Quadratic polynomials and quadratic forms

Applications of quadratic D-forms to generalized quadratic forms

In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.

Annihilating polynomials for quadratic forms

This is a short survey of the main known results concerning annihilating polynomials for the Witt ring of quadratic forms over a field. 1991 A.M.S. Subject Classification : 11E81, 12F10, 19A22

Quadratic Polynomials Represented by Norm Forms

— Let P (t) ∈ Q[t] be an irreducible quadratic polynomial and suppose that K is a quartic extension of Q containing the roots of P (t). Let NK/Q(x) be a full norm form for the extension K/Q. We show that the variety P (t) = NK/Q(x) 6= 0 satisfies the Hasse principle and weak approximation. The proof uses analytic methods.

Quadratic Functions, Optimization, and Quadratic Forms

Linear-quadratic Control and Quadratic Differential Forms

We consider the infinite time linear-quadratic control problem from a behavioral point of view. The performance functional is the integral of a quadratic differential form. A characterization of the stationary trajectories and of the local minima with respect to (left) compact support variations, as well as their relation to stability, are obtained. Finally, several theorems are derived that de...