Hitting times with taboo for a random walk

For a symmetric homogeneous and irreducible random walk on the d-dimensional integer lattice, which have a finite variance of jumps, we study passage times (taking values in [0,??]) determined by a starting point x, a hitting state y, and a taboo state z. We find the probability that these passage times are finite, and study the distribution tail. In particular, it turns out that, for the above-mentioned random walks on ? ^d except for a simple random walk on ?, the order of the distribution tail decrease is specified by dimension d only. In contrast, for a simple random walk on ?, the asymptotic properties of hitting times with taboo essentially depend on mutual location of the points x, y, and z. These problems originated in recent study of a branching random walk on ? ^d with a single source of branching.     

Study of the retention behavior of small polar molecules on different types of stationary phases used in hydrophilic interaction liquid chromatography

The retention behavior of a large group of analytes (35) with varied properties (pK_a and logP) was studied on eight hydrophilic interaction LC columns with different surfaces, stationary phase chemistries, and types of particles. The acetonitrile content (5–95%), buffer concentration (0.5–200 mM), and pH of the mobile phase (3.8 and 6.8) were evaluated for their effects on the retention behavior. The type of stationary phase had a significant impact on the selectivity and retention time of the tested analytes. Completely different selectivity was observed on the aminopropyl stationary phase. In this study, the influence of the buffer concentration was similar for all tested columns, except for the aminopropyl stationary phase. Increasing the buffer concentration led to decreased retention times for the basic compounds and increased retention times for the acidic compounds, while the inverse behavior was observed on the aminopropyl stationary phase. The selectivity of the individual stationary phases was evaluated at pH 3.8 and 6.8. Much lower selectivity differences between the stationary phases were observed at pH 6.8 than pH 3.8. Bare silica stationary phases were used in the comparison of the particles (fused‐core and fully porous particles of 3 and 1.7 μm) and the columns provided by different manufacturers.     

Spread of a catalytic branching random walk on a multidimensional lattice

For a supercritical catalytic branching random walk on ${\mathbb{Z}}^d$, $d\in \mathbb{N}$, with an arbitrary finite catalysts set we study the spread of particles population as time grows to infinity. It is shown that in the result of the proper normalization of the particles positions in the limit there are a.s. no particles outside the closed convex surface in ${\mathbb{R}}^d$ which we call the propagation front and, under condition of infinite number of visits of the catalysts set, a.s. there exist particles on the propagation front. We also demonstrate that the propagation front is asymptotically densely populated and derive its alternative representation.     

Enzymatic synthesis of a chiral chalcogran intermediate

Two lipases, Novozyme 435 (lipase B from Candida Antarctica) and Lipozyme TL IM (Thermomyces lanuginosus) were used successfully for the kinetic resolution of racemic 1-(2-furyl)-3-pentanol, the key intermediate in synthesis of the bark beetle pheromone, chalcogran. The desired S-(+)-enantiomer was prepared in enantiomeric excesses higher than 98 % and with yields of 26.3 % and 32.5 %, respectively. Methyl tert-butyl ether and vinyl acetate were found to be the best reaction media and the acetyl donor to achieve fast and effective resolution.     

In-situ study of Ag nanoparticle hydrosol optical spectra evolution during laser ablation/fragmentation

The results of in-situ monitoring of a laser fragmentation process of a largely polydisperse and morphologically heterogeneous citrate-reduced Ag hydrosol containing a fraction of Ag nanowires are presented. The laser fragmentation was performed using several wavelengths of the incident laser pulses (1064, 532 and 355 nm). Surface plasmon extinction spectra monitoring the nanoparticle fragmentation process were acquired pulse by pulse and related to transmission electron microscopy (TEM) images and statistical TEM image analysis of Ag nanoparticles collected in selected stages of the fragmentation. It was found that, due to different interactions of the laser pulses of various wavelengths with a specific fraction of the Ag nanoparticles in the hydrosol, the course of the fragmentation process depends on the wavelength, leading to different size distributions of the nanoparticles in the resulting hydrosol. The laser pulses of 532 nm wavelength are the most effective for the fragmentation process of the citrate-reduced Ag hydrosol, yielding the narrowest size distribution and the smallest mean radius of the Ag nanoparticles. PACS 81.07.-b; 73.21.-b; 81.16.-c     

Accurate relations for the isotopically invariant spectroscopic parameters of diatomic molecules

Equations are obtained relating the isotopically invariant spectroscopic parameters U_mj, which must be considered as conditions in the least-squares method in spectral analysis. Expressions are given for the first seven Dankhem potential parameters in terms of U_m0 and U_m1. The contribution to the spectroscopic coefficients Y_mj due to violation of the Born-Oppenheimer approximation is calculated for¹²C¹⁶O.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 18–21, November, 1984.It remains to thank Yu. S. Makushkin, V. Ya. Galin, andV. F. Golovko for valuable discussions of the work.     

Determination of phosphorus traces in platinum alloys by two-phase isotope exchange

The method of ZEMAN and KRATZER for the determination of phosphorus traces by means of two-phase isotope exchange was modified for the determination of phosphorus in pure platinum or pure platinum alloys. It was found that Pt, Rh, Ag, and As do not interfere with the determination. Among the elements usually present in platinum metal or platinum alloys, only gold interferes. It was removed by extraction from 7M HCl by MIBK and AmOAc. Hydrochloric acid also interferes but it can be removed by evaporation. The analytical procedure is given for the solution obtained by pressure decomposition of the sample (0.5 g) in a steel bomb with PTFE inlay. It is possible to determine >2 ppm P (approximate error −10%). Using a calibration dependence instead of the well known equation for isotope exchange, the content of P in the standard solution labelled with³²P need not be known.