Arithmetic progressions in sets of fractional dimension

Let E\subset\rr be a closed set of Hausdorff dimension $\alpha$. We prove that if $\alpha$ is sufficiently close to 1, and if $E$ supports a probabilistic measure obeying appropriate dimensionality and Fourier decay conditions, then $E$ contains non-trivial 3-term arithmetic progressions.Comment: 42 page

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

The Influence of PEDOT to PSS Ratio on the Optical Properties of PEDOT:PSS Thin Solid Films - Insight from Spectroscopic Ellipsometry

In this work, we study the influence of the PEDOT to PSS ratio on the optical properties of PEDOT:PSS thin solid films using spectroscopic ellipsometry and UV-vis spectrometry. In the data analysis, we develop a consisted composition dependent optical model of PEDOT:PSS. This enabled us to account for contributions from PSS part within the Tauc-Lorentz optical model and from PEDOT part within the Drude-Lorentz optical model. Moreover, we relate the optical properties of PEDOT:PSS thin solid films to their electrical specific conductivities in the frame of the generalized effective medium theory. Determined in this manner electrical conductivities of five commercially available water dispersions of PEDOT:PSS are compared with their nominal values

Studying of Perovskite Nanoparticles in PMMA Matrix Used As Light Converter for Silicon Solar Cell

The nanoparticles of CH3NH3PbBr3 hybrid perovskites were synthesized. These perovskite nanoparticles we embedded in polymethyl methacrylate (PMMA) in order to obtain the composite, which we used as light converter for silicon solar cells. It was shown that the composite emit the light with the intensity maximum at about 527 nm when exited by a short wavelength (300÷450 nm) of light. The silicon solar cells were used to examine the effect of down-conversion (DC) process by perovskite nanoparticles embedded in PMMA. For experiments, two groups of monocrystalline silicon solar cells were used. The first one included the solar cells without surface texturization and antireflection coating. The second one included the commercial cells with surface texturization and antireflection coating. In every series of the cells one part of the cells were covered by composite (CH3NH3PbBr3 in PMMA) layer and second part of cells by pure PMMA for comparison. It was shown that External Quantum Efficiency EQE of the photovoltaic cells covered by composite (CH3NH3PbBr3 in PMMA) layer was improved in both group of the cells but unfortunately the Internal Quantum Efficiency was reduced. This reduction was caused by high absorption of the short wavelength light and reabsorption of the luminescence light. Therefore, the CH3NH3PbBr3 perovskite nanoparticles embedded in PMMA matrix were unable to increase silicon solar cell efficiency in the tested systems

Studying of Perovskite Nanoparticles in PMMA Matrix Used as Light Converter for Silicon Solar Cell

The nanoparticles of CH3NH3PbBr3 hybrid perovskites were synthesized. These perovskite nanoparticles we embedded in polymethyl methacrylate (PMMA) in order to obtain the composite, which we used as light converter for silicon solar cells. It was shown that the composite emit the light with the intensity maximum at about 527 nm when exited by a short wavelength (300÷450 nm) of light. The silicon solar cells were used to examine the effect of down-conversion (DC) process by perovskite nanoparticles embedded in PMMA. For experiments, two groups of monocrystalline silicon solar cells were used. The first one included the solar cells without surface texturization and antireflection coating. The second one included the commercial cells with surface texturization and antireflection coating. In every series of the cells one part of the cells were covered by composite (CH3NH3PbBr3 in PMMA) layer and second part of cells by pure PMMA for comparison. It was shown that External Quantum Efficiency EQE of the photovoltaic cells covered by composite (CH3NH3PbBr3 in PMMA) layer was improved in both group of the cells but unfortunately the Internal Quantum Efficiency was reduced. This reduction was caused by high absorption of the short wavelength light and reabsorption of the luminescence light. Therefore, the CH3NH3PbBr3 perovskite nanoparticles embedded in PMMA matrix were unable to increase silicon solar cell efficiency in the tested systems