The linear discrepancy of a poset P is the least k such that there is a linear extension L of P such that if x and y are incomparable, then |hL(x)− hL(y)| ≤ k. Whereas the weak discrepancy is the least k such that there is a weak extension W of P such that if x and y are incomparable, then |hW (x)− hW (y)| ≤ k. This paper resolves a question of Tanenbaum, Trenk, and Fishburn on characterizing w...

Let K be an algebraically closed field of characteristic zero and let I = (f1, . . . , fn) be a homogeneous R+-primary ideal in R := K[X, Y, Z]. If the corresponding syzygy bundle Syz(f1, . . . , fn) on the projective plane is semistable, we show that the Artinian algebra R/I has the Weak Lefschetz property if and only if the syzygy bundle has a special generic splitting type. As a corollary we...

In this paper, we obtain the existence and uniqueness of weak pullback mean random attractors for non-autonomous deterministic \begin{document}$ p $\end{document}-Laplacian equations with initial data stochastic id="M3">\begin{document}$ general diffusion terms in Bochner spaces, respectively.

In this study, some existing results dealing with the weak approximation property of Banach spaces are considered for $p$-weak property. Also, an observation on bounded and $p$-bounded properties is given. Moreover, proof solution duality problem which exists in literature given a shorter way as alternative.