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Search results for: Lie group
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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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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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A Hopf type theorem for equivariant local maps
PublicationWe study otopy classes of equivariant local maps and prove a Hopf type theorem for such maps in the case of a real finite-dimensional orthogonal representation of a compact Lie group.
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General solution of quantum mechanical equations of motion with time-dependent Hamiltonians: A Lie algebraic approach
PublicationThe unitary operators U(t), describing the quantum time evolution of systems with a time-dependent Hamiltonian, can be constructed in an explicit manner using the method of time-dependent invariants. We clarify the role of Lie-algebraic techniques in this context and elaborate the theory for SU(2) and SU(1,1). In these cases we give explicit formulae for obtaining general solutions from special ones. We show that the constructions...
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Equivariant Morse equation
PublicationThe paper is concerned with the Morse equation for flows in a representation of a compact Lie group. As a consequence of this equation we give a relationship between the equivariant Conley index of an isolated invariant set of the flow given by x˙ = − ∇f(x) and the gradient equivariant degree of ∇f. Some multiplicity results are also presented.
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The Hopf type theorem for equivariant gradient local maps
PublicationWe construct a degree-type otopy invariant for equivariant gradient local maps in the case of a real finite-dimensional orthogonal representation of a compact Lie group. We prove that the invariant establishes a bijection between the set of equivariant gradient otopy classes and the direct sum of countably many copies of Z.
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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
PublicationConsider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient...
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The equivariant spectral flow and bifurcation of periodic solutions of Hamiltonian systems
PublicationWe define a spectral flow for paths of selfadjoint Fredholm operators that are equivariant under the orthogonal action of a compact Lie group as an element of the representation ring of the latter. This G-equivariant spectral flow shares all common properties of the integer valued classical spectral flow, and it can be non-trivial even if the classical spectral flow vanishes. Our main theorem uses the G-equivariant spectral flow...
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''Povery islands'' - a study on poverty concentration across nations
PublicationPoverty problems, its definition and measurement aspects, constitute a broadly identified discussion. However, there are some widely recognized poverty definitions and statistics, but the detailed overview still remains not clearly visible. There are many economies where the poverty problems lie in the very centre of policy makers` strategies. Also there exist many international statistic databases where some poverty data are reviled....
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The Perception of an Entrepreneur’s Structural, Relational and Cognitive Social Capital among Young People in Poland - An Exploratory Study
PublicationThe goal of the current paper is to verify how an entrepreneur’s structural, relational and cognitive social capital levels are perceived by young people in Poland. The research involved a group of 374 undergraduate business students from a Polish university as participants. Participants completed a survey on entrepreneurial cognitions. It was found that participants assess the level of an entrepreneur’s social capital as relatively...
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9-Cyano-10-methylacridinium hydrogen dinitrate
PublicationThe title compound, C15H11N2+·HN2O6−, crystallizes in the monoclinic space group C2/c with four molecules in the unit cell. The planar 9-cyano-10-methylacridinium cations lie on crystallographic twofold axes and are arranged in layers, almost perpendicular to the ac plane, in such a way that neighbouring molecules are positioned in a `head-to-tail' manner. These cations and the hydrogen dinitrate anions are linked through C—H⋯O...
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Marek Czachor prof. dr hab.
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Topological invariants for equivariant flows: Conley index and degree
PublicationAbout forty years have passed since Charles Conley defined the homotopy index. Thereby, he generalized the ideas that go back to the calculus of variations work of Marston Morse. Within this long time the Conley index has proved to be a valuable tool in nonlinear analysis and dynamical systems. A significant development of applied methods has been observed. Later, the index theory has evolved to cover such areas as discrete dynamical...
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How to stop salami science: promotion of healthy trends in publishing behavior
PublicationThe career of scientists often depends on the number of their published works. This fact leads to the overproduction of low quality papers burying the important articles and making the knowledge less accessible. One of the methods to counteract these negative aspects might lie in the promotion of healthy trends in publishing behavior. In the present work, the theoretical analysis of a new bibliometric measure is presented, and...
