First-return integrals

First Integrals of a Special System of Odes (TECHNICAL NOTE)

In this paper we suggest a method to calculate the first integrals of a special system of the first order of differential equations. Then we use the method for finding the solutions of some differential equations such as, the differential equation of RLC circuit.

Projective dynamics and first integrals

We show the relation between Appell's remark on the central projection in the dynamic of a particle and T.-Y. Thomas and Nijenhuis studies of the polynomial first integrals of the geodesic flow on a space of constant curvature. Among the consequences: the space of leading terms of a quadratic first integral of an equation¨q = f (q), q ∈ IR n , is isomorphic to the space of quadrilin-ear forms o...

The First Tax Return Assessment

In realising the first Tax Return Assessment Expert System in Switzerland we had first to make a convincing business case for an AI innovation in a traditional governmental environment, secondly to show in the daily business environment that what can be demonstrated to be viable in theory does also work in practice, thirdly to minimize the gap between the tacit knowledge in the head of assessme...

The Fundamental Theorem on Quadratic First Integrals.

Stabilization of positive systems with first integrals

Positive systems possessing %rst integrals are considered. These systems frequently occur in applications. This paper is devoted to two stabilization problems. The %rst is concerned with the design of feedbacks to stabilize a given level set. Secondly, it is shown that the same feedback allows to globally stabilize an equilibrium point if it is asymptotically stable with respect to initial cond...