International audienceVibrations of non-uniform and functionally graded (FG) beams with various boundary conditions and varying cross-sections are investigated using the Euler–Bernoulli theory and Haar matrices. It is assumed that the cross-section and material properties vary along the beam in the axial direction. The system of the governing equations is transformed with the aid of a set of simplest wavelets. To validate the present results, the non-homogeneity of the beams is discussed in detail and the calculated frequencies are compared with those of the existing literature. The results show that the Haar wavelet approach is capable of calculating frequencies for the beams with different shapes, rigidity, mass density, small or large translational and rotational boundary coefficients. The advantage of the novel approach consists in its simplicity, accuracy and swiftness

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In every course, there are learners who successfully pass assessments and complete the course. However, there are also those who fail the course for various reasons. One of such reasons may be related to success in assessment. Although performance in assessments has been studied before, there is a lack of knowledge on the degree of variance between different types of learners in terms of scores and the number of resubmissions. In the paper, we analyse the performance in assessments demonstrated by non-completers and completers and by completers with different engagement levels and difficulty-resolving patterns. The data have been gathered from the Moodle statistics source based on the performance of 1065 participants, as regards their completion status, the number of attempts made per each programming task and quiz, and the score received per quiz. Quantitative analysis was performed with descriptive statistics and non-parametric tests. Non-completers and completers were similar in resubmissions per quiz, but the former, expectedly, made more resubmissions per programming task and received lower quiz scores. Completers made more attempts per task than per quiz. They could provide a correct solution with a few resubmissions and receive good scores already at a pragmatic engagement level. At the same time, the increased use of help sources in case of difficulties was also associated with a higher number of attempts and lower quiz scores received. The study may have implications in understanding the role of assessments in dropouts and how completers with different engagement and difficulty-resolving patterns cope with assessments.

This study investigates the depth and location of cracks in homogeneous Euler-Bernoulli beams with free vibrations. The problem is frequently encountered in industrial design and modeling, where an exact model requires the frequency output to be calibrated with a physical measure. The crack is simulated by a line spring model. The boundary value problem is solved using the Haar wavelets. The characteristic parameters are predicted with the aid of neural networks. The proposed method is compared to an alternative approach based on neural networks and several frequencies only. The significance of the complex approach of Haar wavelets and neural networks lies in its ability to make fast accurate model-independent predictions calculating only one natural frequency and training the network only once.

This paper presents the research results of language problems to the point of financial regulation for the students educated for international programme in German-speaking countries and the materials schemed out for the practical using of linguistic means for the solution of these problems in the process of formation of the foreign communicative competence of the students studying German as the second foreign language.