The paper presents and discusses a method of azimuth determination of ultrasonic echo arrival in air. The basis of the presented approach is the assumption that the received signal is a narrowband one. In this way, the direction of the signal arrival can be determined based on its phase shift using two receivers. When the distance between the receivers exceeds half of the wavelength of the received signal, a problem of ambiguity in determining the angle of arrival arises. To solve this, a method using multiple pairs of receivers was used. Its robustness and temperature dependence is analysed. The most important advantages of the presented approach are simplified computations and low hardware requirements. Experimental data made it possible to show that for strong echoes, the accuracy is higher than 0.5X. In the case of weak echos, it is reduced to about 2X. Because the method is based on phase shift measurement, the ultrasonic sonar that uses this method can be compact in size. Moreover, owing to the theoretical analysis, certain properties of the mutual location of the receivers were found and formally proved. They are crucial for determining proper receivers’ inter-distances.

A kind of generalized proportional-integral(GPI) observer for descriptor linear systems is introduced. We first propose two complete parametric solutions to generalized Sylvester matrix equation corresponding to the left eigenvector matrices in the case of Jordan form. Then a parametric design approach for the observer is presented. The proposed method provides all parametric expression of the gain matrices and the corresponding finite left eigenvector matrix and guarantees the regularity and impulse-freeness of the expanded error system. Two numerical examples are given to explain the design procedure and illustrate the effectiveness of the proposed method.

Adam Mickiewicz's epic poem Pan Tadeusz, published in Paris in 1834, can be seen as an expression of a romantic culture of remembrance which emerged in Poland and Lithuania in the aftermath of a traumatic political event, the January Uprising of 1830–1831. This article discusses the poet's transformation of the devices and generic model of heroic epic for the double purpose of expressing a notion of historical time which holds out an open future for both the individual and the national community, and of promoting the acceptance of a complicated past through the resolution of its conflicts. Both in Poland and in Lithuania, Pan Tadeusz was regarded as a monumental tribute to the culture of the Polish-Lithuanian Commonwealth and a major influence on the modern national literatures in Lithuanian, Belarusian and Yiddish, sprouting on the territory of the former Grand Duchy of Lithuania.