Limit theorems in the space of analytic functions for the Hurwitz zeta-function with an algebraic irrational parameter

We prove a limit theorem in the space of analytic functions for the Hurwitz zeta-function with algebraic irrational parameter.     

Spectrophotometric Study of Catechol Oxidation by Aerial O2 in Alkaline Aqueous Solutions Containing Mg(II) Ions.

Electronic absorption spectroscopy was employed to study the aerial oxidation of catechol (1,2-benzenediol) in alkaline aqueous solution containing an excess of Mg(II) ions. Graphical analysis by the matrix method of UV spectra recorded at regular time intervals gave a good fit for two absorbing species in solution. Based on this result and our earlier ESR spectroscopic investigations we concluded that two main absorbing species in this system are Mg(II)-spin stabilized o-benzosemiquinone anion radical and C-C dimer formed by the nucleophilic attack of catecholate anion on o-benzoquinone. Although the formation of 1,2,4-benzenetriol during the catechol oxidation has been detected in some ESR studies its presence was not indicated by this analysis probably because of the low and/or stable steady state concentration throughout the experiment.     

Principal component analysis of the main factors of line intensity enhancements observed in oscillating direct current plasma

Enhancement of emission line intensities by induced oscillations of direct current (DC) arc plasma with continuous aerosol sample supply was investigated using multivariate statistics. Principal component analysis (PCA) was employed to evaluate enhancements of 34 atomic spectral lines belonging to 33 elements and 35 ionic spectral lines belonging to 23 elements. Correlation and classification of the elements were done not only by a single property such as the first ionization energy, but also by considering other relevant parameters. Special attention was paid to the influence of the oxide bond strength in an attempt to clarify/predict the enhancement effect. Energies of vaporization, atomization, and excitation were also considered in the analysis. In the case of atomic lines, the best correlation between the enhancements and first ionization energies was obtained as a negative correlation, with weak consistency in grouping of elements in score plots. Conversely, in the case of ionic lines, the best correlation of the enhancements with the sum of the first ionization energies and oxide bond energies was obtained as a positive correlation, with four distinctive groups of elements. The role of the gas-phase atom-oxide bond energy in the entire enhancement effect is underlined.     

A simple line shape technique for electron number density diagnostics of helium and helium-seeded plasmas

The results of an experimental study of the He I 447.1 nm line and its forbidden component at high electron number density are presented and compared with profiles calculated using computer simulation method. Michelson interferometer at 632.8 nm was used to measure plasma electron number density in the range (1–7) × 10²³ m^− 3 while electron temperatures for the same experimental conditions in the range of 25 000 K to 35 000 K were determined using several spectroscopic techniques. The agreement of experimental overall line shape with computer simulation results is within 10% of what is well within theoretical and experimental uncertainty. This favorable comparison enabled the development of a simple approximate formula for the evaluation of electron number density from the measurement of wavelength separation between peaks of allowed and forbidden lines. This technique of plasma diagnostics is not sensitive to the presence of self-absorption of strong He I allowed line. The derivation of approximate formula with estimated accuracy of 15% was followed by detailed comparison with other experimental and theoretical data.     

Vapor pressure of selected aliphatic alcohols by ebulliometry. Part 2

Vapor pressures of six pentanols, 2-methyl-1-butanol (CAS Registry Number 137-32-6), 2-methyl-2-butanol (CAS Registry Number 75-85-4), 3-methyl-1-butanol (CAS Registry Number 123-51-3), 3-methyl-2-butanol (CAS Registry Number 598-75-4), 2-pentanol (CAS Registry Number 6032-29-7) and 3-pentanol (CAS Registry Number 584-02-1), were measured by the precision ebulliometry over an approximate pressure range from 9 to 99 kPa. The absolute uncertainties in pressure and temperature are estimated to be less than or equal to 7 Pa and 0.02 K, respectively. The results are represented by the Antoine equation and compared with available literature data.     

Limit theorems for the Mellin transform of the fourth power of the Riemann zeta-function

We prove limit theorems in the sense of weak convergence of probability measures on the complex plane as well as in the space of analytic functions for the Mellin transform of {ie88-01}