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Full-Text Articles in Physical Sciences and Mathematics
Power Distribution In The European Union, Dayton Steele
Power Distribution In The European Union, Dayton Steele
Honors Theses
The Treaty of Lisbon, the latest treaty governing law-making in the European Union (EU), was ratified in 2009 and goes fully into effect in 2014. This treaty, with its change to voting procedures in the Council of Ministers, claims to make decision-making in the EU more democratic and more efficient. Since the EU serves as an economic and political entity, we will assess these claims by comparing each member state's GDP and population to its power as modeled using the concept of a power index from the game theory literature. We will utilize the normalized Banzhaf index, the Shapley-Shubik index, …
Difference Sets In Non-Abelian Groups Of Order 256, Taylor Applebaum
Difference Sets In Non-Abelian Groups Of Order 256, Taylor Applebaum
Honors Theses
This paper considers the problem of determining which of the 56092 groups of order 256 contain (256; 120; 56; 64) difference sets. John Dillon at the National Security Agency communicated 724 groups which were still open as of August 2012. In this paper, we present a construction method for groups containing a normal subgroup isomorphic to Z4 Z4 Z2 . This construction method was able to produce difference sets in 643 of the 649 unsolved groups with the correct normal subgroup. These constructions elimated approximately 90% of the open cases, leaving 81 remaining unsolved groups.
One-Pot Reactions Of Ethyl Propiolate, Ana Maria Neferu
One-Pot Reactions Of Ethyl Propiolate, Ana Maria Neferu
Honors Theses
Through an efficient one-pot reaction sequence, ethyl propiolate can be transformed into a complex, usefully functionalized bicyclic product. Thioconjugate addition yielding Z-selective enoates has been developed for both aromatic thiols (trialkylamine-catalyzed) and aliphatic thiols (KOt-Bu-catalyzed). The oxidation of the thioenoates thus generated is followed by Li-catalyzed oxidation to sulfones using mCPBA, and Li-catalyzed Diels–Alder addition of cyclopentadiene. These subsequent steps are performed in situ, without any purification of intermediates. The yields obtained using the described synthesis are acceptable for a one-pot three-step sequence. Preliminary conjugate addition results with alcohols and amines as nucleophiles are also presented.