By John S. McClenahen The U.S. dollar is likely to remain weak against the European euro and the Japanese yen for this year and next -- even weaker than some economists are generally predicting, says UBS Warburg LLC. The explanations are highly technical and mind-numbingly complicated. But the bottom line is that UBS Warburg expects the euro to be trading at $1.20 at the end of this year and at $1.25 at the end of 2004. The dollar will bring just 108 Japanese yen at yearend 2003 and an even lower 105 yen at the end of next year, the financial firm's economists forecast. This month the euro has been trading at about $1.10 and the dollar would buy about 118 yen. "It's ironic, in a way, that the [U.S. dollar] may indeed be subject to undershooting in the coming year or so -- for, as best we can judge, America does not suffer a competitiveness problem," says UBS Warburg. The problem is "that the rest of the world lacks demand growth."