Concrete quantum logics with covering properties

LetL be a concrete (=set-representable) quantum logic. Letn be a natural number (or, more generally, a cardinal). We say thatL admits intrinsic coverings of the ordern, and writeL C _n , if for any pairA, BL we can find a collection {C _i iI}, where cardI<n andC _i L for anyiI, such thatA B= _il C _i . Thus, in a certain sense, ifLC _n , then the rate of noncompatibility of an arbitrary pairA,BL is less than a given numbern. In this paper we first consider general and combinatorial properties of logics ofC _n and exhibit typical examples. In particular, for a givenn we construct examples ofL C _n+1\C _n . Further, we discuss the relation of the classesC _n to other classes of logics important within the quantum theories (e.g., we discover the interesting relation to the class of logics which have an abundance of Jauch-Piron states). We then consider conditions on which a class of concrete logics reduce to Boolean algebras. We conclude with some open questions.     

The first tetranuclear vanadium(V) peroxo complex: Preparation, vibrational spectra and X-ray crystal structure of K6[V4O4(O2)8(PO4)]·9H2O

The vanadium(V) peroxo phosphato complex K₇[V₄O₄(O₂)₈(PO₄)]·9H₂O has been obtained from the KVO₃---KH₂PO₄---KOH---H₂O₂---H₂O---C₂H₅OH system. The X-ray structural analysis revealed a tetranuclear anionic structure in which two dinuclear [V₂O₂(O)₂)₂(μ-η¹ : η²-O₂)₂] units are connected by the μ₄-PO₄ group.     

Correlation between Small-Angle X-ray Scattering spectra and apparent diffusion coefficients in the study of structure and interaction of sodium taurodeoxycholate micelles

Small-Angle X-ray Scattering (SAXS) and Dynamic Light Scattering (DLS) measurements were carried out on aqueous micellar solutions of the ionic biological detergent sodium taurodeoxycholate (NaTDC). Apparent diffusion coefficients (D(app)) and SAXS spectra of NaTDC 0.1 M solutions at different ionic strengths (0.1-0.3 M NaCl) were reported. A comparative analysis of SAXS spectra and D(app) data was performed to infer information on particle structure and interaction potential. Uniform particles with a spherical, an oblate, and a prolate symmetry were used to model the micelles in the data interpretation. A hard-core interaction shell of suitable thickness and a screened Coulomb potential of the electric double layer (EDL potential) were alternatively used to represent the long-range repulsive tail of the interaction potential. The Percus Yevick and the Rescaled Mean Spherical Approximation were applied. To compare the data of the two techniques, for each sample, a D(app) was calculated from the SAXS best-fitting geometrical parameters and interparticle structure factor of the micelles. Hence, a fitting procedure involving both the scattering and D(app) data was performed. The interpretation of SAXS spectra does not allow the discrimination between the oblate and the prolate symmetries of the aggregates. On the other hand, the comparison of calculated and experimental D(app) values indicates that the prolate ellipsoid is better suited to represent the micelle shape. Moreover, the agreement between calculated and experimental D(app) values is sensitively better at the lowest NaCl concentration when the EDL potential is used. A rodlike micellar growth and a progressive screening of the electrostatic interactions is testified by the trends of best-fitting parameters as a function of the added electrolyte.     

RP-HPLC analysis of phenolic compounds and flavonoids in beverages and plant extracts using a CoulArray detector

Methods were developed for the analysis of natural antioxidants including phenolic compounds and flavonoids in beverages and plant extracts using gradient HPLC with multi-channel electrochemical coulometric detection. Suitability of various reversed-phase columns for this purpose was compared; pH and mobile phase gradients were optimized with respect to the separation selectivity and sensitivity of detection. Because of different target compounds in various sample types, the overlapping resolution maps and the normalized resolution product approaches described earlier were used to select optimum columns and gradients to suit the analysis of the individual sample types. The methods were applied to the analysis of phenolic compounds and flavonoids in beer, wine, tea, and yacon extracts. 32 phenolic compounds were identified and determined, including derivatives of benzoic and cinnamic acids, flavones, and a few related glycosides. Eight-channel CoulArray detection offers high selectivity and sensitivity with limits of detection in the low microg L(-1) range, at least an order of magnitude lower than single-channel coulometric detection using the Coulochem detector. No special sample pretreatment is necessary and, because of the compatibility of the CoulArray detector with gradient elution, phenolic antioxidants of different polarities can be determined in a single run. In addition to the retention times, the ratios of the areas of the pre-dominant and post-dominant peaks to the area of the dominant peak can be used for improved identification of natural antioxidants.     

