Theorems dilation

Ht( y) = H(t ) = H (t ) / H( z) for complex values of the dilatation parameter jj, i.e., H( ) is non-Hermitian and as such, the variational theorem does not apply. However, there exists a bi-variational theorem /57,58/ for non-Hermitian operators. The bi-variational SCF equations for the dilated Hamiltonians are derived by extremizing the generalized functional... 

The Aquilar, Balslev, Combes and Simon (ABCS) theorems concerning spectrum of analytically dilated (complex rotated) Hamiltonians were published in the early seventies (1-3). They caused an explosive development of techniques using complex coordinates and their applications, which have been reviewed in numerous articles (4-13). 

Here Q is the area enclosed by the loop, and we utilized the Stokes theorem to see that, in the area of dislocations V x ii 5 0 / i-e-, bend ((V x ii) x n ) and twist Vxn) n) deformations are possible. Parabolic focalconic arrays induced by dilation of layers have importance in lyotropic lamellar systems, too.2 ... 

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