Continuous symmetries of Lagrangians and exact solutions of discrete equations

One of the difficulties encountered when studying physical theories in discrete space-time is that of describing the underlying continuous symmetries (like Lorentz, or Galilei invariance). One of the ways of addressing this difficulty is to consider point transformations acting simultaneously on difference equations and lattices. In a previous article we have classified ordinary difference schemes invariant under Lie groups of point transformations. The present article is devoted to an invariant Lagrangian formalism for scalar single-variable difference schemes. The formalism is used to obtain first integrals and explicit exact solutions of the schemes. Equations invariant under two- and three- dimensional groups of Lagrangian symmetries are considered.Comment: 31 pages, submitted to Journal of Mathematical Physic

Stabilizing Neighborhoods Impacted by Concentrated Foreclosures: Scattered-Site Rental Housing Challenges and Opportunities

The negative impacts of concentrated foreclosures have been destabilizing communities across the country. Community development corporations (CDCs) and other nonprofits that are active in these neighborhoods face falling property values, decreased lending activity and other consequences that are complicating their efforts at community revitalization through acquisition, rehabilitation and resale of vacant and foreclosed housing stock. Given the current crisis in the housing and credit markets, community development corporations aiming for neighborhood stabilization may wish to acquire foreclosed single-family properties and operate them as scattered-site rental units instead. This study presents the challenges that nonprofits pursuing such a plan are likely to face. It discusses the main management, financing and political issues associated with developing and operating scattered-site rental housing while providing a foundation upon which CDCs considering such activities can evaluate their capacity and willingness to meet the challenges. The paper explores how local market conditions, internal organizational capacity and the current policy environment affect nonprofit efforts to acquire, rehabilitate and rent foreclosed properties. The study includes operational and advocacy recommendations for improving the context in which scattered-site rental housing can be managed. The paper also considers the unique difficulties of the current situation and concludes that comprehensive revitalization efforts that emphasize cross-sectoral partnerships and enjoy strong local government support are most likely to exert a positive impact on a community

Pennington to Newberg City Council, May 14, 1947

Pennington writing to the Newberg City Council stating his case for why he believes they should not go through with their planned changes to Newberg\u27s roads.https://digitalcommons.georgefox.edu/levi_pennington/1153/thumbnail.jp

Pennington to The Geneva Newlins, July 11, 1948

Pennington writing to the Geneva Newlins about relief, personal life, politics, Quakerism, and writing.https://digitalcommons.georgefox.edu/levi_pennington/1273/thumbnail.jp