Many-body systems in the presence of the random interaction and the $J$   pairing interaction
  In this talk I shall discuss some regularities of many-body systems in the presence of random interactions and regularities of a single-$j$ shell for the $J$ pairing interaction which works only when two particles are coupled to spin $J$. I shall first explain an empirical rule to predict the spin $I$ ground state probability.   Then I shall present some interesting results of a single-$j$ shell under the $J$ pairing interaction. Last I shall discuss some preliminary results of binding energies in the presence of random two-body interactions. 
A. Arima