Nonstandard Hulls of Locally Exponential Lie Algebras

We show how to construct the nonstandard hull of certain infinite-dimensional Lie algebras in order to generalize a theorem of Pestov on the enlargeability of Banach-Lie algebras. In the process, we consider a nonstandard smoothness condition on functions between locally convex spaces to ensure that the induced function between the nonstandard hulls is smooth. We also discuss some conditions on a function between locally convex spaces which guarantee that its nonstandard extension maps finite points to finite points

Officer-Involved Domestic Violence: The Mediating Factors

Domestic and family violence has been a critical issue in contemporary society. Efforts have been made in researching the causes, effects, and mediating factors of domestic violence in relation to the workplace. Studies demonstrate that a relationship between conflict crossing over from the work to the home environment exist. Additional studies demonstrate that domestic violence does affect the workplace; however, there is little to no scientific data on the reverse relationship. The reverse relationship regards whether the workplace affects the occurrence of domestic violence. This research paper will dive into this topic, and on the lack of data available. Supporting data will illustrate that factors from the workplace do affect the likelihood of domestic and/or family violence occurring in police families. Not considering or viewing police family violence as an effect of workplace factors is shortsighted, and it demonstrates the need for education on this topic. With new data, comes new policies and implications that are reconfigurations of the existing policies. There is a need to bring this subject to light, and in view of the law enforcement community

Ends of groups: a nonstandard perspective

We give a nonstandard treatment of the notion of ends of proper geodesic metric spaces. We then apply this nonstandard treatment to Cayley graphs of finitely generated groups and give nonstandard proofs of many of the fundamental results concerning ends of groups. We end with an analogous nonstandard treatment of the ends of relatively Cayley graphs, that is Cayley graphs of cosets of finitely generated groups.Comment: 23 page