TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: The Bronsted base solution comprises N-methyl-2-pyrrolidone, dimethylformamide, dimethylacetamide, pyrrolidone, or N-dodecylpyrrolidone. The bismaleimide is of formula (II) or (III) (preferably N,N'-bismaleimide-4,4'-diphenylmethane, 1,1'-(methylenedi-4,1-phenylene)bismaleimide, N,N'-(1,1'-biphenyl-4,4'-diyl)bismaleimide, N,N'-(4-methyl-1,3-phenylene)bismaleimide, 1,1'-(3,3'dimethyl-1,1'-biphenyl-4,4'-diyl)bismaleimide, N,N'-ethylenedimaleimide, N,N'-(1,2-phenylene)dimaleimide, N,N'-(1,3-phenylene)dimaleimide, N,N'-thiodimaleimid, N,N'-dithiodimaleimid, N,N'-ketonedimaleimid, N,N'-methylene-bis-maleinimid, bis-maleinimidomethyl-ether, 1,2-bis-(maleimido)-1,2-ethandiol, N,N'-4,4'-diphenylether-bis-maleimid, or 4,4'-bis(maleimido)-diphenylsulfone). The maleimide comprises N-phenylmaleimide or N-cyclohexylmaleimide. The multi-maleimide comprises tris(4-phenymaleimide) amine or polyphenylmethane maleimide.R4=-R-, -R-NH2-R-, -C(O)-, -R-C(O)-R-, -R-C(O)-, -O-, -O-O-, -S-, -S-S-, -S(O)-, -R-S(O)-R-, -SO2-, -(C6H5)-, -R-(C6H5)-R-, -R-(C6H5)-O-, -(C6H5)-(C6H5)-, -R-(C6H5)-(C6H5)-R-, or -R-(C6H5)-(C6H5)-O-;Y'=-R-, -C(O)-, -O-, -O-O-, -S-, -S-S-, -S(O)-, or -SO2-;X1-X8=halo, H, 1-8C alkyl, 1-8C cycloalkyl, or 1-8C silylalkyl;R=1-8C alkyl, phenyl (C6H5), or biphenyl ((C6H5)-(C6H5)).    TECHNOLOGY FOCUS - POLYMERS - Preparation (Claimed): Preparation of the compound (I) involves adding a bismaleimide and a barbituric acid into a Bronsted base solution, and reacting the mixture at 20-100 degrees C to form a hyper-branched polymer. Preferred Process: The method further involves adding a maleimide and/or multi-maleimide into the Bronsted base solution. Preferred Compounds: The hyper-branched polymer (I) further contains maleimide and/or multi-maleimide. In the hyper-branched polymer (I), the bismaleimide and the barbituric acid have a molar ratio of 40:1 to 0.4:1; and the bismaleimide; and the multi-maleimide and/or the maleimide) have a molar ratio of 99:1 to 1:1. EXAMPLE - No suitable example given.