It is shown that a simple closed curve in $${\mathbb {C}}^n$$ uniform limit of rectifiable curves each which has nontrivial polynomial hull itself hull. In case the rectifiable, to be hulls. also every , $$n\ge 2$$ can approximated total variation norm by polynomially convex, coincides with original except on an arbitrarily small segment. As corollary, it arc contained curve.

For i = 0, 1, . . . , n, let Ci be independent and identically distributed random variables with distribution F with support (0,∞). The number of zeros of the random tropical polynomials T fn(x) = mini=1,...,n(Ci + ix) is also the number of faces of the lower convex hull of the n + 1 random points (i, Ci) in R. We show that this number, Zn, satisfies a central limit theorem when F has polynomia...

We present an algorithm that computes the convex hull of multiple rational curves in the plane. The problem is reformulated as one of nding the zero-sets of polynomial equations in one or two variables; using these zero-sets we characterize curve segments that belong to the boundary of the convex hull. We also present a preprocessing step that can eliminate many redundant curve segments.

We describe a common generalization of the weighted matching problem and the weighted matroid intersection problem. In this context we establish common generalizations of the main results on those two problems--polynomial-time solvability, rain-max theorems, and totally dual integral polyhedral descriptions. New applications of these results include a strongly polynomial separation algorithm fo...

A novel moving horizon control strategy for input-saturated nonlinear polynomial systems is proposed. The control strategy makes use of the so called sum-of-squares (SOS) decomposition, i.e. a convexification procedure able to give sufficient conditions on the positiveness of polynomials. The complexity of SOS-based numerical methods is polynomial in the problem size and, as a consequence, comp...

In this paper we give upper and lower bounds as well as a heuristic estimate on the number of vertices of the convex closure of the set Gn = {(a, b) : a, b ∈ Z, ab ≡ 1 (mod n), 1 ≤ a, b ≤ n − 1} . The heuristic is based on an asymptotic formula of Rényi and Sulanke. After describing two algorithms to determine the convex closure, we 1 compare the numeric results with the heuristic estimate. The...

Given a graph G = (V,E), the closed interval of a pair of vertices u, v ∈ V , denoted by I[u, v], is the set of vertices that belongs to some shortest (u, v)-path. For a given S ⊆ V , let I[S] = ⋃ u,v∈S I[u, v]. We say that S ⊆ V is a convex set if I[S] = S. The convex hull Ih[S] of a subset S ⊆ V is the smallest convex set that contains S. We say that S is a hull set if Ih[S] = V . The cardina...

The mathematical modeling of the large deflections for the cantilever beams leads to a nonlinear differential equation with the mixed boundary conditions. Different numerical methods have been implemented by various authors for such problems. In this paper, two novel numerical techniques are investigated for the numerical simulation of the problem. The first is based on a spectral method utiliz...

We give an algorithm for constructing the algebraic hull of a given matrix Lie algebra. It is based on an algorithm for finding integral linear dependencies of the roots of a polynomial, that is probably of independent interest.

In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix polynomials. Some algebraic and geometrical properties are investigated. We also study the relationship between the C-numerical range of a matrix polynomial and the joint C-numerical range of its coefficients.