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Search results for: PERIODIC AND APERIODIC PERTURBATIONS
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Minimal number of periodic points for smooth self-maps of simply-connected manifolds
Open Research DataThe problem of finding the minimal number of periodic points in a given class of self-maps of a space is one of the central questions in periodic point theory. We consider a closed smooth connected and simply-connected manifold of dimension at least 4 and its self-map f. The topological invariant D_r[f] is equal to the minimal number of r-periodic points...
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Estimates for minimal number of periodic points for smooth self-maps of simply-connected manifolds
Open Research DataWe consider a closed smooth connected and simply-connected manifold of dimension at least 4 and its self-map f. The topological invariant Dr[f] is equal to the minimal number of r-periodic points in the smooth homotopy class of f. We assume that r is odd and all coefficients b(k) of so-called periodic expansion of Lefschetz numbers of iterations are...
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Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 4 and homology groups with the sum of ranks less or equal to10
Open Research DataAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of self-maps of a space. A closed smooth and simply-connected manifolds of dimension 4 and its self-maps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...
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Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 6 and homology groups with the sum of ranks less or equal to10
Open Research DataAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of self-maps of a space. A closed smooth and simply-connected manifolds of dimension 6 and its self-maps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...
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Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 5 and homology groups with the sum of ranks less or equal to10
Open Research DataAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of self-maps of a space. A closed smooth and simply-connected manifolds of dimension 5 and its self-maps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...
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Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 8 and homology groups with the sum of ranks less or equal to 10
Open Research DataAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of self-maps of a space. A closed smooth and simply-connected manifolds of dimension 8 and its self-maps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...
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Minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of simply-connected manifolds of dimension 7 and homology groups with the sum of ranks less or equal to10
Open Research DataAn important problem in periodic point theory is minimization of the number of periodic points with periods <= r in a given class of self-maps of a space. A closed smooth and simply-connected manifolds of dimension 7 and its self-maps f with periodic sequence of Lefschetz numbers are considered. The topological invariant Jr[f] is equal to the minimal...
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Database of the minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms of a connected sum of g real projective planes.
Open Research DataMorse–Smale diffeomorphisms, structurally stable and having relatively simple dynamics, constitute an important subclass of diffeomorphisms that were carefully studied during past decades. For a given Morse–Smale diffeomorphism one can consider “Minimal set of Lefschetz periods”, which provides the information about the set of periodic points of considered...
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The database of odd algebraic periods for quasi-unipotent self-maps of a space having the same homology group as the connected sum of g tori
Open Research DataThe dataset consists of 20 files indexed by numbers g=1,...,20. Each file provides sets of odd algebraic periods for all quasi-unipotent self-maps of a space having the same homology groups as the connected sum of g tori. Let us remark that each data set covers all algebraical restrictions that come from zeta functions for the sets of minimal Lefschetz...
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Tax preferences in PIT in numbers 2009-2015
Open Research DataThe follwoing data contain information prepared by the Ministry of Finance on the value of tax preferences by areas of support in Personal Income TAX (PIT) between 2009-2015.
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Database of the minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms of a connected sum of g tori
Open Research DataMorse–Smale diffeomorphisms, structurally stable and having relatively simple dynamics, constitute an important subclass of diffeomorphisms that have been carefully studied during past decades. For a given Morse–Smale diffeomorphism one can consider “Minimal set of Lefschetz periods”, which provides the information about the set of periodic points of...
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Framework for extracting rails and setting-out railway line axis based on UAV photogrammetric measurements
Open Research DataTechnical diagnostics enables assessing the current technical condition of a railway line and adjacent infrastructure, and to forecast its changes over a specific time horizon. One of its elements is the periodic monitoring of rail position and their geometry. The data set presents a new framework for the setting-out of a railway track axis. The process...
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Life expectancy and GDP per capita in selected countries (selected years)
Open Research DataThe dataset presents information on life expectancy in selected countries in 10-year periods. The list covers the years 1950-2020. The dataset also includes GDP values per capita in a given country in the years studied.
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Detection of the acoustic interferences during AFM operation
Open Research DataAtomic force microscopy is a particularly complicated surface imaging technique due to the large number of factors that affect the quality of the resulting images. They are obviously difficult and sometimes even impossible to control at the same time. One of such factors may even be the seismological location of the building or the influence of mechanical...
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Colvolutional calibration of AFM probe
Open Research DataAtomic force microscopy is based on the interaction of the examined surface with a probe of a pyramidal shape, tipped with a sharp end with a radius of curvature ranging from single nanometers to hundreds of nanometers. The resolution of the obtained image is of course dependent on the above-mentioned geometric size, and the resulting image is a convolutional...
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Database of algebraic periods of quasi-unipotent orientation-preserving homeomorphisms of orientable surfaces
Open Research DataThe set of algebraic periods of a map contains important information about periodic points and, in addition, is a homotopy invariant of the map. It is determined by indices of nonzero Dold coefficients which are computed purely algebraically from maps induced on homology groups of a considered space. In this dataset, we include for a given g=1,2,...,30,...
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Ocean mixed layer dynamics: high-resolution simulations of wind, wave and convective effects
Open Research DataThis dataset contains results of high-resolution numerical simulations of the ocean mixed layer (OML) forced by wind, waves and cooling from the atmosphere, i.e., under strongly turbulent, convective conditions. The goal is to provide detailed, three-dimensional information about OML circulation, turbulent kinetic energy, and temperature and salinity...
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Dynamics of S-unimodal maps used in population modeling.
Open Research DataS-unimodal maps are maps of the interval with negative Schwarzian derivative and having only one turning point (such that the map is increasing to the left of the turning point and decreasing to the right of it). Theory of S-unimodal maps is now a well-developed branch of discrete dynamical systems, including famous Singer theorem which implies existence...
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The short-term flicker severity level measured in the industrial power system supplying the rolling mill motors
Open Research DataThe dataset presents a short-term flicker severity level measured on the bus bars of the main switchgear of the industrial power network for the supply of rolling mills. The data were obtained during an experiment whose purpose was to determine a level of short-term and long-term flicker caused by voltage fluctuations. In the virtual application of...
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Simulation of the weight averaging of pulse frequency modulated sensor output signal
Open Research DataThe aim of the research is investigation of the efficiency of weight averaging of pulse frequency modulated signal. It was shown that from the point of view of the reduction of the sampling error the best are polynomial weighing functions, for which the maximum of this component error decreases proportionally to the appropriate power of the number of...