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

Cannabis shenanigans: advocating for the restoration of an effective treatment of pain following spinal cord injury.

Cannabis is an effective treatment for pain following spinal cord injury that should be available to patients and researchers. The major argument against the rescheduling of cannabis is that the published research is not convincing. This argument is disingenuous at best, given that the evidence has been presented and rejected at many points during the political dialog. Moreover, the original decision to criminalize cannabis did not utilize scientific or medical data. There is tension between the needs of a society to protect the vulnerable by restricting the rights of others to live well and with less pain. It is clear that this 70-year war on cannabis has had little effect in controlling the supply of cannabis. Prohibition can never succeed; it is a tyranny from which every independent mind revolts. People living with chronic pain should not have to risk addiction, social stigma, restrictions on employment and even criminal prosecution in order to deal with their pain. It is time to end the shenanigans and have an open, transparent discussion of the true benefits of this much-beleaguered medicine

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