A conjugacy invariant for reducible sofic shifts and its semigroup characterizations

We introduce a notion of magic words and, through them, we present a lattice of sub-synchronizing subshifts which describes the synchronizing parts of a sofic shiftS. We show that topological conjugacy maps subsynchronizing subshifts onto sub-synchronizing subshifts, it preserves their mutual relationship (i.e. the corresponding lattices are isomorphic) and the corresponding covers within the Krieger covers are topologically conjugate. Using the magic words, a full characterization of the syntactic monoid of a shift of finite type is given. We show that a synchronizing deterministic presentation of every sub-synchronizing subshift ofS can be seen within a two-sided ideal of the syntactic monoid ofS.     

Chemometric Approach to Prediction of Antibacterial Agent Production by Streptomyces hygroscopicus

The nutritional requirements for antimicrobial agent production using Streptomyces hygroscopicus were analyzed in shake flask experiments. Antimicrobial activity was tested against Staphylococcus aureus and Bacillus cereus. The mathematical models have been generated with relative high complexity in order to give an adequate fit to the data. All the results suggest a high dependence of produced antimicrobial agent quantities on the amount of carbon, nitrogen, and phosphorus in cultivation medium. The statistical results of the generated models reflect the high predictive ability. The derived models were validated using leave-one-out cross-validation technique, and from statistical point of view, they have significantly high values of the cross-validation parameters.     

Natural radioactivity around former uranium mine,Gabrovnica in Eastern Serbia

Gabrovnica near Kalna village was the first uranium mine established in Yugoslavia. In 1963, the Nuclear Energy Commission began operating the mine and mill. Between 1964 and 1966, the staff at Kalna extracted and produced an estimated 900 kg of UO₂ and 400 kg of uranium metal. The Kalna ore was of poor quality, containing very low uranium content, which required higher-cost mining and refining methods. That was the main reason for closing this mine. This paper presents results obtained by measuring the activity concentration of soil samples measured by gamma spectrometry and also indoor ²²²Rn activity concentrations in houses in the nearby village Kalna. There is a presence of elevated radioactivity levels in the most of the measured samples. The mine was never officially decommissioned. The results obtained might be useful for the future decommissioning procedure.     

Holographic screening length in a hot plasma of two sphere

We study the screening length \(L_{\mathrm{max}}\) of a moving quark–antiquark pair in a hot plasma, which lives in a two sphere, \(S^2\), using the AdS/CFT correspondence in which the corresponding background metric is the four-dimensional Schwarzschild–AdS black hole. The geodesic of both ends of the string at the boundary, interpreted as the quark–antiquark pair, is given by a stationary motion in the equatorial plane by which the separation length L of both ends of the string is parallel to the angular velocity \(\omega \). The screening length and total energy H of the quark–antiquark pair are computed numerically and show that the plots are bounded from below by some functions related to the momentum transfer \(P_c\) of the drag force configuration. We compare the result by computing the screening length in the reference frame of the moving quark–antiquark pair, in which the background metrics are “Boost-AdS” and Kerr–AdS black holes. Comparing both black holes, we argue that the mass parameters \(M_{\mathrm{Sch}}\) of the Schwarzschild–AdS black hole and \(M_{\mathrm{Kerr}}\) of the Kerr–AdS black hole are related at high temperature by \(M_{\mathrm{Kerr}}=M_{\mathrm{Sch}}(1-a^2l^2)^{3/2}\), where a is the angular momentum parameter and l is the AdS curvature.     

A Simple NMR‐Based Method for Studying the Spatial Distribution of Linkers within Mixed‐Linker Metal–Organic Frameworks

The spatial distribution of different linkers within mixed‐linker metal–organic frameworks crucially influences the properties of such materials. A simple and robust approach based on ¹H spin‐diffusion magic‐angle‐spinning nuclear magnetic resonance measurements and modeling of spin‐diffusion curves is presented; this approach facilitates the distinction between homogeneous and clustered distributions. The performance of the approach is demonstrated with an example of an aluminum‐based metal–organic material DUT‐5, which has framework consisting of biphenyl and bipyridyl dicarboxylic linkers. The distribution is shown to be homogeneous in this material. The approach could be applied to studying other spatially disordered crystalline materials.     

Thermodynamics of Solution of Some Alkyl Acetates in Water

 The temperature dependence of the solubility of methyl acetate (MeOAc), ethyl acetate (EtOAc), 1-propyl acetate (1-PrOAc), 1-butyl acetate (1-BuOAc), 2-methyl-1-propyl acetate (iso-BuOAc), 2-butyl acetate (sec-BuOAc), and 2-methyl-2-propyl acetate (tert-BuOAc) in water in the temperature range from 298.2 to 318.2 K was determined. The experimental solubility data together with some literature values are presented as a function of temperature and given in analytical form. The solubilities of the investigated compounds at 298.2 K were correlated with the number of carbon atoms in the solute molecule. The standard thermodynamic functions for solubility, i.e. Gibbs free energy, enthalpy, heat capacity, and entropy, were calculated. The Gibbs free energy is positive and increases linearly with the number of carbon atoms, whereas the enthalpy and entropy are negative. The standard thermodynamic functions were converted to thermodynamic quantities for hydration. The Gibbs free energies of hydration of alkyl acetates, which are negative, are compared with the Gibbs free energy of hydration of some n-alkanes, 1-alcohols, and 1-alkylamines. The standard thermodynamic functions of hydration were analyzed using a modified version of the theoretical approach developed by Lee and Graziano [1].     

Thermodynamics of the Solubility of Water in 1-Hexanol, 1-Octanol, 1-Decanol, and Cyclohexanol

Summary. The solubility of water in 1-hexanol, 1-octanol, 1-decanol, and cyclohexanol was determined as a function of water activity by the isopiestic method at 298.2K. The solubility of water in the alcohol was expressed by a Setchenov type of equation and the correlation coefficients were related to the virial coefficients of the McMillan-Mayer theory of solution. From the solubility data both the activities and the osmotic coefficients of the alcohols were calculated. The Henrys law constants for the solubility of water in the alcohols are given. They depend linearly on the Gibbs energy of hydration. The excess Gibbs energy of mixing of water and alcohols is positive as a consequence of the strong intermolecular interactions of the two pure components of the mixture.     

On the thermodynamic stability of (Eu,Y)-doped barium cerate

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