Nadler. E., Nonnegativity of bivariate quadratic functions on a triangle. Computer Aided Geometric Design 9 (1992) 19.5-205. A necessary and sufficient condition for the nonnegativity of a bivariate quadratic defined on a triangle is presented in terms of the Bernstein-Bkzier form of the function. Keywfords. Nonnegativity, bivariate quadratic function, Bernstein-BCzier form, positiviry preservi...

Orthogonal families of bicircular quartics are naturally viewed as pairs singular foliations C^ by vertical and horizontal trajectories a non-vanishing quadratic differential. Yet the identification these with real in CP2 is subtle. Here, we give an efficient, geometric argument course updating classical theory confocal modern language differentials Edwards normal form for elliptic curves. In p...

We outline a specialization theory of quadratic and (symmetric) bilinear forms with respect to a place λ : K → L∪∞. Here K,L denote fields of any characteristic. We have to make a distinction between bilinear forms and quadratic forms and study them both over fields and valuation rings. For bilinear forms this turns out to be essentially as easy as in the case char L 6= 2, albeit no general can...

Abstract. We introduce and study a canonical quadratic form, called the torsion quadratic form, of the determinant line of a flat vector bundle over a closed oriented odd-dimensional manifold. This quadratic form caries less information than the refined analytic torsion, introduced in our previous work, but is easier to construct and closer related to the combinatorial Farber-Turaev torsion. In...

We find fundamental solutions in closed form for a family of parabolic equations with two spatial variables, whose symmetry groups had been determined in an earlier paper by Ferdinando Finkel [12]. We show how these results can be applied in finance to yield closed form solutions for special affine and quadratic two factor term structure models as well as a new class of models with inverse squa...