Let R be a commutative ring with non-zero identity. The annihilator-inclusion ideal graph of R , denoted by ξR, is a graph whose vertex set is the of allnon-zero proper ideals of $R$ and two distinct vertices $I$ and $J$ are adjacentif and only if either Ann(I) ⊆ J or Ann(J) ⊆ I. In this paper, we investigate the basicproperties of the graph ξR. In particular, we showthat ξR is a connected grap...

Let $R$ be a commutative Noetherian ring with non-zero identity, $fa$ an ideal of $R$, and $X$ an $R$--module. Here, for fixed integers $s, t$ and a finite $fa$--torsion $R$--module $N$, we first study the membership of $Ext^{s+t}_{R}(N, X)$ and $Ext^{s}_{R}(N, H^{t}_{fa}(X))$ in the Serre subcategories of the category of $R$--modules. Then, we present some conditions which ensure the exi...

In this chapter, we propose two novel and curvature-free features: run-lengths of Local Binary Pattern (LBPruns) and Cloud Of Line Distribution (COLD) features for writer identification. The LBPruns is the joint distribution of the traditional run-length and local binary pattern (LBP) methods, which computes the run-lengths of local binary patterns on both binarized images and gray scale images...

In this chapter, we propose two novel and curvature-free features: run-lengths of Local Binary Pattern (LBPruns) and Cloud Of Line Distribution (COLD) features for writer identification. The LBPruns is the joint distribution of the traditional run-length and local binary pattern (LBP) methods, which computes the run-lengths of local binary patterns on both binarized images and gray scale images...

In this chapter, we propose two novel and curvature-free features: run-lengths of Local Binary Pattern (LBPruns) and Cloud Of Line Distribution (COLD) features for writer identification. The LBPruns is the joint distribution of the traditional run-length and local binary pattern (LBP) methods, which computes the run-lengths of local binary patterns on both binarized images and gray scale images...