Diferratricarbaboranes of the subcloso-[(eta5-C5H5)2Fe2C3B8H11] type, the first representatives of the 13-vertex dimetallatricarbaborane series

Treatment of the [2-Cp-9-tBuNH-closo-2,1,7,9-FeC(3)B(8)H(10)] (1) ferratricarbollide (Cp = eta(5)-C(5)H(5) (-)) with Na(+) C(10)H(8) (-) in 1,2-dimethoxyethane (DME) at room temperature produced an air-sensitive transient anion with a tentatively identified nido-[tBuNH-CpFeC(3)B(8)H(10)](2-) constitution. In-situ reaction of this low-stability ion with [CpFe(CO)(2)I] or [CpFe(CO)(2)](2) generated three violet diferratricarbaboranes identified as paramagnetic subcloso complexes [4,5-Cp(2-)-4,5,1,6,7-Fe(2)C(3)B(8)H(11)] (2; yield 2 %), [4,5-Cp(2-)-4,5,1,7,12-Fe(2)C(3)B(8)H(11)] (3; yield 2 %), and [7-tBuNH-4,5-Cp(2-)-4,5,1,7,12-Fe(2)C(3)B(8)H(10)] (4; yield 14 %). These first representatives of the 13-vertex dimetallatricarbaborane family were characterized by EPR and IR spectroscopy, and mass spectrometry, and their structures were determined by X-ray diffraction analysis.     

Rapid speciation of Se(IV) and Se(VI) by flow injection–capillary electrophoresis system with contactless conductivity detection

A flow injection–capillary electrophoresis system with contactless conductivity detection and hydrostatic-pressure-generated flow was used for the fast and sensitive speciation of Se(IV) and Se(VI). The sample throughput was 25 samples per hour using a background electrolyte solution containing 8.75 mM l-histidine (His) adjusted to pH 4.00 with acetic acid. The repeatability of peak areas (n=8) was better than 1.41% and the limits of detection were 190 g L^–1 and 7.5 g L^–1 for Se(IV) and Se(VI), respectively. The interference from carbonate, typically present in water samples, was eliminated by using a low-pH electrolyte in which carbonate is uncharged and migrates at the EOF front. The method was applied to the analysis of Se(IV) and Se(VI) in soil samples that were spiked with both selenium species and the results for recovery of both selenium species were in good agreement with their introduced concentrations.     

Mixed valence in YBaFe(2)O(5)

YBaFe(2)O(5) has been synthesized by heating a nanoscale citrate precursor in a carefully controlled reducing environment. Successful synthesis of a single-phase sample can only be achieved in a narrow window of oxygen partial pressures and temperatures. YBaFe(2)O(5) adopts an oxygen-deficient perovskite-type structure, which contains double layers of corner sharing FeO(5) square pyramids separated by Y(3+) ions. At T(N) congruent with 430 K, tetragonal (P4/mmm) and paramagnetic YBaFe(2)O(5) orders antiferromagnetically (AFM) experiencing a slight orthorhombic distortion (Pmmm). Around this temperature, it can be characterized as a class-III mixed valence (MV) compound, where all iron atoms exist as equivalent MV Fe(2.5+) ions. The magnetic structure is characterized by AFM Fe-O-Fe superexchange coupling within the double layers and a ferromagnetic Fe-Fe direct-exchange coupling between neighboring double layers. Upon cooling below approximately 335 K, a premonitory charge ordering (2Fe(2.5+) --> Fe(2.5+delta) + Fe(2.5)(-delta)) into a class-II MV phase takes place. This transition is detected by differential scanning calorimetry, but powder diffraction techniques fail to detect any volume change or a long-range structural order. At approximately 308 K, a complete charge ordering (2Fe(2.5+) --> Fe(2+) + Fe(3+)) into a class-I MV compound takes place. This charge localization triggers a number of changes in the crystal, magnetic, and electronic structure of YBaFe(2)O(5). The magnetic structure rearranges to a G-type AFM structure, where both the Fe-O-Fe superexchange and the Fe-Fe direct-exchange couplings are antiferromagnetic. The crystal structure rearranges (Pmma) to accommodate alternating chains of Fe(2+) and Fe(3+) running along b and an unexpectedly large cooperative Jahn-Teller distortion about the high-spin Fe(2+) ions. This order of charges does not fulfill the Anderson condition, and it rather corresponds to an ordering of doubly occupied Fe(2+) d(xz) orbitals. Comparisons with YBaMn(2)O(5) and YBaCo(2)O(5) are made to highlight the impact of changing the d-electron count.     

