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Abstract:

This paper is mainly devoted to the study of the differentiation index and the order for quasi-regular implicit ordinary differential algebraic equation (DAE) systems. We give an algebraic definition of the differentiation index and prove a Jacobi-type upper bound for the sum of the order and the differentiation index. Our techniques also enable us to obtain an alternative proof of a combinatorial bound proposed by Jacobi for the order. As a consequence of our approach we deduce an upper bound for the Hilbert-Kolchin regularity and an effective ideal membership test for quasi-regular implicit systems. Finally, we prove a theorem of existence and uniqueness of solutions for implicit differential systems. © 2008 Elsevier Inc. All rights reserved.

Registro:

Documento: Artículo
Título:On the index and the order of quasi-regular implicit systems of differential equations
Autor:D'Alfonso, L.; Jeronimo, G.; Massaccesi, G.; Solernó, P.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina
Palabras clave:Differential membership problem; Differentiation index; Existence and uniqueness; Implicit systems of differential equations; Order of a differential ideal; Differential membership problem; Differentiation index; Existence and uniqueness; Implicit systems of differential equations; Order of a differential ideal
Año:2009
Volumen:430
Número:8-9
Página de inicio:2102
Página de fin:2122
DOI: http://dx.doi.org/10.1016/j.laa.2008.11.029
Título revista:Linear Algebra and Its Applications
Título revista abreviado:Linear Algebra Its Appl
ISSN:00243795
CODEN:LAAPA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00243795_v430_n8-9_p2102_DAlfonso

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Citas:

---------- APA ----------
D'Alfonso, L., Jeronimo, G., Massaccesi, G. & Solernó, P. (2009) . On the index and the order of quasi-regular implicit systems of differential equations. Linear Algebra and Its Applications, 430(8-9), 2102-2122.
http://dx.doi.org/10.1016/j.laa.2008.11.029
---------- CHICAGO ----------
D'Alfonso, L., Jeronimo, G., Massaccesi, G., Solernó, P. "On the index and the order of quasi-regular implicit systems of differential equations" . Linear Algebra and Its Applications 430, no. 8-9 (2009) : 2102-2122.
http://dx.doi.org/10.1016/j.laa.2008.11.029
---------- MLA ----------
D'Alfonso, L., Jeronimo, G., Massaccesi, G., Solernó, P. "On the index and the order of quasi-regular implicit systems of differential equations" . Linear Algebra and Its Applications, vol. 430, no. 8-9, 2009, pp. 2102-2122.
http://dx.doi.org/10.1016/j.laa.2008.11.029
---------- VANCOUVER ----------
D'Alfonso, L., Jeronimo, G., Massaccesi, G., Solernó, P. On the index and the order of quasi-regular implicit systems of differential equations. Linear Algebra Its Appl. 2009;430(8-9):2102-2122.
http://dx.doi.org/10.1016/j.laa.2008.11.029