Let Ξ be a one-relator group with presentation & — ($i, •" ,%n R ) where R is not a proper power and p ^ 2. Then given any integer q, relatively prime to p, we can construct the Lens space ^(pf q) for Ξ from the cellular model C(&) of the presentation & by attaching a 3-cell via the attaching map R — 1, which generates the ideal ZΞ(R — 1) « τr2(C(^)). In this paper we classify these Lens spaces...

A short proof, using graphs and groupoids, is given of Brodskĭı’s theorem that torsion-free one-relator groups are locally indicable.

in this paper we investigate generalized topologies generated by a subbase ofpreorder relators and consider its application in the concept of the complement. we introducethe notion of principal generalized topologies obtained from the new type of open sets andstudy some of their important properties.

We give experimental support for a conjecture of Louder and Wilton saying that words imprimitivity rank greater than two yield hyperbolic one-relator groups.

The United States Court of Appeals for the Second Circuit recently issued a decision that could narrow the scope of the prosecution of cases brought against health care providers under the False Claims Act, 31 U.S.C. § 3729, et seq. (the “Act”). This decision, United States ex rel. Mikes v. Straus, (http://caselaw.lp.findlaw.com/scripts/getcase.pl?court=2nd&navby=case&no=006269) does significan...

This paper presents a supervised method for the detection and extraction of Causal Relations from open domain text. First we give a brief outline of the definition of causation and how it relates to other Semantic Relations, as well as a characterization of their encoding. In this work, we only consider marked and explicit causations. Our approach first identifies the syntactic patterns that ma...