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J. R. Sendra

Publications and source records attributed to J. R. Sendra.

6 recordsLinked to original sources
arXiv2022

On a class of formal power series and their summability

A family of formal power series, such that its coefficients satisfy a recursion formula, is characterized in terms of the summability, in the sense of J. P. Ramis, of its elements along certain well chosen directions. We describe a set of ordinary differential equations which have, as a formal solution, one of such formal power series, and also describe the actual solutions which own such formal power series as Gevrey asymptotic expansion. The main results are extended into the framework of $q-$Gevrey series and $q-$difference equations, and also to the case of moment-differential equations, whose formal solutions have their coefficients' growth governed by a so-called strongly regular sequence, appearing as a generalization of the Gevrey-like sequences.

math.CV↗
arXiv2011

Computing the Singularities of Rational Surfaces

Given a rational projective parametrization $\cP(\ttt,\sss,\vvv)$ of a rational projective surface $\cS$ we present an algorithm such that, with the exception of a finite set (maybe empty) $\cB$ of projective base points of $\cP$, decomposes the projective parameter plane as $\projdos\setminus \cB=\cup_{k=1}^{\ell} \cSm_k$ such that if $(\ttt_0:\sss_0:\vvv_0)\in \cSm_k$ then $\cP(\ttt_0,\sss_0,\vvv_0)$ is a point of $\cS$ of multiplicity $k$.

math.AG↗
arXiv2009

Rational Conchoids of Algebraic Curves

We study the rationality of the components of the conchoid to an irreducible algebraic affine plane curve, excluding the trivial cases of the isotropic lines, of the lines through the focus and the circle centered at the focus and radius the distance involved in the conchoid. We prove that conchoids having all their components rational can only be generated by rational curves. Moreover, we show that reducible conchoids to rational curves have always their two components rational. In addition, we prove that the rationality of the conchoid component, to a rational curve, does depend on the base curve and on the focus but not on the distance. Also, we provide an algorithm that analyzes the rationality of all the components of the conchoid and, in the affirmative case, parametrizes them. The algorithm only uses a proper parametrization of the base curve and the focus and, hence, does not require the previous computation of the conchoid. As a corollary, we show that the conchoid to the irreducible conics, with conchoid-focus on the conic, are rational and we give parametrizations. In particular we parametrize the {\it Limaçons of Pascal}. We also parametrize the conchoids of {\it Nicomedes}. Finally, we show to find the focuses from where the conchoid is rational or with two rational components.

math.AG↗
arXiv2007

Applications of Level Curves to Some Problems on Algebraic Surfaces

In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some topological features of surfaces (reality, compactness, connectivity) and to the problem of plotting.

math.AG↗
arXiv2006

Partial Degree Formulae for Plane Offset Curves

In this paper we present several formulae for computing the partial degrees of the defining polynomial of the offset curve to an irreducible affine plane curve given implicitly, and we see how these formulae particularize to the case of rational curves. In addition, we present a formula for computing the degree w.r.t the distance variable.

math.AG↗