Data

NameCastro Jiménez, Francisco Jesús
DepartmentAlgebra
Knowledge areaÁlgebra
Professional categoryCatedrático de Universidad
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  Statistics

  • Items

    39

  • Visits

    2886

  • Downloads

    3675

  Publications

 

Article
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Linear nested Artin approximation theorem for algebraic power series

Castro Jiménez, Francisco Jesús; Popescu, Dorin; Rond, Guillaume (Springer, 2018-01-01)
We give an elementary proof of the nested Artin approximation Theorem for linear equations with algebraic power series ...
Article
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Echelons of power series and Gabrielov’s counterexample to nested linear Artin Approximation

Alonso García, María Emilia; Castro Jiménez, Francisco Jesús; Hauser, Herwig; Koutschan, Christoph (London Mathematical Society, 2018-01-01)
Gabrielov’s famous example for the failure of analytic Artin approximation in the presence of nested subring conditions ...
Article
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Encoding algebraic power series

Alonso García, María Emilia; Castro Jiménez, Francisco Jesús; Hauser, Herwig (Springer, 2017-01-01)
The division algorithm for ideals of algebraic power series satisfying Hironaka’s box condition is shown to be finite when ...
Final Degree Project
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Bases de Gröbner: eliminación y programación lineal entera

Castro Jiménez, Francisco Jesús; González Parra, Alba (2015-06-01)
Gröbner basis is a basic concept in Computational Algebra; it was introduced by the Austrian mathematician Bruno Buchberger ...
Article
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Gevrey expansions of hypergeometric integrals I

Castro Jiménez, Francisco Jesús; Granger, Michel (Oxford University Press, 2015-01-01)
We study integral representations of the Gevrey series solutions of irregular hypergeometric systems. In this paper we ...
Article
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Irregular modified A-Hypergeometric systems

Castro Jiménez, Francisco Jesús; Fernández Fernández, María Cruz; Koike, Tatsuya; Takayama, Nobuki (American Mathematical Society, 2015-01-01)
A modified A-hypergeometric system is a system of differential equations for the function f(t w · x) where f(y) is a ...
Article
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On irregular binomial D-modules

Fernández Fernández, María Cruz; Castro Jiménez, Francisco Jesús (Springer, 2012-12-01)
We prove that a holonomic binomial D–module MA(I, β) is regular if and only if certain associated primes of I determined ...
Article
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Exact cost minimization of a series-parallel system

Castro Jiménez, Francisco Jesús; Gago Vargas, Manuel Jesús; Hartillo Hermoso, Isabel; Ucha Enríquez, José María (Cornell University, 2012-01-01)
The redundancy allocation problem is formulated minimizing the design cost for a series-parallel system with multiple ...
Article
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Gevrey solutions of irregular hypergeometric systems in two variables

Fernández Fernández, María Cruz; Castro Jiménez, Francisco Jesús (Elsevier, 2011-08-01)
We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated ...
Article
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An algebraic approach to Integer Portfolio problems

Castro Jiménez, Francisco Jesús; Gago Vargas, Manuel Jesús; Hartillo Hermoso, Isabel; Puerto Albandoz, Justo; Ucha Enríquez, José María (2011-05-01)
Integer variables allow the treatment of some portfolio optimization problems in a more realistic way and introduce the ...
Article
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Gevrey solutions of the irregular hypergeometric system associated with an affine monomial curve

Fernández Fernández, María Cruz; Castro Jiménez, Francisco Jesús (American Mathematical Society, 2011-01-01)
We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated ...
Chapter of Book
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Computer algebra and algebraic analysis

Lambán Pardo, Laureano; Romero Ibáñez, Ana; Rubio García, Julio; Castro Jiménez, Francisco Jesús (Universidad de La Rioja, 2010-01-01)
Este artículo describe algunas aplicaciones del Álgebra Computacional al Análisis Algebraico, también conocido como teoría ...
PhD Thesis
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Soluciones Gevrey de sistemas hipergeométricos

