A problem in distance geometry is to find the location of an unknown point in a given convex set in Rk such that its farthest distance to n fixed points is minimum. In this paper we present an algorithm based on subgradient method and convex hull computation for solving this problem. A recent improvement of Quickhull algorithm for computing the convex hull of a finite set of planar points is ap...

Recently introduced invariants copoint pre-hull number and convex pre-hull number are both numerical measures of nonconvexity of a graph G that is a convex space. We consider in this work both on the Cartesian and the strong product of graphs. Exact values in terms of invariants of the factors are presented for the first mentioned product. For strong product it is shown that such a result does ...

in this paper, a numerical efficient method is proposed for the solution of time fractionalmobile/immobile equation. the fractional derivative of equation is described in the caputosense. the proposed method is based on a finite difference scheme in time and legendrespectral method in space. in this approach the time fractional derivative of mentioned equationis approximated by a scheme of order o...

We introduce control curves for trigonometric splines and show that they have properties similar to those for classical polynomial splines. In particular, we discuss knot insertion algorithms, and show that as more and more knots are inserted into a trigonometric spline, the associated control curves converge to the spline. In addition, we establish a convex-hull property and a variation-dimini...

Let S be used to denote a nite set of planar geometric objects. Deene a polygon transversal of S as a closed simple polygon that simultaneously intersects every object in S, and a minimum polygon transversal of S as a polygon transversal of S with minimum perimeter. If S is a set of points then the minimum polygon transversal of S is the convex hull of S. However, when the objects in S have som...

Let G be a connected and simply connected nilpotent Lie group with Lie algebra g and unitary dual Ĝ. The moment map for π ∈ Ĝ sends smooth vectors in the representation space of π to g∗. The closure of the image of the moment map for π is called its moment set. N. Wildberger has proved that the moment set for π coincides with the closure of the convex hull of the corresponding coadjoint orbit. ...

The classical Gauss-Lucas Theorem states that all the critical points (zeros of the derivative) of a nonconstant polynomial p lie in the convex hull Ξ of the zeros of p. It is proved that, actually, a subdomain of Ξ contains the critical points of p.

We show how to efficiently model binary constraint problems (BCP) as integer programs. After considering tree-structured BCPs first, we show that a Sherali-Adams-like procedure results in a polynomial-size linear programming description of the convex hull of all integer feasible solutions when the BCP that is given has bounded tree-width.

Let r > 1 and let Q be a probability measure on a measurable space (X, .4). In this note, we present a proof of a useful bound in Lr ( Q)-norm for the entropy of a convex hull in the case that covering numbers for a class of measurable functions are polynomial.

in this paper, solution of nonlinear optimal control problems and the controlled duffing oscillator, as a special class of optimal control problems, are considered and an efficient algorithm is proposed. this algorithm is based on state parametrization as a polynomial with unknown coefficients. by this method, the control and state variables can be approximated as a function of time. also, the ...