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Open Research Data
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Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0, γ^(1/p)].
Open Research DataPresented dataset is a result of the convergence analysis of the Mickens-type, nonlinear, finite-difference discretization of a generalized Burgers–Huxley partial differential equation. The generalized Burgers–Huxley equation is a diffusive partial differential equation with nonlinear advection and diffusion. The boundary problem for this equation possesses...
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Electronic transition dipole moment functions of the fourth singlet Sigma gerade plus state of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the fourth singlet Sigma gerade plus (4sSg+) state have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the five ETDMFs have been obtained by the nonrelativistic multireference...
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Electronic transition dipole moment functions of the second singlet Sigma gerade plus state of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the second singlet Sigma gerade plus (2sSg+) state have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the five ETDMFs have been obtained by the nonrelativistic multireference...
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Electronic transition dipole moment functions of the fifth singlet Sigma gerade plus state of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the fifth singlet Sigma gerade plus (5sSg+) state have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the five ETDMFs have been obtained by the nonrelativistic multireference...
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Electronic transition dipole moment functions of the fifth triplet Sigma ungerade plus state of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the fifth triplet Sigma ungerade plus (5tSu+) state have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the five ETDMFs have been obtained by the nonrelativistic multireference...
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Electronic transition dipole moment functions of the first singlet Sigma gerade plus state of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the first singlet Sigma gerade plus (1sSg+) state have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the five ETDMFs have been obtained by the nonrelativistic multireference...
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Electronic transition dipole moment functions of the first triplet Sigma ungerade plus state of the Lithium dimer
Open Research DataElectronic transition dipole moment functions (ETDMF) of the first triplet Sigma ungerade plus (1tSu+) state have been calculated for the Lithium dimer. ETDMFs are needed in understanding processes like photodissociation, photoassociation, cooling, and trapping of molecules. The results of the five ETDMFs have been obtained by the nonrelativistic multireference...
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Adiabatic potential energy curves of the singlet Pi and Delta gerade states of the Lithium dimer
Open Research DataAdiabatic potential energy curves of the singlet Pi and Delta gerade states have been calculated for the Lithium dimer. The results of the three excited states of the symmetries singlet Pi and Delta gerade have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing the interaction...
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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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Adiabatic potential energy curves of the triplet Sigma ungerade plus states of the Lithium dimer
Open Research DataAdiabatic potential energy curves of the triplet Sigma ungerade plus states have been calculated for the Lithium dimer. The results of the five excited states of the symmetry triplet Sigma ungerade plus have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing the interaction...
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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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Adiabatic potential energy curves of the triplet Pi gerade states of the Lithium dimer
Open Research DataAdiabatic potential energy curves of the triplet Pi gerade states have been calculated for the Lithium dimer. The results of the two excited states of the symmetry triplet Pi gerade have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing the interaction of valence electrons...
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Adiabatic potential energy curves of the singlet Sigma gerade plus states of the Lithium dimer
Open Research DataAdiabatic potential energy curves of the singlet Sigma gerade plus states have been calculated for the Lithium dimer. The results of the ground state and three excited states of the symmetry singlet Sigma gerade plus have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing...
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Adiabatic potential energy curves of the singlet Sigma ungerade plus states of the Lithium dimer
Open Research DataAdiabatic potential energy curves of the singlet Sigma ungerade plus states have been calculated for the Lithium dimer. The results of the three excited states of the symmetry singlet Sigma ungerade plus have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing the interaction...
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Adiabatic potential energy curves of the triplet Sigma gerade plus states of the Lithium dimer
Open Research DataAdiabatic potential energy curves of the triplet Sigma gerade plus states have been calculated for the Lithium dimer. The results of the three excited states of the symmetry triplet Sigma gerade plus have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing the interaction...
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Adiabatic potential energy curves of the triplet Pi and Delta ungerade states of the Lithium dimer
Open Research DataAdiabatic potential energy curves of the triplet Pi and Delta ungerade states have been calculated for the Lithium dimer. The results of the three excited states of the symmetries triplet Pi and Delta ungerade have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing the interaction...
