A novel algorithm of matching synthetic aperture radar(SAR) image to optical image and SAR got by different sensor based on ratio-gradient and cross-cumulative residual entropy is proposed.

Moreover,survival entropies define broad classes of measures that contain the cumulative residual entropy of a particular case.

We show that C is a crossed coproduct if and only if C_R is free.

This paper gives a new method to prove the following three statements are equivalent: C/E is an H cleft coextension; C is isomorphic to a Hopf crossed coproduct E× α H with α convolution invertible; C/E is an H Galois coextension with a conormal basis property.

By using method of twisted module coalgebras, this paper shows that there are correspondings between the crossed coproducts C× α H and twisted tensor coalgebras ( CH) τ .

This paper reviews the new progress in the residual entropy of glass systems and the entropy -freezing in spin-glass systems and proposes a new explanations of the existence of residual en tropy.