• 대한수학회논문집
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• 제32권3호
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• pp.779-787
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• 2017

Let m be the Lebesgue measure on ${\mathbb{C}}$ normalized to $m(D)=1,{\mu}$ be an invariant measure on D defined by $d_{\mu}(z)=(1-{\mid}z{\mid}^2)^{-2}dm(z)$. For $f{\in}L^1(D^n,m{\times}{\cdots}{\times}m)$, Bf the Berezin transform of f is defined by, $$(Bf)(z_1,{\ldots},z_n)={\displaystyle\smashmargin{2}{\int\nolimits_D}{\cdots}{\int\nolimits_D}}f({\varphi}_{z_1}(x_1),{\ldots},{\varphi}_{z_n}(x_n))dm(x_1){\cdots}dm(x_n)$$. We prove that if $f{\in}L^1(D^2,{\mu}{\times}{\mu})$ is radial and satisfies ${\int}{\int_{D^2}}fd{\mu}{\times}d{\mu}=0$, then for every bounded radial function ${\ell}$ on $D^2$ we have $$\lim_{n{\rightarrow}{\infty}}{\displaystyle\smashmargin{2}{\int\int\nolimits_{D^2}}}(B^nf)(z,w){\ell}(z,w)d{\mu}(z)d{\mu}(w)=0$$. Then, using the above property we prove n-harmonicity of bounded function which is invariant under the Berezin transform. And we show the same results for the weighted the Berezin transform in the polydisc.

• 정보과학회 논문지
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• 제42권6호
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• pp.699-706
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• 2015

최근 이미지 컨텐츠에 쉽게 접근할 수 있는 인터넷 환경과 이미지 편집 기술들의 보급으로 근-복사 이미지가 폭발적으로 증가하면서 관련 연구가 활발하게 이루어지고 있다. 그러나 근-복사 이미지 검출 방법으로 주로 쓰이는 BoF(Bag-of-Feature)는 고차원의 지역 특징을 저차원으로 근사화하는 양자화과정에서 서로 다른 특징들을 같다고 하거나 같은 특징을 다르다고 하는 한계가 발생할 수 있으므로 이를 극복하기 위한 후-검증 방법이 필요하다. 본 논문에서는 BoF의 후-검증 방법으로 SIFT(Scale Invariant Feature Transform) 기술자를 128bit의 이진 코드로 변환한 후 BoF 방법에 의하여 추출된 짧은 후보 리스트에 대하여 변환한 코드들간의 거리를 비교하는 방법을 제안하고 성능을 분석하였다. 1500장의 원본이미지들에 대한 실험을 통하여 기존의 BoF 방법과 비교하여 근-복사 이미지 검출 정확도가 4% 향상됨을 보였다.

• 한국콘텐츠학회논문지
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• 제4권4호
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• pp.205-213
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• 2004

본 논문에서는 크기 불변 패턴인식을 위하여 광 웨이브렛 PO-fSDF(WPOfSDF) 필터 및 개선된 필터 합성알고리듬을 제안하였다. 제안한 필터는 크기가 변화된 영상을 학습영상으로 사용하여 PO-fSDF로 합성한 후 입력을 위한 웨이브렛 함수를 필터에 곱하여 합성한다. 컴퓨터 모의실험을 통하여 제안된 필터가 크기불변 인식을 할 수 있고, 잡음을 가지는 입력영상의 경우 SNR이 개선되며 필터합성시 반복횟수도 줄어듦을 확인할 수 있었다. 그리고 광실험시 발생하는 광축정렬 문제는 전체 시스템을 FSJTC로 구성함으로써 해결하였다.

• East Asian mathematical journal
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• 제14권2호
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• pp.237-247
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• 1998

In this paper, we prove a translation theorem for the analytic Feynman integral for functions in $\mathcal{F}_{A_1,A_2}$(B) and show how this integral can be modified so as to be translation invariant.

• 대한수학회보
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• 제50권4호
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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.

• 대한수학회논문집
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• 제21권1호
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• pp.177-183
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• 2006

The purpose of this paper is to introduce an L-metrical non-linear connection $N_j^{*i}$ and investigate a conformal change in the Finsler space with $({\alpha},\;{\beta})-metric$. The (v)h-torsion and (v)hvtorsion in the Finsler space with L-metrical connection $F{\Gamma}^*$ are obtained. The conformal invariant connection and conformal invariant curvature are found in the above Finsler space.

• 대한수학회지
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• 제56권3호
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• pp.825-855
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• 2019

We establish the existence of $C^1$ stable invariant manifolds for differential equations $u^{\prime}=A(t)u+f(t,u,{\lambda})$ obtained from sufficiently small $C^1$ perturbations of a nonuniform exponential dichotomy. Since any linear equation with nonzero Lyapunov exponents has a nonuniform exponential dichotomy, this is a very general assumption. We also establish the $C^1$ dependence of the stable manifolds on the parameter ${\lambda}$. We emphasize that our results are optimal, in the sense that the invariant manifolds are as regular as the vector field. We use the fiber contraction principle to establish the smoothness of the invariant manifolds. In addition, we can also consider linear perturbations, and thus our results can be readily applied to the robustness problem of nonuniform exponential dichotomies.

• 대한수학회지
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• 제59권1호
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• pp.105-127
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• 2022

It is known that the maximal invariant set of a continuous iterative dynamical system in a compact Hausdorff space is equal to the intersection of its forward image sets, which we will call the first minimal image set. In this article, we investigate the corresponding relation for a class of discontinuous self maps that are on the verge of continuity, or topologically almost continuous endomorphisms. We prove that the iterative dynamics of a topologically almost continuous endomorphisms yields a chain of minimal image sets that attains a unique transfinite length, which we call the maximal invariance order, as it stabilizes itself at the maximal invariant set. We prove the converse, too. Given ordinal number ξ, there exists a topologically almost continuous endomorphism f on a compact Hausdorff space X with the maximal invariance order ξ. We also discuss some further results regarding the maximal invariance order as more layers of topological restrictions are added.

• 충청수학회지
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• 제26권4호
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• pp.821-829
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• 2013

Let f be a diffeomorphism of a closed $C^{\infty}$ manifold M, and let ${\Lambda}{\subset}M$ be a closed f-invariant set. We show that if $f{\mid}_{\Lambda}$ is robustly chain transitive with shadowing, then ${\Lambda}$ is the hyperbolic homoclinic class.

• 대한수학회논문집
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• 제19권1호
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• pp.159-167
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• 2004

In [1], a relative root Nielsen number $N_{rel}(f;\;c)$ is introduced which is a homotopy invariant lower bound for the number of roots at $c\;{\in}\;Y$ for a map of pairs of spaces $f\;:\;(X,\;A)\;{\rightarrow}\;(Y,\;B)$. In this paper, we obtain a minimum theorem for $N_{rel}(f;\;c)$ under some new assumptions on the spaces and maps which are different from those in [1].