IN PRAISE OF ORDER UNITS

2012 ◽  
Vol 11 (06) ◽  
pp. 1250120
Author(s):  
DAVID HANDELMAN
Keyword(s):  
Compact Convex ◽  
Convex Polyhedra ◽  
Order Unit ◽  
Positivity Property

We show that the ordered rings naturally associated to compact convex polyhedra with interior satisfy a positivity property known as order unit cancellation, and obtain other general positivity results as well.

Closed covers of compact convex polyhedra

1991 ◽  
Vol 20 (2) ◽  
pp. 161-169 ◽  
Author(s):  
T. Ichiishi ◽  
A. Idzik
Keyword(s):  
Compact Convex ◽  
Convex Polyhedra

A characterization of compact convex polyhedra in hyperbolic 3-space

1993 ◽  
Vol 111 (1) ◽  
pp. 77-111 ◽  
Author(s):  
Craig D. Hodgson ◽  
Igor Rivin
Keyword(s):  
Compact Convex ◽  
Convex Polyhedra

scholarly journals Data-based polyhedron model for optimization of engineering structures involving uncertainties

2021 ◽  
Vol 2 ◽  
Author(s):  
Zhiping Qiu ◽  
Han Wu ◽  
Isaac Elishakoff ◽  
Dongliang Liu
Keyword(s):  
Linear Programming ◽  
Convex Polyhedron ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Composite Plates ◽  
Convex Polyhedra ◽  
Chebyshev Inequality ◽  
Engineering Structures ◽  
Load Bearing ◽  
Polyhedron Model

Abstract This paper studies the data-based polyhedron model and its application in uncertain linear optimization of engineering structures, especially in the absence of information either on probabilistic properties or about membership functions in the fussy sets-based approach, in which situation it is more appropriate to quantify the uncertainties by convex polyhedra. Firstly, we introduce the uncertainty quantification method of the convex polyhedron approach and the model modification method by Chebyshev inequality. Secondly, the characteristics of the optimal solution of convex polyhedron linear programming are investigated. Then the vertex solution of convex polyhedron linear programming is presented and proven. Next, the application of convex polyhedron linear programming in the static load-bearing capacity problem is introduced. Finally, the effectiveness of the vertex solution is verified by an example of the plane truss bearing problem, and the efficiency is verified by a load-bearing problem of stiffened composite plates.

Spectral resolution in an order-unit space

2008 ◽  
Vol 62 (3) ◽  
pp. 323-344 ◽  
Author(s):  
David J. Foulis ◽  
Sylvia Pulmannová
Keyword(s):  
Spectral Resolution ◽  
Order Unit ◽  
Unit Space ◽  
Order Unit Space

scholarly journals Vector spaces with an order unit

2009 ◽  
Vol 58 (3) ◽  
pp. 1319-1360 ◽  
Author(s):  
Vern I. Paulsen ◽  
Mark Tomforde
Keyword(s):  
Vector Spaces ◽  
Order Unit

Consistency conditions for a finite set of projections of a function

1979 ◽  
Vol 85 (1) ◽  
pp. 61-68 ◽  
Author(s):  
K. J. Falconer
Keyword(s):  
Lebesgue Measure ◽  
Convex Subset ◽  
Compact Convex ◽  
Unit Vector ◽  
Compact Convex Subset ◽  
Finite Collection ◽  
Finite Set ◽  
Almost All ◽  
Dimensional Lebesgue Measure ◽  
Unit Vectors

Let H(μ, θ) be the hyperplane in Rn (n ≥ 2) that is perpendicular to the unit vector 6 and perpendicular distance μ from the origin; that is, H(μ, θ) = (x ∈ Rn: x. θ = μ). (Note that H(μ, θ) and H(−μ, −θ) are the same hyperplanes.) Let X be a proper compact convex subset of Rm. If f(x) ∈ L1(X) we will denote by F(μ, θ) the projection of f perpendicular to θ; that is, the integral of f(x) over H(μ, θ) with respect to (n − 1)-dimensional Lebesgue measure. By Fubini's Theorem, if f(x) ∈ L1(X), F(μ, θ) exists for almost all μ for every θ. Our aim in this paper is, given a finite collection of unit vectors θ1, …, θN, to characterize the F(μ, θi) that are the projections of some function f(x) with support in X for 1 ≤ i ≤ N.

Sign in / Sign up

Export Citation Format

Share Document