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Search results for: INVARIANT MANIFOLDS
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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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The Chow Ring of flag manifolds
Open Research DataSchubert calculus is the intersection theory of 19th century. Justifying this calculus is the content of the 15th problem of Hilbert. In the course to establish the foundation of algebraic geometry, Van der Vaerden and A. Weil attributed the problem to the determination of the chow ring of flag manifolds G/P, where G is a compact Lie group and P is...
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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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Harmonic Analysis
Open Research DataWe construct a decomposition of the identity operator on a Riemannian manifold M as a sum of smooth orthogonal projections subordinate to an open cover of M. This extends a decomposition on the real line by smooth orthogonal projection due to Coifman and Meyer (C. R. Acad. Sci. Paris, Sér. I Math., 312(3), 259–261 1991) and Auscher, Weiss, Wickerhauser...
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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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Testing an evaporator operation with a bifurcation manifold, condenser temperature 20 and evaporator temperature 85
Open Research DataThe experiment was conducted to test the evaporator operation. The heat exchanger was equipped with minigeometry (set of 50 parallel minichannels or single minigap). The studies were conducted for various mass flow rate of the working fluid and for various temperatures at the inlet of the evaporator. Accurate information about the test rig, the parameters...
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Testing an evaporator operation with a trapezoidal manifold, condenser temperature 90 and evaporator temperature 90
Open Research DataThe experiment was conducted to test the evaporator operation. The heat exchanger was equipped with minigeometry (set of 50 parallel minichannels or single minigap). The studies were conducted for various mass flow rate of the working fluid and for various temperatures at the inlet of the evaporator. Accurate information about the test rig, the parameters...
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Testing an evaporator operation with a bifurcation manifold, condenser temperature 20 and evaporator temperature 70
Open Research DataThe experiment was conducted to test the evaporator operation. The heat exchanger was equipped with minigeometry (set of 50 parallel minichannels or single minigap). The studies were conducted for various mass flow rate of the working fluid and for various temperatures at the inlet of the evaporator. Accurate information about the test rig, the parameters...
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Testing an evaporator operation with a rectangular manifold, condenser temperature 30 and evaporator temperature 90
Open Research DataThe experiment was conducted to test the evaporator operation. The heat exchanger was equipped with minigeometry (set of 50 parallel minichannels or single minigap). The studies were conducted for various mass flow rate of the working fluid and for various temperatures at the inlet of the evaporator. Accurate information about the test rig, the parameters...
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Testing an evaporator operation with a trapezoidal manifold, condenser temperature 70 and evaporator temperature 60
Open Research DataThe experiment was conducted to test the evaporator operation. The heat exchanger was equipped with minigeometry (set of 50 parallel minichannels or single minigap). The studies were conducted for various mass flow rate of the working fluid and for various temperatures at the inlet of the evaporator. Accurate information about the test rig, the parameters...
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Testing an evaporator operation with a bifurcation manifold, condenser temperature 20 and evaporator temperature 95
Open Research DataThe experiment was conducted to test the evaporator operation. The heat exchanger was equipped with minigeometry (set of 50 parallel minichannels or single minigap). The studies were conducted for various mass flow rate of the working fluid and for various temperatures at the inlet of the evaporator. Accurate information about the test rig, the parameters...
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Testing an evaporator operation with a bifurcation manifold, condenser temperature 20 and evaporator temperature 90
Open Research DataThe experiment was conducted to test the evaporator operation. The heat exchanger was equipped with minigeometry (set of 50 parallel minichannels or single minigap). The studies were conducted for various mass flow rate of the working fluid and for various temperatures at the inlet of the evaporator. Accurate information about the test rig, the parameters...
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Testing an evaporator operation with a concave manifold, condenser temperature 30, evaporator temperature 70 and preheater temperature 60
Open Research DataThe experiment was conducted to test the evaporator operation. The heat exchanger was equipped with minigeometry (set of 50 parallel minichannels or single minigap). The studies were conducted for various mass flow rate of the working fluid and for various temperatures at the inlet of the evaporator. Accurate information about the test rig, the parameters...
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Testing an evaporator operation with a concave manifold, condenser temperature 30, evaporator temperature 70 and preheater temperature 40
Open Research DataThe experiment was conducted to test the evaporator operation. The heat exchanger was equipped with minigeometry (set of 50 parallel minichannels or single minigap). The studies were conducted for various mass flow rate of the working fluid and for various temperatures at the inlet of the evaporator. Accurate information about the test rig, the parameters...
