Exorcising Maxwell’s Demon from Liboff’s Three-Channel Conundrum

We study a model proposed by Liboff (Found. Phys. Lett. 10:89, 1997) to violate the second law of thermodynamics. Discs are moving without friction in three connected channels inclined by π/3 with respect to each other. Based on the geometry considerations, it was argued that eventually all the discs end up in the middle channel regardless of their initial positions. This would mean a decrease of the entropy of the system and violation of the second law. We argue that no such anomalous behavior occurs in the system.     

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.     

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).     

The Generalized Dolbeault Complex in Two Clifford Variables

The Penrose transform is used to construct a complex starting with the Dirac operator in two Clifford variables. The corresponding relative BGG complex and its direct image is computed for cohomology with values in line bundles induced by representations in singular infinitesimal character. The limit of the induced spectral sequence is computed in cases connected with the Dirac operator in two Clifford variables. The work presented here is a part of the research project MSM 0021620839 and was supported also by the grants GAUK 447/2004 and GA ČR 201/05/2117.