En estas páginas vamos a considerar la tarea de buscar raíces de la unidad que son soluciones de un polinomio en dos variables con coeficientes algebraicos. Esta pregunta, aparentemente inocente, nos llevará por un precioso ...

Kolaitis and Kopparty have shown that for any first-order formula with parity quantifiers over the language of graphs, there is a family of multivariate polynomials of constant-degree that agree with the formula on all but ...

Edge-distance-regularity is a concept recently introduced by the authors which is similar to that of distance-regularity, but now the graph is seen from each of its edges instead of from its vertices. More precisely, a ...

Monitoring spatiotemporal variations of ionospheric vertical total electron content (VTEC) is crucial for space weather and satellite positioning. In the present study, an enhanced neural network (ENN) model is proposed ...

We prove that both Polynomial Calculus and Sums-of-Squares proof systems admit a strong form of feasible interpolation property for sets of polynomial equality constraints. Precisely, given two sets P(x, z) and Q(y, z) of ...

We bound the location of roots of polynomials that have nonnegative coefficients with respect to a fixed but arbitrary basis of the vector space of polynomials of degree at most d. For this, we interpret the basis polynomials ...

Let (K, v) be a discrete valued field with valuation ring O, and let Ov be the completion of O with respect to the v-adic topology. In this paper we discuss the advantages of manipulating polynomials in Ov[x] on a computer ...

A simplified class B laser system is a family of differential polynomial systems of degree two depending on the parameters a and b. Its rich dynamics has already been observed in 1980s, see Arecchi et al. [Opt. Commun. 51, ...

We recall in this note a theorem of Kac which gives an assymptotic equivalent of the expected number of real roots of a random polynomial, and we get from it some estimations on the average complexity of several algorithms ...

In the main part of this paper we present polynomial expressions for the cardinalities of some sets of interest of the nice distance-layer structure of the well-known De Bruijn and Kautz digraphs. More precisely, given a ...