• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.719-725
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• 2001

For a p-compact group G, if G-space X is of finite S-type then we show that the localization $S^{-1}H^*(X_{hG})$is zero. By using this result, we prove the localization theorem for the pair G-space (X, A)

• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.1101-1114
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• 2004

We generalize a result of Dror Farjoun and Zabrodsky on the relationship between fixed point sets and homotopy fixed point sets, which is related to the generalized Sullivan Conjecture. As an application, we discuss extension problems considering actions on homogeneous spaces of p-compact groups.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.299-309
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• 2010

The Weyl group of a compact connected Lie group is a reflection group. If such Lie groups are locally isomorphic, the representations of the Weyl groups are rationally equivalent. They need not however be equivalent as integral representations. Turning to the invariant theory, the rational cohomology of a classifying space is a ring of invariants, which is a polynomial ring. In the modular case, we will ask if rings of invariants are polynomial algebras, and if each of them can be realized as the mod p cohomology of a space, particularly for dihedral groups.

• Journal of Korean Neurosurgical Society
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• v.67 no.4
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• pp.431-441
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• 2024

Objective : Gamma Knife radiosurgery (GKRS) is an effective and noninvasive treatment for high-risk arteriovenous malformations (AVMs). Since differences in GKRS outcomes by nidus type are unknown, this study evaluated GKRS feasibility and safety in patients with brain AVMs. Methods : This single-center retrospective study included patients with AVM who underwent GKRS between 2008 and 2021. Patients were divided into compact- and diffuse-type groups according to nidus characteristics. We excluded patients who performed GKRS and did not follow-up evaluation with magnetic resonance imaging or digital subtraction angiography within 36 months from the study. We used univariate and multivariate analyses to characterize associations of nidus type with obliteration rate and GKRS-related complications. Results : We enrolled 154 patients (mean age, 32.14±17.17 years; mean post-GKRS follow-up, 52.10±33.67 months) of whom 131 (85.1%) had compact- and 23 (14.9%) diffuse-type nidus AVMs. Of all AVMs, 89 (57.8%) were unruptured, and 65 (42.2%) had ruptured. The mean Spetzler-Martin AVM grades were 2.03±0.95 and 3.39±1.23 for the compact- and diffuse-type groups, respectively (p<0.001). During the follow-up period, AVM-related hemorrhages occurred in four individuals (2.6%), three of whom had compact nidi. Substantial radiation-induced changes and cyst formation were observed in 21 (13.6%) and one patient (0.6%), respectively. The AVM complete obliteration rate was 46.1% across both groups. Post-GKRS complication and complete obliteration rates were not significantly different between nidus types. For diffuse-type nidus AVMs, larger AVM size and volume (p<0.001), lower radiation dose (p<0.001), eloquent area location (p=0.015), and higher Spetzler-Martin grade (p<0.001) were observed. Conclusion : GKRS is a safe and feasible treatment for brain AVMs characterized by both diffuse- and compact-type nidi.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.207-218
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• 2020

Some modular representations of reflection groups related to Weyl groups are considered. The rational cohomology of the classifying space of a compact connected Lie group G with a maximal torus T is expressed as the ring of invariants, H*(BG; ℚ) ≅ H*(BT; ℚ)^W(G), which is a polynomial ring. If such Lie groups are locally isomorphic, the rational representations of their Weyl groups are equivalent. However, the integral representations need not be equivalent. Under the mod p reductions, we consider the structure of the rings, particularly for the Weyl group of symplectic groups Sp(n) and for the alternating groups A_n as the subgroup of W(SU(n)). We will ask if such rings of invariants are polynomial rings, and if each of them can be realized as the mod p cohomology of a space. For n = 3, 4, the rings under a conjugate of W(Sp(n)) are shown to be polynomial, and for n = 6, 8, they are non-polynomial. The structures of H*(BT^n-1; 𝔽_p)^A_n will be also discussed for n = 3, 4.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.149-161
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• 2002

We study the torsions in the integral homology of the double loop space of the compact simple Lie groups by determining the higher Bockstein actions on the homology of those spaces through the Bockstein lemma and computing the Bockstein spectral sequence.

• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.171-180
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• 2018

In this paper, the necessary and sufficient conditions are considered for biprojectivity of Banach algebras $E_p(I)$. As an application, we investigate biprojectivity of convolution Banach algebras A(G) and $L^2(G)$ on a compact group G.

• Restorative Dentistry and Endodontics
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• v.26 no.6
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• pp.485-491
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• 2001

The purpose of this study was to compare the mechanical properties of three condensable composite resins and one hybrid composite resin. The compressive strength, diametral tensile strength, Vicker's microhardness were tested for mechanical properties of condensable composite resins (SureFil, Ariston pHc, Synergy compact), and hybrid composite resin (Z 100). The tested materials were divided into four groups: control group Z 100 (3M Co. USA), experimental group I Ariston pHc, (Vivadent, Co., Liechtenstein) experimental group II SureFil (Dentsply, Co., U.S.A.), experimental group III Synergy Compact (Coltene, Co., Swiss). According to the above classification, we made samples of SureFil, Ariston pHc, Synergy Compact, Z 100 with separable cylindrical metal mold. And then, we measured and compared the value of compressive strength, diametral tensile strength and Vicker's microhardness of each sample. (omitted)

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.691-699
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• 1997

The following statement is known as the generalized Hilbert-Smith conjecture : If G is a compact group and acts effectively on a manifold, then G is a Lie group. In this paper we prove that the generalized Hilbert-Smith conjecture is equivalent to the following : A known, but has never been published before.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1193-1200
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• 2013

The center of the Lie group $SU(n)$ is isomorphic to $\mathbb{Z}_n$. If $d$ divides $n$, the quotient $SU(n)/\mathbb{Z}_d$ is also a Lie group. Such groups are locally isomorphic, and their Weyl groups $W(SU(n)/\mathbb{Z}_d)$ are the symmetric group ${\sum}_n$. However, the integral representations of the Weyl groups are not equivalent. Under the mod $p$ reductions, we consider the structure of invariant rings $H^*(BT^{n-1};\mathbb{F}_p)^W$ for $W=W(SU(n)/\mathbb{Z}_d)$. Particularly, we ask if each of them is a polynomial ring. Our results show some polynomial and non-polynomial cases.