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Mostrando ítems 1-10 de 13
Artículo
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 with an affine plane monomial curve. We also describe the irregularity complex of such a system with ...
Artículo
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 consider the case of the systems associated with a one row matrix, for which the integration domains ...
Artículo
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 solution of an A-hypergeometric system in n variables and w is an n dimensional integer vector, which is ...
Artículo
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 Rf = R[f −1 ] for nonzero f ∈ R as a DX-module amounts to computing the annihilator A = ...
Artículo
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 possibility of adding some natural features to the model. We propose an algebraic approach to ...
Artículo
On irregular binomial D-modules
(Springer, 2012-12)
We prove that a holonomic binomial D–module MA(I, β) is regular if and only if certain associated primes of I determined by the parameter vector β ∈ Cd are homogeneous. We further describe the slopes of MA(I, β) along a ...
Artículo
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 expressed suitably in terms of the defining polynomial codes of the series. In particular, the codes ...
Artículo
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 coefficients. Moreover, for any Noetherian local subring of the ring of formal power series, we clarify ...
Artículo
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 assumptions. We prove that, for such systems, any Gevrey series solution, along a coordinate hyperplane of ...
Artículo
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 is shown to be due to a growth phenomenon in standard basis computations for echelons, a generalization ...