arXiv subjects

Aline Hosry

Publications and source records attributed to Aline Hosry.

6 recordsLinked to original sources

arXiv2025

Solving Fredholm integro-differential equations using Hybrid and Block-Pulse functions

In this paper, hybrid and block-pulse functions are used to approximate the solution of a class of Fredholm integro-differential equations that was first studied by Hemeda. By employing suitable approximations, the equation has been converted into a system of algebraic equations that can be solved with classical methods. Finally, the method is explained with illustrative examples and results are compared to the results obtained by Hemeda's method to show the usefulness and efficiency of the block-pulse and hybrid functions approach.

math.FA↗

arXiv2019

Hybrid functions approach to solve a class of Fredholm and Volterra integro-differential equations

In this paper, we use a numerical method that involves hybrid and block-pulse functions to approximate solutions of systems of a class of Fredholm and Volterra integro-differential equations. The key point is to derive a new approximation for the derivatives of the solutions and then reduce the integro-differential equation to a system of algebraic equations that can be solved using classical methods. Some numerical examples are dedicated for showing efficiency and validity of the method that we introduce.

math.NA↗

arXiv2014

Uniform Artin-Rees Bounds for Syzygies

Let $(R,m)$ be a local Noetherian ring, let $M$ be a finitely generated $R$-module and let $(F_{\bullet},\partial_{\bullet})$ be a free resolution of $M$. We find a uniform bound $h$ such that the Artin-Rees containment $I^n F_i\cap Im \, \partial_{i+1} \subseteq I^{n-h} Im \, \partial_{i+1}$ holds for all integers $i\ge d$, for all integers $n\ge h$, and for all ideals $I$ of $R$. In fact, we show that a considerably stronger statement holds. The uniform bound $h$ holds for all ideals and all resolutions of $d$th syzygy modules. In order to prove our statements, we introduce the concept of Koszul annihilating sequences.

math.AC↗

arXiv2013

On the Equality of Ordinary and Symbolic Powers of Ideals

We consider the following question concerning the equality of ordinary and symbolic powers of ideals. In a regular local ring, if the ordinary and symbolic powers of a one-dimensional prime ideal are the same up to its height, then are they the same for all powers? We provide supporting evidence of a positive answer for classes of prime ideals defining monomial curves or rings of low multiplicities.

math.AC↗

arXiv2010

The Briançon-Skoda Theorem and Coefficient Ideals for Non m-Primary Ideals

We generalize a Briançon-Skoda type theorem first studied by Aberbach and Huneke. With some conditions on a regular local ring $(R,\m)$ containing a field, and an ideal $I$ of $R$ with analytic spread $\ell$ and a minimal reduction $J$, we prove that for all $w \geq -1$, $ \bar{I^{\ell+w}} \subseteq J^{w+1} \mathfrak{a} (I,J),$ where $\mathfrak{a}(I,J)$ is the coefficient ideal of $I$ relative to $J$, i.e. the largest ideal $\mathfrak{b}$ such that $I\mathfrak{b}=J\mathfrak{b}$. Previously, this result was known only for $\m$-primary ideals.

math.AC↗

arXiv2010

A Less Restrictive Briançon-Skoda Theorem with Coefficients

The Briançon-Skoda theorem in its many versions has been studied by algebraists for several decades. In this paper, under some assumptions on an F-rational local ring $(R,\m)$, and an ideal $I$ of $R$ of analytic spread $\ell$ and height $g < \ell$, we improve on two theorems by Aberbach and Huneke. Let $J$ be a reduction of $I$. We first give results on when the integral closure of $I^\ell$ is contained in the product $J I_{\ell-1}$, where $I_{\ell-1}$ is the intersection of the primary components of $I$ of height $\leq \ell-1$. In the case that $R$ is also Gorenstein, we give results on when the integral closure of $I^{\ell-1}$ is contained in $J$.

math.AC↗