Root data with group actions

Suppose $k$ is a field, $G$ is a connected reductive algebraic $k$-group, $T$ is a maximal $k$-torus in $G$, and $\Gamma$ is a finite group that acts on $(G,T)$. From the above, one obtains a root datum $\Psi$ on which $\text{Gal}(k)\times\Gamma$ acts. Provided that $\Gamma$ preserves a positive system in $\Psi$, not necessarily invariant under $\text{Gal}(k)$, we construct an inverse to this process. That is, given a root datum on which $\text{Gal}(k)\times\Gamma$ acts appropriately, we show how to construct a pair $(G,T)$, on which $\Gamma$ acts as above. Although the pair $(G,T)$ and the action of $\Gamma$ are canonical only up to an equivalence relation, we construct a particular pair for which $G$ is $k$-quasisplit and $\Gamma$ fixes a $\text{Gal}(k)$-stable pinning of $G$. Using these choices, we can define a notion of taking "$\Gamma$-fixed points" at the level of equivalence classes, and this process is compatible with a general "restriction" process for root data with $\Gamma$-action.Comment: v2: one word inserted, one citation inserted, one reference updated, one misspelling correcte

Dr. J. E. McPherson, Educator and Researcher Extraordinaire: Biographical Sketch and List of Publications

(excerpt) Like many outstanding naturalists, John E. (“Jay”) McPherson grew up with a strong interest in the natural world, especially insects. This innate curiosity led him to enroll as a zoology major at San Diego State University in 1959. Upon completion of his undergraduate degree, he continued on to pursue his interest in insect biology, completing a Master’s thesis on the life history and morphology of a poorly known species of Notonectidae. Shortly thereafter, a teaching assistantship enabled him to pursue a Ph.D. at Michigan State University in East Lansing, where his research involved distinguishing two closely related species of bark beetles. During this period, Jay also worked on various pest species, including the cereal leaf beetle, pine tip beetle, and pine cone beetle

Guides for the Journey: Supporting High-Risk Youth with Paid Mentors and Counselors

Strategies to concentrate resources on high-risk youth have long been a goal in the youth field, but the practical means of doing so frequently have eluded practitioners. High-risk youth often are highly transient, and they may need sustained, costly services to address their needs effectively. Guides for the Journey explores a concrete, flexible approach to the problem: the use of paid counselors who stay with young people for extended periods of time. The report profiles three programs now using this strategy and discusses how public funding to support wider use of paid mentors and counselors may be mobilized

An example of limit of Lempert Functions

The Lempert function for several poles $a_0, ..., a_N$ in a domain $\Omega$ of $\mathbb C^n$ is defined at the point $z \in \Omega$ as the infimum of $\sum^N_{j=0} \log|\zeta_j|$ over all the choices of points $\zeta_j$ in the unit disk so that one can find a holomorphic mapping from the disk to the domain $\Omega$ sending 0 to $z$. This is always larger than the pluricomplex Green function for the same set of poles, and in general different. Here we look at the asymptotic behavior of the Lempert function for three poles in the bidisk (the origin and one on each axis) as they all tend to the origin. The limit of the Lempert functions (if it exists) exhibits the following behavior: along all complex lines going through the origin, it decreases like $(3/2) \log |z|$, except along three exceptional directions, where it decreases like $2 \log |z|$. The (possible) limit of the corresponding Green functions is not known, and this gives an upper bound for it.Comment: 16 pages; references added to related work of the autho

Unique Contractile and Structural Protein Expression in Dog Ileal Inner Circular Smooth Muscle

This study was designed to test the hypothesis that there is heterogeneous expression of contractile and structural proteins between the smooth muscle cells (SMCs) in the inner and outer circular muscle (ICM and OCM) layers of the ileum. Immunohistochemical staining and quantitation of fresh frozen sections of the dog ileum was performed using protein specific antibodies. Smooth muscle (SM) SMA myosin heavy chain (MHC), α- and γ-SM actin, and vinculin all show greater expression in the ICM relative to the OCM. SMB MHC and fibronectin show the opposite pattern, with greater expression in the OCM relative to the ICM. Differences in expression of these proteins are consistent with proposed differences in function of these muscle layers. Hypotheses regarding muscle tone and the coordination and regulation of peristalsis via these different muscle layers based on this data can now be made and tested