The Discounted Limit Theorems

The large deviation theorems, exponential inequalities and a non-uniform estimate of the Berry–Esséen theorem in a discounted version are proved.Dedicated to Professor Vytautas Statulevičius on the occasion of his 75th birthday.     

Discrete limit theorems for general Dirichlet series. III

Here we prove a limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for a general Dirichlet series. The explicit form of the limit measure in this theorem is given. Partially supported by Lithuanian Foundation of Studies and Science     

Synthesis of Polysiloxane Xerogels Using Tetraethoxysilane/(Diethylphosphatoethyl)triethoxysilane System

The xerogels, containing phosphonic acid groups ≡Si(CH₂)₂P(O)(OC₂H₅)₂ in the surface layer of their particles, are synthesized by the sol-gel method (ethanol as a solvent and fluoride ion as a catalyst). It is shown that, when 2 : 1, 3 : 1, and 4 : 1 tetraethoxysilane/(diethylphosphatoethyl)triethoxysilane ratios are used, nonporous substances are formed, whereas, at 6 : 1, 8 : 1, and 10 : 1 ratios, the xerogels with highly porous structures are produced (the specific surface area is 505–534 m²/g, the sorption pore volume is 0.34–0.53 cm³/g, and the pore diameter is 3.6–4.6 nm).     

Application of cosmogenic radionuclides in ozone tracer studies

Downward flux of stratospheric ozone contributes to the near ground level ozone concentrations. The intensity, amount of vertical ozone flow can be evaluated by the ratio of two cosmogenic radionuclides (³³P/³²P, ⁷Be/³²P). Some examples presented in this paper are demonstrating the possibilities of this method. The application of tracer method makes evident the seasonal variations (with maxima during the spring — summer months and minima during winter) of the amount of stratospheric ozone in the ground air. Average monthly contribution from stratospheric ozone in the lower level of the atmosphere ranged from 0 to 18% in 1998–99. During short term intervals (2–3 days) the amount of the stratospheric ozone can increase up to ∼90%.     

The preparation of polysiloxane xerogels containing amide derivatives of phosphonic and thiophosphonic acids in the surface layer

Xerogels containing residues of amide derivatives of phosphonic and thiophosphonic acids, ≡Si(CH₂)₃NHP(S, O)(OC₂H₅)₂ (functional group concentration of 1.3–2.2 mmol/g) have been prepared by a sol-gel method. It has been shown that xerogels having a developed porous structure (with specific surface areas of 240–485 m²/g, pore volumes of 0.20–0.50 cm³/g, and pore diameters of 3.6–6.5 nm) are formed at tetraethoxysilane-to-trifunctional silane ratios of 4: 1 (and above) and 6: 1 (and above) for the derivatives of phosphonic and thiophosphonic acids, respectively. The IR and ¹³C CP/MAS NMR spectroscopy data have demonstrated that the surface layer of the xerogels contains not only (thio)phosphonic acid residues, but also silanol groups and water molecules participating in hydrogen bonding. The ²⁹Si CP/MAS NMR spectroscopy data have indicated that structural groups are, for the most part, contained in structural units T³ [(≡SiO)₃Si(CH₂)₃NHP(O, S)(OC₂H₅)₂] and T² [(≡SiO)₂Si(OR)[(CH₂)₃NHP(O, S)(OC₂H₅)₂] (R = H or C₂H₅).     

Pulse plating effect on microstructure and corrosion properties of Zn–Ni alloy coatings

The influence of pulse plating parameters on the surface morphology, grain size, lattice imperfection and corrosion properties of Zn–Ni alloy has been studied. The coatings were electrodeposited in an alkaline cyanide-free solution. AFM was applied for surface morphology examination, XRD measurements were carried out for phase composition and texture analysis, electron probe microanalysis was used for alloy chemical composition studies, while electrochemical techniques were applied for corrosion performance evaluation. The pulse plated Zn–Ni coatings appeared to consist of the γ-Zn₂₁Ni₅ phase and the composition of the alloy depended on the plating parameters. The grain size, lattice imperfection and homogeneity of grain distribution were established to be the main factors determining corrosion behaviour of the coating. Presented at the 4th Baltic Conference on Electrochemistry, Greifswald, March 13–16, 2005     

Synthesis and optical properties of nanohybrids in the system constituted by silica and lanthanide phosphoramide complexes

Sol-gel process of hydrolytic polycondensation of tetramethoxysilane with trimethoxysilyl derivatives of lanthanide phosphoramide complexes was studied in order to obtain photoluminescent organic-inorganic hybrid materials. Original Russian Text N.N. Khimich, Yu.L. Zub, L.A. Koptelova, T.S. Mashchenko, E.P. Troshina, M.G. Voronkov, 2006, published in Zhurnal Prikladnoi Khimii, 2006, Vol. 79, No. 11, pp. 1789–1794.     

Estimation scheme for level-dependent uncertainty of analytical result: application for determination of 1-hydroxypyrene in urine

The estimation scheme of uncertainty of determination of 1-hydroxypyrene (1-OHP) in urine was developed analysing the main stages of the analytical procedure: (1) preparation of 1-OHP standards, (2) creation of the calibration curve for the high performance liquid chromatography (HPLC) analysis method with the evaluation of recovery, (3) measuring procedure of aliquot of urine, (4) adjusting the pH of aliquot and hydrolysis with enzyme, (5) solid phase extraction, (6) concentration of the extract, (7) injection of the extract to chromatograph and analysing by the HPLC method, (8) calculation of 1-OHP mass from the calibration curve, (9) calculation of 1-OHP concentration in urine. The evaluation of the uncertainty is based on quantification of individual components. Combined uncertainty was calculated using the law of propagation of uncertainties according to the EURACHEM/CITAC guidelines. Level dependence of the uncertainty arises from the calibration curve. The limits of detection and quantification were found to be equal to 0.03 and 0.1 ng/mL, respectively. The calculated expanded level-dependent uncertainty covers 47–27–25% within the concentration range 0.03–0.1–0.4 ng/mL with the materials and equipment used. These parameters could easily be recalculated according to the proposed scheme if there are some changes in the analysis procedure.     

Copper(II) Chelate Complex with N′-(2,4-Dichlorophenoxy)acetyl-N,N-Dimethylhydrazine: Crystal and Molecular Structure

X-ray diffraction analysis of the copper(II) chelate complex CuL₂ (where L is the deprotonated imid-ol form of N,N-dimethyl-2,4-dichlorophenoxyacetohydrazide (HL)) was performed (3826 reflections, R = 0.039, wR = 0.043). Crystals are monoclinic, a = 8.365(7) Å, b = 23.090(7)Å, c = 12.713(3) Å, = 95.12(6)°, space group P2₁/c, Z = 4. The slightly distorted square environment of the copper cation is composed of two N atoms of the dimethylamino groups and two O atoms of the deprotonated imidol groups. Both N and O atoms are located in trans-positions relative to each other. Additional coordination of electron-donor atoms is prevented by methyl groups, in which the C atoms are at a distance of 2.837 to 2.918 Å from the central ion.