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Tagged images with LEGO bricks part 2
Open Research DataThe data set conatins tagged images conatining LEGO bricks used for traning LEGO bricks detecting network. The images contain random number of the same LEGO bricks on white background. Only the whole bricks are labeled.
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Crystallization of space: Space-time fractals from fractal arithmetic
PublicationFractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to the fractal in question, and one can formulate classical and quantum physics within the fractal set. In particular, fractals in space-time can be generated by means of homogeneous spaces associated...
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Studies of the mechanism of metal metal dusting of 10CrMo9-10 steel after 10 years of operation in trhe semi-regenerative catalytic reformer
PublicationThe study showed that metal dusting mechanism of 10CrMo9-10 steel operated in industrial environment differs from models developed in laboratories. Significant differences lie in the fact that the models developed in laboratories only assume the formation of metastable carbide M3C, while studies have shown that the formation of M3C carbides is associated with the transformation of primary carbides and in the next stage is preceded...
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237Np Mössbauer effect study on NpFeAsO
PublicationWe report 237Np Mössbauer measurements on NpFeAsO. The Np atoms were found to occupy only one crystallographic site. The value of the isomer shift (δ ∼ 9.1 mm s−1 versus NpAl2) indicates a 5f4 electronic configuration (Np3+ ions). The magnetic ordering of the Np sublattice below 60 K is established and the saturated ordered magnetic moment is determined to be 1.73μB at 3.6 K. The unique set of hyperfine parameters exclude a modulated...
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INVESTIGATIONS OF THE EMISSION CHARACTERISTICS OF A DUAL-FUEL GAS TURBINE COMBUSTION CHAMBER OPERATING SIMULTANEOUSLY ON LIQUID AND GASEOUS FUELS
PublicationT his study is dedicated to investigations of the working process in a dual-fuel low-emission combustion chamber for a floating vessel’s gas turbine. As the object of the research, a low-emission gas turbine combustion chamber with partial premixing of fuel and air inside the outer and inner radial-axial swirls was chosen. The method of the research is based on the numerical solution of the system of differential...
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Tagged images with LEGO bricks
Open Research DataThe data set conatins tagged images conatining LEGO bricks used for traning LEGO bricks detecting network. The dataset contains two types of images:
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Decision-Making Models of the Human-Operator as an Element of the Socio-Technical Systems
PublicationThe authors of the chapter proved that the fundamental intellectual processes, which lie on the basis of decision-making behavior of the human-operator, could be identified on the bases on the analogies with the devices (elements). The basic intellectual processes of the Rational decision-making models can be adequately identified by the transient processes of the PID-controller; the intellectual processes of the Bounded Rationality...
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Computational methods for calculation of binding free energy for ligand-receptor complexes
PublicationAccurate description of the molecular complexes energetic influence is required for understanding of many biological functions carried out by proteins. Therefore, estimation of binding free energy for ligand-receptor complexes is of highest importance for structure-based ligand design and drug discovery approaches.Experimental methods of determination of difference in Gibbs'es free energy have many limitations. Thus, computational...
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On extending open source IMS platform for integrated IPTV and VoIP services over IPv6
PublicationEven when IMS is the most popular platform for multimedia services, the open versions of IMS ecosystem are lacking in specified functionalities for IPTVv6 and VoIPv6 services. In this paper, we extend current client and server open source software in order to provide reliability and security to these multimedia services. As a part of our work the IMS architecture for conferencing system with proposed mechanisms to improve system...
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Bifractal receiver operating characteristic curves: a formula for generating receiver operating characteristic curves in credit-scoring contexts
PublicationThis paper formulates a mathematical model for generating receiver operating characteristic (ROC) curves without underlying data. Credit scoring practitioners know that the Gini coefficient usually drops if it is only calculated on cases above the cutoff. This fact is not a mathematical necessity, however, as it is theoretically possible to get an ROC curve that keeps the same Gini coefficient no matter how big a share of lowest...
