Abstract: This article discusses plausible reasoning use for solution to practical problems. Such reasoning is the major driver of motivation and implementation of mathematical, scientific and educational research activity. A general, practical problem solving algorithm is presented which includes an analysis of specific problem content to build, solve and interpret the underlying mathematical model. The author explores the role of practical problems such as the stimulation of students' interest, the development of their world outlook and their orientation in the modern world at the different stages of learning mathematics in secondary school. Particular attention is paid to the characteristics of those problems which were systematized and presented in the conclusions.
Abstract: Accurately predicting non-peak traffic is crucial to
daily traffic for all forecasting models. In the paper, least squares
support vector machines (LS-SVMs) are investigated to solve such a
practical problem. It is the first time to apply the approach and analyze
the forecast performance in the domain. For comparison purpose, two
parametric and two non-parametric techniques are selected because of
their effectiveness proved in past research. Having good
generalization ability and guaranteeing global minima, LS-SVMs
perform better than the others. Providing sufficient improvement in
stability and robustness reveals that the approach is practically
promising.