The Picone-type identity for the half-linear second order partial differential equation n i=1 ∂ ∂xi Φ ∂u ∂xi + c(x)Φ(u) = 0, Φ(u) := |u|u, p > 1, is established and some applications of this identity are suggested.

In this work we characterize the combinatorial metrics admitting a MacWilliams-type identity and describe the group of linear isometries of such metrics. Considering coverings that are not connected, we classify the metrics satisfying the MacWilliams extension property.

In this article, a Picone-type identity for the weighted p-biharmonic operator is established and comparison results for a class of half-linear partial differential equations of fourth order based on this identity are derived.

Recent work has demonstrated that Canadians overreport church attendance at rates similar to respondents in the United States. Overreporting in the United States has been attributed to the importance of religious identity; causes of Canadian overreporting have not been examined. This article draws upon Stryker’s identity theory to explain why Canadian survey respondents overreport church attend...

Reductive dehalogenases are the critical enzymes for anaerobic organohalide respiration, a microbial metabolic process that has been harnessed for bioremediation efforts to resolve chlorinated solvent contamination in groundwater and is implicated in the global halogen cycle. Reductive dehalogenase sequence diversity is informative for the dechlorination potential of the site or enrichment cult...

A Picone type identity is established for homogeneous differential operators involving the pseudo p-Laplacian with variable exponent p = p(x). Using this identity, it is shown that the classical Sturmian theory extends to the associated partial differential equations.