subscript being used to distinguish between the two different function

indices. Variable indices are designated by the letter "j." Since in

the original representation of the function,the indices on the variables

were functions of the indices on the functions, the variable indices

must be expressed as functions of the function indices.

 First, some restrictions will be made on the possible values which

the function indices can assume. Function indices will always have

their possible values defined by a "range" which consists of a lower

limit, an upper limit, and an increment. An index range is very similar

to a FORTRAN do-loop range and consequently makes the eventual writing

of the solution procedure in the form of do-loops convenient. Examples

of function index ranges are:

 a) ii: L = 1 b) i2: L = 2 c) i3: L = 1

 U = 10 U = 29 U = 13

 A= 1 A = 1 A = 2

In case a) the function index would have possible index values of all

integers between 1 and 10 inclusive, in case b) i2 would have possible

index values of all integers between 2 and 29 inclusive, and in cazs c)

13 would have possible index values of all odd integer values between

1 and 13 inclusive. Although restricting the function indices to this

form reduces the possible values that function indices in a function

index set can have, it does not exclude any of the index sets an

engineer is likely to create in modeling a chemical process. The stages

in a staged process are numbered consecutively; a distillation column

which has a third and fifth stage has a fourth stage. Certainly the

index sets which arise from staged processes and from discretization of

models are describable in terms of index ranges.