Polynomial interpretations are a useful technique for proving termination of term rewrite systems. We show how polynomial interpretations with negative coefficients, like x− 1 for a unary function symbol or x− y for a binary function symbol, can be used to extend the class of rewrite systems that can be automatically proved terminating.

We propose a new realization of the elliptic quantum group equipped with the H-Hopf algebroid structure on the basis of the elliptic algebra Uq,p(ŝl2). The algebra Uq,p(ŝl2) has a constructive definition in terms of the Drinfeld generators of the quantum affine algebra Uq(ŝl2) and a Heisenberg algebra. This yields a systematic construction of both finite and infinite-dimensional dynamical repre...

The theory of apolarity was first developed by Clebsch, Lasker, Richw x mond, Sylvester, and Wakeford 10, 17, 20 . They were first interested in studying homogeneous polynomials of degree p and in q variables, and in expressing them as sums of pth powers of linear terms. The problem is to minimize the number of pth powers which are required in such a sum. For instance, a result due to Sylvester...

Polynomial interpretations are a useful technique for proving termination of term rewrite systems. They come in various flavors: polynomial interpretations with real, rational and integer coefficients. As to their relationship with respect to termination proving power, Lucas managed to prove in 2006 that there are rewrite systems that can be shown polynomially terminating by polynomial interpre...

to investigate the effect of preprocessing techniques including contrast enhancement and illumination correction on retinal imagequality, a comparative study was carried out. we studied and implemented a few illumination correction and contrast enhancementtechniques on color retinal images to find out the best technique for optimum image enhancement. to compare and choose thebest illumination c...