Let M be a compact manifold with smooth boundary. We study the heat content asymptotics on M defined by a time dependent heat source and time dependent boundary conditions. We adopt the following notational conventions: let M be a compact Riemannian manifold with smooth boundary ∂M , let ∆ = δd be the scalar Laplacian on M , let x be a point of the interior of M , let y be a point of the bounda...

K e y w o r d s A c o u s t i c scattering, Boundary value problems, Potential theory, Explicit solution, Cuts, Cracks, Screens. 1. I N T R O D U C T I O N In the jump problem for the Helmholtz equation outside cuts in a plane we specie" the jump of the solution and the jump of its normal derivative at the cuts. This problem is closely related to the Dirichlet and Neumann problems outside cuts ...

Here we will present some deeper results in renewal theory such as a central limit theorem for counting processes, stationary versions of renewal processes, renewal equations, the key renewal theorem, weak convergence. 1 Central limit theorem for counting processes Consider a renewal process {t n : n ≥ 1} with iid interarrival times X n = t n − t n−1 , n ≥ 0, such that 0 < E(X) = 1/λ < ∞ and 0 ...

We consider the problem of multi-dimensional linearized stability of planar, inviscid detonation waves. For an abstract, multi-step reaction model a normal mode analysis leads to a stability function similar to the Lopatinski determinant for gas dynamics. In the lowfrequency/long wave limit of the perturbation we obtain explicit criteria for uniform stability, weak stability, and strong instabi...

In this paper, we discuss the semantics of disjunctive programs and databases and show how multivalued mappings and their fixed points arise naturally within this context. A number of fixed-point theorems for multivalued mappings are considered, some of which are already known and some of which are new. The notion of a normal derivative of a disjunctive program is introduced. Normal derivatives...

A consistent approach to Cosmology requires an explicit averaging of the Einstein equations, to describe a homogeneous and isotropic geometry. Such an averaging will in general modify the Einstein equations. The averaging procedure due to Buchert has attracted considerable attention recently since it offers the tantalizing hope of explaining the phenomenon of dark energy through such correction...

Emission of fast energetic nucleons in intermediate energy nuclear collisions is investigated in the framework of two specific non-equilibrium models. In the lower energy region considered, the Fermi Jet mechanism dominates whereas results in the higher energy region are suggestive of emission from a hot dense source formed inside cold nuclear matter.

In Rutten [13] the theoretical basis was given for the synthesis of binary Mealy machines from specifications in 2-adic arithmetic. This construction is based on the symbolic computation of the coalgebraic notion of stream function derivative, a generalisation of the Brzozowski derivative of regular expressions. In this paper we complete the construction of Mealy machines from specifications in...