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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)
      This paper deals with the notion of Gr¨obner δ-base for some rings of linear differential operators by adapting the works ...
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      Free divisors and duality for D-modules 

      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. ...
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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)
      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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      Specializations of MacMahon symmetric functions and the polynomial algebra 

      Rosas Celis, Mercedes Helena (Elsevier, 2002-03-06)
      A MacMahon symmetric function is a formal power series in a finite number of alphabets that is invariant under the diagonal ...
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      Ordering pure braid groups on compact, connected surfaces 

      González-Meneses López, Juan (University of California, 2002-04)
      We prove that the pure braid groups on compact, connected, orientable surfaces are bi-orderable, and that the pure braid groups on compact, connected non-orientable surfaces have generalized torsion, thus they are not bi-orderable.
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      Constructions in R[x_1, ..., x_n]. Applications to K-Theory 

      Gago Vargas, Manuel Jesús (2002-06-25)
      A classical result in K-Theory about polynomial rings like the Quillen-Suslin theorem admits an algorithmic approach when ...
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      Computing the rational torsion of an elliptic curve using Tate normal form 

      García Selfa, Irene; Olalla Acosta, Miguel Ángel; Tornero Sánchez, José María (Elsevier, 2002-09)
      It is a classical result (apparently due to Tate) that all elliptic curves with a torsion point of order n (4 ≤ n ≤ 10, ...
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      The module Dfs for locally quasi-homogeneous free divisors 

      Calderón Moreno, Francisco Javier; Narváez Macarro, Luis (Springer, 2002-10)
      We find explicit free resolutions for the D-modules Dfs and D[s]fs/D[s]f s+1, where f is a reduced equation of a locally ...
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      A combinatorial overview of the Hopf algebra of MacMahon symmetric functions 

      Rosas Celis, Mercedes Helena; Rota, Gian-Carlo; Stein, Joel (Springer, 2002-11)
      A MacMahon symmetric function is a formal power series in a finite number of alphabets that is invariant under the diagonal ...
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      Explicit models for perverse sheaves 

      Gudiel Rodríguez, Félix; Narváez Macarro, Luis (European Mathematical Society, 2003)
      We consider categories of generalized perverse sheaves, with relaxed constructibility conditions, by means of the process ...
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      Computation of centralizers in braid groups and Garside groups 

      Gonçalves Soares Franco, Nuno María; González-Meneses López, Juan (Consejo Superior de Investigaciones Científicas, 2003)
      We give a new method to compute the centralizer of an element in Artin braid groups and, more generally, in Garside groups. ...
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      Los números de (Euler)-Catalan 

      Rosas Celis, Mercedes Helena (Asociación Matemática Venezolana, 2003)
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      Minimal resolutions of lattice ideals and integer linear programming 

      Briales Morales, Emilio; Campillo López. Antonio; Pisón Casares, Pilar; Vigneron Tenorio, Alberto (European Mathematical Society, 2003)
      A combinatorial description of the minimal free resolution of a lattice ideal allows us to the connection of Integer ...
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      La labor docente del profesor de matemáticas 

      Aranda Plata, Antonio (Sociedad Española de Matemática Aplicada, 2003)
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      Sumando la derivada de la serie geométrica 

      Boulton, Lyonell; Rosas Celis, Mercedes Helena (Asociación Matemática Venezolana, 2003)
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      Some geometric aspects of Puiseux surfaces 

      Tornero Sánchez, José María (European Mathematical Society, 2003)
      The following problem is treated: Characterizing the tangent cone and the equimultiple locus of a Puiseux surface (that ...
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      Conservation of the noetherianity by perfect transcendental field extensions 

      Fernández Lebrón, María Magdalena; Narváez Macarro, Luis (European Mathematical Society, 2003)
      Let k be a perfect field of characteristic p>0, k(t)per the perfect closure of k(t) and A a k-algebra. We characterize whether the ring A⊗kk(t)per is noetherian when A is the ring of formal power series in n indeterminates over k.
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      Valuations in fields of power series 

      Herrera Govantes, Francisco Javier; Olalla Acosta, Miguel Ángel; Vicente Córdoba, José Luis (European Mathematical Society, 2003)
      This paper deals with valuations of fields of formal meromorphic functions and their residue fields. We explicitly describe ...
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      Hasse-Schmidt derivations and coefficient fields in positive characteristics 

      Fernández Lebrón, María Magdalena; Narváez Macarro, Luis (Elsevier, 2003-07-01)
      We show how to express any Hasse-Schmidt derivation of an algebra in terms of a finite number of them under natural ...
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      Monomial discrete valuations in k[[X]] 

      Herrera Govantes, Francisco Javier; Olalla Acosta, Miguel Ángel; Vicente Córdoba, José Luis (Cornell University, 2003-07-17)
      Let v be a rank m discrete valuation of k[[X1,...,Xn]] with dimension n-m. We prove that there exists an inmediate extension L of K where the valuation is monomial. Therefore we compute explicitly the residue field of the valuation.