NOT RUNNING. Albert Gore Jr., 43, U.S. Senator from Tennessee and oft-mentioned contender for the Democratic presidential nomination in 1992; announced in Carthage, Tenn. Gore, who finished third in the 1988 nomination bids, explained that duty to his four children, ages 8 to 18, offset the fire in his belly. He thus joins a list of prominent Democratic nonstarters that so far includes Jay Rockefeller, Dick Gephardt, Lloyd Bentsen, Bill Bradley, Sam Nunn and Mario Cuomo.