For sequences of rational functions, analytic in some domain, a theorem of Montel’s type is proved. As an application, sequences of rational functions of the best $L_p$-approximation with an unbounded number of finite poles are considered.
This paper deals with basic stability properties of a two-term linear autonomous fractional difference system involving the Riemann-Liouville difference. In particular, we focus on the case when eigenvalues of the system matrix lie on a boundary curve separating asymptotic stability and unstability regions. This issue was posed as an open problem in the paper J. Čermák, T. Kisela, and L. Nechvátal (2013). Thus, the paper completes the stability analysis of the corresponding fractional difference system.
This study aims at developing an artificial intelligence-based (ANN based) analytical method to analyze earthquake performances of the reinforced concrete (RC) buildings. In the scope of the present study, 66 real RC buildings with four to ten storeys were subject to performance analysis according to 19 parameters considered effective on the performance of RC buildings. In addition, the level of performance of these buildings in case of an earthquake was determined on the basis of the 4-grade performance levels specified in Turkish Earthquake Code-2007 (TEC-2007). Thus, an output performance data group was created for the analyzed buildings, in accordance with the input data. Thanks to the ANN-based fast evaluation algorithm mentioned above and developed within the scope of the proposed project study, it will be possible to make an economic and rapid evaluation of four to ten-storey RC buildings in Turkey with great accuracy (about 80%). Detection of post-earthquake performances of RC buildings in the scope of the present study will facilitate reaching important results in terms of buildings, which will be beneficial for Civil Engineers of Turkey and similar countries.