Monochromatic triangles in two-colored plane

We prove that for any partition of the plane into a closed set C and an open set O and for any configuration T of three points, there is a translated and rotated copy of T contained in C or in O.     

Application potential of gas chromatography high speed time-of-flight mass spectrometry system in analysis of pesticides. Part 1

Analysis of pesticides and polychlorinated biphenyls in food matrices was provided by the method of complete two-dimensional gas chromatography/time-of-flight mass spectrometry. It was shown, that using of technology GC/GC is significantly improves separation of target compounds and decrease the limits of quantification in comparison with the common “one-dimensional” chromatography. Also, the study describes briefly the use of rapid separation for the analysis of trace contamination in food samples. High-speed temperature program, coupled with the possibility of deconvolution of spectra, using the TOF-type detector with the appropriate software, significantly reduces the total time of analysis compared with traditional methods.     

Commutative zeropotent semigroups with few invariant congruences

Commutative semigroups satisfying the equation 2x + y = 2x and having only two G-invariant congruences for an automorphism group G are considered. Some classes of these semigroups are characterized and some other examples are constructed. The first author was supported by the Grant Agency of Czech Republic, grant no. 201/01/D047. This work is a part of the research project MSM 0021620839 financed by MŠMT     

Influence of selected biowaste materials pre-treatment on their anaerobic digestion

The topic of this study is the pre-treatment of substrates for anaerobic digestion. Two different substrates of algae Scenedesmus subspicatus (SAG 86.81), Chlorella kessleri (LARG/1) and foliage of Prunus serrulata were subjected to anaerobic digestion. A mixture of commercially available cellulolytic enzymes (Analytical science s.r.o., Modra, Slovakia) was used for anaerobic treatment of algae while the foliage of Prunus serrulata was pre-treated by lignolytic fungi. The highest production of methane per mass of volatile solids was reached with untreated Chlorella kessleri at (0.59 ± 0.04) L g⁻¹. The addition of cellulolytic enzymes did not increase the production of methane from the algal substrate; however, a faster substrate degradation and thus also higher speed of methane production at the beginning of cultivation was achieved. After foliage pre-treatment by fungal isolate Pleurotus pulmonarius, isolated from natural habitats, the methane production increased five times. In this way we were able to speed up the processes of biological degradation of ligno-cellulose materials and thereby to increase the production of methane. Our results show the possibility of using algae as a suitable substrate for biogas production. On the other hand, also aerobic pre-treatment of foliage (Pleurotus pulmonarius) presents a successful way for speeding up the degradation of ligno-cellulose waste leading to increased methane yields.     

DFT study of optical properties of MoS<Subscript>2</Subscript> and WS<Subscript>2</Subscript> compared to spectroscopic results on liquid phase exfoliated nanoflakes

We calculate the dielectric function within the framework of the random-phase approximation (RPA) based on DFT ground-state calculations, starting from eigenvectors and eigenvalues. The final goal of our theoretical work is a comparison to corresponding experimental data. We compare our computational results with optical measurements on \(\hbox {MoS}_2\) and \(\hbox {WS}_2\) nanoflakes. \(\hbox {MoS}_2\) and \(\hbox {WS}_2\) were exfoliated by ultrasonic treatment in high-boiling point organic solvent and characterized using UV–VIS spectrophotometry. We find that DFT-RPA yields a good, computationally inexpensive first approximation of the imaginary part of the dielectric function, although excitonic effects require more complex code and extra computing power.     

