The interior transmission problem is a boundary value problem that plays a basic role in inverse scattering theory but unfortunately does not seem to be included in any existing theory in partial differential equations.This paper presents old and new results for the interior transmission problem ,in particular its relation to inverse scattering theory and new results on the spectral theory asso...

Abstract. We study a quadratic C0 interior penalty method for the displacement obstacle problem of Kirchhoff plates with general Dirichlet boundary conditions on general polygonal domains. Under the conditions that the obstacles are sufficiently smooth and separated from each other and the boundary displacement, we prove that the magnitudes of the errors in the energy norm and the L∞ norm are O...

We establish a mean value property for harmonic functions on the interior of a hyperbola. This property connects their boundary values with the interior ones on the axis of the hyperbola from the focus to infinity.

we study interior operators and interior structures in a fuzzy setting.we investigate systems of “almost open” fuzzy sets and the relationshipsto fuzzy interior operators and fuzzy interior systems.

Observations are presented from Lake Biwa and Lake Kinneret showing the ubiquitous and often periodic nature of high-frequency internal waves in large stratified lakes. In both lakes, high-frequency wave events were observed within two distinct categories: (1) Vertical mode 1 solitary waves near a steepened Kelvin wave front and vertical mode 2 solitary waves at the head of an intrusive thermoc...

In this section we will give an (extremely) brief Introduction to the concept of interior point methods • Logarithmic Barrier Method • Method of Centers We have previously seen methods that follow a path On the boundary of the feasible region (Simplex). As the name suggest, interior point methods instead Follow a path through the interior of the feasible region.

We give a direct construction of the conformally invariant measure on self-avoiding loops in Riemann surfaces (Werner measure) from chordal SLE8/3. We give a new proof of uniqueness of the measure and use Schramm’s formula to construct a measure on boundary bubbles encircling an interior point. After establishing covariance properties for this bubble measure, we apply these properties to obtain...

We study face numbers of simplicial complexes that triangulate manifolds (or even normal pseudomanifolds) with boundary. Specifically, we establish a sharp lower bound on the number of interior edges of a simplicial normal pseudomanifold with boundary in terms of the number of interior vertices and relative Betti numbers. Moreover, for triangulations of manifolds with boundary all of whose vert...