Computing maximal copies of polytopes contained in a polytope

Kepler (1619) and Croft (1980) have considered largest homothetic copies of one regular polytope contained in another regular polytope. For arbitrary pairs of polytopes we propose to model this as a quadratically constrained optimization problem. These problems can then be solved numerically; in case the optimal solutions are algebraic, exact optima can be recovered by solving systems of equations to very high precision and then using integer relation algorithms. Based on this approach, we complete Croft's solution to the problem concerning maximal inclusions of regular three-dimensional polyhedra by describing inclusions for the six remaining cases.Comment: 13 pages, 7 figure

Effective coaching of parents and professionals supporting children who are deaf or hard of hearing

This literature review examines the relationship between collaboration, adult learning and coaching. The most effective adult learning strategies and coaching strategies are discussed to help improve student outcomes for children who are deaf or hard of hearing

Real Equivariant Bordism for elementary abelian 2-groups

We give a description of real equivariant bordism for elementary abelian 2-groups, which is similar to the description of complex equivariant bordism for the group S^1 x ... x S^1 given by Hanke in 2005.Comment: 21 page

Prognostic value of early magnetic resonance imaging in dogs after traumatic brain injury: 50 cases

Retrospective study of dogs with TBI that underwent 1.5T MRI within 14 days after head trauma. MRI evaluators were blinded to the clinical presentation, and all images were scored based on an MRI grading system (Grade I [normal brain parenchyma] to Grade VI [bilateral lesions affecting the brainstem with or without any lesions of lesser grade]). Skull fractures, percentage of intraparenchymal lesions, degree of midline shift, and type of brain herniation were evaluated. MGCS was assessed at presentation. The presence of seizures was recorded. Outcome was assessed at 48 h (alive or dead) and at 3, 6, 12, and 24 months after TBI

Burleigh, Ed., Confronting The Nazi Past - New Debates On Modern German History

Confronting the Nazi Past is a collection of eleven essays on the social history of Nazi Germany, covering such relatively neglected topics as forced labor, the persecution of "gypsies" and homosexuals, and high society during Nazi rule. Although the essays are uneven in quality, the book is nonetheless a valuable resource for both students and teachers

West Creek Development OSAE

Students will work cooperatively to speculate on the changes humans have made to transform farm fields into a housing development and what the consequences of those changes could be

Young, Cold War Europe

One of the pitfalls of contemporary history is that events outrace even the most facile of writers. John W. Young's Cold War Europe is a case in point, a book that is out of date even before it is published

Franklin v. Gwinnett County Public Schools: The Implication of Remedies for an Implied Cause of Action

According to the common law doctrine of ubi jus, ibi remedium, where there is a right, there is a remedy. The United States Supreme Court has long recognized the validity of this doctrine. Traditionally, the Court was very liberal in recognizing private rights of action, and granting injunctive and monetary relief for violations of constitutional and statutory rights in the absence of explicit congressional authorization. In Bell v. Hood, the Supreme Court stated: [W]here federally protected rights have been invaded, it has been the rule from the beginning that courts will be alert to adjust their remedies so as to grant the necessary relief .... [Flederal courts may use any available remedy to make good the wrong done