Kinetic study of wood chips decomposition by TGA

Pyrolysis of a wood chips mixture and main wood compounds such as hemicellulose, cellulose and lignin was investigated by thermogravimetry. The investigation was carried out in inert nitrogen atmosphere with temperatures ranging from 20°C to 900°C for four heating rates: 2 K min⁻¹, 5 K min⁻¹, 10 K min⁻¹, and 15 K min⁻¹. Hemicellulose, cellulose, and lignin were used as the main compounds of biomass. TGA and DTG temperature dependencies were evaluated. Decomposition processes proceed in three main stages: water evaporation, and active and passive pyrolysis. The decomposition of hemicellulose and cellulose takes place in the temperature range of 200–380°C and 250–380°C, while lignin decomposition seems to be ranging from 180°C up to 900°C. The isoconversional method was used to determine kinetic parameters such as activation energy and pre-exponential factor mainly in the stage of active pyrolysis and partially in the passive stage. It was found that, at the end of the decomposition process, the value of activation energy decreases. Reaction order does not have a significant influence on the process because of the high value of the pre-exponential factor. Obtained kinetic parameters were used to calculate simulated decompositions at different heating rates. Experimental data compared with the simulation ones were in good accordance at all heating rates. From the pyrolysis of hemicellulose, cellulose, and lignin it is clear that the decomposition process of wood is dependent on the composition and concentration of the main compounds.     

Thermodynamic properties of magnetic bilayers

Two models of magnetic bilayers are presented both based on the Heisenberg model. In the first case of ferromagnetically ordered ferromagnetically coupled planes of S=1 the anisotropy is of easy plane/axis type, while in the study of antiferromagnetically ordered antiferromagnetically coupled planes of S=1/2, the anisotropy is of XXZ type. Both systems are treated by Green's function method, which consistently applied within Random Phase Approximation lead to excitation energies and the system of equations for order parameters which can be solved numerically and which satisfies both Mermin-Wagner and Goldston theorem in the corresponding limit and also agrees with the Mean Field results. The basic result is that the transition temperature for magnetic dipole order parameter is unique for both planes. The results are compared with previous theoretical and experimental results.     

Modified hydrotalcites application as precursors for (Na,K)Mg/Al spinel-type compounds formation

In this work, a synthesis route of (Na,K)Mg/Al spinel-type compounds, which combines hydrothermal synthesis at low temperatures (<200 °C) and solid-state sintering (>800 °C) methods, is presented. It was examined that NaOH and KOH additives induce the reaction between initial Mg and Al components and the formation of hydrotalcite during hydrothermal treatment. It should be noted that after 1 h of calcination of synthetic precursors at 850 °C spinel-type compounds are formed only in the samples with alkali addition. Meanwhile in the pure system only traces of the mentioned compounds are observed at 900 °C. Moreover, the increase in solid-state sintering temperature and duration lead to the higher-crystallinity (Na,K)MgAl₂O₄ spinel-type compounds. It should be noted that textural properties of formed (Na,K)Mg/Al spinel-type compounds depend on the chemical composition of precursors. The synthetic and calcined products are characterised by XRD, STA, FT-IR analyses and BET method.     

Stationary polarons in discrete molecular chains

Properties of the large acoustic polarons in discrete molecular chains have been investigated within the adiabatic approximation. It turns out that practically all the polaron features are determined by the single parameter‐coupling constant which represents the ratio between the small polaron binding energy and the electron bandwidth. Three different types of stationary solutions were found corresponding to weak, intermediate, and strong coupling limits, respectively. In the weak coupling regime, that is, for the values of coupling constant exceeding the limit of the applicability of continuum approximation but lower than the critical one ( $g_C$ ), we observe symmetric bond‐centered solution corresponding to the polaron positioned in the middle between the adjacent lattice sites. When coupling constant overgrows, this critical value transition toward the site‐centered state occurs. It takes place continuously through the intermediate asymmetric state whose position gradually approaches lattice site as coupling constant increases. One of the main consequences of the lattice discreteness is the emergence of the periodic potential, Peierls‐Nabarro potential relief, through which polarons have to pass to transfer along the chain. The conditions for the polaron propagation are formulated in terms of the threshold velocity. © 2012 Wiley Periodicals, Inc.     

On the Existence of Rainbow 4-Term Arithmetic Progressions

For infinitely many natural numbers n, we construct 4-colorings of [n]  =  {1, 2, ..., n}, with equinumerous color classes, that contain no 4-term arithmetic progression whose elements are colored in distinct colors. This result solves an open problem of Jungić et al. (Comb Probab Comput 12:599–620, 2003) Axenovich and Fon-der-Flaass (Electron J Comb 11:R1, 2004).