Abstract. In this study we analyse the geometrical visualization as a part of the process of solution. In total 263 students in the first year of study at three different universities in three different countries (Poland, Slovakia and Spain) were asked to solve four mathematical problems. The analysis of the results of all students showed that geometrical visualization for problems where there is a possibility to choose different ways...

We introduce a new analytical method, which allows to find chaotic regimes in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered. The corresponding mathematical model is being studied. We show that the considered dynamical system is a skew product over a piecewise smooth mapping of a segment (the so-called base map). For this base map we demonstrate existence of...

Food products composition analysis is a prerequisite for verification of product quality, fulfillment of regulatory enforcements, checking compliance with national and international food standards, contracting specifications, and nutrient labeling requirements and providing quality assurance for use of the product for the supplemen- tation of other foods. These aspects also apply to the berry fruit and berry juice. It also must...