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On the uniform perfectness of equivariant diffeomorphism groups for principal g manifolds

Fukui K.

Opuscula Mathematica

2017

Vol. 37, no. 3

381--388

We proved in [K. Abe, K. Fukui, On commutators of equivariant diffeomorphisms, Proc. Japan Acad. 54 (1978), 52–54] that the identity component [formula] of the group of equivariant Cr-diffeomorphisms of a principal G bundle M over a manifold B is perfect for a compact connected Lie group G and [formula] In this paper, we study the uniform perfectness of the group of equivariant Cr-diffeomorphisms for a principal G bundle M over a manifold B by relating it to the uniform perfectness of the group of Cr-diffeomorphisms of B and show that under a certain condition, [formula] is uniformly perfect if B belongs to a certain wide class of manifolds. We characterize the uniform perfectness of the group of equivariant Cr-diffeomorphisms for principal G bundles over closed manifolds of dimension less than or equal to 3, and in particular we prove the uniform perfectness of the group for the 3-dimensional case and r ≠ 4.

Selective recovery of lithium from seawater using a novel MnO2 type adsorbent

Yoshizuka K., Fukui K., Inoue K.

Ars Separatoria Acta

2002

No. 1

79-86

A novel ?-type manganese dioxide (?-MnO2) adsorbent has been developed for selectively recovering Li+ from seawater. This adsorbent can be prepared from spinel-type lithium di manganese tetra-oxide (LiMn2O4) using ion exchange of Li+ by hydrogen ion. In batch adsorption, ?-MnO2 adsorbent can effectively adsorb Li+ at elevated pH (like seawater; pH=8.1) with quite high selectivity for Li+ vs. Na+ (molar ratio of Li+/Na+ exceeding 800). In chromatographic separation, Li+ can be effectively adsorbed on the adsorbent packed into column, while Na+ is only scarcely adsorbed. In elution stage, Li+ can be concentrated more than 75 times compared to its initial concentration in the feed solution of adsorption stage, while little Na+ was eluted. The molar selectivity coefficient of Li+/Na+ to 2300 can be achieved.