If the above algorithm generates an

infinite sequence {[y.sup.k]} of incumbent solutions by solving the LRP([Z.sup.k]), let

Now if, by applying these two rules, author create a Cantor's diagonal sequence from all

infinite sequence in Fig.3, it will look like as in fig.4.

For any i [member of] N, let [{[A.sub.i]}.sup.[infinity].sub.i=1] be an

infinite sequence of [[beta].sub.i]-inverse strongly accretive operators in E such that [beta] := [inf.sub.i[less than or equal to]1([[beta].sub.i]} > 0 and [mathematical expression not reproducible] for all r > 0.

Just as before, consider an

infinite sequence of Bernoulli trials with probability of success p in every trial.

For an

infinite sequence w [member of] S, the upper complexity of w is defined by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

By construction, the

infinite sequence f is d-periodic.

Assume that the above algorithm is infinite; then it generates an

infinite sequence of iterations such that along any infinite branch-and-bound tree any accumulation point of the sequence {[LB.sub.k]} will be the global minimum of problem (P).

Among the topics are stationary dynamical systems, the expansion of rational numbers in Mobius number systems, horospheres and Farey fractions, ergodic abelian actions with homogeneous spectrum, the geometric entropy of geodesic currents on free groups, statistics of matrix products in hyperbolic geometry, and the

infinite sequence of fixed point free pseudo-Anosov homeomorphisms on a family of genus two surface.

Infinite sequence A is almost periodic if and only if there is a function f such that for every natural n every word w of length n either doesn't occur in A or occurs in every fragment of A with length more than f(n).

Literature [3] has studied the

infinite sequence astringency, has given the identical equation:

Again, we may now construct an

infinite sequence of PPTs using the longer leg in each successive triangle.

We start by defining a generalized Fibonacci number-sequence as a doubly

infinite sequence A = ([a.sub.n]), where n ranges over all integers (negative, zero and positive), such that for all n we have [a.sub.n+1] = [a.sub.n] + [a.sub.n-1].