This paper, the plane projective graph of knot Lin 3-space was transformed into plane graph of edges with "±1" symbol , the eguivalence and mirrorimage characters of knot L were described by the isomorph and the selfdual quality of G(L).

In this paper,the self-duality is discussed in the sense of Hartley proper efficient solu-ions,and results similar to [1] and [2]are obtained.

Subcode chains of quaternary self-dual code

In the last ten or more years,the cyclic codes and self-dual codes over finite rings have become a hot issue for coding theorists.

2) C(1) is self-dual quaternary code if C is self-dual code and of the type 8(n/2

On the basis of a unified definition of the dual operation and the (anti )self dual operation, the connections of the su(2,2｜1) main cluster was used as the fundamental field variables to construct the self dual Lagrangian of conformal supergravity.

In terms of Dirac matrices the self dual and anti self dual decomposition of a conformal supergravity is given and a self dual conformal supergravity theory is developed as a connection dynamic theory in which the basic dynamic variables include the self dual spin connection i.

The optimizer is global unique,and the resulting foumula is self dual.

By using it,we give a necessary and sufficient condition of which a cyCle is a self-dual cycle,and we also present a structure theorem of self-dual cycled.