Detecting quantum states with a positive Wigner function beyond mixtures of Gaussian states

We propose a criterion giving a sufficient condition for quantum states of a harmonic oscillator not to be expressible as a convex mixture of Gaussian states. This nontrivial property is inherent to, e.g., a single-photon state and the criterion thus allows one to reveal a signature of the state even in quantum states with a positive Wigner function. The criterion relies on directly measurable photon number probabilities and enables detection of this manifestation of a single-photon state in quantum states produced by solid-state single-photon sources in a weak coupling regime.     

The first member of the eleven-vertex azadicarbaborane series, 1,6,9-NC2B8H13, and its N-alkyl derivatives

Reactions between closo-1,2-C(2)B(8)H(10) (1) and amines of general formulation R(1)R(2)NH (where R(1), R(2) = H, H; Me, H; t-Bu, H and Et, Et) resulted in a straightforward cluster expansion and formation of the 11-vertex arachno-azadicarbaboranes of the 1,1-R(1),R(2-)1,6,9-NC(2)B(8)H(11) (2) cluster constitution (where R(1), R(2) = H, H 2a; Me, H 2b; t-Bu, H 2c and Et, Et 2d) in yields 10-75%, depending on the nature of the amine used. The reactions are the first example of a direct closo to arachno transformation in the area of cluster-boron compounds. Compounds 2b and 2c were isolated in two isomeric forms anti- and syn- that differ in the positioning of the t-Bu substituent with respect to the bridging hydrogen site. Deprotonation of compounds 2 generally leads to removal of the bridging proton and formation of the [1,1-R(1),R(2-)1,6,9-NC(2)B(8)H(11)](-) (2-) anions that, in the case of the monoalkylated Me and t-Bu derivatives, adopt only an anti configuration. The structure of anti-2c was determined by X-ray diffraction analysis and the geometries of the parent compound and the corresponding syn and anti isomers were optimised at the RMP2/6-31G* level. The composition of all compounds is consistent with the results of mass spectrometry and multinuclear ((1)H and (11)B) spectroscopy complemented by two-dimensional [(11)B-(11)B]-COSY and (1)H{(11)B(selective)} NMR measurements. Experimental (11)B chemical shifts generally show acceptable agreement with theoretical values calculated by GIAO methods, in particular at GIAO-MP2/II, where possible.     

Closure-based constraints in formal concept analysis

We present a method of imposing constraints in extracting formal concepts (equivalently, closed itemsets or fixpoints of Galois connections) from a binary relation. The constraints are represented by closure operators and their purpose is to mimic background knowledge a user may have of the data. The idea is to consider and extract only these itemsets that are compatible with the background knowledge. As a result, the method extracts less clusters, those that are interesting from the user point of view, in a shorter time. The method makes it also possible to extract minimal bases of attribute dependencies in the input data that are compatible with the background knowledge. We provide examples of several particular types of constraints including those that appeared in the literature in the past and present algorithms to compute the constrained formal concepts and attribute implications.     

Chiral separability of boron cluster species studied by screening approaches utilizing polysaccharide‐based chiral stationary phases

In this study, the screening steps of chiral separation strategies with polysaccharide‐based chiral stationary phases were applied on boron cluster compounds in normal‐phase liquid chromatography (NPLC) and polar organic solvents chromatography (POSC). Since the screening steps were initially developed to analyze organic compounds, their applicability for boron clusters was investigated. Overall, the screening steps in NPLC were applicable for the separation of zwitterions, while for anions mostly no elution was observed. A hypothesis for the latter behavior is precipitation of anions in the nonpolar mobile phases. Ten out of 11 compounds could be partially or baseline separated on the NPLC screening systems. In POSC, all zwitterions were separated on at least one of the screening systems, with an overall lower retention as in NPLC. Anions were detected but not separated in the majority of the experiments. Also their retention on the chiral stationary phases was very limited. This study showed that the chiral discrimination potential of chemically modified polysaccharides is meaningful for chiral separations of structurally chiral boron cluster species, but needs further systematic research, in which recognition mechanisms should be further explored. In addition, some unusual peaks also indicated that conditions with a high separation efficiency must first be searched for some of the tested systems. Copyright © 2014 John Wiley & Sons, Ltd.     

Titania-based stationary phase in separation of ondansetron and its related compounds

Improvements in stationary phase stability have been and remain a great task for research of new stationary phases. Metal oxide-based stationary phases appear as one of perspective alternatives to classical silica based stationary phases regarding to their similar effectiveness, different selectivity, different retention mechanism and mainly better chemical and thermal stability. In this study, the retention behaviour of ondansetron and its five pharmacopoeial impurities on TiO(2)-based reversed phase was investigated. The influence of buffer type, pH and concentration on retention was studied. Different types and amount of organic solvent in mobile phase were tested. The effect of temperature and flow rate on separation was investigated. The separation conditions were optimized and developed method validated. The retention parameters - retention time (t(R)), retention factor (k'), theoretical plate number (N), resolution between peaks due to nearby peaks (R(s)) and symmetry factor (A(s)) have been compared to parameters achieved on polybutadiene-coated zirconia column. The thermodynamic parameters of retention of analysed compounds - enthalpy, entropy and Gibbs free energy - were calculated and compared to those achieved on polybutadiene-coated zirconia column. This work proves similarity of retention behaviour of ondansetron and its five related compounds on zirconia-based and titania-based stationary phases and potential utilisation of polyethylene covered TiO(2)-based reversed stationary phase as an alternative to polybutadiene-coated ZrO(2) stationary phase in pharmaceutical analysis of ondansetron.