Secular Celebration

Following ancient Greek and Hellenistic customs, the emperor Augustus instituted a choir of amphithaleis in 17 b.c. to sing on the Capitoline Hill as part of the emperor s Secular celebration. A hymn of Horace survives that the poet composed for these amphithaleis to perform. The very prominence of these favored amphithaleis highlighted the deprivation of the orphans. As a Byzantine commentator noted, the visibility of the amphithaleis brought obscurity to those who had lost their parents. ... 

Rather than looking at the spectrum obtained from the secular determinant (5), we will here consider the spectrum SG for fixed wavenumber k and than average over k. One can write the spectrum in terms of a periodic orbit trace formula reminiscent to the celebrate Gutzwiller trace formula being a semiclassical approximation of the trace of the Green function (Gutzwiller 1990). We write the density of states in terms of the traces of SG, that is,... 

Thomas Edison and Alexander Graham Bell became celebrities and secular prophets. In Germany, privileged young aristocrats took to dreaming of new machines the way earlier generations dreamed of the hunt. ... 

Symmetry has taken us to a point where still quintic, quartic, and quadratic secular equations must be solved. However, a closer look at this equations shows that they can easily be solved. Apparently, a further symmetry principle is present, which leads to simple analytical solutions of the secular equations. Triphenylmethyl is an alternant hydrocarbon. In an alternant, atoms can be given two different colors in such a way that all bonds are between atoms of different colors hence, no atoms of the same color are adjacent. A graph with this property is bipartite, and its eigenvalue spectrum obeys the celebrated Coulson-Rushbrooke theorem [16]. 

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