Lineability, algebrability and strong algebrability of some sets in RR or CC

Udostępnienie publikacji Wydawnictwa Uniwersytetu Łódzkiego finansowane w ramach projektu „Doskonałość naukowa kluczem do doskonałości kształcenia”. Projekt realizowany jest ze środków Europejskiego Funduszu Społecznego w ramach Programu Operacyjnego Wiedza Edukacja Rozwój; nr umowy: POWER.03.05.00-00-Z092/17-00

Spores and vegetative cells of phenotypically and genetically diverse Bacillus cereus sensu lato are common bacteria in fresh water of Northeastern Poland

Gram-positive rods named B. cereus sensu lato (sl), are common in natural habitats and food products. It is believed that they are restricted to spores, however their ecology in aquatic habitats is still poorly investigated. Thus, the aim of the study was to assess the rain-dependent fluctuations of the concentration of B. cereus sl vegetative cells and spores with evaluation of their phylogenetic and population structure in relation to the toxicity and psychrotolerance. We proved that vegetative cells of B. cereus sl are widely distributed in fresh water of rivers and lakes being as common as spores. Moreover, heavy rain shows huge impact on their concentration in undisturbed environments. The diversity of B. cereus sl reflects multiple sources of bacteria and differences between distinct environments. Next, their diverse genetic structure and phenotypes better fit to their ecological properties than to the taxonomic affiliation.The accepted manuscript in pdf format is listed with the files at the bottom of this page. The presentation of the authors' names and (or) special characters in the title of the manuscript may differ slightly between what is listed on this page and what is listed in the pdf file of the accepted manuscript; that in the pdf file of the accepted manuscript is what was submitted by the author

Lineability within Peano Curves, Martingales, and Integral Theory

This paper is devoted to give several improvements of some known facts in lineability approach. In particular, we prove that (i) the set of continuous mappings from the unit interval onto the unit square contains a closed, c-semigroupable convex subset, (ii) the set of pointwise convergent martingales (Xn)n∈N with EXn→∞ is c-lineable, (iii) the set of martingales converging in measure but not almost surely is c-lineable, (iv) the set of sequences (Xn)n∈N of independent random variables, with EXn=0, ∑n=1∞var Xn=∞, and the property that (X1+⋯+Xn)n∈N is almost surely convergent, is c-lineable, (v) the set of bounded functions f:[0,1]×[0,1]→R for which the assertion of Fubini’s Theorem does not hold is consistent with ZFC  1-lineable (it is not 2-lineable), (vi) the set of unbounded functions f:[0,1]×[0,1]→R for which the assertion of Fubini’s Theorem does not hold (with infinite integral allowed) is c-lineable but not c+-lineable

G la̧b, Independent Bernstein sets and algebraic constructions

Abstract. We present the method of constructing algebras and linear spaces of 2 c generators using independent Bernstein sets. As an application we obtain large algebras of special functions

Biosurfactant and biopolymer producing microorganisms from West Kazakhstan oilfield

Abstract Microbiological enhanced oil recovery (MEOR) uses indigenous or exogenous microorganisms and nutrients to enhance oil production through synthesis of metabolites reducing oil viscosity and surface tension. In order to find bacteria suitable for MEOR, we studied 26 isolates from wells in the Akingen oilfield in West Kazakhstan. Six of them were selected for further analysis based on their ability to reduce surface tension to less than 40 mN/m, with the A9 isolate exhibiting tension reduction values of 32.76 ± 0.3 mN/m. Based on the morphological features, biochemical activities, and the 16S rRNA gene, the isolates were classified to the Bacillus subtilis group. In the phylogenetic analysis the isolates grouped into two main clusters. Genes encoding the surfactin synthetase subunits were found in A2, A8, A9, A12, PW2, only the PW2 strain had lchAA encoding lichenysin, while sacB encoding levan was noted in A2, A8, A9, and A12. The expression of srfAB, srfAC, and sacB tested with qPCR varied among strains. Nevertheless, whereas temperature moderately affects the expression level, with the highest level recorded at 40 °C, salinity significantly impacts the expression of the genes encoding biosurfactants. B. subtilis strains isolated in the study, especially A9, are promising for microbial-enhanced oil recovery