The Kekule structure count K of fluoranthene congeners is studied. It is shown that for such polycyclic conjugated π-electron systems, either K = 0 or K ≥ 3. Moreover, for every t ≥ 3, there are infinitely many fluoranthene con- geners having exactly t Kekule structures. Three classes of Kekulean fluoran- thenes are distinguished: i) Φ0 - fluoranthene congeners in which neither the male nor the female benzenoid fragment has Kekule structures, ii) Φm - fluo- ranthene congeners in which the male benzenoid fragment has Kekule structures, but the female does not, and iii) Φfm - fluoranthene congeners in which both the male and female benzenoid fragments have Kekule structures. Necessary and sufficient conditions are established for each class, Φ = Φ0, Φm, Φfm, such that for a given positive integer t, there exist fluoranthene congeners in Φ with the property K = t.

Network capacity for bidirectional communication between pairs of wireless end users assisted by a relay terminal can be improved by network coding at the physical layer (PNC). Narrowband analog network coding (ANC) was introduced as a simpler implementation of PNC in a flat (i.e., frequency-nonselective fading) channel. Recently, broadband ANC has been studied for communication over a frequency-selective fading channel. In ANC, the end user removes its own information from the received signal before detecting the data of the other user. Clearly, the network performance of ANC scheme depends on the self-information removal at the destination terminal. In this paper, we discuss the impact of imperfect self-information removal on the performance of broadband ANC in terms of the bit error rate (BER) and achievable throughput in a frequency-selective fading channel. The theoretical minimum mean square error (MMSE) equalization weight for ANC based on single carrier with frequency domain equalization (SC-FDE) radio access is derived by taking into account the self-interference. We have used analysis and computer simulation to evaluate how the imperfect removal of self-information influences the achievable BER and throughput.