INVERTIBLE INTERPOLATION PROBLEMS IN ALG(equation omitted)

Multivariable Interpolation Problems

Interpolation theory and shell problems

The shell problem and its asymptotic are investigated. A connection between the asymptotic behavior of the shell energy and real Interpolation Theory is established. Although only the Koiter shells have been considered, the same procedure can be used for other models, such as Naghdi’s one, for example.

Interpolation of Benchmark Problems in Defeasible Reasoning

Defeasible reasoning is the kind of logic in which further inference may cause a retraction of former conclusions. Recently, the research program of defeasible reasoning seems to be driven by a set of simple case studies, called benchmark problems, that are used to indicate the strength (or weakness) of particular modes of defeat. In doing so, the aim is to solve as much benchmark problems as p...

Extremal Problems of Interpolation Theory

We consider problems where one seeks m×m matrix valued H∞ functions w(ξ) which satisfy interpolation constraints and a bound (0.1) w∗(ξ)w(ξ) ≤ ρmin, |ξ| < 1, where the m×m positive semi-definite matrix ρmin is minimal (no smaller than) any other matrix ρ producing such a bound. That is, if (0.2) w∗(ξ)w(ξ) ≤ ρ, |ξ| < 1, and if ρmin − ρ is positive semi-definite, then ρmin = ρ. This is an example...

Hereditary Invertible Linear Surjections and Splitting Problems for Selections

Let A + B be the pointwise (Minkowski) sum of two convex subsets A and B of a Banach space. Is it true that every continuous mapping h : X → A + B splits into a sum h = f + g of continuous mappings f : X → A and g : X → B? We study this question within a wider framework of splitting techniques of continuous selections. Existence of splittings is guaranteed by hereditary invertibility of linear ...