Recently in [7). a new multivariate B-spline scheme based on blending functions and control vertices was developed . This surface scheme allows CIo-1-continuous piecewise polynomial surfaces of degree k over arbitrary triangulations to be modelled . Actually, piecewise polynomial surfaces over a refined triangulation are produced given an arbitrary triangulation . The scheme exhibits both affin...

This paper is a polyhedral study of a generalization of the mixing set where two different, divisible coefficients are allowed for the integral variables. Our results generalize earlier work on mixed integer rounding, mixing, and extensions. They also directly apply to applications such as production planning problems involving lower bounds or start-ups on production, when these are modeled as ...

The projective hull X̂ of a compact set X ⊂ P is an analogue of the classical polynomial hull of a set in C. In the special case that X ⊂ C ⊂ P, the affine part X̂ ∩C can be defined as the set of points x ∈ C for which there exists a constant Mx so that |p(x)| ≤ M x sup X |p| for all polynomials p of degree ≤ d, and any d ≥ 1. Let X̂(M) be the set of points x where Mx can be chosen ≤ M . Using an ...

We present efficient algorithms to construct both C1 and C 2 smooth meshes of cubic and quintic A-patches to approximate a given polyhedron P in three dimensions. The A~patch is a smooth and single-sheeted zero-contour patch of a trivariate polynomial in Bernstein-Bezier (BB) form defined within a tetrahedron. The smooth mesh constructions rely on a novel scheme to build an inner simplicial hul...

The masks for Loop’s triangle subdivision surface algorithm are modified resulting in surfaces with bounded curvature and the convex hull property. New edge masks are generated by a cubic polynomial mask equation whose Chebyshev coefficients are closely related to the eigenvalues of the corresponding subdivision matrix. The mask equation is found to satisfy a set of smoothness constraints on th...

A setC of vertices of a graph is P3-convex if every vertex outside C has at most one neighbor in C. The convex hull σ(A) of a set A is the smallest P3-convex set that contains A. A setM is convexly independent if for every vertex x ∈ M, x / ∈ σ(M− x). We show that the maximal number of vertices that a convexly independent set in a permutation graph can have, can be computed in polynomial time.

One can associate to any bivariate polynomial P (X,Y ) its Newton polygon. This is the convex hull of the points (i, j) such that the monomial X Y j appears in P with a nonzero coefficient. We conjecture that when P is expressed as a sum of products of sparse polynomials, the number of edges of its Newton polygon is polynomially bounded in the size of such an expression. We show that this “τ -c...

One can associate to any bivariate polynomial P (X,Y ) its Newton polygon. This is the convex hull of the points (i, j) such that the monomial X Y j appears in P with a nonzero coefficient. We conjecture that when P is expressed as a sum of products of sparse polynomials, the number of edges of its Newton polygon is polynomially bounded in the size of such an expression. We show that this “τ -c...

This study proposes a new method for the acceleration of the projection method to compute a few eigenvalues with the largest real parts of a large nonsymmetric matrix. In the eld of the solution of the linear system, an acceleration using the least squares polynomial which minimizes its norm on the boundary of the convex hull formed with the unwanted eigenvalues are proposed. We simplify this m...

‎In the present paper‎, ‎optimal heating of temperature field which is modelled as a boundary optimal control problem‎, ‎is investigated in the uncertain environments and then it is solved numerically‎. ‎In physical modelling‎, ‎a partial differential equation with stochastic input and stochastic parameter are applied as the constraint of the optimal control problem‎. ‎Controls are implemented ...