Wyszukiwarka
prof. dr hab. Grzegorz Graff
Zatrudnienie
- Kierownik Studiów Doktoranckich w Wydział Fizyki Technicznej i Matematyki Stosowanej
- Kierownik zakładu w Zakład Równań Różniczkowych i Zastosowań Matematyki
- Profesor w Instytut Matematyki Stosowanej
Obszary badawcze
Publikacje
Filtry
wszystkich: 64
Katalog Publikacji
Rok 2011
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Electrophysiological features in patients with sinus node dysfunction and vasovagal syncope
PublikacjaThe aim of the study was to identify electrophysiological criteria that can be used for identification of patients with sinus node dysfunction and concurrent vasovagal syncope.
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Fixed point indices of iterated smooth maps in arbitrary dimension
PublikacjaWe give a complete description of possible sequences ofindices of iterations of f at an isolated fixed point, answering inaffirmative the Chow, Mallet-Paret and Yorke conjecture posed in[S.N. Chow, J. Mallet-Parret, J.A. Yorke, A periodic point index whichis a bifurcation invariant, in: Geometric Dynamics, Rio de Janeiro,1981, in: Lecture Notes in Math., vol. 1007, Springer, Berlin, 1983,pp. 109-131].
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Local fixed point indices of iterations of planar maps
PublikacjaW artykule podana zostaje postać indeksów iteracji dla pewnej klasy odwzorowań planarnych. Podstawowymi narzędziami stosowanym w pracy są liczba Nielsena i indeks Conleya.
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Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds
PublikacjaLet M be a smooth closed simply-connected 4-dimensional manifold, f be a smooth self-map of M with fast grow of Lefschetz numbers and r be a product of different primes. The authors calculate the invariant equal to the minimal number of r-periodic points in the smooth homotopy class of f.
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Minimizing the number of periodic points for smooth maps. Non-simply connected case
PublikacjaNiech f będzie gładkim odwzorowaniem zamkniętej rozmaitości o wymiarze wiekszym niż 2, a r ustaloną liczbą naturalną. W artykule zdefiniowany został niezmiennik topologiczny równy minimalnej liczbie punktów r-periodycznych w gładkiej klasie homotopii f.
Rok 2012
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Combinatorial scheme of finding minimal number of periodic points for smooth self-maps of simply connected manifolds
PublikacjaLet M be a closed smooth connected and simply connected manifold of dimension m at least 3, and let r be a fixed natural number. The topological invariant D^m_r [f], defined by the authors in [Forum Math. 21 (2009), 491-509], is equal to the minimal number of r-periodic points in the smooth homotopy class of f, a given self-map of M. In this paper, we present a general combinatorial scheme of computing D^m_r [f] for arbitrary dimension...
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Entropy measures of heart rate variability for short ECG datasets in patients with congestive heart failure
PublikacjaWe investigated the usefulness of entropy measures calculated for short ECG series in distinguishing healthy subjects from patients with congestive heart failure (CHF). Four entropy measures were tested: Approximate Entropy (ApEn), Sample Entropy (SampEn), Fuzzy Entropy (FuzzyEn) and Permutation Entropy (PE), each computed for ECG series of 1000, 500, 250 and 100 RR intervals. We found that with a reduction of the data set length...
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Entropy Measures of heart rate variability for short ECG datasets in patients with congestive heart failure
PublikacjaWe investigated the usefulness of entropy measures calculated for short ECG series in distinguishing healthy subjects from patients with congestive heart failure (CHF). Four entropy measures were tested: Approximate Entropy (ApEn), Sample Entropy (SampEn), Fuzzy Entropy (Fuzzy En) and Permutation Entropy (PE), each computed for ECG series of 1000, 500, 250 and 100 RR intervals. We found that with a reduction of the data set length...
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Estimation of the minimal number of periodic points for smooth self-maps of odd dimensional real projective spaces
PublikacjaLet f be a smooth self-map of a closed connected manifold of dimension m⩾3. The authors introduced in [G. Graff, J. Jezierski, Minimizing the number of periodic points for smooth maps. Non-simply connected case, Topology Appl. 158 (3) (2011) 276-290] the topological invariant NJD_r[f], where r is a fixed natural number, which is equal to the minimal number of r-periodic points in the smooth homotopy class of f. In this paper smooth...
