On the Index and the Order of Quasi-regular Implicit Systems of Differential Equations
| dc.creator | D'Alfonso, Lisi | |
| dc.creator | Jeronimo, Gabriela | |
| dc.creator | Massaccesi, Gustavo | |
| dc.creator | Solernó, Pablo | |
| dc.date | 2008-04-30 | |
| dc.date | 2008-11-19 | |
| dc.date.accessioned | 2026-07-07T10:19:02Z | |
| dc.date.available | 2026-07-07T10:19:02Z | |
| dc.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. | |
| dc.identifier | https://arxiv.org/abs/0804.4842 | |
| dc.identifier | http://arxiv.org/abs/0804.4842 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174365 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | On the Index and the Order of Quasi-regular Implicit Systems of Differential Equations | |
| dc.type | text |