The LIL for <Emphasis Type="Italic">U</Emphasis>-Statistics in Hilbert Spaces

We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for U-statistics in Hilbert spaces. As a tool we also develop moment and tail estimates for canonical Hilbert-space valued U-statistics of arbitrary order, which are of independent interest. R. Adamczak’s research partially supported by MEiN Grant 2 PO3A 019 30. R. Latała’s research partially supported by MEiN Grant 1 PO3A 012 29.     

A 2-approximation algorithm for interval data minmax regret sequencing problems with the total flow time criterion

In this paper we discuss a minmax regret version of the single-machine scheduling problem with the total flow time criterion. Uncertain processing times are modeled by closed intervals. We show that if the deterministic problem is polynomially solvable, then its minmax regret version is approximable within 2.     

Coordination modes of 2-mercapto-1,3-benzothiazolate in gallium and indium complexes

2-Mercapto-1,3-benzothiazole (mbztH) may act as a chelating or bridging ligand. In this study, reactions of mbztH with Me₃Ga and Me₃In were examined. The products were characterized by NMR spectroscopy, elemental analyses, melting point, and molecular weight determinations. Formation of mononuclear chelating complexes Me₂M(mbzt) (M = Ga, In) was observed in solutions. Crystallization of Me₂M(mbzt) yielded uncommon non-symmetrical dinuclear complexes Me₄M₂(mbzt)₂, in which one metal is bonded to two sulfurs and the other to two nitrogens.     

Novel Approach to Two-Component Analysis Based on the Generalized Calibration Strategy

The generalized calibration strategy (GCS), developed and previously applied to chemical analysis, has been adapted to two-component (2C) analysis. According to the 2C-GCS procedure, a set of 10 calibration solutions containing a sample and standards of two analytes in well-defined composition was diluted. The measurements performed at a given dilution stage allow the concentration of both analytes in a sample to be evaluated with six apparent concentrations calculated with various mathematical approaches. As a result, the method allows the detection, examination, and elimination of nonlinear and interference effects with multiplicative and additive characteristics. To perform 2C-GCS automatically and effectively, a dedicated flow sequential injection system was designed to be fully controlled by a computer. Caffeine and paracetamol were determined in synthetic and pharmaceutical samples using this calibration approach. The analytes were determined with good precision and accuracy with low consumption of sample and standard solutions. On the basis of this experimental model, the influence of effects and tendencies in the examined analytical system was detected and evaluated.     

Analytical Strategy for the Determination of Selenium in Biological Materials by Inductively Coupled Plasma-Mass Spectrometry with a Dynamic Reaction Cell

Selenium was determined in serum, hair, and tobacco by inductively coupled plasma-mass spectrometry using ⁷⁷Se, ⁷⁸Se, and ⁸²Se. The set of standards method (SSM) and the standard addition method (SAM) were applied to calibration with and without the use of internal standards (⁷²Ge and ¹⁰³Rh). In addition, the usefulness of the dynamic reaction cell (DRC) with methane as the reaction gas was characterized. The results obtained in different conditions were evaluated in terms of precision and accuracy. It was demonstrated theoretically and experimentally that an internal standard is a potential source of systematic errors as it can be influenced multiplicatively and additively by its own interferents (independently of selenium). Furthermore, it was shown that—against common opinion—an internal standard can fail in elimination of chemical interference effects influencing selenium and in increasing of precision of selenium determinations. The DRC was shown to be effective in the elimination of additive effects, although the results obtained by both SSM and SAM with DRC were systematically positively erroneous. Finally, selenium was determined accurately in each examined sample when SAM was applied to calibration, and signals were measured either for ⁸²Se without the use of the DRC, or for ⁷⁷Se or ⁷⁸Se with the use of the DRC. In addition, it has also been shown that samples should be diluted prior to analysis to the greatest acceptable extent.     

Solid state NMR spectroscopy as a precise tool for assigning the tautomeric form and proton position in the intramolecular bridges of o-hydroxy Schiff bases

Two analogous Schiff bases, (S,E)-2-((1-hydroxy-3-methyl-1,1-diphenylbutan-2-ylimino)methyl)phenol (1) and (S,Z)-2-hydroxy-6-((1-hydroxy-3-methyl-1,1-diphenylbutan-2-ylamino)methylene)cyclohexa-2,4-dienone (2), exist in the solid state as phenol-imine and keto-amine tautomers, respectively. Their crystal structures were solved using the X-ray diffraction method. Sample 1 forms orthorhombic crystals of space group P2(1)2(1)2(1), while 2 forms monoclinic crystals of space group P2(1). In each sample, one molecule is in the asymmetric unit of the crystal structure. One-dimensional and two-dimensional solid state NMR techniques were used for structure assignment and for inspection of the (13)C and (15)N δ(ii) of the chemical shift tensor (CST) values. NMR study indicates that the span (Ω = δ(11)-δ(33)) and the skew (κ = 3(δ(22)-δ(iso)/Ω) are extremely sensitive to change in the tautomeric form of the Schiff bases. Theoretical calculations of NMR shielding parameters for 1 and 2 and a model compound with reduced aliphatic residue were performed using the GIAO method with B3LYP functional and 6-311++g(d,p) basis sets. From comparative analysis of the experimental and theoretical parameters, it was concluded that the position of hydrogen in the intramolecular bridge has tremendous influence on (13)C and (15)N CST parameters. Inspection of Ω and κ parameters allowed for the establishment of the nature of the hydrogen bonding and the assignment of the equilibrium proton position in the intramolecular bridges in the solid state.     

