We find a universal norming sequence in strong limit theorems for increments of sums of i.i.d. random variables with finite first moments and finite second moments of positive parts. Under various one-sided moment conditions our universal theorems imply the following results for sums and their increments: the strong law of large numbers, the law of the iterated logarithm, the Erdős-Rényi law of large numbers, the Shepp law, one-sided versions of the Csörgő-Révész strong approximation laws. We derive new results for random variables from domains of attraction of a normal law and asymmetric stable laws with index αЄ(1,2).
The asymptotics of the size of the largest cave is found for a d -dimensional .eld of i.i.d.random variables.For Bernoulli case the problem was investigated by R ´ev ´esz (, p =1 /2)and Deheuvels .We consider distributions of a general structure.
Authors:N. Andreychuk, A. Frolov, K. Rotmanov and V. Vasiliev
Plutonium(III) oxidation under high energy -irradiation in nitric acid solutions has been studied relative to concentrations of both nitric acid (0.12–2.9 mol/l) and plutonium (1.4–10 mmol/l) using spectrophotometric techniques. Curium-244 has been used as the basic alpha-irradiation source. It has been stated that in solutions with nitric acid concentrations lower than 0.5 mol/l plutonium(III) does not oxidize completely. In the course of the process the formation of a plutonium(IV) peroxide complex is observed. Increase in the nitric acid concentration results in that in both the rate and degree of plutonium(III) oxidation. When cHNO3 is higher than 0.5 mol/l the peroxide complex does not form and the process assumes an autocatalytic character. It has also been shown that plutonium(III) oxidation kinetics is significantly affected by nitrous acid, one of the nitrate ion radiolysis products. To describe plutonium chemical transformations under irradiation in nitric acid solutions, a kinetic scheme is proposed. The calculations have been carried out on a BESM-6 computer; a satisfactory agreement between the calculated and experimental data has been obtained.
Authors:A. Frolov, N. Andreychuk, K. Rotmanov, L. Frolova and V. Vasiliev
This paper presents the results of systematic kinetic studies of valence transformation of U, Np, Pu, Am and Bk in nitrate- and perchlorate solutions under the effect of intensive internal alpha-radiation emitted by244Cm nuclides. The high dose rate of solutions (D=1–8 Gy/s) provides a sufficient yield of H2O2, HNO2 and ClO2 — the main products of alpharadiolysis of water, nitrate and perchlorate ions, respectively, which was determined by spectrophotometric methods immediately in the course of the process under study. To describe the results, a kinetic scheme considering the effect of dose rate and solution composition is proposed. The calculations have been carried out on a BESM-6 computer, a satisfactory agreement between the calculated and experimental data has been obtained.
Authors:O. Ordzhonikidze, A. Pivkina, Yu. Frolov, N. Muravyev and K. Monogarov
This study deals with a well-known monocyclic nitramine HMX and a relatively new polycyclic strained-cage nitramine CL-20. Experimental data on the powder morphology, simultaneous thermal analysis (STA) and burning rate of binary formulations Al/HMX and Al/CL-20 are presented. Kinetic modelling for HMX and CL-20 are considered based on analysis of STA data obtained for low heating rates. The processing of STA data by the Kissinger method was shown to need to be supplemented with the construction of a thermokinetic model. The thermal decomposition of HMX is reliably described by the reaction of the first order with the autocatalysis. Obtained kinetic parameters of the HMX thermal decomposition correlate with literature-known data on kinetics of the lead stage of HMX combustion. Two types of aluminium powder, i.e. micron-sized and ultrafine, are used to investigate the interaction with both nitramines. Thermal analysis revealed the higher Al oxidation ability of the solid compounds produced at CL-20 thermolysis, than that one of HMX. Burning rate experiments show the differences in the combustion parameters between CL-20- and HMX-based formulations, specifically along with the burn rate level increase for CL-20 monopropellant as compared to HMX one, the pressure exponent and effect of the aluminium particle size variation are also distinct. Results are analyzed and compared to available literature data.