional parameter responsible for varying the slope. Showing that on a large...
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Monotone method to Volterra and Fredholm integral equations with deviating arguments
PublicationPraca dotyczy problemów istnienia rozwiązań równań całkowych typu Volterry i Fredholma z odchylonymi argumentami. Podano warunki dostateczne na istnienie rozwiązań w odpowiedniej klasie. Pewne nierówności całkowe typu opóźnionego są również przedmiotem badań.
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Simulating propagation of coherent light in random media using the Fredholm type integral equation
PublicationStudying propagation of light in random scattering materials is important for both basic and applied research. Such studies often require usage of numerical method for simulating behavior of light beams in random media. However, if such simulations require consideration of coherence properties of light, they may become a complex numerical problems. There are well established methods for simulating multiple scattering of light (e.g....
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Connection of microcosm with macrocosm in Max Scheler's philosophy: man, logos and ethos
PublicationW eseju pokazałem znaczenie mikrokosmicznego wymiaru w ludzkim personalnym życiu. To jest w świecie Zachodu kompleksowa próba, aby uchwycić związek "mikrokosmosu" z "makrokosmosem w filozoficznym dziele Maxa Schelera. Następnie uwypukliłem, że z racji jego powiązania jako pojęcia "mikrokosmosu" z kwestią kształcenia, wtedy w indywidualnej ludzkiej osobie pojęcie to osiąga "prawo obywatelstwa" w Schelerowskiej...
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An absorbing set for the Chialvo map
PublicationThe classical Chialvo model, introduced in 1995, is one of the most important models that describe single neuron dynamics. In order to conduct effective numerical analysis of this model, it is necessary to obtain a rigorous estimate for the maximal bounded invariant set. We discuss this problem, and we correct and improve the results obtained by Courbage and Nekorkin (2010). In particular, we provide an explicit formula for an...
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Inducing a map on homology from a correspondence
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Shadowing is generic---a continuous map case
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E-learning in tourism and hospitality: A map
PublicationThe impact of information and communication technologies (ICT) on tourism and hospitality industries has been widely recognized and investigated as a one of the major changes within the domains in the last decade: new ways of communicating with prospective tourists and new ways of purchasing products arisen are now part of the industries’ everyday life. Poor attention has been paid so far to the role played by new media in education...
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Journal of Map & Geography Libraries
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Firing map of an almost periodic input function
PublicationIn mathematical biology and the theory of electric networks the firing map of an integrate-and-fire system is a notion of importance. In order to prove useful properties of this map authors of previous papers assumed that the stimulus function f of the system ẋ = f(t,x) is continuous and usually periodic in the time variable. In this work we show that the required properties of the firing map for the simplified model ẋ = f(t) still...