Application of the statistical rate theory of interfacial transport to interpret the relaxation time of proton adsorption from solution onto oxides

A new way to analyze the rate of hydrogen ion adsorption from solution onto oxides was described. The statistical rate theory of interfacial transport (SRT) was applied to interpret relaxation time of ion adsorption. The new procedure for determination of rate constants of surface reaction was compared with the classical theory of activated adsorption and desorption (TAAD). It was found that for adsorption of uncharged species, both models give the same result, but for ion adsorption, their predictions differ considerably. Influence of surface potential and total concentration of adsorption sites on calculated rate constants was also discussed.     

Analytic Rank of Graph Algebras and Quantum Spaces

We show that the analytic rank, as defined by Murphy, of a unitalgraph C*-algebra is either 1 or 0, depending on whether or notthe underlying graph possesses an initial loop. As a corollary,we show that the analytic rank of certain quantum spaces (includingsome quantum spheres, projective spaces and lens spaces) is1. 2000 Mathematics Subject Classification 46L05, 46L65, 46L87.     

Possibilities of Practical Use of Historical Distributions of Ash,Sulfur and Mercury Contents in Commercial Steam Coal of the USCB

In the process of extracting hard coal, extensive databases are created on its quality parameters. A statistical assessment was made of the ash, sulfur, and mercury content of commercial coals produced in the Upper Silesian Coal Basin (USCB). The statistical methods applied: non-parametric tests of compatibility for two populations, parametric significance tests, and non-parametric tests of compatibility for the three populations, showed that the distributions of ash and sulfur content in 2014 and 2015 are comparable and the average values are similar. Statistical tests indicated significant differences in the mercury content distributions and their variances. This demonstrates the need for ongoing monitoring of mercury content in commercial coals, as a prediction of mercury content from historical data is hardly possible.     

LC with Coulometric Detection for Analysis of 5-Methyltetrahydrofolate in Human Plasma

An isocratic high-performance liquid chromatographic method with coulometric electrochemical detection has been used for analysis of 5-methyltetrahydrofolate (5-MTHF) in human plasma. A 250 mm × 4.6 mm i.d., 5-μm particle, C₁₈ column was used with 12:88 (v/v) acetonitrile ?35 mM sodium phosphate buffer pH 3.8 as mobile phase at a flow rate of 1.0 mL min^?1. The method was validated for 5-MTHF plasma concentrations in the range 2.5–100.0 nM. The method was characterized by a good linearity (regression coefficient r ≥ 0.9989) and limits of detection and quantification of 0.72 and 2.16 nM, respectively. Mean recovery at low and high concentrations ranged from 89.1 to 96.3%, respectively, with a relative standard deviation <4.6%. Between-run imprecision (4.2%) was higher than within-run imprecision (3.4%). The proposed separation and detection procedures were successfully applied to analysis of 5-MTHF in human plasma.     

Single-ion anisotropy in a four-spin system: mixing of S-states

A four-spin system with s=1 and the single-ion anisotropy, D∑ _j [s _jz ] ² , is considered. When D≠0 the Hamiltonian of the system does not commute with S ² and, therefore, S cannot be used as an additional label of energy levels. In this work we concentrate on the problem of mixing states with different total spins S. The Hamiltonian matrix is transformed to the symmetry-adapted basis (with subspaces labeled by the irreducible representations of the symmetry group) and next, after solving the eigenproblem for S ², to the basis with vectors labeled by S. Each eigenproblem is solved exactly (at least numerically) and the eigenstates are expressed as ∑ _S a _S |S〉. The coefficients a_S are analyzed, especially for their D-dependence. Even in such a small system different schemes of level mixing can be observed.      

Structures and potential superconductivity in at high pressure: en route to "metallic hydrogen"

A way to circumvent the high pressures needed to metallize hydrogen is to "precompress" it in hydrogen-rich molecules, a strategy probed theoretically for silane. We show that phases with tetrahedral SiH4 molecules should undergo phase transitions with sixfold- and eightfold-coordinate Si appearing above 25 GPa. The most stable structure found can be metallized at under a megabar and at a compression close to the prediction of Goldhammer-Herzfeld criterion. According to a BCS-like estimate, metallic silane should be a high-temperature superconductor.     

Extended Weak Coupling Limit for Pauli-Fierz Operators

We consider the weak coupling limit for a quantum system consisting of a small subsystem and reservoirs. It is known rigorously since [10] that the Heisenberg evolution restricted to the small system converges in an appropriate sense to a Markovian semigroup. In the nineties, Accardi, Frigerio and Lu [1] initiated an investigation of the convergence of the unreduced unitary evolution to a singular unitary evolution generated by a Langevin-Schrödinger equation. We present a version of this convergence which is both simpler and stronger than the formulations which we know. Our main result says that in an appropriately understood weak coupling limit the interaction of the small system with environment can be expressed in terms of the so-called quantum white noise.     

Decomposition of thin titanium deuteride films; thermal desorption kinetics studies combined with microstructure analysis

The thermal evolution of deuterium from thin titanium films, prepared under UHV conditions and deuterated in situ at room temperature, has been studied by means of thermal desorption mass spectrometry (TDMS) and a combination of scanning electron microscopy (SEM), transmission electron microscopy (TEM) and X-ray diffraction (XRD). The observed Ti film thickness dependent morphology was found to play a crucial role in the titanium deuteride (TiD_y) film formation and its decomposition at elevated temperatures. TDMS heating induced decomposition of fine-grained thin Ti films, of 10-20 nm thickness, proceeds at low temperature (maximum peak temperature T_m about 500 K) and its kinetics is dominated by a low energy desorption (E_D = 0.61 eV) of deuterium from surface and subsurface areas of the Ti film. The origin of this process is discussed as an intermediate decomposition state towards recombinative desorption of molecular deuterium. The TiD_y bulk phase decomposition becomes dominant in the kinetics of deuterium evolution from thicker TiD_y films. The dominant TDMS peak at approx. T_m = 670 K, attributed to this process, is characterized by E_D = 1.49 eV.     

Quadratic stochastic operators on Banach lattices

We study the convergence of iterates of quadratic stochastic operators that are mean monotonic. They are defined on the convex set of probability measures concentrated on a weakly compact order interval \(S = [0, f]\) of a fixed Banach lattice F. We study their regularity and identify the limits of trajectories either as the “infimum” or “supremum” of the support of initial distributions.