The sorption of some radiocations on microporous titanosilicate ETS-10

The microporous titanosilicate ETS-10 synthesized from gel with following molar composition: 1.0 Na₂O: 1.49 SiO₂ : 0.2 TiO₂ : 0.6 KF : 1.28 HCl : 39.5 H₂O was subjected to sorption of radioactive cations ¹¹⁵Cd²⁺, ²⁰⁴Hg²⁺, ⁶⁰Co²⁺ and ¹³⁷Cs⁺ (M) from aqueous solution, in the absence of ionic competition. The uptake of these cations on the ETS-10 was compared by means of the distribution coefficient (K_d) versus contact time and sorption capacity (R) at equilibrium. The FT-IR spectra of M-ETS-10 sorption products exhibit a modification of the absorption band, principally at 381 cm^-1.     

Determination of vitamin C and preservatives in beverages by conventional capillary electrophoresis and microchip electrophoresis with capacitively coupled contactless conductivity detection

The separation and detection of commonly used preservatives (benzoate, sorbate) and vitamin C by both conventional CE and microchip electrophoresis with capacitively coupled contactless conductivity detection is presented. The separation was optimized by adjusting the pH-value of the buffer and the use of hydroxypropyl-beta-CD (HP-beta-CD) and CTAB as additives. For conventional CE, optimal separation conditions were achieved in a histidine/tartrate buffer at pH 6.5, containing 0.025% HP-beta-CD and 0.1 mM CTAB. LOD ranged from 0.5 to 3 mg/L (S/N = 3) and the RSDs for migration time and peak area were less than 0.1 and 2%, respectively. A considerable reduction of analysis time can be accomplished by using microchip electrophoresis without significant loss in sensitivity under optimal separation conditions. A histidine/tartrate buffer at pH 6.5, incorporating 0.06% HP-beta-CD and 0.25 mM CTAB, gave detection limits ranging between 3 and 10 mg/L and satisfactory reproducibilities of < or =0.4% for the migration time and < or =3.5% for the peak area. The methods developed are useful for the quantitative determination of food additives in real samples such as soft drinks and vitamin C tablets.     

On geometries of stacked and H-bonded nucleic acid base pairs determined at various DFT, MP2, and CCSD(T) levels up to the CCSD(T)/complete basis set limit level

The geometries and interaction energies of stacked and hydrogen-bonded uracil dimers and a stacked adeninecdots, three dots, centeredthymine pair were studied by means of high-level quantum chemical calculations. Specifically, standard as well as counterpoise-corrected optimizations were performed at second-order Moller-Plesset (MP2) and coupled cluster level of theory with single, double, and perturbative triple excitations [CCSD(T)] levels with various basis sets up to the complete basis set limit. The results can be summarized as follows: (i) standard geometry optimization with small basis set (e.g., 6-31G(*)) provides fairly reasonable intermolecular separation; (ii) geometry optimization with extended basis sets at the MP2 level underestimates the intermolecular distances compared to the reference CCSD(T) results, whereas the MP2/cc-pVTZ counterpoise-corrected optimization agrees well with the reference geometries and, therefore, is recommended as a next step for improving MP2/cc-pVTZ geometries; (iii) the stabilization energy of stacked nucleic acids base pairs depends considerably on the method used for geometry optimization, so the use of reliable geometries, such as counterpoise-corrected MP2/cc-pVTZ ones, is recommended; (iv) the density functional theory methods fail completely in locating the energy minima for stacked structures and when the geometries from MP2 calculations are used, the resulting stabilization energies are strongly underestimated; (v) the self-consistent charges-density functional tight binding method, with inclusion of the empirical dispersion energy, accurately reproduces interaction energies and geometries of dispersion-bonded (stacked) complexes; this method can thus be recommended for prescanning the potential energy surfaces of van der Waals complexes.