In this thesis we study a formal first order system T in the standard language L, of Gentzen’s LK, see [Tak87]. T(tind) extends LK by the following valid first-order inference rule (A is quantifier-free). Γ,A(a), Λ→ ∆,A(s(a)), Θ Γ,A(0), Λ→ ∆,A(sn(0)), Θ (tind) This rule is called term induction, it derives a restricted term built from successor s and the constant 0. We call such terms numerals....

Remember the scene in the original Jurassic Park, when all the Land Rovers sputtered and stalled during the park tour? The rain was drumming hard on the roofs of the vehicles and tension began to rise. Slowly, the camera zoomed onto the surface of a still glass of water, and the surface began to ripple. Here, Spielberg was trying to give the sense of something big about to happen. Because he wa...

Reverse subdivision constructs a coarse mesh of a model from a finer mesh of this same model. In [1] Lanquetin and Neveu propose a reverse mask for the Catmull-Clark scheme which consists in locally reversing Catmull-Clark original formula for even control points, but this mask can not be applied in reversing other variants such as Quad-averaging scheme of Warren and Weimer [2]. In this paper, ...

In this paper we study a large class of resource allocation problems with an important complication, the utilization cost of a given resource is private information of a profit maximizing agent. After reviewing the characterization of the optimal bayesian mechanism, we study the informational cost introduced by the presence of private information. Our main result is to provide an upper bound fo...

This paper presents a marching method for computing intersection curves between two solids represented by subdivision surfaces of Catmull-Clark or Loop type. It can be used in trimming and boolean operations for subdivision surfaces. The main idea is to apply a marching method with geometric interpretation to trace the intersection curves. We first determine all intersecting regions, then find ...