Natural Vector Spaces (inward power and Minkowski norm of a Natural Vector, Natural Boolean Hypercubes) and a Fermat’s Last Theorem conjecture
In order to use the structure and operations of Molecular Similarity semispaces, Natural Vector Semispaces are considered in this study as vector spaces defined over the set of natural numbers, with zero added if necessary. The complete sum and inward power of a vector, defined as basic tools in Qua...
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| Published in | Journal of mathematical chemistry Vol. 55; no. 4; pp. 914 - 940 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
01.04.2017
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0259-9791 1572-8897 |
| DOI | 10.1007/s10910-016-0708-6 |
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| Abstract | In order to use the structure and operations of Molecular Similarity semispaces, Natural Vector Semispaces are considered in this study as vector spaces defined over the set of natural numbers, with zero added if necessary. The complete sum and inward power of a vector, defined as basic tools in Quantum Molecular Similarity, are now applied to a Natural Vector to describe Minkowski norms in these vector spaces. The structure and behavior of the Minkowski norm of Natural Vector inward powers and the Boolean Hypercube vertex translation into natural numbers are further used to conjecture a plausible general set up of Fermat’s Last Theorem. |
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| AbstractList | In order to use the structure and operations of Molecular Similarity semispaces, Natural Vector Semispaces are considered in this study as vector spaces defined over the set of natural numbers, with zero added if necessary. The complete sum and inward power of a vector, defined as basic tools in Quantum Molecular Similarity, are now applied to a Natural Vector to describe Minkowski norms in these vector spaces. The structure and behavior of the Minkowski norm of Natural Vector inward powers and the Boolean Hypercube vertex translation into natural numbers are further used to conjecture a plausible general set up of Fermat’s Last Theorem. |
| Author | Carbó-Dorca, Ramon |
| Author_xml | – sequence: 1 givenname: Ramon orcidid: 0000-0002-9219-0686 surname: Carbó-Dorca fullname: Carbó-Dorca, Ramon email: ramoncarbodorca@gmail.com organization: Secció de Química Quàntica i Matemàtica, Centre Europeu de Recerca Teòrica, Universitat de Girona |
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| Keywords | Inward vector powers Minkowski norms Fermat’s Last Theorem Fermat Natural Vectors Quantum molecular similarity Fermat discrete probability distributions Complete vector sums Natural Vector Semispaces |
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| References_xml | – reference: Carbó-DorcaRJ. Math. Chem.20033322724410.1023/A:1024742724706 – reference: Carbó-DorcaRJ. Math. Chem.19972214314710.1023/A:1019123914357 – reference: CarbóRBesalúEJ. Math. Chem.19931333134210.1007/BF01165573 – reference: CarbóRCalabuigBInt. J. Quant. Chem.1992421681169310.1002/qua.560420607 – reference: CarbóRCalabuigBJ. Chem. Inf. Comp. Sci.19923260060610.1021/ci00010a005 – reference: R. Carbó, B. Calabuig, in Chapter 6 ofMolecular Similarity ed. by M.A. Johnson, G.M. Maggiora. Molecular Similarity and Quantum Chemistry (Wiley, New York, 1990) – reference: Carbó-DorcaRJ. Mol. Struct. Teochem.2001537415410.1016/S0166-1280(00)00661-8 – reference: See, for instance: http://www.mersenne.org/primes/ – reference: G. Shimura, Y. Taniyama; Complex multiplication of Abelian varieties and its applications to number theory. Math. Soc. Jpn. (1961) – reference: Carbó-DorcaRJ. Math. Chem.2016541798180910.1007/s10910-016-0649-0 – reference: L. Euler, Vollständige Anleitung zur Algebra. R. Acad. Sci. St. Petersburg (1770) – reference: Carbó-DorcaRJ. Math. Chem.20002735737610.1023/A:1018832008106 – reference: Carbó-DorcaRJ. Math. Chem2016545171 – reference: R. Carbó-Dorca; Adv. Mol. Simil. 2, 43–72. (1998) (Editors: R. Carbó, P.G. Mezey, JAI Press Inc. Greenwich (Conn.)) – reference: Carbó-DorcaRBarragánDWIREs Comput. Mol. Sci.2015538040410.1002/wcms.1223 – reference: R. Carbó-Dorca, A. Gallegos, in Encyclopedia of Complexity and Systems Science, ed. R. Meyers. Quantum Similarity and Quantum QSPR (QQSPR). Entry: 176, vol. 8. (Springer, New York, 2009), p. 7422–7480 – reference: http://mathworld.wolfram.com/EulersSumofPowersConjecture.html – reference: R. Carbó, Ll. Leida, M. Arnau, Int. J. Quant. Chem. 17, 1185–1189 (1980) – reference: T. Gowers (ed.), The Princeton Companoin to Mathematics (Princeton Univ. Press, Princeton, Oxford, 2008) – reference: Carbó-DorcaRJ. Math. 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| Title | Natural Vector Spaces (inward power and Minkowski norm of a Natural Vector, Natural Boolean Hypercubes) and a Fermat’s Last Theorem conjecture |
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