La borne de Jacobi pour une diffiété définie par un système quasi régulier

TL;DR: A combinatorial optimization problem, independently defined in satellite communication and in scheduling theory, for which the same polynomial-time algorithm was independently published 30 years ago by various authors, and it can be shown that such algorithm directly implements another result contained in the same 1931 paper by Egerváry.

TL;DR: A fast prolongation method for a development of (explicit) symbolic Riquier Bases, suitable for numerical applications of complicated nonlinear systems of pde with constraints, is reviewed.

TL;DR: It is shown that any of these systems can be transformed to a generically equivalent first order DAE system consisting of a single purely algebraic (polynomial) equation plus an under-determined ODE in as many variables as the order of the input system.

TL;DR: In this paper, an algebraic definition of the differentiation index and a Jacobi-type upper bound for the sum of the order and the differential index for quasi-regular DAE systems are presented.

TL;DR: In this article, it was shown that the strong Jacobi bound for the order of differential systems cannot be valid if a very natural conjecture concerning the differential dimension of such systems is false.

TL;DR: In this paper, a decision procedure is found to determine when a sentence is true in almost every Frobenius difference field, which generalizes Cebotarev's density theorem and Weil's Riemann hypothesis for curves.

TL;DR: In this paper, it is shown that the argument on which Jacobi bases his conclusion, in the first of the above mentioned papers, should be whimsical in aspect, and it seems safe to assume that before one can speak with completeness on the question of arbitrary constants, one will have to possess a theory for the decomposition of a system into systems of some normal type.