‎Let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial‎ ‎of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$‎. ‎In this paper we obtain some new results about the dependence of $|p(Rz)|$ on $|p(rz)| $ for $r^2leq rRleq k^2$‎, ‎$k^2 leq rRleq R^2$ and for $Rleq r leq k$‎. ‎Our results refine and generalize certain well-known polynomial inequalities‎.

Why do existing parallelizing compilers and environments fail to parallelize many realistic FORTRAN programs? One of the reasons is that these programs contain a number of linearized array references, such as A(M*N*i+N*j+k) or A(i*(i+1)/2+j). Performing exact dependence analysis for these references requires testing polynomial constraints for integer solutions. Most existing dependence analysis...

‎let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial‎ ‎of degree at most $n-s$ having all its zeros in $|z|geq k$ or in $|z|leq k$‎. ‎in this paper we obtain some new results about the dependence of $|p(rz)|$ on $|p(rz)| $ for $r^2leq rrleq k^2$‎, ‎$k^2 leq rrleq r^2$ and for $rleq r leq k$‎. ‎our results refine and generalize certain well-known polynomial inequalities‎.

It is a well know result that roots of a polynomial depend continuously on its coefficients. Here we review this basic result and produce a proof via the use of Rouché’s Theorem. We also provide a simple result regarding real simple roots of polynomials with real coefficients.

Why do existing parallelizing compilers and environments fail to parallelize many realistic FORTRAN programs? One of the reasons is that these programs contain a number of linearized array references , such as A(M*N*i+N*j+k) or A(i*(i+1)/2+j). Performing exact dependence analysis for these references requires testing polynomial constraints for integer solutions. Most existing dependence analysi...