Let $R$ be an infinite ring. Here we prove that if $0_R$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin X}$ for every infinite subset $X$ of $R$, then $R$ satisfies the polynomial identity $x^n=0$. Also we prove that if $0_R$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in X}$ for every infinite subset $X$ of $R$, then $x^n=x$ for all $xin R$.

Subset Interconnection Design is an NP −hard problem which draws its motivation from various applications, such as the design of scalable overlay networks, the inference of inter-molecular protein connectivity, the design of vacuum systems and several other problems in the industry. In that problem, we are given a set of vertices V and a collection S of subsets of V and we want to find an edge ...

Numerous research works about the extraction of lowlevel features from images and videos have been published. However, only recently the focus has shifted to exploiting low-level features to classify images and videos automatically into semantically broad and meaningful categories. In this paper, novel classification algorithms are presented for three broad and general-purpose categories. In de...

Computational approaches to reference resolution , like Centering Theory, are best at resolving referring expressions which denote familiar referents. We demonstrate how, by taking a proof-theoretic approach to reference resolution within a Centering-type framework, we are able to make sense of referring expressions for unfamiliar referents. These include, in addition to bridging descriptions, ...

The synthetic feasibility of any compound library used for virtual screening is critical to the drug discovery process. TIN, a recursive acronym for 'TIN Is Not commercial', is a virtual combinatorial database enumeration of diversity-orientated multicomponent syntheses (MCR). Using a 'one-pot' synthetic technique, 12 unique small molecule scaffolds were developed, predominantly styrylisoxazole...