The proposed scheme uses an elliptic curve (EC)

isomorphic to a given ordered Mordell elliptic curve (MEC) [E.sub.p,b] over [F.sub.p], where p [equivalent to] 2 (mod 3).

We prove that the C* algebra [T.sup.(n).sub.[[infinity],[infinity]] generated by Toeplitz operator with bounded vertical symbols that have limit values at y = -[infinity], [infinity] acting on Fock space is

isomorphic and isometric to the C*-algebra D.

We can say immediately that [mathematical expression not reproducible], which is

isomorphic to R [??] [S.sub.n] as groups.

In accordance with the previous hypothesis, the positive coefficient on geographical distance interaction indicates that the correlations between spatial distance and

isomorphic diffusion will be greatly weakened after the growth period.

End([G.sub.i]) [congruent to] End(H) for some group H [??] [G.sub.i], then the direct products [G.sub.1] x [??] x [G.sub.n] and [G.sub.1] x [??] x [G.sub.i-1] x H x [G.sub.i+1] x [??] x [G.sub.n] can have

isomorphic endomorphism monoids.

Certainly, the group in this manner and PSL(2, Z) are

isomorphic. In other words, PSL(2, Z) is considered as a group acting on [H.sup.2] by linear fractional transformation, that is,

If [G.sub.1] is weak

isomorphic to [G.sub.2] and if [G.sub.1] is strong then [G.sub.2] is also strong.

Clearly, since marking on each vertex remains the same so their 2-path product signed graphs remain

isomorphic.

If k =0, then G is

isomorphic to S([C.sub.3], [P.sub.l], [C.sub.3]).

Moreover, [A.sub.n] (q) [??] [A.sub.n] ([q.sup.-1]) is

isomorphic to [H.sub.n](p, q) as a Hopf algebra (see [8, Theorem 3.3]).

If [v.sub.2][u.sub.2] [member of] E([bar.G]) then G is

isomorphic to 5(3,1).

(i) [Q.sub.h](111)[W(1 0)] is

isomorphic to [Q.sub.h]-1(111).