• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.709-723
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• 2022

In this note, we revise some vanishing and finiteness results on hypersurfaces with finite index in ℝⁿ⁺¹. When the hypersurface is stable minimal, we show that there is no nontrivial L^2p harmonic 1-form for some p. The our range of p is better than those in [7]. With the same range of p, we also give finiteness results on minimal hypersurfaces with finite index.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.323-330
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• 2008

Some finiteness and non-existence results are proved of 2-dimensional mod 2 Galois representations of quadratic fields unramified outside 2.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.461-466
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• 2016

In general, polygonal products of free groups are not residually finite. Using the residual finiteness of polygonal products of nilpotent groups, we show that certain polygonal products of free groups are residually finite.

• East Asian mathematical journal
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• v.26 no.5
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• pp.649-654
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• 2010

A positive definite Hermitian lattice is said to be 2-universal if it represents all positive definite binary Hermitian lattices. We find some finiteness theorems which ensure 2-universality of Hermitian lattices over several imaginary quadratic number fields.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.109-115
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• 2020

Recently, Lesieutre constructed a 6-dimensional projective variety X over any field of characteristic zero whose automorphism group Aut(X) is discrete but not finitely generated. As an application, he also showed that X is an example of a projective variety with infinitely many non-isomorphic real structures. On the other hand, there are also several finiteness results of real structures of projective varieties. The aim of this short paper is to give a sufficient condition for the finiteness of real structures on a projective manifold in terms of the structure of the automorphism group. To be more precise, in this paper we show that, when X is a projective manifold of any dimension≥ 2, if Aut(X) does not contain a subgroup isomorphic to the non-abelian free group ℤ ∗ ℤ, then there are only finitely many real structures on X, up to ℝ-isomorphisms.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.649-661
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• 2023

Let 𝓜 be a stable Serre subcategory of the category of R-modules. We introduce the concept of 𝓜-minimax R-modules and investigate the local-global principle for generalized local cohomology modules that concerns to the 𝓜-minimaxness. We also provide the 𝓜-finiteness dimension f^𝓜_I (M, N) of M, N relative to I which is an extension the finiteness dimension f_I (N) of a finitely generated R-module N relative to I.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.913-920
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• 2004

We give a characterization for fundamental groups of graphs of groups amalgamating cyclic edge subgroups to be cyclic subgroup separable if each pair of edge subgroups has a non-trivial intersection. We show that fundamental groups of graphs of abelian groups amalgamating cyclic edge subgroups are cyclic subgroup separable, hence residually finite, if each edge subgroup is isolated in its containing vertex group.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.629-634
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• 1998

As most of distributions appearing in applications are finite but with the unknown domain of finiteness, we propose to use the robust minimax approach for the determination of the boundaries of this domain. The obtained least favorable distribution minimizing Fisher information over the class of the approximately Gaussian finite distributions gives the reasonable sizes of the domain of finiteness and the thresholds of truncation.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1061-1078
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• 2020

We prove some results about the finiteness of co-associated primes of generalized local homology modules inspired by a conjecture of Grothendieck and a question of Huneke. We also show some equivalent properties of minimax local homology modules. By duality, we get some properties of Herzog's generalized local cohomology modules.

• The Mathematical Education
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• v.23 no.2
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• pp.41-43
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• 1985