• 대한수학회논문집
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• 제12권3호
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• pp.779-788
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• 1997

In this work, using the exact separatrix map which provides an efficient way to describe dynamics near the separatrix, we study the stochastic layer near the separatrix of a one-degree-of-freedom Hamilitonian system with time periodic perturbation. Applying the twist map theory to the exact separatrix map, T. Ahn, G. I. Kim and S. Kim proved the existence of the uniformly hyperbolic invariant set(UHIS) near separatrix. Using the theorems of Bowen and Franks, we prove this UHIS has measure zero.

• 대한수학회보
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• 제33권4호
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• pp.545-551
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• 1996

It is well known in the theory of distributions and proved in [GS, S] that $$ (i) (Bochner-Schwartz) Every positive definite (tempered) distribution is the Fourier transform of a positive tempered measure \mu. $$ $$ (ii) (Schwartz kernel theorem) Let B(\varphi, \psi) be a bilinear distribution. Then for some u \in D'(R^n \times R^n) B(\varphi, \psi) = u(\varphi(x)\bar{\psi}(y)) for every \varphi, \psi \in C_c^\infty. $$ $$ (iii) A translation invariant positive definite bilinear distribution B(\varphi, \psi) is of the form B(\varphi, \psi) = \smallint \varphi(x)\psi(x) d\mu(x) for every \varphi, \psi \in C_c^\infty (R^n), where \mu is a positive tempered measure.

• Korean Journal of Mathematics
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• 제30권3호
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• pp.459-465
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• 2022

We exhibit various properties of the weighted Berezin operator T_α and its iteration T^k_α on L^p(𝜏), where α > -1 and 𝜏 is the invariant measure on the complex unit ball B_n. Iterations of T_α on L¹_R(𝜏) the space of radial integrable functions have performed important roles in proving 𝓜-harmonicity of bounded functions with invariant mean value property. We show differences between the case of 1 < p < ∞ and p = 1, ∞ under the infinite iteration of T_α or the infinite summation of iterations, most of which are extensions or related assertions to the propositions of the previous results.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.211-217
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• 2012

In this paper, we give the weighted Lebesgue-Radon-Nikodym theorem with respect to $p$-adic invariant integral on $\mathbb{Z}_p$.

• 충청수학회지
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• 제22권1호
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• pp.89-99
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• 2009

Let $\mu$ be a finite positive Borel measure on the unit ball $B{\subset}\mathbb{C}^n$ and $\nu$ be the Euclidean volume measure such that ${\nu}(B)=1$. For the unit sphere $S=\{z:{\mid}z{\mid}=1\}$, $\sigma$ is the rotation-invariant measure on S such that ${\sigma}(S)=1$. Let $\mathcal{P}[f]$ be the invariant Poisson integral of f. We will show that there is a constant M > 0 such that $\int_B{\mid}{\mathcal{P}}[f](z){\mid}^{p}d{\mu}(z){\leq}M\;{\int}_B{\mid}{\mathcal{P}}[f](z)^pd{\nu}(z)$ for all $f{\in}L^p({\sigma})$ if and only if ${\parallel}{\mu}{\parallel_r}\;=\;sup_{z{\in}B}\;\frac{\mu(E(z,r))}{\nu(E(z,r))}\;<\;\infty$.

• 대한임베디드공학회논문지
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• 제12권4호
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• pp.231-238
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• 2017

Detecting small infrared targets from the low-SCR images at a long distance is very hard. The previous Local Contrast Method (LCM) algorithm based on the human visual system shows a superior performance of detecting small targets by a background suppression technique through local contrast measure. However, its slow processing speed due to the heavy multi-scale processing overhead is not suitable to a variety of real-time applications. This paper presents a lightweight real-time small target detection algorithm, called by the Improved Selective Local Contrast Method (ISLCM), to reduce the scale-invariant computational overhead. The proposed ISLCM applies the improved local contrast measure to the predicted selective region so that it may have a comparable detection performance as the previous LCM while guaranteeing low scale-invariant computational load by exploiting both adaptive scale estimation and small target feature feasibility. Experimental results show that the proposed algorithm can reduce its computational overhead considerably while maintaining its detection performance compared with the previous LCM.

