On the index and the order of quasi-regular implicit systems of differential equations

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 di...

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Autores principales:	D'Alfonso, L., Jeronimo, G., Massaccesi, G., Solernó, P.
Formato:	JOUR
Materias:	Differential membership problem Differentiation index Existence and uniqueness Implicit systems of differential equations Order of a differential ideal
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00243795_v430_n8-9_p2102_DAlfonso
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_00243795_v430_n8-9_p2102_DAlfonso
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spelling	todo:paper_00243795_v430_n8-9_p2102_DAlfonso2023-10-03T14:34:46Z On the index and the order of quasi-regular implicit systems of differential equations D'Alfonso, L. Jeronimo, G. Massaccesi, G. Solernó, P. 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 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. Fil:Jeronimo, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Massaccesi, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Solernó, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00243795_v430_n8-9_p2102_DAlfonso
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	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
spellingShingle	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 D'Alfonso, L. Jeronimo, G. Massaccesi, G. Solernó, P. On the index and the order of quasi-regular implicit systems of differential equations
topic_facet	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
description	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.
format	JOUR
author	D'Alfonso, L. Jeronimo, G. Massaccesi, G. Solernó, P.
author_facet	D'Alfonso, L. Jeronimo, G. Massaccesi, G. Solernó, P.
author_sort	D'Alfonso, L.
title	On the index and the order of quasi-regular implicit systems of differential equations
title_short	On the index and the order of quasi-regular implicit systems of differential equations
title_full	On the index and the order of quasi-regular implicit systems of differential equations
title_fullStr	On the index and the order of quasi-regular implicit systems of differential equations
title_full_unstemmed	On the index and the order of quasi-regular implicit systems of differential equations
title_sort	on the index and the order of quasi-regular implicit systems of differential equations
url	http://hdl.handle.net/20.500.12110/paper_00243795_v430_n8-9_p2102_DAlfonso
work_keys_str_mv	AT dalfonsol ontheindexandtheorderofquasiregularimplicitsystemsofdifferentialequations AT jeronimog ontheindexandtheorderofquasiregularimplicitsystemsofdifferentialequations AT massaccesig ontheindexandtheorderofquasiregularimplicitsystemsofdifferentialequations AT solernop ontheindexandtheorderofquasiregularimplicitsystemsofdifferentialequations
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On the index and the order of quasi-regular implicit systems of differential equations

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