LpL^p-Taylor approximations characterize the Sobolev space W1,pW^{1,p}

In this note, we introduce a variant of Calder\'on and Zygmund's notion of $L^p$-differentiability - an \emph{$L^p$-Taylor approximation}. Our first result is that functions in the Sobolev space $W^{1,p}(\mathbb{R}^N)$ possess a first order $L^p$-Taylor approximation. This is in analogy with Calder\'on and Zygmund's result concerning the $L^p$-differentiability of Sobolev functions. In fact, the main result we announce here is that the first order $L^p$-Taylor approximation characterizes the Sobolev space $W^{1,p}(\mathbb{R}^N)$, and therefore implies $L^p$-differentiability. Our approach establishes connections between some characterizations of Sobolev spaces due to Swanson using Calder\'on-Zygmund classes with others due to Bourgain, Brezis, and Mironescu using nonlocal functionals with still others of the author and Mengesha using nonlocal gradients. That any two characterizations of Sobolev spaces are related is not surprising, however, one consequence of our analysis is a simple condition for determining whether a function of bounded variation is in a Sobolev space.Comment: 7 pages. Preprint of an article to appear in Comptes Rendus - the exposition of the two articles is substantially different and the full article will not be available as an arxiv paper. The title and abstract displaying on arxiv have been changed to that of the article in its more polished for

A System Appallingly out of Balance : Morgan v. State and the Rights of Defendants and Victims in Sexual Assault Prosecutions

In a series of three cases that culminate with Morgan v. State, Alaska\u27s courts established a unique protection for defendants in sexual assault cases. This protection, which allows such defendants to attack their victims in court with previous reports of sexual assault that did not result in prosecution, is not afforded to defendants in other cases and is based on a dubious general principle that the credibility of sexual assault victims has special relevance. The protection is problematic in several ways: it is grounded in erroneous stereotypes about the victims of sex crimes; it is detrimental to victims and the pursuit of truth; it is inconsistent with traditional rules of evidence; and it is unnecessary to protect the rights of defendants. For these reasons, this protection for defendants in sexual assault cases should be abrogated by legislative action as proposed herein

Epizooic Diatoms on the Cerci of Ephemeroptera (Caenidae) Naiads

Using scanning electron microscopy, epizooic diatoms were observed growing on the cerci of Caenis amica Hagen naiads (Ephemeroptera, Caenidae). Meridion circulare (Greville) C. Agardh was the most abundant, followed by Synedra rumpens Kützing, then Cocconeis pediculus Ehrenberg. Other diatom species observed from substrates in Cedar Creek, Isabella County, Michigan were not observed on the cerci. No diatoms were observed on Ephemerellidae naiads

Isinglass River Conservation Corridor Project

The New Hampshire Estuaries Project (NHEP) provided a $9,075 grant to Bear-Paw Regional Greenways to support the Isinglass River Conservation Corridor Project. The grant helped fund some of the transaction costs associated with the project that protected high-value conservation land along the Isinglass River and in other areas of the watershed in Strafford, New Hampshire. The$2.9 million project was a collaboration of Bear-Paw, the Trust for Public Land (TPL), and the Town of Strafford that protected five properties and 868 acres of forest, over one mile of road frontage, more than three miles of frontage on streams and rivers (including more than 1½ miles on the Isinglass River), several ponds, and two historic mill sites. All of these properties are in areas that have been identified as important to protect in the Land Conservation Plan for New Hampshire’s Coastal Watersheds, a Conservation Plan produced by Bear-Paw Regional Greenways, the New Hampshire Wildlife Action Plan