Start Action of PSL(2, Z) on GF([2.sup.9]) [union] {[infinity]} Coset diagram for the action Write the elements of GF*([2.sup.9]) in 16 x 16 matrix, in a specific order determined by the coset diagram Consider h : GF*([2.sup.9]) [right arrow] GF([2.sup.8]) defined by h([[alpha].sup.2n]) = [[omega].sup.n] Apply h on each element of the matrix Consider a

bijective map g : GF([2.sup.8]) [right arrow] GF([2.sup.8]) defined by g (z) = [mathematical expression not reproducible] Apply g on each element of the matrix Proposed S-box Step 3.

Hence, we have a

bijective map [f.sup.-1] : Y [right arrow] X, which is an isomorphism from K to H.

(A4) u [member of] [C.sup.6] [[OMEGA]], w(x) : [bar.[OMEGA]] [right arrow] [bar.[OMEGA]] is a

bijective map in [C.sup.3], with w'(x) > 0, [for all]x [member of] [bar.[OMEGA]], w[-.sup.1] [member of] [C.sup.1] [[OMEGA]],

In fact, if lattice DP(X) is isomorphic to lattice DP(Y) then we obtain a

bijective map F: X [right arrow] Y preserving closed nowhere dense sets, which turns out to be a homeomorphism if X and Y are countably compact T3 spaces without isolated points.

Menu M' is a proxy improvement over M if there exists a

bijective map h on [R.sub.n] such that [U.sub.h(x)](M') [greater than or equal to] [U.sub.x] (M) for all x [member of] [R.sub.n], and [U.sub.h(x)](M') > [U.sub.x] (M) for at least one x.

A Standard Young tableau is a

bijective map T: [D.sub.[lambda]] [right arrow] {1, ..., [absolute value of [D.sub.[lambda]]]} which is increasing along rows and down columns, i.e.

(1) [[phi].sub.1]: [0,c] [right arrow] [0, 1], strictly monotone increasingC'

bijective map [[phi].sub.1], [[phi].sup.-1.sub.1] are absolutely continuous

f:X [right arrow] Y is a

bijective map defined by: f(x) = y for all x [member of] X satisfying the conditions:

This correspondence defines a

bijective map k: [T.sub.2]([OMEGA]) [??] G: [[tau].sub.[alpha],[beta]] [right arrow] [g.sub.[alpha],[beta]] and one verifies easily that k: ([T.sub.2]([OMEGA]), [omicron]) [right arrow] (G, [omicron]) is a group homomorphism (using also the sharp 2-transitivity of [T.sub.2]([OMEGA]) on [OMEGA]).

Let k be a weak isomorphism between the neutrosophic graph G2 and G1 so the relation is anti-symmetric that is k : V2 [left arrow] V1 is a

bijective map with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].