Joint discrete limit theorems in the space of analytic functions for general Dirichlet series

We prove joint discrete limit theorems in the sense of weak convergence of probability measures in the space of analytic functions for general Dirichlet series.__________Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 1, pp. 104–116, January–March, 2005.Translated by R. Macaitien     

Fluorescent Probe ABM and Estimation of Immune State in Patients with Different Pathologies (Review Article)

The fluorescent probe ABM (3-aminobenzanthrone derivative) one of the fluorescent probes synthesized in Riga Technical University proved to be an excellent, independent model for studying cell membranes. In our work we have investigated the possibility of using the fluorescent probe ABM for detection of immune state in patients with different pathologies. There is a strong correlation among all studied ABM spectral parameters, immunological characteristics, clinical and laboratory investigations of the all observed patients groups. The obtained results suggest that ABM spectral parameters in cell suspension reflect the alterations of the cellular mechanisms of immunity. Therefore fluorescent method could be used as preliminary screening test in immune diagnostics instead of more expensive, time consuming methods (subset detection, radioisotope method etc.) used as routine in clinics. Spectral parameters of ABM reflect a wide range of interrelated (interdependent) characteristics of cells (physico-chemical state and microviscosity of membrane, proliferating and lipid metabolic activity of cells, distribution of cells among subsets). The observed change of the studied parameters reflects alterations of the cellular mechanisms of immunity which is a main focus for its application as preliminary screening test in immune diagnostics. The fluorescence based method is sensitive, less expensive and time consuming, technically simple and convenient.     

The law of iterated logarithm for logarithmic combinatorial assemblies

The strong convergence of dependent random variables is analyzed and the law of iterated logarithm for real additive functions defined on the class of combinatorial assemblies is obtained. Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 4, pp. 532–547, October–December, 2006.     

Numerical analysis of nonlinear model of excited carrier decay

This paper presents a mathematical model for photo-excited carrier decay in a semiconductor. Due to the carrier trapping states and recombination centers in the bandgap, the carrier decay process is defined by the system of nonlinear differential equations. The system of nonlinear ordinary differential equations is approximated by linearized backward Euler scheme. Some a priori estimates of the discrete solution are obtained and the convergence of the linearized backward Euler method is proved. The identifiability analysis of the parameters of deep centers is performed and the fitting of the model to experimental data is done by using the genetic optimization algorithm. Results of numerical experiments are presented.     

Sonochemical effectiveness factor (eUS) in the reactors for wastewater treatment by sono-Fenton oxidation: Novel considerations

A comprehensive algorithm was recently proposed for calculation of the sonochemical effectiveness factor and wastewater treatment modeling. The presented approach implies that ultrasound is an auxiliary source of free radicals in Fenton type reactions; introduction of ultrasound represents an enhancement of pollutant degradation rates. The sonochemical effectiveness factor was introduced in kinetic models as the e_US factor (Gr?i? et al., 2012 [1]). As a substantial follow-up, this study presents novel considerations. The e_US factor was modeled as a function of employed frequency, actual cavitation-related power intensity of ultrasound and a portion of the cavitationally active zone, i.e. dimensionless active volume. The effect of temperature was disregarded in the present model considerations. Cavitationally active zone in reactors was determined based on the erosion of aluminum foil, resulting in cone-shaped space arising from transducer.In the present study, sonochemical treatment of industrial wastewater containing HCOONa as organic pollutant was performed using different equipment: ultrasonic baths (UB1, UB2 and UB3), cylindrical reactor with homogenizer (HCR) and three-frequency hexagonal cell, i.e. ultrasonic pilot reactor prototype (PP). Explored frequency range was from 20 to 120 kHz. Homogeneous and heterogeneous Fenton-type sonochemical processes, US/Fe(II)(FeSO₄,aq.)/H₂O₂ and US/Fe(II)(steel-plate)/H₂O₂, respectively, applied to industrial wastewater were investigated in terms of mineralization kinetics. Newly modeled e_US factor was introduced in corresponding kinetic models and the overall model was validated. Kinetic parameters of Fenton process were treated as independent of ultrasound, since e_US factor consists of cavitation-related phenomena responsible for the mineralization rate enhancement. In average, a 21% increase of mineralization efficiency was achieved using a single frequency, while more than 70% increase can be achieved by combining 20, 68 and 120 kHz in PP.     

A sharp inequality for the variance with respect to the Ewens sampling formula

Lithuanian Mathematical Journal - We examine the variance of a linear statistic defined on the symmetric group endowed with the Ewens probability. Despite the dependence of the summands, it can be...     

Pressure‐Tuneable Visible‐Range Band Gap in the Ionic Spinel Tin Nitride

The application of pressure allows systematic tuning of the charge density of a material cleanly, that is, without changes to the chemical composition via dopants, and exploratory high‐pressure experiments can inform the design of bulk syntheses of materials that benefit from their properties under compression. The electronic and structural response of semiconducting tin nitride Sn₃N₄ under compression is now reported. A continuous opening of the optical band gap was observed from 1.3 eV to 3.0 eV over a range of 100 GPa, a 540 nm blue‐shift spanning the entire visible spectrum. The pressure‐mediated band gap opening is general to this material across numerous high‐density polymorphs, implicating the predominant ionic bonding in the material as the cause. The rate of decompression to ambient conditions permits access to recoverable metastable states with varying band gaps energies, opening the possibility of pressure‐tuneable electronic properties for future applications.