• Communications of the Korean Mathematical Society
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• v.12 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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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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• v.30 no.3
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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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• v.30 no.1_2
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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 $\mathbb{Z}_p$.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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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 ${\parallel}{\mu}{\parallel_r}\;=\;sup_{z{\in}B}\;\frac{\mu(E(z,r))}{\nu(E(z,r))}\;<\;\infty$.

• IEMEK Journal of Embedded Systems and Applications
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• v.12 no.4
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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.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.1
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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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• v.21 no.5
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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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• v.21 no.12
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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.

• The KIPS Transactions:PartB
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• v.18B no.2
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• pp.51-56
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• 2011

Algorithms for intrinsic images reduce color differences in RGB images caused by the temperature of black-body radiators. Based on the reference light and detecting single invariant direction, these algorithms are weak in real images which can have multiple invariant directions when the scene illuminant is a colored illuminant. To solve these problems, this paper proposes a method of acquiring an intrinsic image by omnidirectional projection of an ROI and a translation of white patch in the ${\chi}$-chromaticity space. Because it is not easy to analyze an image in the three-dimensional RGB space, the ${\chi}$-chromaticity is also employed without the brightness factor in this paper. After the effect of the colored illuminant is decreased by a translation of white patch, an invariant direction is detected by omnidirectional projection of an ROI in this chromaticity space. In case the RGB image has multiple invariant directions, only one ROI is selected with the bin, which has the highest frequency in 3D histogram. And then the two operations, projection and inverse transformation, make intrinsic image acquired. In the experiments, test images were four datasets presented by Ebner and evaluation methods was the follows: standard deviation of the invariant direction, the constancy measure, the color space measure and the color constancy measure. The experimental results showed that the proposed method had lower standard deviation than the entropy, that its performance was two times higher than the compared algorithm.