a2_The town of Litija was hit by four damaging earthquakes in the last 120 years which reached a maximum intensity of VII-VIII MSK. The town is located in a shallow sedimentary basin filled with relatively soft Quaternary sediments in which seismic site amplification is expected. On the other hand no borehole or geophysical data are available to support quantitative assessment of site effects. As a contribution to the first seismic microzonation of the area, we performed a free-field study based on the microtremor HVSR method in order to assess the resonance frequency of th e sediments. In ge neral clear spectral peaks were obtained for 57 measuring points which show distribution of frequencies in a broad range between 4.4 an d 22.7 Hz. The iso-frequency map was prepared by using natural neighbour interpolation algorithm. For soil-structure resonance assessment we considered large building stock from different Slovenian towns, because the building typology is similar in wider area. Low-rise masonry family houses with two or three floors prev ail. By microtremor measurements inside 45 such buildings their fundamental longitudinal and transver se frequencies were determined and statistically analysed in a complementary study. To assess the possible occurrence of soil-structure resonance in general, the average fundamental frequency +/- one standard devia tion interval is obtained for these two building heights, which give s the range 5.6-11.1 Hz. The free-field microtremor data shows that this frequency range occupies 37% of the urban area in the Litija basin. This study has shown that soil-structure resonance issue for low-rise buildings is frequently overlooked, but should be considere d seriously in shallow sedimentary basins, characterized by relatively high free-field frequencies, because many towns are located in such geological environment., a2_Second application of the derived iso-frequency map is to support soil classification, because recent investigations have shown that fundamental frequency of sediments can be used together with the average shear velocity in the upper 30 m to improve classi fications according to di fferent seismic codes., Andrej Gosar., and Obsahuje bibliografické odkazy
A measuring system evaluating a Point Spread Function generated in an ultrasonographic image by scanning a spherical target was developed. The target is moved in measuring bath filled by water over scanned volume via 3D computer controlled positioning system. A video signal obtained is converted to digital form and analyzed by original software to derive various objective parameters of the imager as follows: Focal areas in both the azimuth and the elevation directions, Ultrasound scanning lines visualisation, Manufacturer preloaded TGC, Width of the scanning plane, Side lobe levels and Amplification uniformity in the azimuth direction. The method was verified by testing 18 different equipments in 282 measurements. Samples of particular measurement results in form of graphical outputs are included. Medical and physiological impacts of this approach are discussed., L. Doležal, J. Mazura, J. Tesařík, H. Kolářová, D. Korpas, S. Binder, J. Hálek., and Obsahuje bibliografii
Let $R$ be a prime ring, $I$ a nonzero ideal of $R$, $d$ a derivation of $R$ and $m, n$ fixed positive integers. (i) If $(d[x,y])^{m}=[x,y]_{n}$ for all $x,y\in I$, then $R$ is commutative. (ii) If $\mathop {\rm Char}R\neq 2$ and $[d(x),d(y)]_{m}=[x,y]^{n}$ for all $x,y\in I$, then $R$ is commutative. Moreover, we also examine the case when $R$ is a semiprime ring.
Let $R$ be a prime ring of char $R\ne 2$ with a nonzero derivation $d$ and let $U$ be its noncentral Lie ideal. If for some fixed integers $n_1\ge 0, n_2\ge 0, n_3\ge 0$, $( u^{n_1}[d(u),u]u^{n_2})^{n_3}\in Z(R)$ for all $u \in U$, then $R$ satisfies $S_4$, the standard identity in four variables.
Vsevolod I. Ivanov stated (Nonlinear Analysis 125 (2015), 270-289) the general second-order optimality condition for the constrained vector problem in terms of Hadamard derivatives. We will consider its special case for a scalar problem and show some corollaries for example for ℓ-stable at feasible point functions. Then we show the advantages of obtained results with respect to the previously obtained results.
We consider a nonlinear differential inclusion defined by a set-valued map with nonconvex values and we prove that the reachable set of a certain variational inclusion is a derived cone in the sense of Hestenes to the reachable set of the initial differential inclusion. In order to obtain the continuity property in the definition of a derived cone we use a continuous version of Filippov's theorem for solutions of our differential inclusion. As an application, in finite dimensional spaces, we obtain a sufficient condition for local controllability along a reference trajectory.
We estimated the common seasonal signal (annual oscillation) included in the Global Positioning System (GPS) vertical position time series by using Multichannel Singular Spectrum Analysis (MSSA). We employed time series from 24 International GNSS Service (IGS) stations located in Europe which contributed to the newest ITRF 2014 (International Terrestrial Reference Frame). The MSSA method has an advantage over the traditional modelling of seasonal signals by the Least-Squares Estimation (LSE) and Singular Spectrum Analysis (SSA) approaches because it can extract time-varying and common seasonal oscillations for stations located in the considered area. Having estimated the annual curve with LSE, we may make a misfit of 3 mm when a peak-to-peak variations of seasonal si gnals are to be estimated due to the time-variability of seasonal signal. A variance of data modelled as annual signal with SSA and MSSA differs of 3 % at average what proves that the MSSA-curves contain only time-varying and common seasonal signal and leave the station-specific part, local phenomena and power-law noise intact. In contrast to MSSA, these effects are modelled by SSA. The differences in spectral indices of power-law noise between MSSA and LSE esti mated with Maximum Likelihood Estimation (MLE) are closer to zero than the ones between SSA and LSE, which means that MSSA curves do not contain site-specific noise as much as the SSA curves do., Marta Gruszczynska, Anna Klos, Severine Rosat and Janusz Bogusz., and Obsahuje bibliografické odkazy