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Extended Sobolev and Hilbert spaces and approximate stationary solutions for electronic systems within the non-linear Schrödinger equation
ArticleAbstract: The definition of Sobolev spaces, which has already been shown to be a convenient way to set up thePalabras claves:Extended Hilbert spaces, Kinetic energy distribution, N-electron wavefunctions, Nested sums formalism, Non-linear Schrödinger equation, Quantum self-similarity measures, Sobolev spacesAutores:Besalu E., Ramón Carbö-D̈orcaFuentes:scopusExtending molecular similarity to energy surfaces: Boltzmann similarity measures and indices
ArticleAbstract: Maxwell-Boltzmann statistics provides the adequate mathematical background allowing to define similaPalabras claves:Autores:Besalu E., Ramón Carbö-D̈orcaFuentes:scopusFunction extended spaces
ArticleAbstract: Extended function spaces defined over the real field are defined as vector spaces made by the CartesPalabras claves:Density function (DF), Function extended spaces (FES), Holographic electronic density theorem (HEDT), Holographic general function theorem (HGFT), Molecular fields, Quantum Similarity, Stereographic projection of quantum chemical functionsAutores:Besalu E., Ramón Carbö-D̈orcaFuentes:scopusGeneralized one-electron spin functions and self-similarity measures
ArticleAbstract: A simple method for construction of eigenfunctions of one-electron spin angular momentum operators fPalabras claves:Coupling of angular momenta, One-electron spin functions, Quantum similarity measures, spin densityAutores:Besalu E., Karwowski J., Ramón Carbö-D̈orcaFuentes:scopusGeneration of molecular fields, quantum similarity measures and related questions
ArticleAbstract: A straightforward discussion on how to generate molecular fields is developed within the postulatesPalabras claves:Density functions, Electrostatic molecular potential, Quantum molecular fields, Quantum similarity fields, Quantum similarity measuresAutores:Besalu E., Ramón Carbö-D̈orcaFuentes:scopusGeometry of n-dimensional Euclidean space Gaussian enfoldments
ArticleAbstract: In this study the geometric features and relationships of the points contained into a Gaussian enfolPalabras claves:Enfoldment points, Gaussian enfoldment of n-dimensional Euclidean spaces, Generalized distances and angles in Gaussian enfoldments, Geometry of Gaussian enfoldment, Holographic electronic density theorem (HEDT), Multivariate Gaussian functionsAutores:Besalu E., Ramón Carbö-D̈orcaFuentes:scopusDefinition and quantum chemical applications of nested summation symbols and logical functions: Pedagogical artificial intelligence devices for formulae writing, sequential programming and automatic parallel implementation
ArticleAbstract:Palabras claves:Autores:Besalu E., Ramón Carbö-D̈orcaFuentes:scopusCentroid origin shift of quantum object sets and molecular point clouds description and element comparisons
ArticleAbstract: Shifting the origin of a known quantum object set (QOS) or of some discrete molecular point cloud (MPalabras claves:Centroid origin shift, Density functions, Molecular dissimilarity Euclidian distances, Molecular point clouds (MPC), Molecular point huts (MPH), Molecular similarity Carbó indices (CI), Quantum object sets (QOS), Quantum Similarity, Quantum similarity matrices (SM), Shape functions, Space of descriptors, Space of moleculesAutores:Besalu E., Ramón Carbö-D̈orcaFuentes:scopusEMP as a similarity measure: A geometric point of view
ArticleAbstract: Soft Coulomb potentials constructed by multiplying the classical potential by a Gaussian function (oPalabras claves:Density functions origin shift, Electrostatic molecular potentials (EMP), Similarity integrals, Soft coulomb potentials, Soft EMP, Soft EMP origin shiftAutores:Besalu E., Ramón Carbö-D̈orcaFuentes:scopusA Gaussian holographic theorem and the projection of electronic density functions into the surface of a sphere
ArticleAbstract: A theorem, associated to the holographic nature of general Gaussian functions, is employed to descriPalabras claves:ASA density functions, Electronic density functions (EDF), Gaussian holographic theorem, Projection of EDF into spherical surfacesAutores:Besalu E., Ramón Carbö-D̈orcaFuentes:scopus