• 대한수학회지
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• 제35권2호
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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.

• 대한수학회보
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• 제42권1호
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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.

• 대한수학회논문집
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• 제10권4호
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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.

• 대한수학회지
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• 제50권6호
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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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• 제26권2호
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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.

• 자연과학논문집
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• 제5권1호
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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.

• 대한수학회보
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• 제58권3호
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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.

• 한국인터넷방송통신학회논문지
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• 제24권1호
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• pp.181-187
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• 2024

이미지 공간에서 무작위로 회전된 객체에 대한 분류 성능이 우수한 기법으로는 군 등변 CNN과 steerable 필터를 이용한 CNN 등이 있다. 본 논문에서는 이들의 수학적 구조를 설명하고 구현 방법을 소개한다. 기존의 CNN을 포함한 세 개의 모델에 대하여 동일한 필터 수를 갖도록 구현한 다음, 무작위로 회전된 MNIST를 이용하여 실험하고 이들의 성능을 비교분석한다. 실험 결과에 의하면 steerable CNN은 CNN보다 6.5% 이상의 인식률 향상을 보여준다. 특히, steerable CNN은 학습할 파라미터의 수가 상대적으로 적어서 훈련 데이터셋의 크기를 줄여도 성능 열화가 비교적 크지 않음을 실험 결과로 확인한다.

• ETRI Journal
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• 제15권2호
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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.

• 대한수학회지
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• 제30권1호
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• pp.63-77
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• 1993