On Series of Ordinals and Combinatorics

This paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well-known that for finite ordinals ∑_bT<αβ is the number of 2-element subsets of an α-element set. It is shown here that for any well-ordered set of arbitrary infinite order type α, ∑_bT<αβ is the ordinal of the set M of 2-element subsets, where M is ordered in some natural way. The result is then extended to evaluating the ordinal of the set of all n-element subsets for each natural number n ≥ 2. Moreover, series ∑_β<αf(β) are investigated and evaluated, where α is a limit ordinal and the function f belongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α appears to be quite problematic.     

Existence and Stability for Spherical Crystals Growing in a Supersaturated Solution

We consider the growth of a spherical crystal in a supersaturatedsolution. In the first part, existence and uniqueness resultsfor radially symmetric growth are obtained, provided that thesupersaturation is not too large; conversely, when the far-fieldsupersaturation exceeds a critical value, it is shown that theradially symmetric solution ceases to exist in finite time.In the second part, we examine the linear stability of a radiallysymmetric similarity solution (in which the radius grows ast?) to shape perturbations. The results are compared with previousquasi-static analyses, and, in particular, the critical radiusat which the crystal becomes unstable is found to be largerfor small supersaturations, but smaller for large supersaturations,than those predicted by the quasi-static analysis     

Numerical solutions of the shallow water equations with discontinuous bed topography

A simple scheme is developed for treatment of vertical bed topography in shallow water flows. The effect of the vertical step on flows is modelled with the shallow water equations including local energy loss terms. The bed elevation is denoted with z_b^‐ for the left and z_b⁺ for the right values at each grid point, hence exactly representing a discontinuity in the bed topography. The surface gradient method (SGM) is generalized to reconstruct water depths at cell interfaces involving a vertical step so that the fluxes at the cell interfaces can accurately be calculated with a Riemann solver. The scheme is verified by predicting a surge crossing a step, a tidal flow over a step and dam‐break flows on wet/dry beds. The results have shown good agreements compared with analytical solutions and available experimental data. The scheme is efficient, robust, and may be used for practical flow calculations. Copyright © 2002 John Wiley & Sons, Ltd.     

Effect of trapping centers of luminescent properties of bismuth orthogermanate

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 6, pp. 970–975, June, 1991.     

Self-transparency effect in a twisted nematic liquid crystal cell

In a twisted nematic liquid crystal cell we report and study the self-transparency effect induced by the creation of an isotropic droplet. A simple theoretical model is presented and good agreement with experimental data is found. In a two beams configuration transistor-like behavior is observed and theoretically discussed.     

Franck-Condon factors and relative strengths of the c1Σu → α1Δg,c1Σu → X3Σg electronic transitions in the O2 molecule

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 1, pp. 46–50, January, 1991.     

The frequency scale of speech intonation.

In intonation research, prominence-lending pitch movements have either been described on a linear or on a logarithmic frequency scale. An experiment has been carried out to check whether pitch movements in speech intonation are perceived on one of these two scales or on a psychoacoustic scale representing the frequency selectivity of the auditory system. This last scale is intermediary between the other two scales. Subjects matched the excursion size of prominence-lending pitch movements in utterances resynthesized in different pitch registers. Their task was to adjust the excursion size in a comparison stimulus in such a way that it lent equal prominence to the corresponding syllable in a fixed test stimulus. The comparison stimulus and the test stimulus had pitches running parallel on either the logarithmic frequency scale, the psychoacoustic scale, or the linear frequency scale. In one-half of the experimental sessions, the test stimulus was presented in the low register, while the comparison stimulus was presented in the high register, and, conversely, for the other half of the sessions. The result is that, in all cases, stimuli are matched in such a way that the average excursion sizes in different registers are equal on the psychoacoustic scale.     

The measurement of subcritical electroconvection

Under idealized conditions, electroconvection in a nematic liquid crystal sets in at a well-defined threshold of the driving ac voltage. Fluctuating convection rolls of a small amplitude below that threshold have been observed recently. The measurement of the amplitude of these fluctuations is described in detail in this paper. It is based on averaging the light intensity signals using the structure function and a quantitative analysis of the light deflection.     

Evaluating the Efficiency of US Air Force Real-Property Maintenance Activities

The objective of this research is to evaluate a new methodology, data envelopment analysis (DEA), as a tool for measuring and evaluating the operational efficiency of US Air Force organizations. This study involves the application of DEA to locate possible inefficiencies in the performance of US Air Force real-property maintenance activities. Dynamic behaviour, as exhibited via window analyses, is reviewed along with static counterparts. The testing was done in close coordination with Air Force officials, who reviewed the results for accuracy, validity and relevance. We conclude that this type of efficiency analysis does have value for the Air Force, where it can serve as a guide to auditors, budget programmers, managers and others in measuring, evaluating and enhancing operational efficiency.