Castro Jiménez, Francisco Jesús; Fernández Fernández, María Cruz (2010-01-01)
Esta memoria versa sobre la irregularidad de los D-módulos hipergeométricos MA(β)(cf. Definición 3.1.3), introducidos p ...
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The computation of the logarithmic cohomology for plane curves

Castro Jiménez, Francisco Jesús; Takayama, Nobuki (Elsevier, 2009-12-01)
We will give algorithms of computing bases of logarithmic cohomology groups for square-free polynomials in two variables.
Article
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Localization at hyperplane arrangements: combinatorics and D-modules

Álvarez Montaner, Josep; Castro Jiménez, Francisco Jesús; Ucha Enríquez, José María (Elsevier, 2007-10-15)
We describe an algorithm deciding if the annihilating ideal of the meromorphic function 1 f , where f = 0 defines an ...
Article
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Computational methods in algebra and analysis

Castro Jiménez, Francisco Jesús (Sociedad Española de Matemática Aplicada, 2007-09-01)
This paper describes some applications of Computer Algebra to Algebraic Analysis also known as D-module theory, i.e. the ...
Article
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A flatness property for filtered D-modules

Castro Jiménez, Francisco Jesús; Granger, Michel (European Mathematical Society, 2007-01-01)
Let M be a coherent module over the ring DX of linear differential operators on an analytic manifold X and let Z1, · · · ...
Article
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A vanishing theorem for a class of logarithmic D-modules

Castro Jiménez, Francisco Jesús; Gago Vargas, J.; Hartillo Hermoso, Isabel; Ucha Enríquez, José María (Cornell University, 2007-01-01)
Let OX (resp. DX) be the sheaf of holomorphic functions (resp. the sheaf of linear differential operators with holomorphic ...
Article
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Gröbner bases and logarithmic D-modules

Castro Jiménez, Francisco Jesús; Ucha Enríquez, José María (Elsevier, 2006-01-01)
Let C[x] = C[x1, . . . , xn] be the ring of polynomials with complex coefficients and An the Weyl algebra of order n over ...
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Logarithmic Comparison Theorem and some Euler homogeneous free divisors

Castro Jiménez, Francisco Jesús; Ucha Enríquez, José María (American Mathematical Society, 2005-01-01)
Let D, x be a free divisor germ in a complex manifold X of dimension n > 2. It is an open problem to find out which are ...
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Explicit calculations in rings of differential operators

Castro Jiménez, Francisco Jesús; Granger, Michel (Société Mathématique de France, 2004-01-01)
We use the notion of a standard basis to study algebras of linear differential operators and finite type modules over these ...
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On the computation of Bernstein–Sato ideals

Ucha Enríquez, José María; Castro Jiménez, Francisco Jesús (Elsevier, 2004-01-01)
In this paper we compare the approach of Brianc¸onand Maisonobe for computing Bernstein–Sato ideals—based on computations ...
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Quasi-free divisors and duality

Castro Jiménez, Francisco Jesús; Ucha Enríquez, José María (Elsevier, 2004-01-01)
We prove a duality theorem for some logarithmic D-modules associated with a class of divisors. We also give some results for the locally quasi-homogeneous case.
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Testing the Logarithmic Comparison Theorem for Free Divisors

Castro Jiménez, Francisco Jesús; Ucha Enríquez, José María (Taylor and Francis, 2004-01-01)
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Logarithmic cohomology of the complement of a plane curve

Calderón Moreno, Francisco Javier; Mond, David; Narváez Macarro, Luis; Castro Jiménez, Francisco Jesús (Springer, 2002-03-01)
Let D, x be a plane curve germ. We prove that the complex Ω•(log D)x computes the cohomology of the complement of D, x ...
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Gröbner δ-bases and Gröbner bases for differential operators

