Approximation by a binomial type law

Kaunas Academy of Agriculture, 4324 Noreikiškés, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 32, No. 2, pp. 221–228, April–June, 1992.     

Vertical migration of 85Sr, 137Cs and 131I in various arable and undisturbed soils

The vertical migration of ⁸⁵Sr, ¹³⁷Cs and ¹³¹I in some arable and undisturbed single-contaminated soils was studied by gamma-spectrometry measurements under lysimetric laboratory conditions during irrigation of the soil profiles with wet atmospheric precipitation for about one year, except ¹³¹I. A new simple exponential compartment (box) model was derived, which makes it possible to calculate the migration rate constants and migration rates in the individual soil layers (vertical sections) as well as the total vertical migration rate constants and total vertical migration rates of radionuclides in the bulk soil horizon. The relaxation times of radionuclides in respective soil horizons can also be evaluated.     

Symmetry of electronic states in garnets

The paper presents the classification of the electronic empty lattice eigenvalues and the classification of the Bloch sums for the garnet structureIa3d (O _h ¹⁰ ) at the symmetry points, H, P, andN of the Brillouin zone. This provides a starting point for the energy band studies of these technologically important materials.The author thanks Dr. V. Frei for useful comments.     

On the possibility of measuring the thickness of very thin films using electron probe microanalyzer

The measurement of the thickness of thin aluminum and silver films using an electron probe microanalyzer is described. The method of measurement was studied in order to investigate very thin discontinuous aluminum layers, originated from inorganic residues of photoresists removed from the surface of silicon and other materials by plasma oxidation. The calibration curves, i.e. the dependences of the intensity of the characteristic X-ray emission on the thickness of thin standard films evaporated on the same substrate, were determined for the evaluation of the measurements. These dependences were measured till the smallest thickness 15 nm of the standard film. Then the curves were extrapolated to the origin of coordinates and the film thickness was calculated using the value of the slope of tangent to the calibration curve in the origin. In order to estimate the accuracy of this procedure, the calibration curves were expressed analytically using the mathematical representation of the electron excitation function. It follows from the results that the shape of the calibration curves may be influenced mainly due to electrons scattered from the substrate back into the film and due to fluorescence excitation of X-ray emission. The last effect was markedly observed in Al/Si system.     

Investigation of the separation efficiency in one-stage and multistage extractions by a numerical method

Theoretical separation efficiencies in one-stage static and multistage dynamic models of liquid-liquid extraction have been studied mathematically. By the use of the iterative numerical method the maximum difference between separation efficiencies in these two models, as well as the absolute values of the respective separation efficiencies were calculated at this maximum. The maximum difference between multistage and one-stage separation efficiencies amounts to 20.36%, when the respective separation efficiencies are about 91.89% and 71.56%.     

Factorial regular representation of groups in complete graphs

A necessary and sufficient condition for the group of isomorphisms involved in a factorization of a complete graph into isomorphic factors is established.     

Effect of degradation of montmorillonite by vibration grinding on the dTA curves in the range 20–1500°C

The effect of vibration grinding on the DTA curves of montmorillonite isolated from the most important locality of bentonite in the Slovak Republic (Jel?ovy potok, Middle Slovakia) was studied in the temperature range 20–1500°C. Interpretation is offered for 6 endothermic and 3 exothermic peaks. vibration grinding modified the course of dehydration of the mineral, suppresses the “dehydroxylation’ peak at 700°C, enables the crystallization of high-temperature quartz, cristobalite and cordierite at lower temperatures in comparison with unground natural montmorillonite. Vibration griding slows down the crystallization of mullite which—unlike quartz, cristobalite and cordierite—does not belong to high-temperature phases of Cheto-montmorillonite. The order in which these high-temperature phases occur is not influenced by vibration grinding.     

Sorption of 125I−, 137Cs+, 85Sr2+ and 152,154Eu3+ during their transport in undisturbed vertical and horizontal soil cores under dynamic flow conditions

Transport and sorption of ¹²⁵I^?, ¹³⁷Cs⁺, ⁸⁵Sr²⁺ and ^152,154Eu³⁺ in undisturbed soil cores have been studied under dynamic conditions. Radionuclides were dissolved in synthetic groundwater (SGW) of 0.015 mol/dm³ ionic strength, pH 8.4 and redox potential E_h = 145 mV. The soil samples were taken vertically and horizontally from the river bed at 5–100 cm depths, about 120 m southward of the Dukovany Low and Medium Level Radioactive Waste Repository. The respective water-soluble carriers in the 10^?6 mol/dm³ concentration were added into the SGW prior to the experiments. The soil cores of 9 cm height and 3.8 cm in diameter were placed into columns made of 150 cm³ PE injection syringes of suitable dimensions. The SGW was introduced into columns from the Mariotte’s bottle through a glass manifolds to supply the soil columns by gravity flow at a constant flow-rate about 1.2 cm³/h. Into the water stream, radioactive nuclides were added individually in a form of a short pulse in 0.1 cm³ of demineralized water. In the case of ¹²⁵I^? transport, retardation and hydrodynamic dispersion coefficients were determined, using an integral form of a simple advection-dispersion equation. For each radionuclides, sorption and desorption data have been obtained, evaluated and the results were compared mutually. Residual distributions of the sorbed cationic radionuclides along the soil columns were also presented.