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Theory versus experiment for vacuum Rabi oscillations in lossy cavities. II. Direct test of uniqueness of vacuum
PublicationThe paper continues the analysis of vacuum Rabi oscillations we started in part I [Phys. Rev. A 79, 033836 (2009)]. Here we concentrate on experimental consequences for cavity QED of two different classes of representations of harmonic-oscillator Lie algebras. The zero-temperature master equation, derived in part I for irreducible representations of the algebra, is reformulated in a reducible representation that models electromagnetic...
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Reasons for Implementing Movement in Kinetic Architecture
PublicationThe paper gives insights into different forms of movement in contemporary architecture and examines them based on the reasons for their implementation. The main objective of the paper is to determine: the degree to which the complexity of kinematic architecture results from functional and spatial needs and what other motivations there are. The method adopted to investigate these questions involves theoretical studies and comparative analyses...
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Rozwój Pucka, Kartuz i Nowego Dworu Gdańskiego w latach 2005-2013 = The development of Puck, Kartuzy and Nowy Dwór Gdański In the years 2005-2013
PublicationNa terenie województwa pomorskiego znajdują się 42 miasta. Wśród nich 28 to miejscowości o liczbie do 20 000 mieszkańców. Stanowią one 66% wszystkich miast województwa. Według danych GUS na 2006 rok mieszka w nich 16% całkowitej liczby jego miejskiej ludności.W najbliższym sąsiedztwie Gdańska położone są trzy miasteczka o liczbie ludności w przedziale od 10 000 do 20 000. Są nimi: Puck, Kartuzy i Nowy Dwór Gdański. Choć są one...
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BODIPY‐Perylene Charge Transfer Compounds; Sensitizers for Triplet‐Triplet Annihilation Up‐conversion
PublicationBODIPY heterochromophores, asymmetrically substituted with perylene and/or iodine at the 2 and 6 positions were prepared and investigated as sensitizers for triplet-triplet annihilation up conversion (TTA-UC). Single-crystal X-ray crystallographic analyses show that the torsion angle between BODIPY and perylene units lie between 73.54 and 74.51, though they are not orthogonal. Both compounds show intense, charge transfer absorption...
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Two-spinors, oscillator algebras, and qubits: aspects of manifestly covariant approach to relativistic quantum information
PublicationThe first part of the paper reviews applications of 2-spinor methods to relativistic qubits (analogies between tetrads in Minkowski space and 2-qubit states, qubits defined by means of null directions and their role for elimination of the Peres-Scudo-Terno phenomenon, advantages and disadvantages of relativistic polarization operators defined by the Pauli-Lubanski vector, manifestly covariant approach to unitary representations...
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Dendron to Central Core S1–S1 and S2–Sn (n>1) Energy Transfers in Artificial Special Pairs Containing Dendrimers with Limited Numbers of Conformations
PublicationTwo dendrimers consisting of a cofacial free-base bisporphyrin held by a biphenylene spacer and functionalized with 4-benzeneoxomethane (5-(4-benzene)tri-10,15,20-(4-n-octylbenzene)zinc(II)porphyrin) using either five or six of the six available meso-positions, have been synthesized and characterized as models for the antenna effect in Photosystems I and II. The presence of the short linkers, -CH2O-, and long C8H17 soluble side...
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Medium-sized cyclic bis(anisylphosphonothioyl)- disulfanes and their corresponding cyclic sulfane-structures and most characteristic reactions
PublicationCyclic 8-, 9-, 10-, and 12-membered bis(anisylphosphonothioyl)disulfanes were synthesized. Next, structurally related 7 to 9-membered cis and trans sulfanes were isolated as a result of sulfur atom extrusion from the parent cyclic disulfanes. The results of the desulfurization of the disulfanes were compared to the results obtained for desulfurization of the respective bis(anisylphosphodithioates). Cyclic disulfanes predominantly...
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Structural properties of hydration shell around various conformations of simple polypeptides
PublicationIn this paper we investigate structural properties of water within the solvation shell around the peptide core created by a well-defined conformation of polypeptide chain. The following secondary structures are investigated: linear (straight chain), and three helices PII (polyproline-like), 310, and α. We propose using the two-particle contribution to entropy as a rational measure of the water structural ordering within the solvation...