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.     

Dynamic equilibrium of ion exchange in the system lead-cation exchanger at different temperatures

Summary The relationship between the ion-exchange reaction in a column and temperature was examined in the system lead-ion exchanger resin Lewatit S 1080. Lead binding was performed with 0.01 mol/l HNO₃ and elution with 4.0 mol/l HCl. The working temperature was gradually increased from 273 to 333 K. Thermostat columns were of own construction. The results were statistically analysed and graphically presented and the parameters obtained for elution curves were related to temperature. The elution curves were found to be temperature specific. The parameters such as elution band width, distribution factor, maximal volume of the eluate, maximal lead concentration in the eluate, confirmed this fact. At higher temperatures, larger volumes of elution solution were required for the elution of the same quantity of lead.

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Ionenaustausch im System Blei-Kationischer Austauscher bei verschiedenen Temperaturen

     

Complex coordinates and the Stark effect

The theories of the dilatation, r → r e^iθ, and translation, x → x + iq, transformations as related to the Stark problem are reviewed, and new results obtained. Results for the hydrogen atom n = 1 and n = 2 levels and the ¹P⁰, 2s2p H^? shape resonance in dc fields are presented, and the extension to the ac Stark effect made. Spectral estimates are made using the technique of the numerical range and via discussion of several model problems, using both coordinate rotation and coordinate translation.     

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.