Ligilactobacillus salivarius is an important member of the human and animal gut microbiota, and selected strains are promising probiotics, but knowledge of the characteristics of avian isolates is still limited. In this study, we examined selected phenotypic and genotypic traits of 33 L. salivarius strains from geese, chickens, turkeys and pigeons. The strains varied in terms of cell size, colony morphology, broth growth characteristics, biofilm formation, tolerance to bile, hydrophobicity and phenotypic and genotypic antibiotic resistance profiles. Large variation among strains was noted for the utilization of sorbitol, salicin, trehalose, rhamnose, inulin and N-acetyl-D-glucosamine. The presence of genes related to sugar metabolism, i.e., mipB, tktA, rhaB and LSL_1894, was not always correlated with the biochemical phenotypic profile. Correlations were recorded between the host and utilization of certain sugars as well as tolerance to bile. The repA-type megaplasmid and genes coding for Abp118 bacteriocin were detected in 94% and 51.5% of L. salivarius strains, respectively. Phylogeny based on groEL gene sequences was partly correlated with the origin of the strains and revealed an evolutionary distance between L. salivarius strains from humans and birds. The results of the study contribute to knowledge of the characteristics of the species L. salivarius. Intraspecies variations of L. salivarius strains may affect their ability to colonize specific niches and utilize nutrients and reveal potential strain-dependent effects on host health.
A case study of the tools used by an analyst of the economic aspects of the operation of the water supply network has been undertaken in this paper. All issues discussed here are formulated by using degenerated linear programming models ( PL ). Below, it is noted that the linear dependence of binding constraints ( CO ) distorts standard postoptimization procedures in PL. This observed fact makes postoptimization analysis mostly unhelpful for an average analyst due to problems with the int erpretation of ambiguous sensitivity reports which are obtained from popular computer packages. In standard postoptimization methods, changes to single parameters of the right-hand vector CO are analyzed or referred to parametric linear programming that unfortunately requires prior knowledge of mathematically and economically justified vectors of changes of right-hand sides CO. Therefore, it is suggested that modifications are introduced to some of the postoptimization procedures in this work. For issues in the field of hydrology, the following were presented: interpretation and methods of generating justified vectors of changes of right-hand sides of limiting conditions. And so, the procedure of generating infinitely many solutions of the dual issue based on certain vectors orthogonal to the vector of right-hand sides of constraint conditions was demonstrated. Furthermore, the same orthogonal vectors were used to obtain nodal solutions of the dua0l model and the corresponding vectors of changes of the entire right-hand sides of the constraint conditions. Then, managerial interpretation was applied to this way of proceeding. The methods presented in the work serve to improve the functioning of the system of water supply.
We study problems similar to the Koebe Quarter Theorem for close-to-convex polynomials with all zeros of derivative in $${\mathbb {T}}:=\{z\in {\mathbb {C}}:|z|=1\}$$ T : = { z ∈ C : | z | = 1 } . We found minimal disc containing all images of $${\mathbb {D}}:=\{z\in {\mathbb {C}}: |z|<1\}$$ D : = { z ∈ C : | z | < 1 } and maximal disc contained in all images of $${\mathbb {D}}$$ D through polynomials of degree 3 and 4. Moreover we determine the extremal functions for both problems.
Article citation info: (*) Tekst artykułu w polskiej wersji językowej dostępny w elektronicznym wydaniu kwartalnika na stronie www.ein.org.pl Introduction Fixing the price of water in order to balance water demandAn analysis conducted by the World Bank [64] indicates that water shortages in some regions may reduce GDP by up to 6% and lead to increased migration and in some cases to a greater risk of conflict. Droughts and periods of water scarcity have become a more common and more frequent phenomenon in Europe [17]. The drought experiences in Europe in 2011, 2012, 2015 and 2018 were the worst in a century and affected not only Southern and Western Europe, but also the countries in Northern Europe (including Great Britain, France, Germany, Sweden and Poland). The difference between water supply and its growing demand also determines the key limitations of China's economic development. It is estimated that before 2005 due to a shortage of water in production, China lost $ 28 511 million annually. Brown [7] concluded that the shortage of water in China will soon be a threat to global cereal demand. Therefore, water, alongside cereals and crude oil, is referred to as a strategic resource. Hence, it is suggested that public authorities should shape water pricing for users in order to reflect its true shortage or alternative costs [15].
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