• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.371-386
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• 1998

Let G be a compact Lie group and M a semialgebraic G space in some orthogonal representation space of G. We prove that if G is finite then M has an equivariant semialgebraic triangulation. Moreover this triangulation is unique. When G is not finite we show that M has a semialgebraic G CW complex structure, and this structure is unique. As a consequence compact semialgebraic G space has an equivariant simple homotopy type.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.157-164
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• 2005

Let $RRat_k$ ($CP^n$) denote the space of basepoint-preserving conjugation-equivariant holomorphic maps of degree k from $S^2$ to $CP^n$. A map f ; $S^2 {\to}CP^n$ is said to be full if its image does not lie in any proper projective subspace of $CP^n$. Let $RF_k(CP^n)$ denote the subspace of $RRat_k(CP^n)$ consisting offull maps. In this paper we determine $H{\ast}(RF_k(CP^2); Z/p)$ for all primes p.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.949-961
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• 1995

Let f be a smooth G map from a nonsingular real algebraic G variety to an equivariant Grassmann variety. We use some G vector bundle theory to find a necessary and sufficient condition to approximate f by an entire rational G map. As an application we algebraically approximate a smooth G map between G spheres when G is an abelian group.

• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1369-1400
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• 2013

The concept of "orbifold embedding" is introduced. This is more general than sub-orbifolds. Some properties of orbifold embeddings are studied, and in the case of translation groupoids, orbifold embedding is shown to be equivalent to a strong equivariant immersion.

• Journal of the Korean Statistical Society
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• v.26 no.2
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• pp.245-259
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• 1997

The paper shows that certain hierachical Bayes (HB) predictors for small domain data in repeated surveys "universally" or "stochastically" dominate all linear unbiased predictors. Also, the HB predictors are "best" within the class of all equivariant predictors under a certain group of transformations.tain group of transformations.

• The Journal of Natural Sciences
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• v.5 no.1
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• pp.1-3
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• 1992

G가 compact Lie 군이고 $\pi$ : $E to S^1$이 $S^1$ 상의 G-line bundle 일때, 군 작용이 없다면, 부드러운 trivial G-line bundle $E to S^1$ 은 S(V) $\times$ $\delta to S(V)$ 와 동치이고 부드러운 nontrivial G-line bundle $E to S^1$ 은 S(V) $\times$$z_2$ $\delta to S(V)$/$Z_2$=P(V)와 동치 이다.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.573-591
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• 2021

We study the equivariant Gromov-Witten theory of ℙ^r-1 for all r ≥ 2. We prove a polynomiality property in r of the Gromov-Witten classes of ℙ^r-1. Using this polynomiality property, we define a set of polynomial valued classes in $H^*({\bar{M}}_{g,n})$ which generalize the limit of Witten's s-spin classes studied by Pandharipande, Pixton and Zvonkine.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.24 no.1
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• pp.181-187
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• 2024

There are two kinds of well-known CNN methods, the group equivariant CNN and the CNN using steerable filters, which have excellent classification performances for randomly rotated objects in image space. This paper describes their mathematical structures and introduces implementation methods. We implement them, including the existing CNN, which have the same number of filters, then compare and analyze their performances by simulating them with the randomly rotated MNIST. According to the experimental results, the steerable CNN, which shows a classification improvement over the others, has a relatively small number of parameters to learn, so performance degradation is relatively small even when the size of the training dataset is reduced.

• ETRI Journal
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• v.15 no.2
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• pp.27-34
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• 1993

Pitman-Intransitive triples of estimators are constructed, based on prior work on equivariant estimators and prior work on shrinkage.

• Journal of the Korean Mathematical Society
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• v.30 no.1
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• pp.63-77
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• 1993