In previous work the framework for a hypercomplex function theory in superspace was established and amply investigated. In this paper a Cauchy integral formula is obtained in this new framework by exploiting techniques from orthogonal Clifford analysis. After introducing Clifford algebra valued surfaceand volume-elements first a purely fermionic Cauchy formula is proven. Combining this formula ...

Abstract In this paper we examine necessary conditions for an inhomogeneity to be non‐scattering, or equivalently, by negation, sufficient it scattering. These are formulated in terms of the regularity boundary inhomogeneity. We broad classes incident waves both two and three dimensions. Our analysis is greatly influenced carried out Williams order establish that a domain, which does not posses...

Let Ξ(H) denote the set of all nonzero closed convex cones in a finite dimensional Hilbert space H. Consider this set equipped with the bounded Pompeiu-Hausdorff metric δ. The collection of all pointed cones forms an open set in the metric space (Ξ(H), δ). One possible way of measuring the degree of pointedness of a cone K is by evaluating the distance from K to the set of all nonpointed cones....

In the unit ball B(0, 1), let u and Ω (a domain in RN ) solve the following overdetermined problem: ∆u = χΩ in B(0, 1), 0 ∈ ∂Ω, u = |∇u| = 0 in B(0, 1) \ Ω, where χΩ denotes the characteristic function, and the equation is satisfied in the sense of distributions. If the complement of Ω does not develop cusp singularities at the origin then we prove ∂Ω is analytic in some small neighborhood of t...

In this paper, we extend fundamental notions of control theory to evolving compact subsets of the Euclidean space – as states without linear structure. Dispensing with any restriction of regularity, shapes can be interpreted as nonempty compact subsets of the Euclidean space RN . Their family K(RN ), however, does not have any obvious linear structure, but in combination with the popular Pompei...

We will discuss the regularity theory and the geometry of the free boundary for free boundary problems of obstacle type, but without positivity assumptions, for instance the Pompeiu problem 4:15–5:00 pm Wendell Fleming Brown University Risk Sensitive Stochastic Control Abstract: Risk sensitive control provides a link between deterministic and stochastic modelling of disturbances in control syst...