Permanental bounds for nonnegative matrices via decomposition

If u = J, then U*(A) turns out to be the very bound UJ(A) used by Jurkat and Ryser to obtain J as a special case. If u = M, then U*(A) is a new upper bound UM(A). We believe its sharpened version UGM(A) to be the best extant permanental upper bound for nonnegative matrices as well as for (0, 1)-matrices.