Figure 1.
A geometrical explanation of the e-index.
Without losing generality, we assume that ,
, can be represented by a smooth function
,
. A typical
curve is shown here, where
is equal to the area of the dark gray region.
Figure 2.
A Descartes coordinate system for the h-e plane.
The x-axis indicates the e-index, and the y-axis indicates the h-index. All the horizontal lines are called isohindex lines, on which all the mapping points have identical h-index. One of the isohindex lines is shown. The R-index is equal to , the Euclidean distance between the point
and the origin.
Table 1.
The e-index and some derived h-type indices for three famous chemists.a