In this paper we introduce a family of ordered sets we call k-weak orders which generalize weak orders, semi-orders, and bipartite orders. For each k, we give a polynomial-time recognition algorithm for k-weak orders and a partial characterization. In addition, we prove that among 1-weak orders, the classes of bounded bitolerance orders and totally bounded bitolerance orders are equal. This ena...

Motivated by the heat flow and bubble analysis of biharmonic mappings, we study further regularity issues fourth order Lamm–Rivière system $$\begin{aligned} \Delta ^{2}u=\Delta (V\cdot \nabla u)+\mathrm{div}(w\nabla u)+(\nabla \omega +F)\cdot u+f \end{aligned}$$ in dimension four, with an inhomogeneous term f which belongs to some natural function space. We obtain optimal higher sharp Hölder co...

We study a quasilinear nonlocal hyperbolic initial-boundary value problem that models the evolution of N size-structured subpopulations competing for common resources. We develop an implicit nite di erence scheme to approximate the solution of this model. The convergence of this approximation to a unique bounded variation weak solution is obtained. The numerical results for a special case of th...

We propose a new numerical method for one dimensional stochastic differential equations (SDEs). The main idea of this is based on representation weak solution an SDE using time-changed Brownian motion, which dates back to Doeblin (1940). In cases where the diffusion coefficient bounded and β-Holder continuous with 0<β≤1, we provide rate strong convergence. An advantage our approach that approxi...

In this paper is constructed an aproximate solution to P (x,D)G = H, G|∂Ω = F in the space of generaliaed Colombeau functions on Ω. Here P is a differential operator with coefficients which are generalized functions (for example singular distributions), Ω is a bounded open set, and H and F are generalized functions. Also, solutions to a class of elliptic equations with coefficients in G are obt...

A C* algebra is a closed self-adjoint subalgebra of B(H), the bounded operators on a Hilbert space H. Kirchberg asked whether every C* algebra embeds into an ultrapower of a particular C* algebra, the Cuntz algebra O_2. In this talk, I will explain the model-theoretic content of this problem. In particular, I will show how model-theoretic forcing can be used to give a weak local reformulation o...

The purpose of this paper is to study the approximation of vector valued mappings defined on a subset of a normed space. We investigate Korovkin-type conditions under which a given sequence of linear operators becomes a so-called approximation process. First, we give a sufficient condition for this sequence to approximate the class of bounded, uniformly continuous functions. Then we present som...