Reflection Groups and Polytopes over Finite Fields, III

When the standard representation of a crystallographic Coxeter group is reduced modulo an odd prime p, one obtains a finite group G^p acting on some orthogonal space over Z_p . If the Coxeter group has a string diagram, then G^p will often be the automorphism group of a finite abstract regular polytope. In parts I and II we established the basics of this construction and enumerated the polytopes associated to groups of rank at most 4, as well as all groups of spherical or Euclidean type. Here we extend the range of our earlier criteria for the polytopality of G^p . Building on this we investigate the class of 3-infinity groups of general rank, and then complete a survey of those locally toroidal polytopes which can be described by our construction.Comment: Advances in Applied Mathematics (to appear); 19 page

Reflection groups and polytopes over finite fields, II

When the standard representation of a crystallographic Coxeter group $\Gamma$ is reduced modulo an odd prime $p$, a finite representation in some orthogonal space over $\mathbb{Z}_p$ is obtained. If $\Gamma$ has a string diagram, the latter group will often be the automorphism group of a finite regular polytope. In Part I we described the basics of this construction and enumerated the polytopes associated with the groups of rank 3 and the groups of spherical or Euclidean type. In this paper, we investigate such families of polytopes for more general choices of $\Gamma$, including all groups of rank 4. In particular, we study in depth the interplay between their geometric properties and the algebraic structure of the corresponding finite orthogonal group.Comment: 30 pages (Advances in Applied Mathematics, to appear

Watering the garden of family wellbeing

This report contains the recommendations and outcomes of the national roundtable Empowering Aboriginal and Torres Strait Islander people through the Family Wellbeing program, Adelaide, March 2014. There is an accompanying policy brief. Family Wellbeing (FWB) is an effective social and emotional wellbeing program originally developed and delivered by and for Aboriginal and Torres Strait Islander people. The central objective of FWB is to develop people’s skills and capacity to move from a position of disempowerment to empowerment; to empower people with a way to control and change their lives. In March 2014, the Lowitja Institute convened a national roundtable in Adelaide to consider the impact of FWB and opportunities for future development. Roundtable participants from across community, training and delivery, research and policy sectors, shared their experiences of FWB and focused on finding strategies to support the delivery, research and uptake of the FWB program. Roundtable discussions underlined how the program’s empowerment model builds the evidence base that social and emotional wellbeing programs effectively improve people’s lives and provide a promising and practical way to help bridge the gap between Australia’s First Peoples and the non-Indigenous population

Creating Individualized Self-Scoring Assessments for Agricultural Economics Undergraduates

What is an individualized self-scoring assessment for an agricultural economics major? It is a homework assignment that is unique for each student in the class and provides immediate feedback to the student on the correctness of the work. The principle is to generate unique problems, whether it is as simple as the basic intercept and slope of supply and demand equations for an introductory economics class, the parameters of a production function for a production economics, or the interest rate for agricultural finance. One must be aware in constructing the generator algorithms for problem parameters that any necessary conditions will be satisfied a priori such as downward sloping demand, concavity or convexity for maximization or minimization. These assignments are created in an Excel spreadsheet format. Once the basic template is created, the process for self-scoring immediate feedback is relatively easy. Create a copy of the original uncompleted problem sheet in the same workbook and provide the correct formulae to serve as a key. Create a second copy to serve as a check page and replace the formulae with an IF statement comparing the value or formula in the original to the second. It is best to provide some tolerance in the comparison such as checking that the absolute difference in the original and second sheet is less than some critical value. This is especially true for optimization problems. By hiding the key worksheet and protecting the workbook structure, students can not access the correct formulae. However, if the correct formulae or number is entered in the problem sheet, the student can view the check worksheet to see if the answer is correct. A simple GETFORMULA add-in allows the worksheet to check model setups in optimization problems. The key advantage of this technique to the students is the immediate feedback. Also by generating unique assignments, students can cooperate and learn among themselves without being able to directly copy from their peers. Additionally, graphical representations of their problems can often be provided simultaneously. Lastly, the students find that their spreadsheet skills are greatly enhanced. From the instructor perspective, the assessments are already scored when submitted. Students will seek help prior to turning in the assignment. And there is little need to sacrifice complexity to create problems that work out to neat answers. Empirical evidence of improvement in student evaluations indicates the technique is successful.Teaching/Communication/Extension/Profession,

Dynamic Factor Demands for Aggregate Southeastern United States Agriculture

A four equation input demand system for aggregate Southeastern United States agriculture consistent with dynamic optimizing behavior is specified and estimated. Labor and materials are considered as variable inputs while land and capital are treated as quasi-fixed inputs. It is found that the adjustment rates for capital and land differ considerably and are interdependent. Further, the data appear consistent with the existence of an aggregate production technology and the hypothesized optimizing behavior.Farm Management,

Uniform Silicon Isotope Ratios Across the Milky Way Galaxy

We report the relative abundances of the three stable isotopes of silicon, $^{28}$Si, $^{29}$Si and $^{30}$Si, across the Galaxy using the $v = 0, J = 1 \to 0$ transition of silicon monoxide. The chosen sources represent a range in Galactocentric radii ($R_{\rm GC}$) from 0 to 9.8 kpc. The high spectral resolution and sensitivity afforded by the GBT permit isotope ratios to be corrected for optical depths. The optical-depth-corrected data indicate that the secondary-to-primary silicon isotope ratios $^{29}{\rm Si}/^{28}{\rm Si}$ and $^{30}{\rm Si}/^{28}{\rm Si}$ vary much less than predicted on the basis of other stable isotope ratio gradients across the Galaxy. Indeed, there is no detectable variation in Si isotope ratios with $R_{\rm GC}$. This lack of an isotope ratio gradient stands in stark contrast to the monotonically decreasing trend with $R_{\rm GC}$ exhibited by published secondary-to-primary oxygen isotope ratios. These results, when considered in the context of the expectations for chemical evolution, suggest that the reported oxygen isotope ratio trends, and perhaps that for carbon as well, require further investigation. The methods developed in this study for SiO isotopologue ratio measurements are equally applicable to Galactic oxygen, carbon and nitrogen isotope ratio measurements, and should prove useful for future observations of these isotope systems.Comment: 18 pages, 12 figures, 2 tables. Published in The Astrophysical Journal, Volume 839, Issue

Attached and separated boundary layers on highly cooled, ablating and nonablating models at M equals 13.8

Attached and separated boundary layers on highly cooled, ablating and nonablating models at Mach 13.