Multidimensional objects

The one-dimensional potential curves depicted in Figures 1.1-1.3 represent the dissociation of diatomic molecules for which the potential V(Rab) depends only on the internuclear distance between atoms A and B. However, if one or both constituents are molecules, V is a multidimensional object, a so-called potential energy surface which depends on several (at least three) nuclear coordinates denoted by the vector Q = (Ql,Q2,Q3,---) (Margenau and Kestner 1969 Balint-Kurti 1974 Kuntz 1976 Schaefer III 1979 Kuntz 1979 Truhlar 1981 Salem 1982 Murrell et al. 1984 Hirst 1985 Levine and Bernstein 1987 ch.4 Hirst 1990 ch.3). The intramolecular and intermolecular forces, defined by... 

Langston, L. S. Heat Transfer from Multidimensional Objects Using One-Dimensional Solutions for Heat Loss, Int. J. Heat Mass Transfer, vol. 25, p. 149, 1982. 

Mapping allows the reduction of multidimensional objects to a space of different dimension. 

Distance-Based Similarity Measures Similarity measm-es determine the proximity (or distance) between two data objects. Multidimensional objects can be formalized as numerical vectors O, = oy = 1 data object and p is the number of dimensions for the data object Oy. Figure 5.1 provides an intuitive view of multidimensional data. The similarity between two objects can be measured by a distance function of corresponding vectors Oj and (. ... 

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