We give an estimation for the arithmetic genus of an integral space curve which is not contained in a surface of degree $k-1$. Our main technique is the Bogomolov-Gieseker type inequality for ${\mathbb{P}}^{3}$ proved by Macrì.

In this paper, we will present several necessary and sufficient conditions on a commutative ring such that the algebraic and geometric local cohomologies are equivalent.

A probabilistic communication structure considers the setting with communication restrictions in which each pair of players has a probability to communicate directly. In this paper, we consider a more general framework, called a probabilistic communication structure with fuzzy coalition, that allows any player to have a participation degree to cooperate within a coalition. A maximal product spanning tree, indicating a way of the greatest possibility to communicate among the players, is introduced...

It is well-known that the concentric circle space has no ${G}_{\delta}$-diagonal nor any countable point-separating open cover. In this paper, we reveal two new properties of the concentric circle space, which are the weak versions of ${G}_{\delta}$-diagonal and countable point-separating open cover. Then we introduce two new cardinal functions and sharpen some known cardinal inequalities.

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