×
Carbó-Dorca, Ramon

Definition of norm coherent generalized scalar products and quantum similarity. (English) Zbl 1200.81077

J. Math. Chem. 47, No. 1, 331-344 (2010).
Summary: Complete matrix sums and inward products are employed within vector spaces to define a generalized scalar product, searching at the same time for coherent definitions with the related general order norms. The theoretical background developed in this way permits to connect such mathematical constructs with quantum similarity and QSPR.

Cited in 11 Documents

MSC:

81Q99 General mathematical topics and methods in quantum theory
46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.)

Keywords:

generalized scalar products; generalized norms; inward matrixproducts; vector semispaces; quantum similarity; quantum QSPR
Cite Review PDF
Full Text: DOI

References:

[1] Berberian S.K.: Introduction to Hilbert Space. Oxford University Press, New York (1961) · Zbl 0121.09302
[2] Brody D.C., Hook D.W.: J. Phys. A Math. Theor. 42, 1–33 (2009)
[3] Bultinck P., Carbó-Dorca R.: J. Math. Chem. 36, 191–200 (2004) · Zbl 1052.81669 · doi:10.1023/B:JOMC.0000038793.21806.65
[4] P. Bultinck, X. Gironés, R. Carbó-Dorca, Rev. Comput. Chem., vol. 21, eds. by K.B. Lipkowitz, R. Larter, T. Cundari (Wiley, Hoboken, 2005), pp. 127–207
[5] Carbó R., Calabuig B., Besalú E., Martínez A.: Mol. Eng. 2, 43–64 (1992) · doi:10.1007/BF00999522
[6] Carbó R., Leyda L., Arnau M.: Int. J. Quantum Chem. 17, 1185–1189 (1980) · doi:10.1002/qua.560170612
[7] Carbó-Dorca, R. (eds): Advances in Molecular Similarity, vol. 2. JAI Press, Greenwich pp. 43–72 (1998) · Zbl 0931.92034
[8] Carbó-Dorca R.: J. Mol. Struct. (Teochem) 537, 41–54 (2001) · doi:10.1016/S0166-1280(00)00661-8
[9] Carbó-Dorca R.: J. Math. Chem. 32, 201–223 (2002) · Zbl 1027.81512 · doi:10.1023/A:1021250527289
[10] Carbó-Dorca R.: J. Math. Chem. 36, 241–260 (2004) · Zbl 1172.81334 · doi:10.1023/B:JOMC.0000044222.02974.ef
[11] Carbó-Dorca R.: SAR QSAR Environ. Res. 18, 265–284 (2007) · doi:10.1080/10629360701304113
[12] Carbó-Dorca R.: J. Math. Chem. 44, 228–234 (2008) · Zbl 1192.81409 · doi:10.1007/s10910-007-9305-z
[13] R. Carbó-Dorca, A. Gallegos, ”Quantum Similarity and Quantum QSPR (QQSPR)” Enciclopaedia of Complexity and System Science. (Springer, Berlin, 2009 in press)
[14] Carbó-Dorca R., Van Damme S.: Int. J. Quantum. Chem. 108, 1721–1734 (2007) · doi:10.1002/qua.21703
[15] Carbó-Dorca R., Gallegos A., Sánchez A.J.: J. Comput. Chem. 30, 1146–1159 (2009) · doi:10.1002/jcc.21145
[16] Gröbner W., Hofreiter N.: Integraltafel (zweiter teil) Bestimmte Integrale. Springer, Wien (1966) · Zbl 0142.13504
[17] Horn R.A., Johnson C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1985) · Zbl 0576.15001
[18] Shilov G.E.: Linear Algebra. Dover, New York (1977)
[19] Sneath P.H.A., Sokal R.R.: Numerical Taxonomy. W.H. Freeman, San Francisco (1973)
[20] Vinogradov, I.M. (eds): Encyclopaedia of Mathematics, vol. 5. Kluwer, Dordrecht (1990)
[21] Vinogradov, I.M. (eds): Encyclopaedia of Mathematics, vol. 7. Kluwer, Dordrecht (1990)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.