Among all bodies of constant width in the Euclidean plane, the Reuleaux triangle of the same width has minimal area. But Reuleaux triangles are also minimal in another sense: if a convex body can be covered by a translate of a Reuleaux triangle, then it can be covered by a translate of any convex body of the same constant width. The first result is known as the Blaschke-Lebesgue theorem, and it...

This paper is a collection of thoughts and observations, being partly a review and partly a report of current research, on recent work in various aspects of Grünbaum colorings, their existence and usage. In particular, one of the most striking significances of Grünbaum’s Conjecture in the 2-dimensional case is its equivalence to the 4-Color Theorem. The notion of Grünbaum coloring is extended f...

After first determining criteria for wild ramification of L/K (which can only happen at primes above 2), the above result is obtained for n = 2 (e ≥ 3) by computing TL/K(OL) explicitly, and is then extended to the general case. This approach does not rely on Leopoldt’s Theorem, in contrast to the techniques used in [6]. The explicit nature of the calculations used to compute I(L/K) leads to the...

Bilattices and d-frames are two different kinds of structures with a four-valued interpretation. Whereas d-frames were introduced with their topological semantics in mind, the theory of bilattices has a closer connection with logic. We consider a common generalisation of both structures and show that this not only still has a clear bitopological semantics, but that it also preserves most of the...

Avian necrotic enteritis is a major economic and welfare issue throughout the global poultry industry and is caused by isolates of Clostridium perfringens that produce NetB toxin. Previously we have shown that birds directly vaccinated with inactivated C. perfringens type A culture supernatant (toxoid) combined with recombinant NetB (rNetB) protein were significantly protected from homologous a...

effect of protexin to diminish negative consequences of feeding aflatoxin b1 (afb1) contaminated diet on performance, immune response, meat quality and ileal microbial flora were examined using 320 seven-day-old japanese quails fed four treatments [control diet (without additives), diet containing 2.5 mg afb1/kg, diet containing 150 mg protexin/kg, diet containing 2.5 mg afb1/kg+150 mg protexin...

A total of 448 Ross 308 male broiler chickens were assigned to seven treatments with four replicates, each containing 16 chicks. The birds were reared from d 21 to 42 and effects of physical sizes (ad libitum by a basal commercial broiler diet with 3050 Kcal/Kg ME and 19.06% CP/Kg from 21 to 42 d. The chickens which received clinoptilolite (1.5% with particle size of 0.4-0.8 mm) showed a signif...

Frequent vaccination failures have occurred in the broiler farms in Eurasian countries during Newcastle disease outbreaks. The disease is enzootic in many countries of the region, especially in southwest Asia. I-2 vaccine has been used successfully in village chickens in many Asian and African countries. Our preliminary study showed good efficacy of the vaccine in broiler chickens. Therefore th...

The aim of this study was to recognize the effects of dietary hempseed (HS) and hempseed oil (HO) on performance, egg quality and blood parameters of laying hens. A total of 320 Hy-line 55-weeks laying hens were randomly allotted to eight dietary treatments with five replicates (8 birds each). The experimental treatments were offered as a completely randomized design as follow: control group (n...

Coccidiosis is endemic in the commercial broiler industry capable of inflicting devastating economic losses to poultry operations. Vaccines are relatively effective in controlling the disease; their efficacy could potentially be improved with concurrent use of probiotics as evaluated in this study using an Eimeria challenge. Day of hatch 400 Cobb-500 male broilers were assigned to one of four t...