A sharp inequality for the variance with respect to the Ewens sampling formula

Lithuanian Mathematical Journal - We examine the variance of a linear statistic defined on the symmetric group endowed with the Ewens probability. Despite the dependence of the summands, it can be...     

Evaluation of education scenarios for acquiring digital competences of secondary school students in Slovenia

Central European Journal of Operations Research - Digital competences are among the most important competences in modern society, with the education system playing a key role in the acquisition of...     

Sensitive CE-MS method for monitoring of riociguat and desmethylriociguat levels in human serum

Riociguat is novel antihypertensive drug for treatment of pulmonary hypertension. As such, it is still being tested in many clinical and pharmacokinetic trials. Existing methods that determine serum riociguat and desmethylriociguat (DMR) are based solely on liquid chromatography with mass spectrometry. Therefore, we present a novel capillary electrophoresis with mass spectrometry method (CE-MS) for their determination in human serum as alternative method for ongoing trials. Complete resolution of both analytes was achieved by means of pH optimization of ammonium formate background electrolytes that are fully compatible with ESI/MS detection. Simple liquid-liquid extraction was used as sample pretreatment. The calibration dependence of the method was linear (in the range of 10–1000 ng/mL), with adequate accuracy (90.1–114.9%) and precision (13.4%). LOD and LOQ were arbitrarily set at 10 ng/mL for both analytes. Clinical applicability was validated using serum samples from patients treated with riociguat in pharmacokinetic study and the results corresponded with reference HPLC-MS/MS values. Capillary electrophoresis proved to be sensitive and selective tool for the analysis of riociguat and DMR.     

Differentials on graph complexes III: hairy graphs and deleting a vertex

We continue studying the cohomology of the hairy graph complexes which compute the rational homotopy of embedding spaces, generalizing the Vassiliev invariants of knot theory, after the second part in this series. In that part we have proven that the hairy graph complex \(\mathrm {HGC}_{m,n}\) with the extra differential is almost acyclic for even m. In this paper, we give the expected same result for odd m. As in the previous part, our results yield a way to construct many hairy graph cohomology classes by the waterfall mechanism also for odd m. However, the techniques are quite different. The main tool used in this paper is a new differential, deleting a vertex in non-hairy Kontsevich’s graphs, and a similar map for hairy vertices. We hope that the new differential can have further applications in the study of Kontsevich’s graph cohomology. Namely it is conjectured that the Kontsevich’s graph complex with deleting a vertex as an extra differential is acyclic.

     

Enhancing the Viscosity-Sensitive Range of a BODIPY Molecular Rotor by Two Orders of Magnitude

Molecular rotors are a class of fluorophores that enable convenient imaging of viscosity inside microscopic samples such as lipid vesicles or live cells. Currently, rotor compounds containing a boron-dipyrromethene (BODIPY) group are among the most promising viscosity probes. In this work, it is reported that by adding heavy-electron-withdrawing −NO₂ groups, the viscosity-sensitive range of a BODIPY probe is drastically expanded from 5–1500 cP to 0.5–50 000 cP. The improved range makes it, to our knowledge, the first hydrophobic molecular rotor applicable not only at moderate viscosities but also for viscosity measurements in highly viscous samples. Furthermore, the photophysical mechanism of the BODIPY molecular rotors under study has been determined by performing quantum chemical calculations and transient absorption experiments. This mechanism demonstrates how BODIPY molecular rotors work in general, why the −NO₂ group causes such an improvement, and why BODIPY molecular rotors suffer from undesirable sensitivity to temperature. Overall, besides reporting a viscosity probe with remarkable properties, the results obtained expand the general understanding of molecular rotors and show a way to use the knowledge of their molecular action mechanism for augmenting their viscosity-sensing properties.     

Tailoring thermal development of gamma alumina sorbents material using combustion synthesis: the effect of amino acids (G,A, N) and equivalence ratio

Using a combustion synthesis, the range of achievable textures is broader than using conventional synthesis methods and can be controlled more successfully. As a tool allowing the achievement and control of desired textures, here we bring about wet chemistry synthesis using aluminium nitrate nonahydrate (ANN) precursor systematically combined with different fuels (amino acids). The amino acids; glycine (G), alanine (A) and asparagine (N) have been specifically selected in order to show the role of gradual increase in their: (1) molar mass, (2) enthalpy of combustion, (3) amine groups content and (4) ratio to ANN. Detailed (micro) structural and thermal characterisations confirm that the nanocrystalline character and thermomechanical stability were not diminished in the course of this synthesis. The conditions leading to development of different morphologies from gels to powders were found to be heavily under the influence of fuel/oxygen ratio, i.e. of the smouldering versus flaming mechanism of the combustion. Higher content of nitrates (predominately from amino-rich amino acids) strongly promoted auto-combustion behaviour. As-derived alumina precursors have been thermally treated at various temperatures (quenched and soaked), to monitor γ- and α-alumina crystallisation, with respect to the development of morphology. Different texture types have been observed, such as porous wormhole, porous and porous expanded flakes. Higher fuel levels promote specific surface increase. This combustion synthesis allows facile tailoring of nanocrystalline γ-alumina with different morphological features, whereas samples having optimal parameters were suitable for catalyst support application on behalf of rapid sorption performance.

     

Crystal structure of K[PtCl3(caffeine)] and its interactions with important nitrogen-donor ligands

The crystal structure of K[PtCl₃(caffeine)] was determined. The coordination geometry around platinum is square-planar formed by N9 of the caffeine ligand and three Cl^? ions. The bond lengths and angles of K[PtCl₃(caffeine)] were compared with those reported for [PtCl₃(caffeine)]^? and K[PtCl₃(theobromine)]. At the level of the statistical significance of the data we have compared, no differences in the bond distances and angles for any of these compounds were noticed. Weak interactions between K⁺ and Cl^? are responsible for the formation of 1-D polymeric chains in the crystal structure of the complex. The interactions of K[PtCl₃(caffeine)] with inosine (Ino) and guanosine-5′-monophosphate (5′-GMP) were studied by ¹H NMR spectroscopy at 295 K in D₂O in a molar ratio of 1 : 1. The results indicate formation of the reaction product [PtCl₃(Nu)] (Nu=Ino or 5′-GMP) with the release of caffeine from the coordination sphere of the starting complex. The higher stability of the bond between the Pt(II) ion and Ino or 5′-GMP compared to the stability of the platinum–caffeine bond is confirmed by density functional theory calculations (B3LYP/LANL2DZp) using as models 9-methylhypoxanthine and 9-methylguanine.