Transitive and Co-Transitive Caps

A cap in PG(r,q) is a set of points, no three of which are collinear. A cap is said to be transitive if its automorphism group in PGammaL(r+1,q) acts transtively on the cap, and co-transitive if the automorphism group acts transtively on the cap's complement in PG(r,q). Transitive, co-transitive caps are characterized as being one of: an elliptic quadric in PG(3,q); a Suzuki-Tits ovoid in PG(3,q); a hyperoval in PG(2,4); a cap of size 11 in PG(4,3); the complement of a hyperplane in PG(r,2); or a union of Singer orbits in PG(r,q) whose automorphism group comes from a subgroup of GammaL(1,q^{r+1}).Comment: To appear in The Bulletin of the Belgian Mathematical Society - Simon Stevi

Effect of pH and level of concentrate in the diet on the production of biohydrogenation intermediates in a dual-flow continuous culture

Milk fat depression in cows fed high-grain diets has been related to an increase in the concentration of trans-10 C-18:1 and trans-10, cis-12 conjugated linoleic acid (CLA) in milk. These fatty acids (FA) are produced as a result of the alteration in rumen biohydrogenation of dietary unsaturated FA. Because a reduction in ruminal pH is usually observed when high-concentrate diets are fed, the main cause that determines the alteration in the biohydrogenation pathways is not clear. The effect of pH (6.4 vs. 5.6) and dietary forage to concentrate ratios (F:C; 70:30 F:C vs. 30:70 F:C) on rumen microbial fermentation, effluent FA profile, and DNA concentration of bacteria involved in lipolysis and biohydrogenation processes were investigated in a continuous culture trial. The dual-flow continuous culture consisted of 2 periods of 8 d (5 d for adaptation and 3 d for sampling), with a 2 x 2 factorial arrangement of treatments. Samples from solid and liquid mixed effluents were taken for determination of total N, ammonia-N, and volatile fatty acid concentrations, and the remainder of the sample was lyophilized. Dry samples were analyzed for dry matter, ash, neutral and acid detergent fiber, FA, and purine contents. The pH 5.6 reduced organic matter and fiber digestibility, ammonia-N concentration and flow, and crude protein degradation, and increased nonammonia and dietary N flows. The pH 5.6 decreased the flow of C-18:0, trans-11 C-18:1 and cis-9, trans-11 CLA, and increased the flow of trans-10 C-18:1, C18:2n-6, C18:3n-3, trans-11, cis-15 C-18:2 and trans-10, cis-12 CLA in the 1 h after feeding effluent. The pH 5.6 reduced Anaerovibrio lipolytica (32.7 vs. 72.1 pg/10 ng of total DNA) and Butyrivibrio fibrisolvens vaccenic acid subgroup (588 vs. 1,394 pg/10 ng of total DNA) DNA concentrations. The high-concentrate diet increased organic matter and fiber digestibility, nonammonia and bacterial N flows, and reduced ammonia-N concentration and flow. The high-concentrate diet reduced trans-11 C-18:1 and trans-10 C-18:1, and increased C18:2n-6, C18:3n-3 and trans-10, cis-12 CLA proportions in the 1 h after feeding effluent. The increase observed in trans-10, cis-12 CLA proportion in the 1 h after feeding effluent due to the high-concentrate diet was smaller that that observed at pH 5.6. Results indicate that the pH is the main cause of the accumulation of trans-10 C-18:1 and trans-10, cis-12 CLA in the effluent, but the trans-10, cis-12 CLA proportion can be also affected by high levels of concentrate in the diet

Maximal partial spreads and the modular n-queen problem III

AbstractMaximal partial spreads in PG(3,q)q=pk,p odd prime and q⩾7, are constructed for any integer n in the interval (q2+1)/2+6⩽n⩽(5q2+4q−1)/8 in the case q+1≡0,±2,±4,±6,±10,12(mod24). In all these cases, maximal partial spreads of the size (q2+1)/2+n have also been constructed for some small values of the integer n. These values depend on q and are mainly n=3 and n=4. Combining these results with previous results of the author and with that of others we can conclude that there exist maximal partial spreads in PG(3,q),q=pk where p is an odd prime and q⩾7, of size n for any integer n in the interval (q2+1)/2+6⩽n⩽q2−q+2

A proof of the linearity conjecture for k-blocking sets in PG(n, p3), p prime

In this paper, we show that a small minimal k-blocking set in PG(n, q3), q = p^h, h >= 1, p prime, p >=7, intersecting every (n-k)-space in 1 (mod q) points, is linear. As a corollary, this result shows that all small minimal k-blocking sets in PG(n, p^3), p prime, p >=7, are Fp-linear, proving the linearity conjecture (see [7]) in the case PG(n, p3), p prime, p >= 7