Density of commensurators for uniform lattices of right-angled buildings

Let G be the automorphism group of a regular right-angled building X. The "standard uniform lattice" \Gamma_0 in G is a canonical graph product of finite groups, which acts discretely on X with quotient a chamber. We prove that the commensurator of \Gamma_0 is dense in G. This result was also obtained by Haglund. For our proof, we develop carefully a technique of "unfoldings" of complexes of groups. We use unfoldings to construct a sequence of uniform lattices \Gamma_n in G, each commensurable to \Gamma_0, and then apply the theory of group actions on complexes of groups to the sequence \Gamma_n. As further applications of unfoldings, we determine exactly when the group G is nondiscrete, and we prove that G acts strongly transitively on X.Comment: 29 pages, 10 figures. Version 2: revised abstract and introduction, to appear in J. Group Theor

Transverse thermal velocity broadening of focused beams from liquid metal ion sources

Experiments have shown that the target current density in focused ion beam columns have long ‘‘tails’’ outside the central submicron region. We show that these tails result from a transverse velocity distribution which has a Holtsmark probability density. Both theory and experiment show that the tails are reduced as the system magnification and source current are reduced

Surface quotients of hyperbolic buildings

Let I(p,v) be Bourdon's building, the unique simply-connected 2-complex such that all 2-cells are regular right-angled hyperbolic p-gons and the link at each vertex is the complete bipartite graph K(v,v). We investigate and mostly determine the set of triples (p,v,g) for which there exists a uniform lattice {\Gamma} in Aut(I(p,v)) such that {\Gamma}\I(p,v) is a compact orientable surface of genus g. Surprisingly, the existence of {\Gamma} depends upon the value of v. The remaining cases lead to open questions in tessellations of surfaces and in number theory. Our construction of {\Gamma}, together with a theorem of Haglund, implies that for p>=6, every uniform lattice in Aut(I) contains a surface subgroup. We use elementary group theory, combinatorics, algebraic topology, and number theory.Comment: 23 pages, 4 figures. Version 2 incorporates referee's suggestions including new Section 7 discussing relationships between our constructions, previous examples, and surface subgroups. To appear in Int. Math. Res. No

The FAn Conjecture for Coxeter groups

We study global fixed points for actions of Coxeter groups on nonpositively curved singular spaces. In particular, we consider property FA_n, an analogue of Serre's property FA for actions on CAT(0) complexes. Property FA_n has implications for irreducible representations and complex of groups decompositions. In this paper, we give a specific condition on Coxeter presentations that implies FA_n and show that this condition is in fact equivalent to FA_n for n=1 and 2. As part of the proof, we compute the Gersten-Stallings angles between special subgroups of Coxeter groups.Comment: This is the version published by Algebraic & Geometric Topology on 19 November 200

Update on PISCES

An updated version of the Platform Independent Software Components for the Exploration of Space (PISCES) software library is available. A previous version was reported in Library for Developing Spacecraft-Mission-Planning Software (MSC-22983), NASA Tech Briefs, Vol. 25, No. 7 (July 2001), page 52. To recapitulate: This software provides for Web-based, collaborative development of computer programs for planning trajectories and trajectory- related aspects of spacecraft-mission design. The library was built using state-of-the-art object-oriented concepts and software-development methodologies. The components of PISCES include Java-language application programs arranged in a hierarchy of classes that facilitates the reuse of the components. As its full name suggests, the PISCES library affords platform-independence: The Java language makes it possible to use the classes and application programs with a Java virtual machine, which is available in most Web-browser programs. Another advantage is expandability: Object orientation facilitates expansion of the library through creation of a new class. Improvements in the library since the previous version include development of orbital-maneuver- planning and rendezvous-launch-window application programs, enhancement of capabilities for propagation of orbits, and development of a desktop user interface

Rural Mental Health Matters: Challenges, Opportunities & Resources for Communities

This session will focus on resources and tools available to people in rural areas regarding mental health and community wellbeing. A Q/A – conversation will be hosted about its relevance with particular attention focused on the challenges of accessing help in rural areas, and why improved services, and investments in a robust workforce and infrastructure are needed to ensure the wellbeing and economic prosperity of rural communities

Evaluation of a Group Administered 24-Hour Recall Method for Dietary Assessment

A group administered 24-hour food recall was developed by the Expanded Food and Nutrition Education Program of Texas to expedite dietary assessment of clients. The study reported here evaluated the group recall and an individual recall method. Data for one meal collected with the use of dietary recalls, either group of individual, were compared to observational data. Results suggest that the group recall may be at least as effective as the individual recall to estimate dietary intakes of subjects. The group recall method could be used by programs such as EFNEP to simplify and expedite dietary assessment of clients

The Impact of the Fusarium Mycotoxin Deoxynivalenol on the Health and Performance of Broiler Chickens

The aim of the present experiment was to investigate the effects of feeding grains naturally contaminated with Fusarium mycotoxins on morphometric indices of jejunum and to follow the passage of deoxynivalenol (DON) through subsequent segments of the digestive tract of broilers. A total of 45 1-d-old broiler chickens (Ross 308 males) were randomly allotted to three dietary treatments (15 birds/treatment): (1) control diet; (2) diet contaminated with 1 mg DON/kg feed; (3) diet contaminated with 5 mg DON/kg feed for five weeks. None of the zootechnical traits (body weight, body weight gain, feed intake, and feed conversion) responded to increased DON levels in the diet. However, DON at both dietary levels (1 mg and 5 mg DON/kg feed) significantly altered the small intestinal morphology. In the jejunum, the villi were significantly (P < 0.01) shorter in both DON treated groups compared with the controls. Furthermore, the dietary inclusion of DON decreased (P < 0.05) the villus surface area in both DON treated groups. The absolute or relative organ weights (liver, heart, proventriculus, gizzard, small intestine, spleen, pancreas, colon, cecum, bursa of Fabricius and thymus) were not altered (P > 0.05) in broilers fed the diet containing DON compared with controls. DON and de-epoxy-DON (DOM-1) were analyzed in serum, bile, liver, feces and digesta from consecutive segments of the digestive tract (gizzard, cecum, and rectum). Concentrations of DON and its metabolite DOM-1 in serum, bile, and liver were lower than the detection limits of the applied liquid chromatography coupled with mass spectrometry (LC-MS/MS) method. Only about 10 to 12% and 6% of the ingested DON was recovered in gizzard and feces, irrespective of the dietary DON-concentration. However, the DON recovery in the cecum as percentage of DON-intake varied between 18 to 22% and was not influenced by dietary DON-concentration. Interestingly, in the present trial, DOM-1 did not appear in the large intestine and in feces. The results indicate that deepoxydation in the present study hardly occurred in the distal segments of the digestive tract, assuming that the complete de-epoxydation occurs in the proximal small intestine where the majority of the parent toxin is absorbed. In conclusion, diets with DON contamination below levels that induce a negative impact on performance could alter small intestinal morphology in broilers. Additionally, the results confirm that the majority of the ingested DON quickly disappears through the gastrointestinal tract