All nonclassical correlations can be activated into distillable entanglement

We devise a protocol in which general nonclassical multipartite correlations produce a physically relevant effect, leading to the creation of bipartite entanglement. In particular, we show that the relative entropy of quantumness, which measures all nonclassical correlations among subsystems of a quantum system, is equivalent to and can be operationally interpreted as the minimum distillable entanglement generated between the system and local ancillae in our protocol. We emphasize the key role of state mixedness in maximizing nonclassicality: Mixed entangled states can be arbitrarily more nonclassical than separable and pure entangled states.     

Generation of vorticity motion by sound in a chemically reacting gas and inversion of acoustic streaming in the non-equilibrium regime

Nonlinear stimulation of the vorticity mode caused by losses in the momentum of sound in a chemically reacting gas is considered. The instantaneous dynamic equation for the vorticity mode is derived. It includes a quadratic nonlinear acoustic source, which reflects the fact that the reason for the interaction between sound and the vorticity mode is nonlinear. Both periodic and aperiodic sound may be considered as the origin of the vorticity flow. The equation governing the mean flow (the acoustic streaming) in the field of periodic sound is also derived. In the non-equilibrium regime of a chemical reaction, there may exist streaming vortices whose direction of rotation is opposite to that of the vortices in the standard thermoviscous flows. For periodic sound, this is illustrated by an example. The theory and the example describe both equilibrium and non-equilibrium chemical reactions.     

Ab initio determination of atomic structure and energy of surface states of bare and hydrogen covered GaN (0001) surface — Existence of the Surface States Stark Effect (SSSE)

Density Functional Theory (DFT) calculations indicate that energetically stable structure of clean GaN(0001) surface posses (2 × 1) reconstruction, having every second row of Ga located near plane of N atoms, that gives rise to Ga-related dispersionless surface electronic state, already identified by angle resolved photoelectron spectroscopy (ARPES) measurements [S.S. Dhesi et al. Phys. Rev. B 56 (1997) 10271, L. Plucinski et al. Surf. Sci 507-10 (2002) 223, S. M. Widstrand et al. Surf. Sci. 584 (2005) 169]. The energy reduction in reconstruction proceeds via change of the hybridization of the occupied Ga surface states from sp³ to sp², transforming the empty states to p_z type. It is also shown that the electric subsurface field, modeled in new slab model which allows to simulate electric fields at the semiconductor surfaces [P. Kempisty et al., J. Appl. Phys. 106 (2009) 054901], strongly affects the energy of electronic states of GaN(0001) surfaces. The change of the field may shift the energy of surface states of bare and hydrogen covered GaN(0001) surface, by several eV with respect to the band states. The phenomenon, denoted as Surface States Stark Effect (SSSE), explains various band bending values, measured at differently doped n-type GaN(0001) surfaces. It is shown also that, for the adsorbate density up to one H atom for each Ga surface atom i.e. 1 monolayer coverage (1 ML), the hydrogen adatoms are located at the on-top positions, i.e. directly above Ga atoms. For these adsorbate densities, the H-related quantum surface state is located slightly below the valence band maximum (VBM) in the case of p-type GaN surface. For n-type GaN, the H-related surface state is located deeply in the valence band, about 2 eV below VBM. For higher, 1.25 ML hydrogen coverage, the two H adatoms create either surface attached H₂ ad-molecule (energetically stable) or triple bridge configuration is created (metastable). The H₂ ad-molecule is weekly attached to the surface, having the desorption energy barrier equal to 0.16 eV. For 1.25 ML coverage the DFT results were obtained for p-type GaN only. They show that in the ad-molecule case, a new surface electronic state arises which is located about 6.7 eV below VBM. In the case of the bridge configuration, the bridge related surface state is located closely to the conduction band minimum (CBM).     

Embeddable quantum homogeneous spaces

We discuss various notions generalizing the concept of a homogeneous space to the setting of locally compact quantum groups. On the von Neumann algebra level we recall an interesting duality for such objects studied earlier by M. Izumi, R. Longo, S. Popa for compact Kac algebras and by M. Enock in the general case of locally compact quantum groups. A definition of a quantum homogeneous space is proposed along the lines of the pioneering work of Vaes on induction and imprimitivity for locally compact quantum groups. The concept of an embeddable quantum homogeneous space is selected and discussed in detail as it seems to be the natural candidate for the quantum analog of classical homogeneous spaces. Among various examples we single out the quantum analog of the quotient of the Cartesian product of a quantum group with itself by the diagonal subgroup, analogs of quotients by compact subgroups as well as quantum analogs of trivial principal bundles. The former turns out to be an interesting application of the duality mentioned above.