A preference is invariant with respect to a transformation τ if its ranking of acts is unaffected by a reshuffling of the states under τ . We show that any invariant preference must be parametric: there is a unique sufficient set of parameters such that the preference ranks acts according to their expected utility given the parameters. This property holds for all non-trivial preferences, provid...

A trigonometric curve is a real plane curve where each coordinate is given parametri-cally by a truncated Fourier series. The trigonometric curves frequently arise in various areas of mathematics, physics, and engineering. Some trigonometric curves can be also represented implicitly by bivariate polynomial equations. In this paper, we give algorithms for (a) simplifying a given parametric repre...

In this paper, we establish the equivalence between the half-space representation and the vertex representation of a smooth parametric semiclosed polyhedron. By virtue of the smooth representation result, we prove that the solution set of a smooth parametric piecewise linear program can be locally represented as a finite union of parametric semiclosed polyhedra generated by finite smooth functi...