This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained – by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size were considered, so the resulting discrete time dynamical system was also autonomous. One of the aims of this book is to present new findings on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, and in particular to examine the properties of nonautonomous omega limit sets and their approximations by numerical schemes – results that are also of importance for autonomous systems approximated by a numerical scheme with variable time steps, thus by a discrete time nonautonomous dynamical system.
‛Abdü’s-Selâm ‛Abdü’l-Hafîz ‛Abdü’l-‛Âl, Nakdü’ş-şi‛r beyne İbn Kuteybe ve İbn Tabâtabâ el-‛Alevî, Dâru’l-fikri’l-‛Arabî, Mısır, ts. , 166. ‛Abdü’l-‛Âl, aynı yer. İbn Kuteybe, 12, 13. Ebû ‛Usmân ‛Amr b. Bahr el-Câhiz, el-Beyân ve’t-tebyîn, nşr: ‛Abdü’s-Selâm M. Hârûn, Kahire, 1948, I, 208. İbn Kuteybe, 17. Krş: el-Câhiz, I, 207 ve II, 13. Krş: el-Câhiz, II, 13. Bkz: İbn Kuteybe, 476, 497, 501
Penbegul, Necmettin; Atar, Murat; Kendirci, Muammer; Bozkurt, Yasar; Hatipoglu, Namık Kemal; Verit, Ayhan; Kadıoglu, Ates
In recent years, day by day, robotic surgery applications have increase their role in our medical life. In this article, we reported the discovery of the first primitive robotic applications as automatic machines for the sensitive calculation of liquids such as blood in the literature. Al-Jazari who wrote the book "Elcâmi 'Beyne'l - 'ilm ve'l - 'amel en-nâfi 'fi es-sınaâ 'ti'l - hiyel", lived in Anatolian territory between 1136 and 1206. In this book that was written in the twelfth century, Al-Jazari described nearly fifty graphics of robotic machines and six of them that were designed for medical purposes. We found that some of the robots mentioned in this book are related to medical applications. This book reviews approximately 50 devices, including water clocks, candle clocks, ewers, various automata used for amusement in drink assemblies, automata used for ablution, blood collection tanks, fountains, music devices, devices for water lifting, locks, a protractor, a boat-shaped water clock, and the gate of Diyarbakir City in south-east of Turkey, actually in northern Mesopotamia. We found that automata used for ablution and blood collection tanks were related with medical applications; therefore, we will describe these robots.