Results 11 to 20 of about 71 (42)
Le groupoïde de Galois de P1 et son irréductibilité
, 2008 In this article, the Galois groupoid of the first Painleve equation is computed. This computation uses E. Cartan’s classification of structural equations of pseudogroups acting on C2 and the degeneration of the first Painleve equation on an elliptic ...
G. Casale
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Differential flatness and defect: an overview
, 1995 We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman ...
M. Fliess +3 more
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Algebraic and qualitative remarks about the family yy′ = (αxm+k–1 + βxm–k–1)y + γx2m–2k–1
Open Mathematics, 2019 The aim of this paper is the analysis, from algebraic point of view and singularities studies, of the 5-parametric family of differential ...
Rodríguez-Contreras Jorge +2 more
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Growth properties of functions in Hardy fields
, 1987 This paper continues the author's earlier work on the notion of rank in a Hardy field. Further results are given on functions in Hardy fields of finite rank, including extensions of Hardy's results on the rates of growth of his logarithmicoexponential ...
M. Rosenlicht
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The model theory of differential fields of characteristic ̸=0
, 1973 The theory of differential fields of characteristic p¿¿0 is shown to have a model companion, the theory of differentially closed fields, which is moreover the model completion of the theory of differentially perfect fields.
C. Wood
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Kähler differentials and differential algebra in arbitrary characteristic
, 1974 Let L and K be differential fields with L an extension of K. It is shown how the module of Kahler differentials S41/K can be used to "linearize" properties of a differential field extension L/K.
Joseph Johnson
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An analogue of l’Hospital’s rule
, 1973 Formal power series expansions have proved as useful in differential algebra as in other fields of mathematics. The present work magnifies one small aspect of their theory (leading terms) to get a simple result that is independent of the expansions ...
M. Rosenlicht
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Differential algebraic Lie algebras
, 1979 A class of infinite-dimensional Lie algebras over the field SC of constants of a universal differential field G1i is studied. The simplest case, defined by homogeneous linear differential equations, is analyzed in detail, and those with underlying set ...
P. Cassidy
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An Eisenstein criterion for noncommutative polynomials
, 1972 An analogue of the Eisenstein irreducibility criterion is developed for linear differential operators, or, more generally, noncommutative polynomials, and is applied to a few simple examples. Introduction.
J. Kovacic
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Functions satisfying elementary relations
, 1977 In this paper we deal with the following problems: When do the solutions of a collection of differential equations satisfy an elementary relation, that is, when is there an equation of the form R = 0 where R is some algebraic combination of logarithmic ...
M. Singer
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