Author profile: Castro Jiménez, Francisco Jesús
Institutional data
Name | Castro Jiménez, Francisco Jesús |
Department | Algebra |
Knowledge area | Álgebra |
Professional category | Catedrático de Universidad |
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Statistics
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No. publications
42
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No. visits
3991
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5168
Publications |
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Article
![]() Gevrey Expansions of Hypergeometric Integrals II
(Oxford University Press, 2019-12-01)
We study integral representations of the Gevrey series solutions of irregular hypergeometric systems under certain ... |
Article
![]() Linear nested Artin approximation theorem for algebraic power series
(Springer, 2018-01-01)
We give an elementary proof of the nested Artin approximation Theorem for linear equations with algebraic power series ... |
Article
![]() Echelons of power series and Gabrielov’s counterexample to nested linear Artin Approximation
(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
![]() Encoding algebraic power series
(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
![]() Bases de Gröbner: eliminación y programación lineal entera
(2015-06-01)
Gröbner basis is a basic concept in Computational Algebra; it was introduced by the Austrian mathematician Bruno Buchberger ... |
Article
![]() Gevrey expansions of hypergeometric integrals I
(Oxford University Press, 2015-01-01)
We study integral representations of the Gevrey series solutions of irregular hypergeometric systems. In this paper we ... |
Article
![]() Irregular modified A-Hypergeometric systems
(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
![]() On irregular binomial D-modules
(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
![]() Exact cost minimization of a series-parallel system
(Cornell University, 2012-01-01)
The redundancy allocation problem is formulated minimizing the design cost for a series-parallel system with multiple ... |
Article
![]() Gevrey solutions of irregular hypergeometric systems in two variables
(Elsevier, 2011-08-01)
We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated ... |
Article
![]() An algebraic approach to Integer Portfolio problems
(2011-05-01)
Integer variables allow the treatment of some portfolio optimization problems in a more realistic way and introduce the ... |
Article
![]() Gevrey solutions of the irregular hypergeometric system associated with an affine monomial curve
(American Mathematical Society, 2011-01-01)
We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated ... |
Article
![]() Computing localizations iteratively
(Cornell University, 2011-01-01)
Let R = C[x] be a polynomial ring with complex coefficients and DX = Chx, ∂i be the Weyl algebra. Describing the localization ... |
PhD Thesis
![]() ![]() Soluciones Gevrey de sistemas hipergeométricos
(2010-01-01)
Esta memoria versa sobre la irregularidad de los D-módulos hipergeométricos MA(β)(cf. Definición 3.1.3), introducidos p ... |
Chapter of Book
![]() Computer algebra and algebraic analysis
(Universidad de La Rioja, 2010-01-01)
Este artículo describe algunas aplicaciones del Álgebra Computacional al Análisis Algebraico, también conocido como teoría ... |
Article
![]() The computation of the logarithmic cohomology for plane curves
(Elsevier, 2009-12-01)
We will give algorithms of computing bases of logarithmic cohomology groups for square-free polynomials in two variables. |
Article
![]() Localization at hyperplane arrangements: combinatorics and D-modules
(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
![]() Computational methods in algebra and analysis
(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
![]() A vanishing theorem for a class of logarithmic D-modules
(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
![]() A flatness property for filtered D-modules
(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
![]() Gröbner bases and logarithmic D-modules
(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 ... |
Article
![]() Logarithmic Comparison Theorem and some Euler homogeneous free divisors
(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 ... |
Article
![]() On the computation of Bernstein–Sato ideals
(Elsevier, 2004-01-01)
In this paper we compare the approach of Brianc¸onand Maisonobe for computing Bernstein–Sato ideals—based on computations ... |
Article
![]() Quasi-free divisors and duality
(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. |
Article
![]() Testing the Logarithmic Comparison Theorem for Free Divisors
(Taylor and Francis, 2004-01-01)
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Article
![]() Explicit calculations in rings of differential operators
(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 ... |
Article
![]() Logarithmic cohomology of the complement of a plane curve
(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 ... |
Article
![]() Free divisors and duality for D-modules
(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. ... |
Article
![]() Gröbner δ-bases and Gröbner bases for differential operators
(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
![]() Métodos efectivos en anillos de operadores diferenciales y en sistemas hipergeométricos
(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
![]() The analytic standard fan of a D-module
(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 ... |
Article
![]() Explicit Comparison Theorems for D -modules
(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
![]() A computational approach to free divisors and logarithmic D-modules
(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. |
Article
![]() A computational approach to the D-module of meromorphic functions
(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. |
Article
![]() The Gröbner fan of an An-module
(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 ... |
Article
![]() On some D-modules in dimension 2
(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
![]() Métodos computacionales en los sistemas de ecuaciones en derivadas parciales
(2000-01-01)
"La memoria tiene dos partes: La primera está dedicada a la comparación entre los métodos clásicos de Riquier-Janet (para ... |
PhD Thesis
![]() Presentaciones de módulos teorema de estabilidad de Suslin en Z[X]
(1999-01-01)
La comparación de módulos finitamente generados sobre anillos de polinomios es un problema de gran dificultad no resuelto. ... |
PhD Thesis |
Article
![]() Cohomology of the complement of a free divisor
(American Mathematical Society, 1996-08-01)
We prove that if D is a "strongly quasihomogeneous" free divi- sor in the Stein manifold X, and U is its complement, then ... |
Article
![]() How to calculate the slopes of a D-module
(Foundation Compositio Mathematica, 1996-01-01)
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PhD Thesis
![]() Teorema de división para los operadores diferenciales y cálculo de multiplicidades de D-Modulos
(1984-10-31)
En el capítulo preliminar (Capítulo 0) se estudia la relación entre un módulo filtrado y el módulo graduado asociado y se ... |