The parametric anti-resonance phenomenon as an active damping tool for suppression of externally excited resonant vibration is numerically studied herein. It is well known fact that the anti-resonance phenomenon, i.e. the stiffness periodic variation by subtractive, combination resonance frequency, brings stabilization and cancelling into self-excited vibrations. But this paper aims at a new possibility of its application, namely a damping of externally excited resonant vibration. For estimation of its effect we come both from a characteristic exponent of the analytical solution and numerical solution of forced vibration of 2DOF linear system with additional parametric excitation. The amplitude suppression owing to the parametric anti-resonance is studied on several parameters of the system: a depth of parametric excitation, mass ratio, damping coefficient and small frequency deviations from the parametric anti-resonance.
A trellis coded 4-ary Pulse Amplitude Modulation (4-PAM) is presented, where the encoding algorithm is derived from Distance Preserving Mapping (DPM) algorithm. In this work, we modify the DPM algorithm for 4-PAM and obtain a new construction for mapping binary sequences to permutation sequences, where the permutation sequences are obtained by permuting symbols of a 4-PAM constellation. The resulting codebook of permutation sequences formed this way are termed mappings. We also present several metrics for assessing the performance of the mappings from our construction, and we show that a metric called the Sum of Product of Distances (SOPD) is the best metric to use when judging the performance of the mappings. Finally, performance results are presented, where the mappings from our construction are compared against each other and also against the conventional mappings in the literature.
The paper presents the method of assessment of learning outcomes acquirement by students. The analysis is based on the results of the final matriculation exam in mathematics. For crisp and both types of fuzzy relations, cut scores (passing scores) can be defined along with the method of preparing rankings of students. The advantage of applying type 2 fuzzy relations is the lack of the necessity for experts to agree to one level (one number) of verification of learning outcomes by items created for the examination. Based on the results of the exam and experts’ knowledge, the decision support system for calculating the levels of learning outcomes acquirement, making decisions about passing the examination and preparing rankings of students, can be developed. Additionally, the rank reversal phenomenon does not burden the proposed method.