In 2001, 3269 unidentified individuals were found in a mass grave on the Northern part of Vilnius, Lithuania. Artifactual context indicates that these individuals were likely soldiers that were a part of Napoleon’s Grand Army. Stable oxygen isotope analysis was performed on bone apatite from 9 femoral bone samples to determine whether or not these individuals were Lithuanian locals and to test ratio variation. If individuals were foreigners, then geographical origins were approximated utilizing percentages of C4 plants from Holder (2013) and δ18O values that were extracted from bone apatite. The carbonate oxygen isotope compositions (δ18Ocarbonate) of bone apatite from the femoral samples (-4.4‰ to -6.2‰) indicate that these individuals were from central and western Europe (-4.0‰ to -6.9‰). It is significant that none of the individuals have values consistent with the area around Lithuania (-10.0‰ to -11.9‰), because it means that they all were non-local. It is also indicative that the Lithuanians were not burying their citizens in the grave and therefore strongly support that these individuals were Napoleonic soldiers. Additionally, although C4 percentages in the diet ranged from 17.8% to 31.7%, which overlaps with eastern European consumption patterns (approximately 15% to 25% of C4 plants) (Reitsema et al., 2010), the slight shift towards a higher C4 percentage is more representative of a central and western European diet. These results are significant because they provide stable isotopic evidence that these individuals were Napoleon’s soldiers whom participated in the Russian campaign of 1812.

We investigate binary hypotheses for the formation of bipolar nebulae using the smoothed particle hydrodynamics code Gadget-2. In the general case, we present a parameter study of mass loss from very simple common envelope models, which seems to show a strongly bipolar trend for sufficiently oblate envelopes and low enough spiral-in injection energy. The density profiles of the envelopes produce differing structure within the ejecta. We also investigate 3 specific bipolar mass loss events. In the case of the outer nebula of SN 1987A, we study the effects of fast polar jets interacting with a pre- existing progenitor wind and find that these are consistent with the observed light echoes from the nebula, in particular for the feature known as ’Napoleon’s Hat’. In the case of Cas A, we briefly study the effects of close binarity on supernova ejecta and suggest the influence of a close, compact companion may lead to at least one jet-like disturbance that may be observable in a supernova remnant. Finally, we study whether a fast bipolar wind, similar to that of Eta Car’s present wind, may inflate ejecta similar to that produced in the common envelope models to a shape consistent with that of Eta Car’s Homunculus Nebula.

This diploma thesis is focused on Selected problems in planimetry. The aim of this diploma thesis is description not only planimetric problems and their verification in a dynamic mathematical program GeoGebra, but also presentation of the author after whom it is called. The thesis is illustrated with pictures, which can help the reader to understand the problem and verification. This thesis can be used as a supplement the curriculum in secondary schools, where using dynamic program GeoGebra and subsequent verification may reach a better understanding of the topic.

This diploma thesis studies in depth the progress and endings of both Napoleon's reigns in 1814 and 1815. The first chapter deals with belligerent campaigns in the beginning of 1814, with the first Napoleon's abdication and his deportation to Elba. His exile there is examined in the second chapter which shows his living on a small island in the Mediterranean sea. The third chapter takes place on the Continent again and describes Bonaparte's escape and his sequential armament within France including the view on Allies' forces and problems in Naples. The fourth chapter is genuinely military for it examines number of forces on both sides and mentions all three important battles. The last, fifth, chapter looks at the second Napoleon's abdication, at interlude since his departure for the South, entrance of Allies into Francie and return of Louis XVIII until Bonaparte's final embarking on a British vessel and his deportation to the island of Saint Helena. Key words: Napoleon Bonaparte, Emperor, abdication, Elba island, The Congress of Vienna, Quatre Bras, Ligny, Waterloo, Gebhard von Blücher, Arthur Wellesley, 1st Duke of Wellington, Joseph Fouché, Louis XVIII