Castro Jiménez, Francisco Jesús; Moreno Frías, María Ángeles (Polish Academy of Sciences, Institute of Mathematics, 2002-01-01)
This paper deals with the notion of Gr¨obner δ-base for some rings of linear differential operators by adapting the works ...
PhD Thesis
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Métodos efectivos en anillos de operadores diferenciales y en sistemas hipergeométricos

Castro Jiménez, Francisco Jesús; Hartillo Hermoso, Isabel (2002-01-01)
El Análisis Algebraico, o teoría de D-m&oa cute;dulos, trata el estudio de los sistemas de ecuaciones -- en derivadas ...
Article
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Free divisors and duality for D-modules

Castro Jiménez, Francisco Jesús; Ucha Enríquez, José María (Pleiades, 2002-01-01)
The relationship between D-modules and free divisors has been studied in a general setting by L. Narváez and F.J. Calderón. ...
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The analytic standard fan of a D-module

Assi, Abdallah; Castro Jiménez, Francisco Jesús; Granger, Michel (Elsevier, 2001-10-24)
We extend to the analytic D-module case our results in the algebraic case, namely, we associate with any monogeneous module ...
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A computational approach to the D-module of meromorphic functions

Castro Jiménez, Francisco Jesús; Ucha Enríquez, José María (2001-01-01)
Let D be a divisor in Cn. We present methods to compare the D-module of the meromorphic functions O[∗D] to some natural approximations. We show how the analytic case can be treated with computations in the Weyl algebra.
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Explicit Comparison Theorems for D -modules

Castro Jiménez, Francisco Jesús; Ucha Enríquez, José María (Elsevier, 2001-01-01)
We prove in an explicit way a duality formula between two A2-modules Mlog and Mflog associated to a plane curve and we ...
Presentation
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A computational approach to free divisors and logarithmic D-modules

Ucha Enríquez, José María; Castro Jiménez, Francisco Jesús (Universidad de La Rioja, Departamento de Matemáticas y Computación, 2001-01-01)
We apply algorithmic techniques for comparing some D-modules associated to a kind of divisors in Cn.
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The Gröbner fan of an An-module

Assi, Abdallah; Castro Jiménez, Francisco Jesús; Granger, Michel (Elsevier, 2000-06-14)
Let I be a non-zero left ideal of the Weyl algebra An of order n over a field k and let L:R2n→R be a linear form defined ...
PhD Thesis
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Métodos computacionales en los sistemas de ecuaciones en derivadas parciales

Castro Jiménez, Francisco Jesús; Moreno Frías, María Ángeles (2000-01-01)
"La memoria tiene dos partes: La primera está dedicada a la comparación entre los métodos clásicos de Riquier-Janet (para ...
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On some D-modules in dimension 2

Castro Jiménez, Francisco Jesús; Ucha Enríquez, José María (Cornell University, 2000-01-01)
We prove a duality formula for two D-modules arising from logarithmic derivations w.r.t. a plane curve. As an application we give a differential proof of a logarithmic comparison theorem in [4].
PhD Thesis
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Métodos constructivos en álgebras de operadores diferenciales

Castro Jiménez, Francisco Jesús; Ucha Enríquez, José María (1999-01-01)
PhD Thesis
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Presentaciones de módulos teorema de estabilidad de Suslin en Z[X]

Castro Jiménez, Francisco Jesús; Gago Vargas, Manuel Jesús (1999-01-01)
La comparación de módulos finitamente generados sobre anillos de polinomios es un problema de gran dificultad no resuelto. ...
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How to calculate the slopes of a D-module

Assi, Abdallah; Castro Jiménez, Francisco Jesús; Granger, Michel (Foundation Compositio Mathematica, 1996-01-01)
PhD Thesis
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Teorema de división para los operadores diferenciales y cálculo de multiplicidades de D-Modulos

Vicente Córdoba, José Luis; Castro Jiménez, Francisco Jesús (1984-10-31)
En el capítulo preliminar (Capítulo 0) se estudia la relación entre un módulo filtrado y el módulo graduado asociado y se ...