However, it is important to note that the discrete-time model in the time scale formalism is given in terms of the

difference operator, and not in terms of the more conventional shift operator as, for example, in [1-3,13].

3) generalizes the divided

difference operator for G/B to what we call the highest root Hessenberg variety.

omega]] f(t) = f (t + [omega]) - f(t) / [omega] is the forward

difference operator with stepsize [omega] [32], and [D.

To establish the corresponding relation, let us first recall the definition of the backward

difference operator [nabla].

0]), and [DELTA] denotes the forward

difference operator, that is, [DELTA]x(n) = x(n +1) - x(n) for a sequence x(n).

for central difference, where L denotes the

difference operator generating the corresponding scheme and (*, *)O,h denotes the discrete [L.

where [delta] is the

difference operator, (Y/POP) is gross domestic product per capita, POP is total population, and [epsilon] and [micro] are zero-mean, serially uncorrelated random error terms.

The main concept of the time scale calculus is the so-called delta-derivative that is a generalization of both the time-derivative (in the continuous-time case) and the

difference operator (in the discrete-time case) [5].

1), we associate the linear

difference operator L defined by

Applying twice the basic

difference operator to [f.

By linear algebra, one can prove that a certain multiple of the

difference operator [R.

In this section, we give a theorem which provides some estimates on these type of the inequality (2) about the forward

difference operator.