Order Convergence and Topological Convergence

Topological Scott Convergence Theorem

Recently, J. D. Lawson encouraged the domain theory community to consider the scientific program of developing domain theory in the wider context of T0 spaces instead of restricting to posets. In this paper, we respond to this calling with an attempt to formulate a topological version of the Scott Convergence Theorem, i.e., order-theoretic characterisation of those posets for which the Scott-co...

On Order-convergence

First-Order Convergence and Roots

Nešetřil and Ossona de Mendez introduced the notion of first order convergence, which unifies the notions of convergence for sparse and dense graphs. They asked whether if (Gi)i∈N is a sequence of graphs with M being their first order limit and v is a vertex of M , then there exists a sequence (vi)i∈N of vertices such that the graphs Gi rooted at vi converge to M rooted at v. We show that this ...

Second Order Sliding Mode Control With Finite Time Convergence

In this paper, a new smooth second order sliding mode control is proposed. This algorithm is a modified form of Super Twisting algorithm. The Super Twisting guarantees the asymptotic stability, but the finite time stability of proposed method is proved with introducing a new particular Lyapunov function. The Proposed algorithm which is able to control nonlinear systems with matched structured u...

First order convergence of matroids

The model theory based notion of the first order convergence unifies the notions of the left-convergence for dense structures and the BenjaminiSchramm convergence for sparse structures. It is known that every first order convergent sequence of graphs with bounded tree-depth can be represented by an analytic limit object called a limit modeling. We establish the matroid counterpart of this resul...