z-arcs in the thirty degrees sector

In this detailed study of 3-segment non-convex simple arcs inscribed in the 30 ∘ {30^{\circ}} sector, we show that each such arc of length one fits in the interior of the sector of radius one with the prescribed embedding. We discuss implications of this study for covering problems involving triangular covers and for the worm problem of Leo Moser.

LOWER BOUND FOR CONVEX HULL AREA AND UNIVERSAL COVER PROBLEMS

We provide a technique to obtain a lower bound for the area of the convex hull of a set of points and a rectangle in the plane, and then apply the resulting estimates to improve the lower bound for the convex case of Moser's Worm problem. Specifically, we show that any convex universal cover for unit arcs has an area of at least 0.232239. We also apply our approach to the universal cover problem for closed unit curves.

Seasonal evolution of faecal egg output by gastrointestinal worms in goats on communal farms in eastern Namibia

As a more detailed continuation of a previous study, faecal samples for worm egg counts were collected per rectum from ten marked adult animals in selected flocks of goats, in each of six villages evenly spread out in the communal farming district of Okakarara in eastern Namibia. The study was conducted on a monthly basis from August 1999 to July 2000. Average faecal worm egg counts (FECs) were highest during the warm-wet season, much lower during the cold-dry months and moderate during the hot-dry season. Least square means of FECs were 2 140, 430 and 653 per gram of faeces for the three seasons, respectively. Seasonal variation in egg counts was significant (P < 0.0001). Gastrointestinal strongyles, and to a lesser extent Strongyloides species, were the predominant parasite groups identified in goats. Kidding rates peaked in the cold-dry season and mortality rates in the hot-dry season. Results of this study suggest that gastrointestinal parasitism may be a problem that accentuates the effect of poor nutrition on small ruminants during the season of food shortages in the east of Namibia and that the use of FECs per se to assess the severity of gastrointestinal parasitic infection in goats followed by chemoprophylactic strategic and / or tactical treatment, may not be the best approach to addressing the worm problem under resource-poor conditions. The use of the FAMACHA(c) system that identifies severely affected animals for treatment is technically a better option for communal farmers.