11.   Randy M. Mastro, a deputy mayor, said the mayor appeared at the invitation of the authority.

12.   The crowd burst into wild applause when former mayor Rudolph Giuliani appeared, marching alongside Mayor Michael Bloomberg and ducking into the crowd now and then to shake hands.

13.   The mayor appeared on television and promised not to allow tanks to roll through his city.

14.   The mayor appeared to be trying to burnish his profile among national representatives of a religious group whose members have staunchly backed him in New York.

15.   The mayor will appear in the commercial, scheduled to begin running next Wednesday, along with Gov. George E. Pataki.

16.   The mayor appeared the next day, accompanied by police and militia.

17.   The mayor appeared to be referring to those schools that have had the greatest number of incidents of violence and crime.

18.   The mayor appears driven by a moral conviction that complete abstinence from drugs is the only acceptable course.

19.   The mayor appeared to relish picking a fight with the CUNY board, joking that its members might faint when they heard his proposal.

20.   Unfortunately, the mayor still appears to be committed to giving the Police Department the sole responsibility for investigating and disciplining its members.