Elementary approach to closed billiard trajectories in asymmetric normed spaces

We apply the technique of K\'aroly Bezdek and Daniel Bezdek to study billiard trajectories in convex bodies, when the length is measured with a (possibly asymmetric) norm. We prove a lower bound for the length of the shortest closed billiard trajectory, related to the non-symmetric Mahler problem. With this technique we are able to give short and elementary proofs to some known results.Comment: 10 figures added. The title change

Effect of probiotic strains of

In this paper, the probiotic properties of Bacillus subtilis GM2 and GM5 strains were studied. It is shown that the use of probiotic additives based on the spores of these bacteria leads to an increase in the live weight gain of broiler chickens by 4.16% and 10.76% relative to the control. Metagenomic analysis showed that representatives of the phylum Firmicutes (54.55%) and Bacteroidetes (30.45%), mainly represented by the families Ruminococcacea and Bacteroidaceae, predominate in the caecal microbiota of broiler chickens on day 42. It was found that a probiotic based on the B. subtilis GM5 strain leads to an increase in the proportion of Firmicutes in caecum by 27% and a decrease in Bacteroidetes by 19%. There was also a significant decrease in the number of representatives of opportunistic pathogenic bacteria of the Enterobacteriaceae family relative to the control group

Effect of

The objective of the study was to determine the effect of adding protease obtained from the Bacillus pumilus 3-19 strain to the diet of Hubboard broiler chickens on the growth indicators of poultry and the composition of the cecum microbiota of broiler chickens. As a result of metagenomic analysis of 16S rRNA genes in the contents of the cecum of chickens, it was shown that the control and experimental groups formed two separate clusters, which indicates differences in microbial communities in these two groups. Analysis of alpha diversity showed an increase in species richness in the group of chickens that received protease as a feed additive. On day 35, both groups were dominated by bacterium of Firmicutes (21.13 — 49.01%) and Bacteroidetes (37.68 — 67.72%) groups. It was shown that in the group of chickens receiving protease as a feed additive, the average daily gain in live weight was higher than in the control group by 0.5 kg (P < 0.05). The introduction of protease resulted in an increased F/B ratio, which was positively correlated with chicken body weight. Thus, the addition of B. pumilus 3-19 protease to broiler feed leads to improved feed intake and digestibility, which is of great importance for reducing the cost of the final product. The use of protease regulates the cecum microbiota of broiler chickens and increases microbial diversity on 35 day of chicken growth

Antimicrobial Activities of Secondary Metabolites from Model Mosses

Plants synthetize a large spectrum of secondary metabolites with substantial structural and functional diversity, making them a rich reservoir of new biologically active compounds. Among different plant lineages, the evolutionarily ancient branch of non-vascular plants (Bryophytes) is of particular interest as these organisms produce many unique biologically active compounds with highly promising antibacterial properties. Here, we characterized antibacterial activity of metabolites produced by different ecotypes (strains) of the model mosses Physcomitrium patens and Sphagnum fallax. Ethanol and hexane moss extracts harbor moderate but unstable antibacterial activity, representing polar and non-polar intracellular moss metabolites, respectively. In contrast, high antibacterial activity that was relatively stable was detected in soluble exudate fractions of P. patens moss. Antibacterial activity levels in P. patens exudates significantly increased over four weeks of moss cultivation in liquid culture. Interestingly, secreted moss metabolites are only active against a number of Gram-positive, but not Gram-negative, bacteria. Size fractionation, thermostability and sensitivity to proteinase K assays indicated that the secreted bioactive compounds are relatively small (less than &lt;10 kDa). Further analysis and molecular identification of antibacterial exudate components, combined with bioinformatic analysis of model moss genomes, will be instrumental in the identification of specific genes involved in the bioactive metabolite biosynthesis