in this study, by a non-negative homogeneous kernel k we prove some extensions of hardy's inequalityin two and three dimensions

We give conditions under which near-critical stochastic processes on the half-line have infinitely many or finitely cutpoints, generalizing existing results nearest-neighbour random walks to adapted with bounded increments satisfying appropriate conditional increment moments conditions. apply one of these deduce that a class transient zero-drift Markov chains in $\mathbb{R}^d$, $d \geq 2$, poss...

In this paper, we use the generalized differentiability concept tostudy the fuzzy transport equation. We consider transport equationin the homogeneous and non-homogeneous cases with fuzzy initialcondition. We also present the solution when speed parameter is a fuzzynumber. Our method is based on the construction of the solutionsby employing Zadeh's extension principle.