Automorphisms of the affine Cremona group

We show that every automorphism of the group Gn := Aut(An) of polynomial automorphisms of complex affine n-space An = Cn is inner up to field automorphisms when restricted to the subgroup TGn of tame automorphisms. This generalizes a result of Julie Deserti who proved this in dimension n = 2 where all automorphisms are tame: TG2 = G2. The methods are different, based on arguments from algebraic group actions

On Maximal Subalgebras

Let $\textbf{k}$ be an algebraically closed field. We classify all maximal $\textbf{k}$-subalgebras of any one-dimensional finitely generated $\textbf{k}$-domain. In dimension two, we classify all maximal $\textbf{k}$-subalgebras of $\textbf{k}[t, t^{-1}, y]$. To the authors' knowledge, this is the first such classification result for an algebra of dimension $> 1$. In the course of this study, we classify also all maximal $\textbf{k}$-subalgebras of $\textbf{k}[t, y]$ that contain a coordinate. Furthermore, we give examples of maximal $\textbf{k}$-subalgebras of $\textbf{k}[t, y]$ that do not contain a coordinate.Comment: 30 pages, typos corrected, minor changes, improved expositio

Holomorphically Equivalent Algebraic Embeddings

We prove that two algebraic embeddings of a smooth variety $X$ in $\mathbb{C}^m$ are the same up to a holomorphic coordinate change, provided that $2 \dim X + 1$ is smaller than or equal to $m$. This improves an algebraic result of Nori and Srinivas. For the proof we extend a technique of Kaliman using generic linear projections of $\mathbb{C}^m$.Comment: 17 pages. Version 2 acknowledges the fact that the main result of this paper was previously established by Kaliman, see http://arxiv.org/abs/1309.379

Should I Say Something? Dating and Sexual Aggression Bystander Intervention Among High School Youth

Using data from a sample of 218 high school youth from three high schools in New England (one rural, two urban), this brief discusses dating and sexual aggression bystander intervention among high school youth. Authors Katie Edwards, Robert Eckstein, and Kara Anne Rodenhizer-Stämpfli report that an overwhelming majority (93.6 percent) of high school students reported having the opportunity to intervene during the past year in situations of dating aggression or sexual aggression; however, in over one-third of the episodes (37.4 percent) students reported not intervening. Girls were more likely to intervene in situations of dating and sexual aggression than boys, and youth with histories of dating and sexual aggression were more likely to intervene than youth without these histories. Focus group data revealed that barriers to bystander intervention included avoidance of drama or a desire to fuel drama, social status and personal repercussions, closeness with the victim and/or perpetrator, the victim being male and the perpetrator female, the failure of the dating or sexual aggression to meet a certain threshold, the dating and sexual aggression occurring online, anticipated negative reactions from the perpetrator or victim, and an inability to relate to the situation. Given the mounting evidence that bystander education is a critical component of dat­ing and sexual aggression prevention, the authors urge policy makers and educators to enhance the presence of this type of education in high school health curricula and related course curricula

Species Composition and Standing Crop Variation in an Unfertilized Meadow and Its Relationship to Climatic Variability during Six Years

Year-to-year variability of species composition and hay yield were investigated during a six-year period (1988-1993) in a traditionally mown meadow of great species richness at Negrentino in southern Switzerland. Climatic parameters (temperature, duration of sunshine, global radiation, precipitation, evaporation, relative moisture) measured at a nearby weather station were calculated for ten-day units and compared to quantitative vegetation data. Yields of the first and second harvest were positively correlated with the mean relative moisture during the first and second growth period. Distinct variation patterns were recognized among the 48 species and interpreted as direct or indirect responses of interacting species to climatic conditions during three periods of the year. The first variation pattern including abundant graminoids reflects a strong direct effect by weather conditions in the first growth period. Species of the other variation patterns responded differently to extreme summer droughts with apparent time-lags. Some species reflect warm and humid conditions in early spring followed by dry conditions in a particular year; others combine features of different variation patterns

Automorphisms of C3\mathbb{C}^3 Commuting with a C+\mathbb{C}^+-Action

Let $\rho$ be an algebraic action of the additive group $\mathbb{C}^+$ on the three-dimensional affine space $\mathbb{C}^3$. We describe the group $\textrm{Cent}(\rho)$ of polynomial automorphisms of $\mathbb{C}^3$ that commute with $\rho$. A particular emphasis lies in the description of the automorphisms in $\textrm{Cent}(\rho)$ coming from algebraic $\mathbb{C}^+$-actions. As an application we prove that the automorphisms in $\textrm{Cent}(\rho)$ that are the identity on the algebraic quotient of $\rho$ form a characteristic subgroup of $\textrm{Cent}(\rho)$.Comment: 18 pages, typos corrected, minor changes, improved expositio

After Thirty Years, Is it Time to Change the Vehicle Inventory Search Doctrine?

Part II of this Comment will describe the inventory search as it has developed in the Supreme Court\u27s jurisprudence in order to provide background and understanding of the procedure as it stands today. Part III will address the difficulties in applying the Supreme Court\u27s approach by comparing the differences in police department policies. Part IV will then closely examine Washington\u27s somewhat laudable approach to inventory searches, the limits the state has placed on the scope of inventory searches, and the steps the state has taken to impose a consent requirement. Last, Part V will suggest much needed reforms for Washington and the rest of the nation to ensure that the rights of individuals are protected while inventory searches continue to serve their purpose