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.     

An experiment to discover mathematical talent in a primary school in Kampong Air

It is often said that many pupils have hidden talent in mathematics. This hidden ability is rarely seen in a normal classroom teaching and learning situation if the focus of the teacher is on drilling with routine exercises. To allow pupils to display their mathematical talent and to break from mental set and fixation in mathematics, they must be given opportunity to think by themselves with mininum cue or guidance. The pupils could be left entirely on their own to show their mathematical creativity even on mathematical topics which have not been exposed to them. With this approach, five non-routine questions were administered one at a time to a standard 5 class. One out of the 25 pupils in the class consistently exhibited mathematical creativity and talent is answering the questions. Her responses were shown and discussed in this paper.     

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.     

Ab initio calculation of the heptamer (NH3)7 as a reasonable starting point for a description of the ammonia crystal

Quasi-Wannier functions for the ammonia crystal have been determined from optimized ab initio calculations of the heptamer (NH₃)₇, thus accounting for all the first neighbor interactions. The calculated geometry and binding energy are in good agreement with their experimental counterparts.     

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.