When does the subadditivity theorem for multiplier ideals hold?

Demailly, Ein and Lazarsfeld proved the subadditivity theorem for multiplier ideals on nonsingular varieties, which states the multiplier ideal of the product of ideals is contained in the product of the individual multiplier ideals. We prove that, in the two-dimensional case, the subadditivity theorem holds on log terminal singularities. However, in the higher dimensional case, we have several counterexamples. We consider the subadditivity theorem for monomial ideals on toric rings and construct a counterexample on a three-dimensional toric ring.

     

Polymerization of 1,3‐dienes with functional groups. III. Free‐radical polymerization of N,N‐diethyl‐2‐methylene‐3‐butenamide

Free‐radical homo‐ and copolymerization behavior of N,N‐diethyl‐2‐methylene‐3‐butenamide (DEA) was investigated. When the monomer was heated in bulk at 60 °C for 25 h without initiator, rubbery, solid gel was formed by the thermal polymerization. No such reaction was observed when the polymerization was carried out in 2 mol/L of benzene solution with with 1 mol % of azobisisobutyronitrile (AIBN) as an initiator. The polymerization rate (R_p) equation was R_p ∝ [DEA]^1.1[AIBN]^0.51, and the overall activation energy of polymerization was calculated 84.1 kJ/mol. The microstructure of the resulting polymer was exclusively a 1,4‐structure where both 1,4‐E and 1,4‐Z structures were included. From the product analysis of the telomerization with tert‐butylmercaptan as a telogen, the modes of monomer addition were estimated to be both 1,4‐ and 4,1‐addition. The copolymerizations of this monomer with styrene and/or chloroprene as comonomers were also carried out in benzene solution at 60 °C. In the copolymerization with styrene, the monomer reactivity ratios obtained were r₁ = 5.83 and r₂ = 0.05, and the Q and e values were Q = 8.4 and e = 0.33, respectively. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 999–1007, 2004     

Magnetism in electron-doped copper oxides

We report muon spin relaxation/rotation measurements on sintered powder samples of Nd_2−x Ce _x CuO_4−y and a large single crystal of Nd₂CuO_4−y . We find an electronic phase diagram which is quite similar to that of hole-doped superconductors such as La_2−x Sr _x CuO_4−y , although the doping of electrons into the system is less efficient in destroying the static moments on the copper spins. Static magnetic order in Nd₂CuO_4−y appears below about 250 K, and two spin reorientations are seen atT=75 K andT=35 K. Measurements of the magnetic field penetration depth have been unsuccessful due to the rare-earth paramagnetism of these materials.     

Application of novel SIMS technique for imaging the active sites of oxygen reduction at the SOFC cathode/electrolyte interfaces

The oxygen reduction active sites were visualized around the O₂/SOFC cathode/electrolyte triple phase boundaries (TPB) by the¹⁶O/¹⁸O exchange techniques and secondary ion mass spectrometry (SIMS) analysis. The higher¹⁸O concentration is observed on the cathode top surfaces (La_0.9Sr_0.1MnO₃-mesh, Au-mesh, and Ag-porous), which suggested the promotion of oxygen adsorption and oxygen surface exchange at the cathode. The oxygen diffusion through the bulk of cathode occurred at the La_0.9Sr_0.1MnO₃-mesh and the Ag-porous cathodes, not at the Au-mesh cathode. On the YSZ surfaces after removing the cathode, the active sites for oxygen incorporation were analyzed by SIMS. The active sites for oxygen incorporation were at the La_0.9Sr_0.1MnO₃/YSZ interface as well as the TPB. On the other hand, the active sites for oxygen incorporation are limited to the TPB in the case of the Au-mesh removed YSZ surface. From the SIMS analysis, the expansion of the active sites for oxygen incorporation is less than a few μm from the TPB lines. Paper presented at the 8th EuroConference on Ionics, Carvoeiro, Algarve, Portugal, Sept. 16–22, 2001.