A concept of strong necessary conditions for extremum of functional has been applied for analysis an existence of dual equations for a system of two nonlinear Partial Differential Equations (PDE) in 1+1 dimensions. We consider two types of the dual equations: the Bäcklund transformations and the Bogomolny equations. A general form of the second order PDE with a derivative-less non-linear term has been considered. In the case of a coupled system of equations the general conditions for the existence of the Bogomolny decomposition are derived. In the case of an uncoupled system of equations the Bogomolny equations become the Bäcklund transformations. It has been found a denumerable classes of coupled systems possessing the Bogomolny relationship. Weaken the method into semi-strong necessary conditions is presented together with an application to the Lax hierarchy. The method basing on both the strong and the semi-strong necessary condition concept reduces the derivation of the dual equations to an algorithm.
A Stokes viscometer made and launched by the authors in the Physical Laboratory of the State Higher Vocational School in Tarnów was presented. The construction of the viscometer is discussed and the theoretical description of the physical phenomena occurring there is given. The results of measurements on the device, statistical analysis of the measurement uncertainties and confrontation with the literature value are presented - the obtained results correspond very well to the literature values. A possible further development in the accuracy of theoretical description and experimental measurements related to the ellipsoid analysis of the shape of water droplets was suggested. The didactic aspects of the new experiment in the context of the understanding of molecular physics, especially by students of material engineering, were discussed.
The general aim of this article is to present didactic aspects of familiarizing students with the Fourier analysis. This didactic process issues through the use of IT tools of Laboratory of Technical Aids of Teaching is discussed. There are four separate computer stations, differing in software, where students learn step by step: composing signals from single harmonics, visualization through images of rotating vectors of harmonic signal composition, operation of a virtual generator of a given number of harmonics and elements of the CMA Coach system in the context of signal analysis. The applied didactic methods are aimed at students of biophysics for whom the Fourier analysis is of practical importance.
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