ETHYLENE POLYMERIZATION AND COPOLYMERIZATION WITH POLAR MONOMERS BY A NEUTRAL NICKEL CATALYST COMBINED WITH CO-CATALYST OF Ni（COD）2 OR AL（i-Bu）3

A neutral nickel (Ⅱ) catalyst D, { [O-(3-cyclohexyl)(5-Cl)C6H2-ortho-C(H)=N-2,6-C6H3(i-Pr)2]Ni(Ph3P)(Ph)} has been synthesized and characterized by 1H-NMR, FTIR and elemental analysis. The results indicate that Al(i-Bu)3 is an effective cocatalyst for the neutral nickel catalyst. With bis(1,5-cyclooctadiene) nickel(0) [Ni(COD)2] or Al(i-Bu)3 as a cocatalyst, the neutral nickel catalyst D is active for ethylene polymerisation and copolymerisation with polar monomers (tertbutyl 10-undecenoate(BU), methyl 10-undecenoate (MU), allyl alcohol (AA) and 4-penten-1-ol (PO)) under mild conditions.The resulting polymers were characterized by 1H-NMR, FTIR, DSC, and GPC. From the comparative studies, Ni(COD)2 is more active than Al(i-Bu)3 for ethylene homopolymerization, while Al(i-Bu)3 is more effective than Ni(COD)2 for ethylene copolymerisation with polar monomers. The polymerization parameters which affect both the catalytic activity and properties of the resulting polyethylene were investigated in detail. Under the conditions of 20 μmol catalyst D and Ni(COD)2/D = 3(molar ratio) in 30 mL toluene solution at 45℃, 12 × 105 Pa ethylene for 20 min, the polymerization activity reaches as High as7.29×105gPE.(mol.Ni·h)-1and Mηis 7.16×104g.mol-1.For ethylene copolymerization with polar monomers,the effect of comonomer concentrations was examined. As high as 0.97 mol% of MU, 1.06 mol% of BU, 1.04 mol% of AA and 1.37 mol% of PO were incorporated into the polymer, respectively, catalyzed by D/Al(i-Bu)3 system.     

ON THE SEPARATION PROPERTY OF SYMMETRIC ORDINARY SECOND-ORDER DIFFERENTIAL EXPRESSIONS

A 1-variable calculus type argument is used to show that, for a function f : R ² → R, if for all (a, b) ? R ² we have that f o c is smooth for every smooth curve c : R → R ² nonsingular except at 0 and with c(0) = (a, b), then f is smooth. This strengthens Boman's theorem. In fact, we use an even more special collection of smooth curves to prove Boman's theorem. It is shown using a related special collection of smooth curves how the upper half cone can be viewed largely as a model for polar coordinates. Our proof here shows how the use of Frölicher spaces can reduce questions in several dimensions to those of one real variable.