The reduction to normal form of a non-normal system of differential equations

Carl Gustav Jacob Jacobi; François Ollivier

doi:10.1007/s00200-009-0088-2

The reduction to normal form of a non-normal system of differential equations

Carl Gustav Jacob Jacobi, François Ollivier

Research output: Contribution to journal › Article › peer-review

Abstract

This paper was edited by Sigismund Cohn, C. W. Borchardt and A. Clebsch from posthumous manuscripts of C. G. J. Jacobi. The solution of the following problem: "to transform a square table of m ² numbers by adding minimal numbers ℓ_i to each horizontal row, in such a way that it possess m transversal maxima", determines the order and the shortest normal form reduction of the system: the equations u _i = 0 must be respectively differentiated ℓ_i times. One also determines the number of differentiations of each equation of the given system needed to produce the differential equations necessary to reduce the proposed system to a single equation.

Original language	English
Pages (from-to)	33-64
Number of pages	32
Journal	Applicable Algebra in Engineering, Communication and Computing
Volume	20
Issue number	1 SPEC. ISS.
DOIs	https://doi.org/10.1007/s00200-009-0088-2
Publication status	Published - 1 Jan 2009

Keywords

Assignment problem
Differential algebra
Differential resolvent
Jacobi's bound
Order of a differential system
Shortest reduction in normal form

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10.1007/s00200-009-0088-2

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abstract = "This paper was edited by Sigismund Cohn, C. W. Borchardt and A. Clebsch from posthumous manuscripts of C. G. J. Jacobi. The solution of the following problem: {"}to transform a square table of m 2 numbers by adding minimal numbers ℓi to each horizontal row, in such a way that it possess m transversal maxima{"}, determines the order and the shortest normal form reduction of the system: the equations u i = 0 must be respectively differentiated ℓi times. One also determines the number of differentiations of each equation of the given system needed to produce the differential equations necessary to reduce the proposed system to a single equation.",

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AU - Ollivier, François

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N2 - This paper was edited by Sigismund Cohn, C. W. Borchardt and A. Clebsch from posthumous manuscripts of C. G. J. Jacobi. The solution of the following problem: "to transform a square table of m 2 numbers by adding minimal numbers ℓi to each horizontal row, in such a way that it possess m transversal maxima", determines the order and the shortest normal form reduction of the system: the equations u i = 0 must be respectively differentiated ℓi times. One also determines the number of differentiations of each equation of the given system needed to produce the differential equations necessary to reduce the proposed system to a single equation.

AB - This paper was edited by Sigismund Cohn, C. W. Borchardt and A. Clebsch from posthumous manuscripts of C. G. J. Jacobi. The solution of the following problem: "to transform a square table of m 2 numbers by adding minimal numbers ℓi to each horizontal row, in such a way that it possess m transversal maxima", determines the order and the shortest normal form reduction of the system: the equations u i = 0 must be respectively differentiated ℓi times. One also determines the number of differentiations of each equation of the given system needed to produce the differential equations necessary to reduce the proposed system to a single equation.

KW - Assignment problem

KW - Differential algebra

KW - Differential resolvent

KW - Jacobi's bound

KW - Order of a differential system

KW - Shortest reduction in normal form

U2 - 10.1007/s00200-009-0088-2

DO - 10.1007/s00200-009-0088-2

M3 - Article

AN - SCOPUS:65049090331

SN - 0938-1279

VL - 20

SP - 33

EP - 64

JO - Applicable Algebra in Engineering, Communication and Computing

JF - Applicable Algebra in Engineering, Communication and Computing

IS - 1 SPEC. ISS.

ER -

The reduction to normal form of a non-normal system of differential equations

Abstract

Keywords

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