Extracting relations from text corpora is an important task in text mining. It becomes particularly challenging when focusing on weakly-supervised relation extraction, that is, utilizing a few relation instances (i.e., a pair of entities and their relation) as seeds to extract more instances from corpora. Existing distributional approaches leverage the corpus-level co-occurrence statistics of e...

Let R be a commutative ring with identity and M an R-module. The Scalar-Product Graph of M is defined as the graph GR(M) with the vertex set M and two distinct vertices x and y are adjacent if and only if there exist r or s belong to R such that x = ry or y = sx. In this paper , we discuss connectivity and planarity of these graphs and computing diameter and girth of GR(M). Also we show some of...

We present a numerical study of spatially quasi-periodic gravity-capillary waves finite depth in both the initial value problem and travelling wave settings. adopt conformal mapping formulation Euler equations, where one-dimensional functions are represented by periodic on higher-dimensional torus. compute time evolution free surface presence background flow bottom boundary observe formation pa...

Let T be a Noetherian ring and f a nonzerodivisor on T . We study concrete necessary and sufficient conditions for a module over R = T/(f) to be weakly liftable to T , in the sense of Auslander, Ding and Solberg. We focus on cyclic modules and get various positive and negative results on the lifting and weak lifting problems. For a module over T we define the loci for certain properties: liftab...

The notions of pure ideals and pure submodules play an important role in the study of rings and their module categories. In this paper, we introduce right t-pure fuzzy ideals and pure fuzzy submodules of an R-module. We establish their basic properties, and use them to obtain fuzzy theoretic characterizations of right weakly regular rings. Among other results, we prove that a ring R is right we...