let r be a commutative ring with non-zero identity and m be a unital r-module. then the concept of quasi-secondary submodules of m is introduced and some results concerning this class of submodules is obtained

The notions of a S fuzzy ∧ sub semi lattice, a S fuzzy ideal and a S fuzzy prime ideal of a bounded lattice with truth values in a bounded ∧ sub semi lattice S are introduced which generalize the existing notions with truth values in a unit interval of real numbers. Finally, S fuzzy prime ideal theorem is proved. 2010 AMS Classification: 03G10, 46H10, 06D50, 08A72

The abundance of unlabeled data makes semi-supervised learning (SSL) an attractive approach for improving the accuracy of learning systems. However, we are still far from a complete theoretical understanding of the benefits of this learning scenario in terms of sample complexity. In particular, for many natural learning settings it can in fact be shown that SSL does not improve sample complexit...

Let Ω be an open set of R and let f : Ω × R × R be a nonnegative continuous function, convex with respect to ξ ∈ R. Following the well known theory originated by Serrin [14] in 1961, we deal with the lower semicontinuity of the integral F (u,Ω) = ∫ Ω f (x, u(x), Du(x)) dx with respect to the Lloc (Ω) strong convergence. Only recently it has been discovered that dependence of f (x, s, ξ) on the ...

in this paper we introduce the notion of classical quasi-primary submodules that generalizes the concept of classical primary submodules. then, we investigate decomposition and minimal decomposition into classical quasi-primary submodules. in particular, existence and uniqueness of classical quasi-primary decompositions in finitely generated modules over noetherian rings are proved. moreover, w...