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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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Adiabatic potential energy curves of the singlet Pi ungerade states of the Lithium dimer
Open Research DataAdiabatic potential energy curves of the singlet Pi ungerade states have been calculated for the Lithium dimer. The results of the two excited states of the symmetry singlet Pi ungerade have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing the interaction of valence electrons...
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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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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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Dataset of non-isomorphic graphs of the coloring types (K3,Km;n), 2<m<7, 1<n<R(3,m)
Open Research DataFor K3 and Km graphs, a coloring type (K3,Km;n) is such an edge coloring of the full Kn graph, which does not have the K3 subgraph in the first color (representing by no edges in the graph) or the Km subgraph in the second color (representing by edges in the graph).The Ramsey number R(3,m) is the smallest natural number n such that for any edge coloring...
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Potential energy curve, rovibrational energies and nuclear wave functions of 2 singlet Pi state in KLi dimer
Open Research DataThis data sets contains potential energy curve, energy levels and nuclear wave functions of rovibrational states of KLi dimer in 2 singlet Pi electronic state. Potential energy curve (PEC) for the electronic state was calculated in the Born-Oppenheimer approximation by the means of effective core potentials and MRCI method. Nuclear wave functions and...
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Data obtained by computation for X-ray focusing using oriented Gaussian beams
Open Research DataThe propagation of X-ray waves through an optical system consisting of several X-ray refractive lenses is considered. Gaussian beams are exact solutions of the paraxial equation. The Helmholtz equation describes the propagation of a monochromatic electromagnetic wave. Since the widths of the beams are much larger than the wavelength of X-rays, Gaussian...
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A Fortran-95 algorithm to solve the three-dimensional Higgs boson equation in the de Sitter space-time
Open Research DataA numerically efficient finite-difference technique for the solution of a fractional extension of the Higgs boson equation in the de Sitter space-time is designed. The model under investigation is a multidimensional equation with Riesz fractional derivatives of orders in (0,1)U(1,2], which considers a generalized potential and a time-dependent diffusion...
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Data on solutions of Hes1 system
Open Research DataHes1 protein (hairy and enhancer of split 1) belongs to the helix-loop-helix (bHLH) family of transcription proteins, i.e. DNA-binding proteins in the promoter region or in another region where regulation of transcription processes occurs. The database collects data on solutions of the Hes1 systems with multiple binding sites and the dimer formation...
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Dataset of non-isomorphic graphs of the coloring types (K4,Km-e;n), 2<m<5, 1<n<R(K4,Km-e)
Open Research DataFor K4 and Km-e graphs, a coloring type (K4,Km-e;n) is such an edge coloring of the full Kn graph, which does not have the K4 subgraph in the first color (representing by no edges in the graph) or the Km-e subgraph in the second color (representing by edges in the graph). Km-e means the full Km graph with one edge removed.The Ramsey number R(K4,Km-e)...
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Database of the thermal ablation model
Open Research DataThermal ablation is a low invasive technique which eliminates cancerous tissue using high temperature. The presented database was used to show the temperature distribution for t=600[s] in two cases: when the value of the thermal conductivity of tissue k(x;T) is constant and for the variable k(x;T). In addition, using these data we showed the difference...
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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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Dataset of non-isomorphic graphs of the coloring types (Km,K3-e;n), 4<m<8, 1<n<R(Km,K3-e)
Open Research DataFor Km and K3-e graphs, a coloring type (Km,K3-e;n) is such an edge coloring of the full Kn graph, which does not have the Km subgraph in the first color (representing by no edges in the graph) or the K3-e subgraph in the second color (representing by edges in the graph). K3-e means the full Km graph with one edge removed.The Ramsey number R(Km,K3-e)...
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Dataset of non-isomorphic graphs of the coloring types (K4,K4;n), 1<n<R(4,4)
Open Research DataFor K4 graph, a coloring type (K4,K4;n) is such an edge coloring of the full Kn graph, which does not have the K4 subgraph in the first color (representing by no edges in the graph) or the K4 subgraph in the second color (representing by edges in the graph).The Ramsey number R(4,4) is the smallest natural number n such that for any edge coloring of...
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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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Dataset of non-isomorphic graphs of the coloring types (K3,Km-e;n), 2<m<7, 1<n<R(K3,Km-e).
