This paper considers the optimal control problem for constrained discrete–time systems affected by measured and bounded disturbances and uncertainties in the underlying system equations. This problem setting leads to the sup–inf robust optimal control problems. Three classes of discrete–time systems permitting the characterization of the sup–inf value functions and robust optimal control polici...

Let X be a Banach space and let S(X)= {x ∈ X , ‖x‖ = 1} be the unit sphere of X . Parameters E(X) = sup{α(x), x ∈ S(X)}, e(X) = inf{α(x), x ∈ S(X)}, F(X) = sup{β(x), x ∈ S(X)}, and f (X) = inf{β(x), x ∈ S(X)}, where α(x) = sup{‖x + y‖2 + ‖x − y‖2, y ∈ S(X)}, and β(x) = inf{‖x + y‖2 + ‖x− y‖2, y ∈ S(X)} are introduced and studied. The values of these parameters in the lp spaces and function spac...

Interpolation by radial basis functions and interpolation by polynomials are both popular methods for function reconstruction from discrete data given on spheres. Recently, there has been an increasing interest in employing these function families together in hybrid schemes for scattered data modeling and the solution of partial differential equations on spheres. For the theoretical analysis of...

BACKGROUND The symptoms and functional limitations due to obstructive lung disease (OLD) are the direct results of airway and lung parenchymal destruction. In these conditions, airflow obstruction leads to increased work of breathing, and gas exchange abnormalities. Hyperinflation, which is inferred from a standard chest radiograph (CXR), may imply increased total lung capacity that can be seen...

The so called ”Pierce-Birkhoff Conjecture” asserts that a continuous function h on Rn piecewise polynomial on a finite number of pieces may be written as finitely many Sup and Inf of polynomials. Up to now a positive answer is known for n ≤ 2. In this paper we show that for n = 3 such an Inf-Sup description may be obtained outside an arbitrarily small neighborhood of a finite fixed set of point...

and Applied Analysis 3 With respect to the pointwise order u ≤ v ⇐⇒ ( ∀x ∈ Ω : u (x) ≤ v (x) ) (11) the setNL(Ω) is a Dedekind complete lattice. In particular, the supremum and infimum of a setA ⊂ NL(Ω) is given by inf A = (I ∘ S) (φ) , (12) supA = (I ∘ S) (ψ) , (13) respectively, where φ : Ω ∋ x 󳨃→ inf{u(x) : u ∈ A} and ψ : Ω ∋ x 󳨃→ sup{u(x) : u ∈ A}. Furthermore, the lattice NL(Ω) is fully di...

tributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Let (s n) be a real sequence, let (σ n) denote the sequence of averages of its first n partial sums. Let lim sup n σ n = β and lim inf n σ n = α, where β = α. We prove that lim sup n s n = β and lim inf n s ...

We study the distance-profile of the random rooted plane graph Gn with n edges (by a plane graph we mean a planar map with no loops nor multiple edges). Our main result is that the profile and radius of Gn (with 2 O. Bernardi, G. Collet, and É. Fusy In this article, we prove this type of result on the profile for rooted simple maps, that is, maps without loops nor multiple edges, which are clas...

| A formula for the optimistic capacity of arbitrary channels is established. It is shown to equal the supremum, over all input processes, of the inputoutput zero-sup-information rate. A general expression for optimistic "-capacity is also provided. I. Overview The conventional de nition of channel capacity C [1] requires the existence of reliable block codes for all su ciently large blocklengt...