We consider the following problem, arising within a geological model of sedimentationerosion: For a given vector field g and a given nonnegative function F defined on a oneor twodimensional domain Ω, find a vector field under the form g̃ = ug, with 0 ≤ u(x) ≤ 1 for a.e. x ∈ Ω, such that divg̃ + F ≥ 0 and (u − 1)(divg̃ + F ) = 0 in Ω. We first give a weak formulation of this problem, and we prove a...

It is known that B(l) is not amenable for p = 1, 2,∞, but whether or not B(l) is amenable for p ∈ (1,∞) \ {2} is an open problem. We show that, if B(l) is amenable for p ∈ (1,∞), then so are l(B(l)) and l(K(l)). Moreover, if l(K(l)) is amenable so is l(I,K(E)) for any index set I and for any infinite-dimensional Lspace E; in particular, if l(K(l)) is amenable for p ∈ (1,∞), then so is l(K(l ⊕ l...

We show that it is possible to apply the DPG methodology without reformulating a second order boundary value problem into a first order system, by considering the simple example of the Poisson equation. The result is a new weak formulation and a new DPG method for the Poisson equation, which has no numerical trace variable, but has a numerical flux approximation on the element interfaces, in ad...

In this paper, a weak formulation of the discontinuous variable co-eecient Poisson equation with interfacial jumps is introduced. The existence, uniqueness and regularity of solutions of the Poisson equation are obtained. Finite diierence methods can be derived from the weak formulation. An abstract framework is given for proving convergence of the nite diierence methods for such problems. The ...

In a recent paper, probabilistic processes are used to generate Borel probability measures on topological spaces X that are equipped with a representation in the sense of Type-2 Theory of Effectivity. This gives rise to a natural representation of the set M(X) of Borel probability measures on X. We compare this representation to a canonically constructed representation which encodes a Borel pro...

A supersimple theory eliminates hyperimaginaries. In particular, in a supersimple theory Lascar strong type is the same as strong type, and every strong type has a canonical base in C . It follows that the Amalgamation Theorem (Independence Theorem) holds for types over algebraically closed sets.

We study roles of quark-quark correlations in the baryons for the deep inelastic structure function and the I = 1=2 rule of the non-leptonic weak hyperon decay. The quark-quark correlation is incorporated phenomenologically as diquarks within the Nambu and Jona-Lasinio model. The strong diquark correlations in the spin-0 channel enhance the I = 1=2 weak matrix elements, and account for the I = ...

Abstract. We discuss the multiplicity of the non-trivial zeros of the Riemann zetafunction and the summatory function M(x) of the Möbius function. The purpose of this paper is to consider two open problems under some conjectures. One is that whether all zeros of the Riemann zeta-function are simple or not. The other problem is that whether M(x) ≪ x holds or not. First, we consider the former pr...

I propose an approximation scheme for asymptotically free field theories combining both weak coupling and strong coupling series. The weak coupling expansion is used to integrate the high frequency modes and the resulting low energy effective theory is solved using the strong coupling expansion. In some models there exists an intermediate scale at which both expansions make sense. The method is...