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Classification of self-dual torsion-free LCA groups

100%

Wu S. L.

Fundamenta Mathematicae

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1991-1992

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tom 140

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nr 3

255-278

EN

In this paper we seek to describe the structure of self-dual torsion-free LCA groups. We first present a proof of the structure theorem of self-dual torsion-free metric LCA groups. Then we generalize the structure theorem to a larger class of self-dual torsion-free LCA groups. We also give a characterization of torsion-free divisible LCA groups. Consequently, a complete classification of self-dual divisible LCA groups is obtained; and any self-dual torsion-free LCA group can be regarded as an open subgroup of a well-understood torsion-free divisible LCA group.

2

The Bohr compactification, modulo a metrizable subgroup

51%

Comfort W. W., Trigos-Arrieta F. J., Wu S. L.

Fundamenta Mathematicae

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1993

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tom 143

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nr 2

119-136

EN

The authors prove the following result, which generalizes a well-known theorem of I. Glicksberg [G]: If G is a locally compact Abelian group with Bohr compactification bG, and if N is a closed metrizable subgroup of bG, then every A ⊆ G satisfies: A·(N ∩ G) is compact in G if and only if {aN:a ∈ A} is compact in bG/N. Examples are given to show: (a) the asserted equivalence can fail in the absence of the metrizability hypothesis, even when N ∩ G = {1}; (b) the asserted equivalence can hold for suitable G and N with N closed in bG but not metrizable; (c) an Abelian group may admit two topological group topologies U and T, with U totally bounded, T locally compact,U ⊆ T, with U and T sharing the same compact sets, and such that nevertheless U is not the topology inherited from the Bohr compactification of ⟨ G, T⟩. There are applications to topological groups of the form kG for G a totally bounded Abelian group.

3

Improved fuzzy feedback linearization and Sinswat-transformation control of inverted pendulum

39%

Chien T. L., Chen C. C., Chen Y. C., Wu S. L.

Control and Cybernetics

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2010

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tom 39

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nr 4

1069-1093

Ograniczanie wyników

2 Fundamenta Mathematicae

1 Control and Cybernetics

3 Wu S. L.

1 Chen C. C.

1 Chen Y. C.

1 Chien T. L.

1 Comfort W. W.

1 Trigos-Arrieta F. J.

1 2010

1 1993

1 1992

Classification of self-dual torsion-free LCA groups

The Bohr compactification, modulo a metrizable subgroup

Improved fuzzy feedback linearization and Sinswat-transformation control of inverted pendulum