A Note on Coincidence Isometries of Modules in Euclidean Space

It is shown that the coincidence isometries of certain modules in Euclidean $n$-space can be decomposed into a product of at most $n$ coincidence reflections defined by their non-zero elements. This generalizes previous results obtained for lattices to situations that are relevant in quasicrystallography.Comment: 8 page

RCIA and the Formation of Liturgical Piety

(Excerpt) Here is what I think the formation of liturgical piety means. You will recognize at once, I believe, these words which in December 1988 will celebrate their 25th birthday, words taken from the Constitution on the Sacred Liturgy, the first work of Vatican II. In what seems to me to be the very clearest and most amazing statement of its own zeal for putting the renewal of the liturgy as its first and foundational work, the Council said

Discrete Tomography of Icosahedral Model Sets

The discrete tomography of B-type and F-type icosahedral model sets is investigated, with an emphasis on reconstruction and uniqueness problems. These are motivated by the request of materials science for the unique reconstruction of quasicrystalline structures from a small number of images produced by quantitative high resolution transmission electron microscopy.Comment: 21 pages, 3 figures; revised version, figures adde

The Grace of Leading the Assembly

(Excerpt) It is good in nearly every Christian liturgy there comes a moment when all present pray to be forgiven just as they are themselves now offering forgiveness. Thus do assemblies and presiders provide a ground for meeting again next Sunday and giving it another go

What Gets Changed? Sam Gets Changed?

(Excerpt) Most of what I learn about ritual and liturgy and church I learn from places that aren\u27t about ritual and liturgy and church-novels and poems and music and dance-and from people who don\u27t know the jargon but often know the Lord and the church. The tide of this presentation comes from one such fellow named Sam. He is a member of St. Henry Church on the southwest side of Cleveland. You\u27ll see a little of that church later on in this hour. We were there last fall, some of us from LTP, to make a video about the communion rite at Sunday mass. We had been looking for some parish where they really did the rite, and here we found one. So on one weekend we shot the video at their church and the producer interviewed a dozen or so parishioners and the clergy

Reproductive Den Habitat Characterization of American Badgers (\u3cem\u3eTaxidea taxus\u3c/em\u3e) in Central California

The American badger (Taxidea taxus) is a species of special concern in California, and, as such, conservation measures are necessary. The goal of this study was to identify potential reproductive den habitat characteristics in order to more accurately predict critical reproductive habitat in central California grasslands. A paired study design was used to examine differences between reproductive and non-reproductive sites, and logistical regression was used to analyze the variables and produce two predictive models, one with biotic factors and one with abiotic factors. Badgers in central Californian grasslands appear to rely on both biotic and abiotic factors when selecting locations for reproductive den sites. Predictive biotic variables included amount of ground vegetation, presence of predators, presence of prey, and nearest shrub width. Predictive abiotic variables included distance to a drainage point and slopes at 10, 30, and 40 m from the den entrance. Integrating information from these models into conservation efforts will identify critical reproductive habitat and help form viable conservation strategies for the species

Magic numbers in the discrete tomography of cyclotomic model sets

We report recent progress in the problem of distinguishing convex subsets of cyclotomic model sets $\varLambda$ by (discrete parallel) X-rays in prescribed $\varLambda$-directions. It turns out that for any of these model sets $\varLambda$ there exists a `magic number' $m_{\varLambda}$ such that any two convex subsets of $\varLambda$ can be distinguished by their X-rays in any set of $m_{\varLambda}$ prescribed $\varLambda$-directions. In particular, for pentagonal, octagonal, decagonal and dodecagonal model sets, the least possible numbers are in that very order 11, 9, 11 and 13.Comment: 6 pages, 1 figure; based on the results of arXiv:1101.4149 [math.MG]; presented at Aperiodic 2012 (Cairns, Australia

Comparative statics for a three player differential game in resource economics - the case of exhaustible resources and varying allocations of initial stocks

Differential games combine strategic interactions between agents and optimization concerning time. Decisions made in the past determine the present and even the future .in pay off as well as in the opportunities available . for oneself and for the rival players, eventually too. Unfortunately, due to high complexity it is hard to find a Nash-equilibrium within a differential game and it is even harder to get some results in comparative statics. It is the purpose of the paper at hand to present findings concerning comparative statics in a differential game discussed by Wacker and Blank (1999). Comparative statics become available due to a routine solving for the open-loop Nash equilibrium for each parameter combination under consideration. A description of the routine . a 4 step simulation run which approximates the equilibrium numerically . was presented in an earlier Working Paper. In the earlier Paper Excel was applied as it is a wild spread tool. Here again Excel, its Solver and Macros constitute the main instruments; they are used to get repeated simulation runs for varying parameter constellations. The findings presented here concern varying allocations in initial stocks. Generalization to comparative statics in further parameters is in progress.

Discrete Tomography of Penrose Model Sets

Various theoretical and algorithmic aspects of inverse problems in discrete tomography of planar Penrose model sets are discussed. These are motivated by the demand of materials science for the reconstruction of quasicrystalline structures from a small number of images produced by quantitative high resolution transmission electron microscopy.Comment: 7 pages, 1 figure; paper presented at Aperiodic 2006 (Zao, Japan