It is well known that the dynamics of vortices in an ideal incompressible two-dimensional fluid contained a bounded not necessarily simply connected smooth domain described by Kirchhoff–Routh point vortex system. In this paper, we revisit classical problem how solutions to Euler equations approximate these dynamics, and extend previous rigorous results case where vorticity field unbounded. More...

We develop a notion of non-commutative hull for left ideal the [Formula: see text]-algebra compact quantum group text]. A spectral synthesis groups is proposed as well. It shown that certain Ditkin’s property at infinity (which includes those text] where dual has approximation property) equivalent to every having synthesis. use this work extend recent White characterizes weak[Formula: closed id...

we survey the recent investigations on (bounded, sequential) approximate connesamenability and pseudo-connes amenability for dual banach algebras. we will discuss thecore problems concerning these notions and address the signicance of any solutions to themto the development of the eld.

in this paper, we study the arens regularity properties of module actions and we extend some proposition from baker, dales, lau and others into general situations. we establish some relationships between the topological centers of module actions and factorization properties of them with some results in group algebras. in 1951 arens shows that the second dual of banach algebra endowed with the e...

Let and be randomly chosen subsets of the first positive integers cardinalities , such that their sumset has size . We show asymptotically almost surely are fully contained in arithmetic progressions with same common difference approximately also prove a counting theorem for pairs sets arbitrary abelian groups. The results hold Our main tool is an asymmetric version method hypergraph containers...

This article shows the existence of weak solutions of a resonance problem for nonuniformly p-Laplacian system in a bounded domain in $mathbb{R}^N$‎. ‎Our arguments are based on the minimum principle and rely on a generalization of the Landesman-Lazer type condition‎.