Linear stability of convective motion in a tall vertical annulus was analysed in the paper. The base flow was generated by a non-uniform distribution of heat sources in the radial direction. The base flow velocity and temperature were obtained analytically solving the system of Navier-Stokes equations under the Boussinesq approximation. The linear stability problem was solved for axi-symmetric and asymmetric perturbations by a collocation method based on the Chebyshev polynomials. Numerical results showed that there were three destabilising factors: (1) increase of the gap between the cylinders, (2) increase of the density of internal heat sources towards to the outer boundary of the annulus and (3) increase of the Prandtl number.
Abstract. Questions about the quality improvement of the school system are topical at the moment. Universities must be prepared to offer the young person an education that prepares him/her to be competitive in these new work conditions, which is why the main goal of the university in this changing time is development of the of mental skills, cognitive research attitudes and IT skills. That is why mathematics study programmes and didactics must be improved, based on IT, creating more modern learning materials based on modern technologies and offering access to them via the Internet. During the period 2005 to 2014, students from the Faculty of Computer Science and Information Technologies, parallel to the regular teaching of mathematics, were taught a program package MATHEMATICA. In the last two years it was changed to a program package MATLAB. For two semesters the first course students have had laboratory work at computers, where students are acquiring the ability to solve tasks that are similar to those in their practical work with the help of a mathematical program. This year's first course students were questioned about MATLAB classes. 172 students took part in a survey, and the majority of them believe that MATLAB classes are useful and necessary for students and that they help them understand mathematical algorithms to solve tasks.
More than twenty years have passed since the adoption of the Bologna agreements, and disputes between their supporters and opponents do not cease. In general, in Europe until recently two education systems dominated: Anglo-Saxon, i.e. German, and Latin. As a result of the adoption of the Bologna agreements, it turned out that the Latin system won. As math teachers of Higher School, we are interested in changes regarding the teaching of mathematics in Higher education. In this article the changes that had occurred as a result of the signing of the Bologna Convention were analyzed using the examples of Latvia and Russia.
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