29 research outputs found
Algebra versus analysis in the theory of flexible polyhedra
Two basic theorems of the theory of flexible polyhedra were proven by
completely different methods: R. Alexander used analysis, namely, the Stokes
theorem, to prove that the total mean curvature remains constant during the
flex, while I.Kh. Sabitov used algebra, namely, the theory of resultants, to
prove that the oriented volume remains constant during the flex. We show that
none of these methods can be used to prove the both theorems. As a by-product,
we prove that the total mean curvature of any polyhedron in the Euclidean
3-space is not an algebraic function of its edge lengths.Comment: 5 pages, 5 figures; condition (iii) in Theorem 5 is correcte
On the total mean curvature of non-rigid surfaces
Using Green's theorem we reduce the variation of the total mean curvature of
a smooth surface in the Euclidean 3-space to a line integral of a special
vector field and obtain the following well-known theorem as an immediate
consequence: the total mean curvature of a closed smooth surface in the
Euclidean 3-space is stationary under an infinitesimal flex.Comment: 4 page
Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds
We study curvature functionals for immersed 2-spheres in a compact,
three-dimensional Riemannian manifold M. Under the assumption that the
sectional curvature of M is strictly positive, we prove the existence of a
smoothly immersed sphere minimizing the L^{2} integral of the second
fundamental form. Assuming instead that the sectional curvature is less than or
equal to 2, and that there exists a point in M with scalar curvature bigger
than 6, we obtain a smooth 2-sphere minimizing the integral of 1/4|H|^{2} +1,
where H is the mean curvature vector
Market Power and Collusion on Interconnection Phone Market in Tunisia : What Lessons from International Experiences
We try in this paper to characterize the state of mobile phone market in Tunisia. Our study is based on a survey of foreign experience (Europe) in detecting collusive behavior and a comparison of the critical threshold of collusion between operators in developing countries like Tunisia. The market power is estimated based on the work of Parker Roller (1997) and the assumption of "Balanced Calling Pattern". We use then the model of Friedman (1971) to compare the critical threshold of collusion. We show that the "conduct parameter" measuring the intensity of competition is not null during the period 1993-2011. Results show also that collusion is easier on the Tunisian market that on the Algerian, Jordanian, or Moroccan one