2016
DOI: 10.1007/s10958-016-2712-6
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Bases and Dimension of Vector Spaces Over Lattices

Abstract: In this paper, we give a consistent presentation of dimension properties and properties of bases for vector spaces over distributive lattices. The bases consisting of join irreducible vectors are studied and their uniqueness is proved. Criteria for the following are proved: the set of join irreducible vectors is a generating set for a vector space; this set is a vector space basis; all bases contain the same number of vectors. A criterion of uniqueness for the basis is proved. The basis containing the greatest… Show more

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Cited by 3 publications
(2 citation statements)
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“…The calculated ionization potential (I) value was used as a control and compared with the experimental I value of melatonin, 7.70 eV [32]. To simulate aqueous and lipid environments, we use the continuum solvation model based on density (SMD) [33], used to simulate solvent effects (water, ε = 78.36 and pentyl ethanoate as a model for lipidic ones, ε = 4.73).…”
Section: Computational Methodologymentioning
confidence: 99%
“…The calculated ionization potential (I) value was used as a control and compared with the experimental I value of melatonin, 7.70 eV [32]. To simulate aqueous and lipid environments, we use the continuum solvation model based on density (SMD) [33], used to simulate solvent effects (water, ε = 78.36 and pentyl ethanoate as a model for lipidic ones, ε = 4.73).…”
Section: Computational Methodologymentioning
confidence: 99%
“…We then generated 110 configurations with the water molecule located at varying distances from the μ3-OH, μ3-O and Olinker interaction sites for which the interaction energies were calculated at the DFT level of theory and corrected for the basis set superposition error (BSSE) using the counterpoise method. 65,66 Finally, the partial charges of the atoms in the metal node and organic linkers were calculated using the Charge Model 5 (CM5) 67 as implemented in Gaussian 16 68 with the same DFT functional and basis set used for the single point energy refinements.…”
Section: Force Fieldmentioning
confidence: 99%