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FLQ, the Fastest Quadratic Complexity Bound on the Values of Positive Roots of Polynomials

Akritas, Alkiviadis, Argyris, Andreas, Strzeboński, Adam (2008)

Serdica Journal of Computing

In this paper we present F LQ, a quadratic complexity bound on the values of the positive roots of polynomials. This bound is an extension of FirstLambda, the corresponding linear complexity bound and, consequently, it is derived from Theorem 3 below. We have implemented FLQ in the Vincent-Akritas-Strzeboński Continued Fractions method (VAS-CF) for the isolation of real roots of polynomials and compared its behavior with that of the theoretically proven best bound, LM Q. Experimental results indicate...

Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation

Nicola Garofalo, Ermanno Lanconelli (1990)

Annales de l'institut Fourier

A recent result of Bahouri shows that continuation from an open set fails in general for solutions of u = V u where V C and = j = 1 N - 1 X j 2 is a (nonelliptic) operator in R N satisfying Hörmander’s condition for hypoellipticity. In this paper we study the model case when is the subelliptic Laplacian on the Heisenberg group and V is a zero order term which is allowed to be unbounded. We provide a sufficient condition, involving a first order differential inequality, for nontrivial solutions of u = V u to have a finite order...

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