Classification of Multidimensional Darboux Transformations: First Order and Continued Type

We analyze Darboux transformations in very general settings for multidimensional linear partial differential operators. We consider all known types of Darboux transformations, and present a new type. We obtain a full classification of all operators that admit Wronskian type Darboux transformations of first order and a complete description of all possible first-order Darboux transformations. We introduce a large class of invertible Darboux transformations of higher order, which we call Darboux transformations of continued Type I. This generalizes the class of Darboux transformations of Type I, which was previously introduced. There is also a modification of this type of Darboux transformations, continued Wronskian type, which generalize Wronskian type Darboux transformations

Traffic Analysis in Random Delaunay Tessellations and Other Graphs

In this work we study the degree distribution, the maximum vertex and edge flow in non-uniform random Delaunay triangulations when geodesic routing is used. We also investigate the vertex and edge flow in Erd\"os-Renyi random graphs, geometric random graphs, expanders and random $k$-regular graphs. Moreover we show that adding a random matching to the original graph can considerably reduced the maximum vertex flow.Comment: Submitted to the Journal of Discrete Computational Geometr

Resolving Range Conflict in Nevada? The Potential for Compensation via Monetary Payouts and Grazing Alternatives

In response to environmental pressure, public land agencies in Nevada have reduced animal unit months (AUMs) of grazing on public lands. This has resulted in economic losses to ranchers, increased conflict between ranchers and the public land agencies, and general unrest in the ranch community. One approach to resolving the problems might be to compensate ranchers for lost grazing privileges. In this study, we employ the results of the Nevada Ranch Survey to examine ranchers’ willingness to accept a one-time payment to retire grazing rights, as well as three other means of “compensating” ranchers that enable them to earn a living from the public lands despite reduced access to public forage. The results suggest that ranchers are not keen on being compensated in any form, expressing a desire to continue ranching. However, those most amenable to compensation and a reworking of the social contract are those who have the best relationship with the public land manager and view the public agencies in a positive light.range economics, environmental services from public land, compensation for grazing rights, social capital and trust

African Missions of the Church of Christ in Northern Rhodesia

A pamphlet detailing several of the Church of Christ missions in Northern Rhodesia, now Zimbabwe. Provides information about mission schools, evangelistic work, and missionaries. Contains black and white photos of African Christians and American missionaries.https://digitalcommons.acu.edu/crs_books/1461/thumbnail.jp

Ann-Marie Priest. My Tongue Is My Own: A Life of Gwen Harwood: La Trobe University Press in conjunction with Black Inc, 2022. 471 pages. AU$37.99 ISBN 9781760642341 (Paperback)

Nathan Hobby reviews Ann-Marie Priest's My Tongue Is My Own: A Life of Gwen Harwood (2022)

Lawyers Take Heed! A De Novo Review of Rule 11 in North Carolina - Turner v. Duke Univ.

This Note will propose the standard of review which best balances both concerns. First, this Note will summarize the facts of Turner, to introduce the setting of the Rule 11 decision. Second, in the Background section, this Note will explore the history of Rule 11 in the federal courts and in North Carolina, and the various standards of review adopted in the federal courts. Third, this Note will analyze the Turner decision and the standard of appellate review adopted by the North Carolina Supreme Court. Fourth, this Note will compare the standards of review and suggest which of the standards furthers or hinders the purposes of Rule 11. Through this Note, the reader should have a sharper understanding of Rule 11, and its treatment in the federal courts and in North Carolina. Finally, this Note urges the reader to consider the impact which a particular standard of review may have on a decision under Rule 11 and on litigation generally