A Szemeredi-Trotter type theorem in R4\mathbb{R}^4

We show that $m$ points and $n$ two-dimensional algebraic surfaces in $\mathbb{R}^4$ can have at most $O(m^{\frac{k}{2k-1}}n^{\frac{2k-2}{2k-1}}+m+n)$ incidences, provided that the algebraic surfaces behave like pseudoflats with $k$ degrees of freedom, and that $m\leq n^{\frac{2k+2}{3k}}$. As a special case, we obtain a Szemer\'edi-Trotter type theorem for 2--planes in $\mathbb{R}^4$, provided $m\leq n$ and the planes intersect transversely. As a further special case, we obtain a Szemer\'edi-Trotter type theorem for complex lines in $\mathbb{C}^2$ with no restrictions on $m$ and $n$ (this theorem was originally proved by T\'oth using a different method). As a third special case, we obtain a Szemer\'edi-Trotter type theorem for complex unit circles in $\mathbb{C}^2$. We obtain our results by combining several tools, including a two-level analogue of the discrete polynomial partitioning theorem and the crossing lemma.Comment: 50 pages. V3: final version. To appear in Discrete and Computational Geometr

Authentic leadership, followership, and psychological capital as antecedents of work engagement

The present study investigated authentic leadership, psychological capital, and followership behaviour influences on work engagement of employees . Respondents were 901 South African employees within the healthcare industry organisation (n = 647) and mining industry (n = 254) . The employees completed questionnaires on authentic leadership, psychological capital, and followership behaviour, and work engagement . Results following structural equation modelling and mediation analysis suggest work engagement to be explained by the psychological capital of the employee rather than by authentic leadership qualities . Improving employee psychological capital has the potential to enhance the levels of work engagement of employees

Zastosowanie grzybów Trichoderma do uwalniania cukrów prostych z roślinnych surowców odpadowych

The aim of the presented work was to examine the applicability of selected agri-food industry waste materials as substrates for microbial hydrolytic enzymes biosynthesis (mostly celulases, xylanases and poligalacturonases) as well as to determine the quantitative and qualitative composition of mono- and disaccharides released from non-starch polysaccharides. (sucrose, glucose, galactose, fructose, cellobiose, etc). Two strains of Trichoderma fungi were tested: T. citrinoviride C1 and T. harzianum T33 in SSF culture on six different waste materials from agro-food industries (pulp from: cherries with seeds, pears, red cabbage, cornelian cherry and grapes with seeds).W pracy przedstawiono ocenę możliwości zagospodarowania wybranych odpadów przemysłu rolno-spożywczego jako substratu do mikrobiologicznej biosyntezy enzymów hydrolitycznych (głównie celulaz, ksylanaz i poligalakturonaz) a także, określenie składu ilościowego i jakościowego uwalnianych z polisacharydów nieskrobiowych mono- i disacharydów (sacharozy, glukozy, galaktoza, fruktozy, celobiozy itd). Testowano dwa szczepy grzybów z rodzaju Trichoderma: T. citri-noviride C1 i T. harzianum T33 w hodowlach SSF na sześciu różnych surowcach pochodzących z przemysłu rolno-spożywczego (wytłoki z: wiśni z pestkami, gruszki, czerwonej kapusty, derenia, winogron z pestkami)

Compositing of keratinous waste with bacterial inoculum in a rotary bioreactor

Odpady keratynowe w postaci piór kurzych kompostowano w bioreaktorze obrotowym z udziałem szczepionki bakterii Bacillus subtilis. Skład mikroflory kompostu oraz aktywności enzymatyczne, a także końcowa mineralizacja, sugerowały aktywny udział tych bakterii w biodegradacji białek keratynowych. W bioreaktorze obrotowym kompostowanie miało bardziej dynamiczny przebieg, a szczególnie zaawansowana była nitryfi-kacja, czego nie uzyskano w warunkach kontrolnych.Composting of chicken feathers was conducted in a rotary bioreacto: with an addition of Bacillus subtilis inoculum. A microbial profile anc enzymatic activities revealed active participation of introduced bacte ria in keratin proteins biodegradation. In the rotary bioreactor thi composting process was more dynamic with exceptionally advancec nitrification in contrast to obtained in controlled conditions

Application of bacterial inoculum in compostingof keratinous waste in a static bioreactor

W bioreaktorze statycznym kompostowano pióra kurze z udziałem szczepionki bakterii Bacillus subtilis P22. Inokulacja kompostu była niezbędnym warunkiem prawidłowego przebiegu tego procesu, a także dynamicznej biotransformacji substancji organicznych do składników mineralnych, co wykazano na podstawie ilościowej analizy mikroflory kompostowej, badań enzymatycznych oraz chemicznych wskaźników dojrzałości.Composting of chicken feathers was carried out in the presence ofBa cillus subtilis P22 inoculum in a static bioreactor. Inoculation of com post was essential for proper dynamic biotransformation of organ! matter to mineral components, which was proved by analysis of com post microflora, enzymatic tests and chemical maturity indexes