Open Research DataFor K3 and Km-e graphs, a coloring type (K3,Km-e;n) is such an edge coloring of the full Kn graph, which does not have the K3 subgraph in the first color (representing by no edges in the graph) or the Km-e subgraph in the second color (representing by edges in the graph). Km-e means the full Km graph with one edge removed.The Ramsey number R(K3,Km-e)...
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An facile Fortran-95 algorithm to simulate complex instabilities in three-dimensional hyperbolic systems
Open Research DataIt is well know that the simulation of fractional systems is a difficult task from all points of view. In particular, the computer implementation of numerical algorithms to simulate fractional systems of partial differential equations in three dimensions is a hard task which has no been solved satisfactorily. Here, we provide a Fortran-95 code to solve...
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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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Adiabatic potential energy curves of the 3, 4 and 5^1Σ^+ excited states of LiCs molecule
Open Research DataAdiabatic potential energy curves of the 3, 4, and 5^1Σ^+ excited states have been calculated for the LiCs molecule. The results of three excited states of the symmetry Σ^+ have been obtained by the nonrelativistic multireference configuration interaction (MRCI) method used with pseudopotentials describing the interaction of valence electrons with atomic...
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Computing dynamical curlicues
Open Research DataA curlicue is a piece-wise linear curve in the complex plane which can be generated by an arbitrary sequence of real numbers u_n. It can be interpreted as a trajectory of a particle in the plane which starts in the origin at time t=0 and moves with a constant velocity, changing its direction at instances t=0,1,2,3,..., where the new direction is given...
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Stochastic intervals for the family of quadratic maps
Open Research DataNumerical analysis of chaotic dynamics is a challenging task. The one-parameter families of logistic maps and closely related quadratic maps f_a(x)=a-x^2 are well-known examples of such dynamical systems. Determining parameter values that yield stochastic-like dynamics is especially difficult, because although this set has positive Lebesgue measure,...
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Database of the illustrative simulations of the nonstandard approximation of the generalized Burgers–Huxley equation
Open Research DataThe presented dataset is a result of numerical analysis of a generalized Burgers–Huxley partial differential equation. An analyzed diffusive partial differential equation consist with nonlinear advection and reaction. The reaction term is a generalized form of the reaction law of the Hodgkin–Huxley model, while the advection is a generalized form of...
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Potential energy curves of NaRb dimer
Open Research DataThis data presents potential energy curves of NaRb dimer in Hund's case (a). Calculated using Born-Oppenheimer approximation with scalar relativistic effects are included via large effective core potentials. Core polarization potentials and MRCI method is used to describe electron correlation. Dataset consists of 18 potential energy curves of ground...
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A collection of directed graphs for the minimum cycle mean weight computation
Open Research DataThis dataset contains definitions of the 16 directed graphs with weighted edges that were described in the following paper: Paweł Pilarczyk, A space-efficient algorithm for computing the minimum cycle mean in a directed graph, Journal of Mathematics and Computer Science, 20 (2020), no. 4, 349--355, DOI: 10.22436/jmcs.020.04.08, URL: http://dx.doi.org/10.22436/jmcs.020.04.08 These...
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Data obtained by numerical simulation for X-ray focusing using a finite difference method
Open Research DataThe propagation of X-ray waves through an optical system consisting of many X-ray refractive lenses is considered. For solving the problem for an electromagnetic wave, a finite-difference method is applied.
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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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Potential energy surfaces of the low-lying electronic states of the Li+LiCs system
Open Research DataThis data presents potential energy surfaces of Li atom interacting with LiCs dimer for the ground and first excited state. They were calculated using effective core potentials and MRCI method and include relativistic effects. The interatomic distance in the dimer is kept constant and equal to experimental value of 6.931704423 bohrs (3.6681 A). Energy...
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The set of 22 sessions of 14-channel eeg signals recorded during watching pictures
Open Research DataThe data were collected in order to perform research on the possibility of controlling the content displayed on the monitor screen using human emotional states extracted from EEG signals. The dataset contains recordings of 14-channel EEG signals collected from 10 persons within 22 sessions, during which 45 different random photos taken from the ImageNet...
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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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Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0,1].
Open Research DataThe presented dataset is a result of the convergence analysis of the Mickens-type, nonlinear, finite-difference discretization of a generalized Burgers–Huxley partial differential equation.