This article generalizes the geometric quadratic Chabauty method, initiated over Q \mathbb {Q}</mml:annotation...

This work addresses the problem of identifiability, that is, question whether parameters can be recovered from data, for linear compartmental models. Using standard differential algebra techniques, a given model is generically locally identifiable equivalent to asking Jacobian matrix certain coefficient map, arising input-output equations, full rank. A natural next step study set parameter valu...

There are nontrivial dualities and parallels between polynomial algebras and the Grassmann algebras. This paper is an attempt to look at the Grassmann algebras at the angle of the Jacobian conjecture for polynomial algebras (which is the question/conjecture about the Jacobian set – the set of all algebra endomorphisms of a polynomial algebra with the Jacobian 1 – the Jacobian conjecture claims ...

A new Jacobian approximation is developed for use in quasi-Newton methods for solving systems of nonlinear equations. The new hypersecant Jacobian approximation is intended for the special case where the evaluation of the functions whose roots are sought dominates the computation time, and additionally the Jacobian is sparse. One example of such a case is the solution of the discretized transpo...

y 00 (except at t = 0). One additional differentiation to get y 000 guarantees full column rank equal to three for the coefficient matrix of vector x. For the example, this rank condition is equivalent to the 1-full condition on the Jacobian O j; k of (11) for the time-varying linearization. (We may take j = 1 and k = 3.) Thus we have smooth observability on the interval [0; T ] for the time-va...