Pit your wits against young minds!

This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, suprising, or appealing that one has an urge to pass them on. Contributions are most welcome.     

Analogy of thermogravimetric measurements

Dimensionless number has been developed and introduced for quantitative analysis of the effect of thermogravimetric measuring factors like sample quantity, heating rate, etc. The TG, DTG and T data of different thermogravimetric measurements can be used directly for calculation of the three constants of analogy. TG data of CaCO₃ measured in very different conditions show the method of transformation and its applicability for calculation of the correlation of measurements.     

Synchronization Analysis of Coupled Noncoherent Oscillators

We present two different approaches to detect and quantify phase synchronization in the case of coupled non-phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the R?ssler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators.     

Scattering of scalar fields by rough surfaces. Accounting for multiple scattered waves

Physical Engineering Institute, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 5, pp. 565–574, May, 1991.     

Growth of InP/InGaAs multiple quantum well structures by chemical beam epitaxy

InP/InGaAs multiple quantum well structures with up to 200 periods have been grown by CBE. These structures exhibit exceptional lateral uniformity, measured as ±1 Å in period, ±13 ppm in lattice mismatch and ±0.5 nm in wavelength across a 2 inch wafer. Good surface morphology, sharp interfaces and excellent growth control have all been demonstrated.     

On a class of elliptic operators with nonpolynomial degeneracy on a boundary

Rostov-on-Don. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 33, No. 5, pp. 91–99, September–October, 1992.