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Database of the estimations of the numbers of simplices of triangulation of some classical Lie groups
Open Research DataIt is know that any smooth manifold can be triangulated. The number of simplices of triangulation of a given manifold depends on its topological and combinatorial structure. The data consists of the lower bounds for the numbers of simplices of each dimension of any triangulation of classical Lie groups U(n), SU(n), Sp(n), and SO(n) for n up to 25. Each...
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Atomic force microscopy images of copper electrical contacts wear under the influence of friction
Open Research DataMeasurement of wear of copper electrical contacts under the influence of friction. Imaging in contact mode in the variant of scanning spreading resistance microscopy. Additionally, there are spectroscopic current-voltage curves showing local changes in electrical conductivity. NTEGRA Prima (NT-MDT) device. Probe NSG 01Pt.
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The structure of revenues of non-public universities in 2010 from didactic activity by sources of financing (in%)
Open Research DataIncome from teaching activities of non-public universities accounted for almost 1/5 of income from teaching activities of all types of universities. Non-public universities generated the highest revenues from fees for teaching classes, which accounted for over half of the revenues from this title in relation to all universities.The average cost of education...
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Initial geometries and MD trajectories of right- and left-handed G-quadruplexes
Open Research DataDataset contains initial geometries of 12 monomeric, 2-tetrad G-quadruplexes featuring three different loop lengths (T1, T2 and T3), adapted by the sequence GGTnGGTnGGTnGG where n=(1-3). For each loop length variant two directions of strand progression (clockwise (+) and anti-clockwise (-)) and two helicities (left-handed (LH) and right-handed (RH))...
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Vident-synth: a synthetic intra-oral video dataset for optical flow estimation
Open Research DataWe introduce Vident-synth, a large dataset of synthetic dental videos with corresponding ground truth forward and backward optical flows and occlusion masks. It can be used for:
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The surface of a fragment of the structure of an integrated circuit in the semi-contact mode.
Open Research DataThe surface of a fragment of the structure of an integrated circuit. Topographic measurements in the semi-contact mode. NTEGRA Prima (NT-MDT) device. NSG 01 probe.
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The scanning tunnelling micrographs of highly oriented pyrolytic graphite
Open Research DataThe dataset contains the results imaging of a sample of highly oriented pyrolytic graphite obtained using scanning tunneling microscopy. The above variant of scanning probe microscopy is one of the most convenient research techniques at atomic scales. The file contains images corresponding to increasing magnifications from the 1 um scale to a few nanometers....
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The dataset of simulations for optimal and non-optimal rotating receiver angles of multicoil dynamic wireless power transfer system
Open Research DataThe provided dataset is part of the simulation results shown in related journal paper "Optimal Rotating Receiver Angles Estimation for Multicoil Dynamic Wireless Power Transfer".
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AFM investigation of electrode fabricated by 3D printing
Open Research Data3D printing, also known as additive manufacturing, has enjoyed great interest in recent years due to the versatility of this method of producing various shapes and details. Due to the possibility of precise control of the shape and composition of the printed elements, the discussed technique can be widely used in electrochemistry, including electrochemical...
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Visualization of the surface of the Nafion membrane
Open Research DataFuel cells use the chemical energy of hydrogen or other fuels to produce electricity. If the fuel is hydrogen, the only products are electricity, water and heat. Fuel cells are unique in the variety of their potential applications, they can use a wide variety of fuels. They are also highly scalable devices that can power both cars and mobile phones....
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Data on LEGO sets release dates and retail prices combined with aftermarket transaction prices between June 2018 and June 2023.
Open Research DataThe dataset contains LEGO bricks sets item count and pricing history for AI-based set pricing prediction.
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A set of data constituting the basis for the publication entitled "Mitochondria dysfunction is one of the causes of diclofenac toxicity in the green alga Chlamydomonas reinhardtii"
Open Research DataNon-steroidal anti-inflammatory drugs (NSAIDs), such as diclofenac (DCF), form a significant group of environmental contaminants. When the toxic effects of DCF on plants are analyzed, authors often focus on photosynthesis, whilemitochondrial respiration is usually overlooked. Therefore, an in vivo investigation of plant mitochondria functioning under...