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  • 1
    Electronic Resource
    Electronic Resource
    Analysis of the topological dependency of the characteristic polynomial in its chebyshev expansion (1983)
    Springer
    Theoretical chemistry accounts 63 (1983), S. 473-495 
    Details
    ISSN: 1432-2234
    Keywords: Characteristic polynomial ; Chebyshev polynomial ; Topological index ; Structure factor ; Graph
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The structural dependency (effect of branching and cyclisation) of an alternative form, the Chebyshev expansion, for the characteristic polynomial were investigated systematically. Closed forms of the Chebyshev expansion for an arbitrary star graph and a bicentric tree graph were obtained in terms of the “structure factor” expressed as the linear combination of the “step-down operator”. Several theorems were also derived for non-tree graphs. Usefulness and effectiveness of the Chebyshev expansion are illustrated with a number of examples. Relation with the topological index (Z G ) was discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02394808
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Analysis of the topological dependency of the characteristic polynomial in its chebyshev expansion (1983)
    Springer
    Theoretical chemistry accounts 63 (1983), S. 473-495 
    Details
    ISSN: 1432-2234
    Keywords: Characteristic polynomial ; Chebyshev polynomial ; Topological index ; Structure factor ; Graph
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The structural dependency (effect of branching and cyclisation) of an alternative form, the Chebyshev expansion, for the characteristic polynomial were investigated systematically. Closed forms of the Chebyshev expansion for an arbitrary star graph and a bicentric tree graph were obtained in terms of the “structure factor” expressed as the linear combination of the “step-down operator”. Several theorems were also derived for non-tree graphs. Usefulness and effectiveness of the Chebyshev expansion are illustrated with a number of examples. Relation with the topological index (Z G ) was discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00552651
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Back-of-envelope derivation of the analytical formulas of the atomic wave functions of a D-dimensional atom (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 64 (1997), S. 35-42 
    Details
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A simple algebraic manipulation is presented for obtaining the analytical rectangular coordinate expressions of the atomic orbital wave functions with angular quantum number l of a D-dimensional atom, where no hyperspherical harmonics or any differential calculus is involved. A general expression of the D-dimensional f-orbitals is given which supplements the previously obtained result of D-dimensional d-orbitals.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 35-42, 1997
    Additional Material: 6 Tab.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
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