Delaunay variables

We consider first a body of negligible mass moving around a body of finite mass m in an elliptic orbit. It can be proved (Murray and Dermott, 1999) that the action-angle variables of the two-body problem in the inertial frame, in the plane, are the Delaunay variables defined by... 

Since we employed the concept of electronegativity combined with Delaunay tciiellation of protein-ligand complexes we termed these unique characteristics of the protein-ligand interface the EnTess descriptors We have applied the variable selection A -nearest neighbor (A NN) QSAR approach to establish correlations between binding affinities and the EnTess descriptors as described below. 

The variable-metric total-energy approach [12] is adopted here for the matrix. As illustrated in Fig. 1, the periodic system is described by the scaling matrix [13,14] H = [ABC], where A, B, and C are the overall system s continuation vectors. Two kinds of nodal points are specified in the matrix One (x ) on the inclusion boundary and the other (x ) in the continuum (throughout this text, vectors are written as column matrices). For convenience, the scaled coordinates [13,14] (s and s ) are chosen as degrees of freedom via x = Hs and x = Hs. These nodal points are used as vertices of a periodic network of Delaunay tetrahedra. The Delaunay network uniquely tessellates space without overlaps or fissures the circumsphere of the four nodal points of any tetrahedron does not contain another nodal point of the system [15,16]. For each tetrahedron p, the local scaling matrix = [a b c ] is defined in the same manner as H for the overall system. The local (Lagrange) strain is assumed to be constant inside each tetrahedron and defined as [13,14]... 

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