• 대한전기학회논문지:전력기술부문A
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• 제48권1호
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• pp.76-81
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• 1999

The degree of relative similarity between 2D patterns is obtained using Open-Ball Scheme. Open-Ball Scheme employs a method of transforming the geometrical information on 3D objects or 2D patterns into the features to measure the relative similarity for object(patten) recognition, with invariance on scale, rotation, and translation. The feature of an object is used to obtain the relative similarity and mapped into [0, 1] the interval of real line. For decades, Moment-Invariant Method has been used as one of the excellent methods for pattern classification and object recognition. Open-Ball Scheme uses the geometrical structure of patterns while Moment Invariant Method uses the statistical characteristics. Open-Ball Scheme is compared to Moment Invariant Method with respect to the way that it interprets two-dimensional patten classification, especially the paradigms are compared by the degree of closeness to human's intuitive understanding. Finally the effectiveness of the proposed Open-Ball Scheme is illustrated through simulations.

• International Journal of Computer Science & Network Security
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• 제21권5호
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• pp.211-216
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• 2021

This study intended to test the structure of the latent factor of a subjective happiness scale and the stability of invariance across groups of students' classifications (gender and students' status). In the large, non-clinical sample (619), students completed the subjective happiness scale. The (CFA) confirmatory factor analysis was used to investigate the factor-structure of the measure, and multiple-group confirmatory factor analysis (MGCFA) model was used to test the stability of invariance across groups of students classifications. The findings of the CFA indicated support for the original one-factor model. Additional analyses of the MGCFA method support the measurement (configural, metric and strong) invariant and practical invariant components of this model. There was an invariant across gender. There was partially invariant across groups of students' statuses. The scale exists in both groups to assess the same concepts of (single and married), excluding Items 3 and 4. Given that this study is the first investigation for the structure of the subjective happiness scale.

• International Journal of Computer Science & Network Security
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• 제21권12호
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• pp.149-156
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• 2021

This study intended to test the structure of the latent factor of an effectiveness scale and the stability of invariance across groups of students' classifications (gender and levels of education). In the large, non-clinical sample (850), students completed the effectiveness scale. The (CFA) confirmatory factor analysis was used to investigate the factor-structure of the measure, and multiple-group confirmatory factor analysis (MGCFA) model was used to test the stability of invariance across groups of students' classifications. The findings of the CFA indicated support for the original four-factor model. Additional analyses of the MGCFA method support the measurement (configural, metric and strong) invariant and practical invariant components of this model. There was an invariant across gender. There was partially invariant across groups of levels of education. The scale exists in groups of levels of education assess the same concepts of, excluding Items 15 and 10. Given that this study is the first investigation for the structure of the effectiveness scale.

• 정보처리학회논문지B
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• 제18B권2호
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• pp.51-56
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• 2011

흑체의 온도 변화에 대한 영상의 색차를 줄이는 본질 영상은 단일 불변 방향을 검출하고 백색 장면 조명체를 기반으로 하기 때문에 실영상에 존재하는 다수의 불변 방향과 유색 장면 조명체에 취약하다. 이러한 문제를 해결하기 위해 본 논문에서는 ${\chi}$-색도 공간에서 ROI의 전방향프로젝션과 백색패치의 평행이동을 통해 불변 방향을 검출하는 본질 영상 획득 기법을 제안한다. 3차원 RGB 공간 분석의 어려움으로 인하여, 본 논문 또한 밝기가 고려되지 않은 ${\chi}$-색도 공간을 사용한다. 이 공간에서 유색 조명체의 효과는 백색패치의 평행이동을 통해 감소시키고, 색차에 따라 가상의 선분으로 나타나는 불변 방향은 ROI의 전방향 프로젝션을 통해 검출한다. 다수의 불변 방향을 고려하여 ROI 선택은 3D 히스토그램에서 빈도수에 의해 결정한다. 검출 후, 본질 영상은 불변 방향의 직교 방향으로의 프로젝션과 RGB영상으로의 역변환 과정을 통해 획득된다. 실험에서 Ebner가 제안한 데이터집합을 실험 영상으로 이용하였고, 불변 방향의 표준편차와 색항등성 측도를 평가 측도로 사용하였다. 제안한 기법의 실험 결과는 엔트로피 기법보다 불변 방향의 표준 편차가 낮았으며, 기존의 기법에 비해 색항등성이 2배 이상 높았다.