Quantum polyhedra, definitions, statistics and the construction of a collective quantum similarity index

DOI10.1007/s10910-014-0419-9zbMath1310.81023OpenAlexW2091981389WikidataQ62511097 ScholiaQ62511097MaRDI QIDQ2263691

Ramon Carbó-Dorca

Publication date: 19 March 2015

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-014-0419-9

zbMATH Keywords

quantum similaritydensity functions (DF)quantum object sets (QOS)DF origin shiftsgeneralized collective distancesmultimolecular polyhedra (MP)QP variancequantum polyhedra (QP)shape functions (shf)

Mathematics Subject Classification ID

Molecular physics (81V55) Molecular structure (graph-theoretic methods, methods of differential topology, etc.) (92E10) Quantum state spaces, operational and probabilistic concepts (81P16)

Related Items (17)

A study on the centroid vector of a polyhedron ⋮ \(N\)-dimensional Boolean hypercubes and the Goldbach conjecture ⋮ Analysis of solutions of time-dependent Schrödinger equation of a particle trapped in a spherical box ⋮ On the nature of the collective quantum mechanical description of molecular atoms and bonds ⋮ Time vectors and particle swarms defined as polyhedra in spherically enfolded spaces ⋮ Universal transformation and non-linear connection between experimental and calculated property vectors in QSPR ⋮ A quantum similarity discussion about Einstein-Podolsky-Rosen (EPR) paradox in Gaussian enfolded spaces ⋮ Topological characterization of statistically clustered networks for molecular similarity analysis ⋮ Quantum similarity and QSPR in Euclidean-, and Minkowskian-Banach spaces ⋮ Least squares estimation of unknown molecular properties and quantum QSPR fundamental equation ⋮ An isometric representation problem in quantum multimolecular polyhedra and similarity ⋮ An isometric representation problem in quantum multimolecular polyhedra and similarity: II: Synisometry ⋮ A theorem on the Gram matrix of a polyhedron ⋮ Natural vector spaces (inward power and Minkowski norm of a natural vector, natural Boolean hypercubes) and a Fermat's last theorem conjecture ⋮ Hypercubes defined on \(n\)-ary sets, the Erdös-Faber-Lovász conjecture on graph coloring, and the description spaces of polypeptides and RNA ⋮ Average energy and quantum similarity of a time dependent quantum system subject to Pöschl-Teller potential ⋮ Shadows' hypercube, vector spaces, and non-linear optimization of QSPR procedures

Cites Work

• Shells, point cloud huts, generalized scalar products, cosines and similarity tensor representations in vector semispaces
• Scaled Euclidean distances: a general dissimilarity index with a suitably defined geometrical foundation
• Multimolecular polyhedra and QSPR
• Molecular quantum similarity measures in Minkowski metric vector semispaces
• Quantum similarity and discrete representation of molecular sets
• Quantum similarity, volume functions and generalized Carbó indices
• Centroid origin shift of quantum object sets and molecular point clouds description and element comparisons
• Definition of norm coherent generalized scalar products and quantum similarity
• On quantum molecular similarity measures (QMSM) and indices (QMSI)
• Quantum similarity matrices column set as holograms of DF molecular point clouds
• Collective Euclidian distances and quantum similarity
• Mathematical aspects of the LCAO MO first order density function. V: Centroid shifting of MO shape functions basis set, properties and applications
• Variational principle, Hohenberg-Kohn theorem, and density function origin shifts

This page was built for publication: Quantum polyhedra, definitions, statistics and the construction of a collective quantum similarity index