We present in this paper a new direction finding algorithm for non circular sources that is based on polynomial rooting. Due to the non circularity characteristics of the impinging sources, the proposed method is able to handle more sources than sensors. By using a polynomial rooting instead of a searching technique the method is limited to linear uniformly spaced arrays. However, polynomial ro...

To identify polynomials one usually requires the value of the polynomial at d + 1 points where d is the degree of the polynomial. In this note we show that every polynomial with non-negative integral coeecients can be identiied by knowing its value at two cleverly chosen points irrespective of the degree and the number of terms in the polynomial.

Given p polynomials with coefficients in a commutative unitary integral ring C containing Q, we define the notion of a generic Bernstein-Sato polynomial on an irreducible affine scheme V ⊂ Spec(C). We prove the existence of such a non zero rational polynomial which covers and generalizes previous existing results by H. Biosca. When C is the ring of an algebraic or analytic space, we deduce a st...

This paper defines a new invariant of virtual knots and flat virtual knots. We study this invariant in two forms: the extended bracket invariant and the arrow polyomial. The extended bracket polynomial takes the form of a sum of virtual graphs with polynomial coefficients. The arrow polynomial is a polynomial with a finite number of variables for any given virtual knot or link. We show how the ...

This paper presents the first quantum computational characterization of the Graph Non-Isomorphism problem (GNI). We show that GNI is in a quantum non-deterministic polynomial-time class, i.e., quantum Merlin-Arthur game class (QMA) or quantum probabilistic NP (BQNP). In other words, given two graphs (G0, G1) ∈ GNI, (G0, G1) has a polynomial-size quantum certificate with which (G0, G1) ∈ GNI can...

In this paper, we extend the method proposed by Cochelin and Vergez in [A high order purely frequency based harmonic balance formulation for continuation of periodic solutions, Journal of Sound and Vibration, 324:243–262, 2009] to the case of non polynomial non-linearities. This extension allows for the computation of branches of periodic solutions of a broader class of nonlinear dynamical syst...