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Lefschetz periodic point free self-maps of compact manifolds
PublikacjaLet f be a self-map of a compact connected manifold M. We characterize Lefschetz periodic point free continuous self-maps of M for several classes of manifolds and generalize the results of Guirao and Llibre [J.L.G. Guirao, J. Llibre, On the Lefschetz periodic point free continuous self-maps on connected compact manifolds,
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Lefschetz periodic point free self-maps of compact manifolds
PublikacjaLet f be a self-map of a compact connected manifold M. We characterize Lefschetz periodic point free continuous self-maps of M for several classes of manifolds and generalize the results of Guirao and Llibre [J.L.G. Guirao, J. Llibre, On the Lefschetz periodic point free continuous self-maps on connected compact manifolds, Topology Appl. 158 (16) (2011) 2165-2169].
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Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers
PublikacjaLet f be a smooth self-map of m-dimensional, m ≥ 4, smooth closed connected and simply-connected manifold, r a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math....
Rok 2013
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A Strategy to Locate Fixed Points and Global Perturbations of ODE’s: Mixing Topology with Metric Conditions
PublikacjaIn this paper we discuss a topological treatment for the planar system z' = f (t, z) + g(t, z) where f and g are T -periodic in time and g(t, z) is bounded. Namely, we study the effect of g(t, z) in two different frameworks: isochronous centers and time periodic systems having subharmonics. The main tool employed in the proofs consists of a topological strategy to locate fixed points in the class of orientation preserving embedding...
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O Centrum Zastosowań Matematyki
PublikacjaCentrum Zastosowań Matematyki to projekt realizowany w ramach Programu Operacyjnego Kapitał Ludzki wyłoniony w drodze konkursu zorganizowanego przez Narodowe Centrum Badań i Rozwoju.
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Ordinal pattern statistics for the assessment of heart rate variability
PublikacjaThe recognition of all main features of a healthy heart rhythm (the so-called sinus rhythm) is still one of the biggest challenges in contemporary cardiology. Recently the interesting physiological phenomenon of heart rate asymmetry has been observed. This phenomenon is related to unbalanced contributions of heart rate decelerations and accelerations to heart rate variability. In this paper we apply methods based on the concept...
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Reducing the number of periodic points in the smooth homotopy class of a self-map of a simply-connected manifold with periodic sequence of Lefschetz numbers
PublikacjaLet f be a smooth self-map of an m-dimensional (m >3) closed connected and simply-connected manifold such that the sequence of the Lefschetz num- bers of its iterations is periodic. For a fixed natural r we wish to minimize, in the smooth homotopy class, the number of periodic points with periods less than or equal to r. The resulting number is given by a topological invariant J[f] which is defned in combinatorial terms and is...
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Relationship between heart rate variability, blood pressure and arterial wall properties during air and oxygen breathing in healthy subjects
PublikacjaPrevious studies reported that normobaric hyperoxia influences heart rate, arterial pressure, cardiac output and systemic vascular resistance, but the mechanisms underlying these changes are still not fully understood. Several factors are considered including degeneration of endothelium-derived nitric oxide by reactive oxygen species, the impact of oxygen-free radicals on tissues and alterations of autonomic nervous system function....
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The Efficiency of Polish Stock Market: Ordinal Patterns Approach
PublikacjaZunino et al. analyzed the problem of discrimination of developed and emergent markets by the use of ordinal patterns methods: number of forbidden patterns and ordinal pattern probability distribution as a basis for entropy and statistical measure of complexity. In this paper we apply the same methodology for the analysis of Polish stock market (index WIG). The results indicate that Polish market belongs neither to developed, nor...
Rok 2014
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Network Approach to Increments of RR-intervals for Visualization of Dynamics of Cardiac Regulation
PublikacjaThe transition network for RR -increments is pre- sented in a directed and weighted graph, with vertices represent- ing RR -increments and edges corresponding to the order in a sequence of increments. The adjacency matrix and the transition matrix of this network provide a graphical tool which could be useful in the assessment of cardiac regulation. As an example, the method is applied in detecting differences between diurnal activity...
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Ordinal Pattern Statistics for RR Intervals during Head-Up Tilt Test in Patients with the History of Vasovagal Syncope
PublikacjaWe apply ordinal pattern analysis to quantify differences in distribution of patterns of length 3 and 4 in basal state and during head-up tilt test (HUTT) in patients with the history of syncope and positive (HUTT(+)) or negative (HUTT(-)) responses to the test. We identify the patterns related to prevalence of sympathetic or parasympathetic cardiac modulation as well as describe the relations between the response to the test and...
wyświetlono 4722 razy