Lie algebras and triple systems

This thesis is dedicated to the Tits-Kantor-Koecher (TKK) construction which establishes a bijective correspondence between unital Jordan algebras and shortly graded Lie algebras with Z-grading induced by an sl_2-triple. It is based on the observation that if g is a Lie algebra with a short Z-grading and f lies in g_1, then the formula ab=[[a,f],b] defines a structure of a Jordan algebra on g_{-1}. The TKK construction has been extended to Jordan triple systems and, more recently, to the so-called Kantor triple systems. These generalizations are studied in the thesis.

Isoxazolidines and oxazines: preliminary studies for the synthesis of N,O-heterocyclic systems via an organocatalyzed 1,3-Dipolar Cycloaddiction and a tandem reaction mediated by TEMPO salts

This thesis is the result of the study of two reactions leading to the formation of important heterocyclic compounds of potential pharmaceutical interest. The first study concerns the reaction of (1,3)-dipolar cycloaddition between nitrones and activated olefins by hydrogen bond catalysis of thioureas derivatives leading to the formation of a five-membered cyclic adducts, an interesting and strategic synthetic intermediate, for the synthesis of benzoazepine. The second project wants to explore the direct oxidative C(sp3)-H α-alkylation of simple amides with subsequent addition of an olefin and cyclization in order to obtain the corresponding oxazine. Both reactions are still under development.

OFDM-based schemes for next generation wireless systems

The purpose of this study is to investigate two candidate waveforms for next generation wireless systems, filtered Orthogonal Frequency Division Multiplexing (f-OFDM) and Unified Filtered Multi-Carrier (UFMC). The evaluation is done based on the power spectral density analysis of the signal and performance measurements in synchronous and asynchronous transmission. In f-OFDM we implement a soft truncated filter with length 1/3 of OFDM symbol. In UFMC we use the Dolph-Chebyshev filter, limited to the length of zero padding (ZP). The simulation results demonstrates that both waveforms have a better spectral behaviour compared with conventional OFDM. However, the induced inter-symbol interference (ISI) caused by the filter in f-OFDM, and the inter-carrier interference (ICI) induced in UFMC due to cyclic prefix (CP) reduction , should be kept under control. In addition, in a synchronous transmission case with ideal parameters, f-OFDM and UFMC appear to have similar performance with OFDM. When carrier frequency offset (CFO) is imposed in the transmission, UFMC outperforms OFDM and f-OFDM.