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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42
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Publications |
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Article
Gevrey Expansions of Hypergeometric Integrals II
(Oxford University Press, 2019)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Integer variables allow the treatment of some portfolio optimization problems in a more realistic way and introduce the ... |
Article
Computing localizations iteratively
(Cornell University, 2011)
Let R = C[x] be a polynomial ring with complex coefficients and DX = Chx, ∂i be the Weyl algebra. Describing the localization ... |
Article
Gevrey solutions of the irregular hypergeometric system associated with an affine monomial curve
(American Mathematical Society, 2011)
We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated ... |
PhD Thesis
Soluciones Gevrey de sistemas hipergeométricos
(2010)
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)
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)
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)
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)
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)
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)
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)
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)
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)
In this paper we compare the approach of Brianc¸onand Maisonobe for computing Bernstein–Sato ideals—based on computations ... |
Article
Testing the Logarithmic Comparison Theorem for Free Divisors
(Taylor and Francis, 2004)
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Article
Explicit calculations in rings of differential operators
(Société Mathématique de France, 2004)
We use the notion of a standard basis to study algebras of linear differential operators and finite type modules over these ... |
Article
Quasi-free divisors and duality
(Elsevier, 2004)
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
Logarithmic cohomology of the complement of a plane curve
(Springer, 2002)
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 ... |
PhD Thesis
Métodos efectivos en anillos de operadores diferenciales y en sistemas hipergeométricos
(2002)
El Análisis Algebraico, o teoría de D-m&oa cute;dulos, trata el estudio de los sistemas de ecuaciones -- en derivadas ... |
Article
Gröbner δ-bases and Gröbner bases for differential operators
(Polish Academy of Sciences, Institute of Mathematics, 2002)
This paper deals with the notion of Gr¨obner δ-base for some rings of linear differential operators by adapting the works ... |
Article
Free divisors and duality for D-modules
(Pleiades, 2002)
The relationship between D-modules and free divisors has been studied in a general setting by L. Narváez and F.J. Calderón. ... |
Article
The analytic standard fan of a D-module
(Elsevier, 2001)
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)
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)
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)
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)
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)
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)
"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)
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)
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)
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PhD Thesis
Teorema de división para los operadores diferenciales y cálculo de multiplicidades de D-Modulos
(1984)
En el capítulo preliminar (Capítulo 0) se estudia la relación entre un módulo filtrado y el módulo graduado asociado y se ... |