Now showing items 1-20 of 33

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      A computational approach to the D-module of meromorphic functions  [Article]

      Castro Jiménez, Francisco Jesús; Ucha Enríquez, José María (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.
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      A flatness property for filtered D-modules  [Article]

      Castro Jiménez, Francisco Jesús; Granger, Michel (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, · · · , Zk be k germs of transverse hypersurfaces at a point x ∈ X. The Malgrange-Kashiwara V-filtrations ...
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      A vanishing theorem for a class of logarithmic D-modules  [Article]

      Castro Jiménez, Francisco Jesús; Gago Vargas, J.; Hartillo Hermoso, Isabel; Ucha Enríquez, José María (Cornell University, 2007)
      Let OX (resp. DX) be the sheaf of holomorphic functions (resp. the sheaf of linear differential operators with holomorphic coefficients) on X = Cn. Let D X be a locally weakly quasi-homogeneous free divisor defined by ...
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      An algebraic approach to Integer Portfolio problems  [Article]

      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 possibility of adding some natural features to the model. We propose an algebraic approach to ...
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      Bases de Gröbner: eliminación y programación lineal entera  [Final Degree Work]

      González Parra, Alba (2015-06)
      Gröbner basis is a basic concept in Computational Algebra; it was introduced by the Austrian mathematician Bruno Buchberger in 1965. A Gröbner basis of an ideal in a polinomial ring with coefficients over a field is a ...
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      Computational methods in algebra and analysis  [Article]

      Castro Jiménez, Francisco Jesús (Sociedad Española de Matemática Aplicada, 2007-09)
      This paper describes some applications of Computer Algebra to Algebraic Analysis also known as D-module theory, i.e. the algebraic study of the systems of linear partial differential equations. Gröbner bases for rings ...
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      Computer algebra and algebraic analysis  [Chapter of Book]

      Castro Jiménez, Francisco Jesús (Universidad de La Rioja, 2010)
      Este artículo describe algunas aplicaciones del Álgebra Computacional al Análisis Algebraico, también conocido como teoría de D-módulos, es decir, el estudio algebraico de sistemas lineales de ecuaciones en derivadas ...
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      Echelons of power series and Gabrielov’s counterexample to nested linear Artin Approximation  [Article]

      Alonso García, María Emilia; Castro Jiménez, Francisco Jesús; Hauser, Herwig; Koutschan, Christoph (London Mathematical Society, 2018)
      Gabrielov’s famous example for the failure of analytic Artin approximation in the presence of nested subring conditions is shown to be due to a growth phenomenon in standard basis computations for echelons, a generalization ...
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      Encoding algebraic power series  [Article]

      Alonso García, María Emilia; Castro Jiménez, Francisco Jesús; Hauser, Herwig (Springer, 2017)
      The division algorithm for ideals of algebraic power series satisfying Hironaka’s box condition is shown to be finite when expressed suitably in terms of the defining polynomial codes of the series. In particular, the codes ...
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      Explicit calculations in rings of differential operators  [Article]

      Castro Jiménez, Francisco Jesús; Granger, Michel (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 algebras. We consider the polynomial and the holomorphic cases as well as the formal case. Our ...
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      Explicit Comparison Theorems for D -modules  [Article]

      Castro Jiménez, Francisco Jesús; Ucha Enríquez, José María (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 give an application of this duality to the comparison between Mflog and the A2-module of rational ...
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      Free divisors and duality for D-modules  [Article]

      Castro Jiménez, Francisco Jesús; Ucha Enríquez, José María (Pleiades, 2002)
      The relationship between D-modules and free divisors has been studied in a general setting by L. Narváez and F.J. Calderón. Using the ideas of these works we prove in this article a duality formula between two D-modules ...
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      Gevrey expansions of hypergeometric integrals I  [Article]

      Castro Jiménez, Francisco Jesús; Granger, Michel (Oxford University Press, 2015)
      We study integral representations of the Gevrey series solutions of irregular hypergeometric systems. In this paper we consider the case of the systems associated with a one row matrix, for which the integration domains ...
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      Gevrey solutions of irregular hypergeometric systems in two variables  [Article]

      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 with an affine plane monomial curve. We also describe the irregularity complex of such a system with ...
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      Gevrey solutions of the irregular hypergeometric system associated with an affine monomial curve  [Article]

      Fernández Fernández, María Cruz; Castro Jiménez, Francisco Jesús (American Mathematical Society, 2011)
      We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine monomial curve. We also describe the irregularity complex of such a system with respect ...
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      Gröbner bases and logarithmic D-modules  [Article]

      Castro Jiménez, Francisco Jesús; Ucha Enríquez, José María (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 C. Elements in An are linear differential operators with polynomial coefficients. For each polynomial ...
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      Gröbner δ-bases and Gröbner bases for differential operators  [Article]

      Castro Jiménez, Francisco Jesús; Moreno Frías, María Ángeles (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 of W. Trinks, A. Assi, M. Insa and F. Pauer. We compare this notion with the one of Gröbner base for ...
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      How to calculate the slopes of a D-module  [Article]

      Assi, Abdallah; Castro Jiménez, Francisco Jesús; Granger, Michel (Foundation Compositio Mathematica, 1996)
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      Irregular modified A-Hypergeometric systems  [Article]

      Castro Jiménez, Francisco Jesús; Fernández Fernández, María Cruz; Koike, Tatsuya; Takayama, Nobuki (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 solution of an A-hypergeometric system in n variables and w is an n dimensional integer vector, which is ...
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      Linear nested Artin approximation theorem for algebraic power series  [Article]

      Castro Jiménez, Francisco Jesús; Popescu, Dorin; Rond, Guillaume (Springer, 2018)
      We give an elementary proof of the nested Artin approximation Theorem for linear equations with algebraic power series coefficients. Moreover, for any Noetherian local subring of the ring of formal power series, we clarify ...