In a fit of frustration over a continuing $23 million securities arbitration claim at the New York Stock Exchange, a plaintiffs attorney is cracking open the guarded, almost secretive, process of securities arbitration. Thomas R. Ajamie of Ajamie LLP in Houston listed the exchange as one of the parties in a lawsuit filed in the Supreme Court of the State of New York, over the proceedings of the NYSE arbitration, which was filed in August. In his petition, he said that the NYSE should remove one of three securities arbitrators in the massive case against the former Prudential Securities Inc., and a few of its New York brokers and managers.