Inward matrix product algebra and calculus as tools to construct space-time frames of arbitrary dimensions

Journal of Mathematical Chemistry

Volumn 30, Issue 2, 2001, Pages 227-245

  Carbó Dorca, Ramon ^a  

^a UNIVERSITY OF GIRONA   (Spain)

Author keywords

Classical mechanics in N dimensional spaces; Hypermatrix space time structures; Inward matrix derivation and integration; Inward matrix product; N dimensional time dependent schr dinger equation; Physical measures in N dimensional spaces

Indexed keywords

EID: 0035413418     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1017931905397     Document Type: Article

References (32)

1. K.D. Sen and R. Carbo-Dorca, J. Mol. Struct. (Theochem) 501-502 (2000) 173-176.
2. R. Carbo-Dorca, E. Besalu and X. Girones, Extended density functions, Adv. Quant. Chem. 38 (2001) 1-63.
3. R. Carbó-Dorca, Quantum Quantitative Structure-Activity Relationships (QQSAR): A comprehensive discussion based on inward matrix products, employed as a tool to find approximate solutions of strictly positive linear systems and providing a QSAR-Quantum Similarity Measures connection, in: Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000, Barcelona (11-14 September 2000) pp. 1-31.
4. A Fortran 95 connection: LF95 Language Reference, Lahey Computer Systems (Incline Village, NV, 1998)http://www.lahey.com
5. R. Carbó-Dorca, Int. J. Quant. Chem. 79 (2000) 163-177.
6. R. Carbó-Dorca, J. Math. Chem. 27 (2000) 357-376.
7. R. Carbó-Dorca, J. Mol. Struct. (Theochem) 537 (2001) 41-54.
8. I.M. Vinogradov (ed.), Enciclopaedia of Mathematics, Vol. 4 (Kluwer, Dordrecht, 1989).
9. R. Carbo and E. Besalu, Theoretical foundations of quantum similarity, in: Molecular Similarity and Reactivity: From Quantum Chemical to Phenomenological Approaches, ed. R. Carbo (Kluwer Academic Publishers, Amsterdam, 1995) pp. 3-30.
10. R. Carbo-Dorca, E. Besalu, Ll. Amat and X. Fradera, Quantum molecular similarity measures: Concepts, definitions and applications to QSAR, in: Advances in Molecular Similarity, Vol. 1, eds. R. Carbo-Dorca and P.G. Mezey (JAI Press, London, 1996) pp. 1-42.
11. R. Carbo-Dorca, Ll. Amat, E. Besalu and M. Lobato, Quantum molecular similarity, in: Advances in Molecular Similarity, Vol. 2, eds. R. Carbo-Dorca and P. G. Mezey (JAI Press, London, 1998) pp. 1-42.
12. R. Carbo-Dorca, Ll. Amat, E. Besalu, X. Girones and D. Robert, Quantum mechanical origin of QSAR: Theory and applications, J. Mol. Struct. (Theochem) 504, Special Issue on Computational Medicinal Chemistry (2000) 181-228.
13. R. Carbó-Dorca, Ll. Amat, E. Besalú, X. Girones and D. Robert, Quantum molecular similarity: Theory and applications to the evaluation of molecular properties, biological activities and toxicity, in: Fundamentals of Molecular Similarity, eds. R. Carbó-Dorca, X. Gironés and P.G. Mezey (Kluwer Academic/Plenum Publishers, New York, 2001) pp. 187-320.
14. C. Roos, T. Terlaky and J.-P. Vial. Theory and Algorithms for Linear Optimization (Wiley, New York, 1997).
15. R.A. Horn and Ch.A. Johnsonm, Matrix Analysis (Cambridge University Press, Cambridge, 1985).
16. R. Carbo and E. Besalu, J. Math. Chem. 13 (1993) 331-342.
17. R. Carbo and E. Besalu, Comput. Chem. 18 (1994) 117-126.
18. R. Carbo and E. Besalu, J. Math. Chem. 18 (1995) 37-72.
19. R. Carbo and E. Besalu, Applications of nested summation symbols to quantum chemistry: Formalism and programming techniques, in: Strategies and Applications in Quantum Chemistry, eds. Y. Ellinger and M. Defranceschi (Kluwer Academic Publishers, Dordrecht, 1996) pp. 229-248.
20. R. Carbo-Dorca, Fuzzy sets and Boolean tagged sets, vector semispaces and convex sets, quantum similarity measures and ASA density functions, diagonal vector spaces and quantum chemistry, in: Advances in Molecular Similarity, Vol. 2, eds. R. Carbo-Dorca and P.G. Mezey (JAI Press, London, 1998) pp. 43-71.
21. R. Carbo-Dorca, J. Math. Chem. 22 (1997) 143-147.
22. R. Carbo-Dorca, J. Math. Chem. 23 (1998) 353-364.
23. R. Carbo-Dorca, J. Math. Chem. 23 (1998) 365-375.
24. R. Carbo-Dorca and E. Besalu, J. Mol. Struct. (Theochem) 451 (1998) 11-23.
25. H. Eyring, J. Walter and G.E. Kimball, Quantum Chemistry (Wiley, New York, 1940).
26. L. Pauling and E.B. Wilson, Jr., Introduction to Quantum Mechanics (Dover, New York, 1985).
27. G. Joos, Theoretical Physics (Dover Publications, New York, 1986).
28. G. Stephenson and C.W. Kilmister, Special Relativity for Physicists (Dover, New York, 1986).
29. G. Wentzel, Quantum Theory of Fields (Interscience Publishers, New York, 1949).
30. W.D. McComb, The Physics of Fluid Turbulence, Oxford Science Publications (Clarendon Press, Oxford, 2000).
31. W. Pauli, Theory of Relativity (Dover, New York, 1981).
32. M. Kriele, Spacetime (Springer Verlag, Berlin, 1999).