‎in the present paper we investigate the $l_1$-weak ergodicity of‎ ‎nonhomogeneous continuous-time markov processes with general state‎ ‎spaces‎. ‎we provide a necessary and sufficient condition for such‎ ‎processes to satisfy the $l_1$-weak ergodicity‎. ‎moreover‎, ‎we apply‎ ‎the obtained results to establish $l_1$-weak ergodicity of quadratic‎ ‎stochastic processes‎.

In this paper we study the notion of strong non-reflection, and its contrapositive weak reflection. We say θ strongly non-reflects at λ iff there is a function F : θ −→ λ such that for all α < θ with cf(α) = λ there is C club in α such that F 1 C is strictly increasing. We prove that it is consistent to have a cardinal θ such that strong non-reflection and weak reflection each hold on an unboun...

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...