Search results for "Hull"

The Linear Ordering Polytope

2010

So far we developed a general integer programming approach for solving the LOP. It was based on the canonical IP formulation with equations and 3-dicycle inequalities which was then strengthened by generating mod-k-inequalities as cutting planes. In this chapter we will add further ingredients by looking for problem- specific inequalities. To this end we will study the convex hull of feasible solutions of the LOP: the so-called linear ordering polytope.

The simplex dispersion ordering and its application to the evaluation of human corneal endothelia

2009

A multivariate dispersion ordering based on random simplices is proposed in this paper. Given a R^d-valued random vector, we consider two random simplices determined by the convex hulls of two independent random samples of sizes d+1 of the vector. By means of the stochastic comparison of the Hausdorff distances between such simplices, a multivariate dispersion ordering is introduced. Main properties of the new ordering are studied. Relationships with other dispersion orderings are considered, placing emphasis on the univariate version. Some statistical tests for the new order are proposed. An application of such ordering to the clinical evaluation of human corneal endothelia is provided. Di…

The Bourgain property and convex hulls

2007

Let (Ω, Σ, μ) be a complete probability space and let X be a Banach space. We consider the following problem: Given a function f: Ω X for which there is a norming set B ⊂ BX * such that Zf,B = {x * ○ f: x * ∈ B } is uniformly integrable and has the Bourgain property, does it follow that f is Birkhoff integrable? It turns out that this question is equivalent to the following one: Given a pointwise bounded family ℋ ⊂ ℝΩ with the Bourgain property, does its convex hull co(ℋ) have the Bourgain property? With the help of an example of D. H. Fremlin, we make clear that both questions have negative answer in general. We prove that a function f: Ω X is scalarly measurable provided that there is a n…

A Novel Multi-Scale Strategy for Multi-Parametric Optimization

2017

The motion of a sailing yacht is the result of an equilibrium between the aerodynamic forces, generated by the sails, and the hydrodynamic forces, generated by the hull(s) and the appendages (such as the keels, the rudders, the foils, etc.), which may be fixed or movable and not only compensate the aero-forces, but are also used to drive the boat. In most of the design, the 3D shape of an appendage is the combination of a plan form (2D side shape) and a planar section(s) perpendicular to it, whose design depends on the function of the appendage. We often need a section which generates a certain quantity of lift to fulfill its function, but the lift comes with a penalty which is the drag. Th…

Numerical and experimental analysis of a high innovative hydrofoil

2020

The hydrofoil is a craft where the weight is entirely supported by the lift generated by the submerged part of wings. The particular structure of the craft requires a thorough study of the architecture of the hull, whose structure differs from others high speed vessels since the lift on wing surfaces are transmitted to the hull in limited areas (wing attacks). The authors have developed a research to optimize geometry of hull and wing system on a hydrofoil capable to carry 250 passengers at a speed of 35 knots, operating among Sicilian island. The principal goals of the new hydrofoil concern both the fuel reduction that the improvement of the comfort in terms of seakeeping and levels of aco…

A four vertex theorem for strictly convex space curves

1993

Monotonicity and enclosure methods for the p-Laplace equation

2018

We show that the convex hull of a monotone perturbation of a homogeneous background conductivity in the $p$-conductivity equation is determined by knowledge of the nonlinear Dirichlet-Neumann operator. We give two independent proofs, one of which is based on the monotonicity method and the other on the enclosure method. Our results are constructive and require no jump or smoothness properties on the conductivity perturbation or its support.

Derivation of high-resolution leaf area index maps in support of validation activities: Application to the cropland Barrax site

2009

The validation of coarse satellite-derived products from field measurements generally relies on up-scaling the field data to the corresponding satellite products. This question is commonly addressed through the generation of a reference high-resolution map of an area covering several moderate resolution pixels. This paper describes a method by which reference leaf area index (LAI) maps can be generated from ground-truth LAI measurements. The method is based on a multivariate ordinary least squares (OLS) algorithm which uses an iteratively re-weighted least squares (IRLS) algorithm. It provides an empirical relationship (i.e. a transfer function) between in situ measurements and concomitant …

Robust l2-gain control for 2D nonlinear stochastic systems with time-varying delays and actuator saturation

2013

Abstract This paper is concerned with the problems of stability analysis and l2-gain control for a class of two-dimensional (2D) nonlinear stochastic systems with time-varying delays and actuator saturation. Firstly, a convex hull representation is used to describe the saturation behavior, and a sufficient condition for the existence of mean-square exponential stability of the considered system is derived. Then, a state feedback controller which guarantees the resulting closed-loop system to be mean-square exponentially stable with l2-gain performance is proposed, and an optimization procedure to maximize the estimation of domain of attraction is also given. All the obtained results are for…

A constructive theory of shape

2021

We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of qualitatively similar shapes are constructed giving as input a finite ordered set of characteristic points (landmarks) and the value of a continuous parameter $\kappa \in (0,\infty)$. We prove that all shapes belonging to the same family are located within the convex hull of the landmarks. The theory is constructive in the sense that it provides a systematic means to build a mathematical model for any shape taken from the physical world. We illustrate this with a va…