We extend the Wermer’s theorem, to describe the polynomial hull of compact sets lying on the boundary of a smooth strictly convex domain of Cn. We also extend the result to polynomial p-hulls and apply it to get properties of pluriharmonic or p.s.h. positive currents. RÉSUMÉ. Nous décrivons à la suite des travaux de Wermer, l’enveloppe polynomiale des ensembles compacts contenus dans le bord d’...

We say that a subset of C n is hypoconvex if its complement is the union of complex hyperplanes. Let be the closed unit disk in C , ? = @. We prove two conjectures of Helton and Marshall. Let be a smooth function on ? C n whose sublevel sets have compact hypoconvex bers over ?. Then, with some restrictions on , if Y is the set where is less than or equal to 1, the polynomial convex hull of Y is...

In this paper we give some evidence for M Kontsevich’s homological mirror symmetry conjecture [13] in the context of toric varieties. Recall that a smooth complete toric variety is given by a simplicial rational polyhedral fan ∆ such that |∆| = Rn and all maximal cones are non-singular (Fulton [10, Section 2.1]). The convex hull of the primitive vertices of the 1–cones of ∆ is a convex polytope...

a class of new methods based on a septic non-polynomial spline function for the numerical solution one-dimensional bratu's problem are presented. the local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. the inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. associated bound...

We present a sixth-order non-polynomial spline method for the solutions of two-point nonlinear boundary value problem u(4)+f(x,u)=0, u(a)=α1, u''(a)= α2, u(b)= β1,u''(b)= β2, in off step points. Numerical method of sixth-order with end conditions of the order 6 is derived. The convergence analysis of the method has been discussed. Numerical examples are presented to illustrate the applications ...

We present the class of binary automaton, a new representation for the subsets of N that naturally extends the NDD ([25], [10]). We prove that the affine hull of the set of vectors represented by a binary automaton is computable in polynomial time. As application, we show that the set of place invariants [11] of a counter system (an extension of the Broadcast Protocols [16], [13], [12], the Res...

We prove that, for a tropical rational map if any point the convex hull of Jacobian matrices at smooth points in neighborhood does not contain singular then is an isomorphism. also show that polynomial on plane isomorphism all Jacobians have same sign (positive or negative). In addition, we and its preimage singleton least one regular

We study dynamical properties of asymptotically extremal polynomials associated with a non-polar planar compact set E. In particular, we prove that if the zeros such are uniformly bounded then their Brolin measures converge weakly to equilibrium measure addition, E is regular and sufficiently close show filled Julia sets polynomial convex hull in Klimek topology.

A new multivariate B-spline scheme based on blending functions and control ver-tices has recently been developed by Dahmen, Micchelli, and Seidel 4]. This surface scheme allows to model piecewise polynomial surfaces of degree k over arbitrary triangulations, such that the resulting surfaces are C k?1-continuous everywhere. The scheme exhibits both aane invariance and the convex hull property, a...