• The Pure and Applied Mathematics
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• v.8 no.1
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• pp.71-78
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• 2001

In 1984, Johnson[A bounded convergence theorem for the Feynman in-tegral, J, Math. Phys, 25(1984), 1323-1326] proved a bounded convergence theorem for hte Feynman integral. This is the first stability theorem of the Feynman integral as an $L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$ theory. Johnson and Lapidus [Generalized Dyson series, generalized Feynman digrams, the Feynman integral and Feynmans operational calculus. Mem, Amer, Math, Soc. 62(1986), no 351] studied stability theorems for the Feynman integral as an $L(L_2 (\mathbb{R}^N), L_2(\mathbb{R}^{N}))$ theory for the functional with arbitrary Borel measure. These papers treat functionals which involve only a single integral. In this paper, we obtain the stability theorems for the Feynman integral as an $L(L_1 (\mathbb{R}^N), L_{\infty}(\mathbb{R}^{N}))$theory for the functionals which involve double integral with some Borel measures.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.609-631
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• 2021

Let C[0, T] denote a generalized analogue of Wiener space, the space of real-valued continuous functions on the interval [0, T]. Define $Z_{\vec{e},n}$ : C[0, T] → ℝⁿ⁺¹ by $$Z_{\vec{e},n}(x)=\(x(0),\;{\int}_0^T\;e_1(t)dx(t),{\cdots},\;{\int}_0^T\;e_n(t)dx(t)\)$$, where e₁,…, e_n are of bounded variations on [0, T]. In this paper we derive a simple evaluation formula for Radon-Nikodym derivatives similar to the conditional expectations of functions on C[0, T] with the conditioning function $Z_{\vec{e},n}$ which has an initial weight and a kind of drift. As applications of the formula, we evaluate the Radon-Nikodym derivatives of various functions on C[0, T] which are of interested in Feynman integration theory and quantum mechanics. This work generalizes and simplifies the existing results, that is, the simple formulas with the conditioning functions related to the partitions of time interval [0, T].

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1531-1548
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• 2016

Let C[0, t] denote the space of real-valued continuous functions on [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}\mathbb{R}^n$ by $Z_n(x)=(\int_{0}^{t_1}h(s)dx(s),{\ldots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $ t_n=t$ is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. Using a simple formula for a conditional expectation on C[0, t] with $Z_n$, we evaluate a generalized analytic conditional Wiener integral of the function $G_r(x)=F(x){\Psi}(\int_{0}^{t}v_1(s)dx(s),{\ldots},\int_{0}^{t}v_r(s)dx(s))$ for F in a Banach algebra and for ${\Psi}=f+{\phi}$ which need not be bounded or continuous, where $f{\in}L_p(\mathbb{R}^r)(1{\leq}p{\leq}{\infty})$, {$v_1,{\ldots},v_r$} is an orthonormal subset of $L_2[0,t]$ and ${\phi}$ is the Fourier transform of a measure of bounded variation over $\mathbb{R}^r$. Finally we establish various change of scale transformations for the generalized analytic conditional Wiener integrals of $G_r$ with the conditioning function $Z_n$.

• Journal of the Korean Home Economics Association
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• v.17 no.3
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• pp.1-11
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• 1979

The purposes of this study were ; (1) to investigate attitudes toward Korean clothing in relation to 3 aspects of clothing behavior , and in relation to attitudes toward women's role, age and education, and (2) to ascertain the extent to which Korean clothing was used and valued. Clothing measures consisted of statements dealing with positive and negative attitudes toward psychological and practical aspects of Korean clothing, frequency of use of Korean clothing, and modesty and confirmity -individuality measure. The measure of attitudes toward women's role consisted of items selected form the Inventory of Feminie Values and the Sex Role Ideology Scale. Product-moment correlation was used to analyze the data which consisted of the responses of 700 adult Korean women to questionnaires administered by the researcher. The results obtained are as follows : 1) Positive attitudes toward Korean clothing for both psychological and practical aspects were, (1) related negatively to nontraditional attitudes toward women's role and education, and (2) related positively to age, frequency of wearing Korean clothing and modesty in clothing. 2) Negative attitudes toward Korean clothing for practical aspect was related negatively to age and education , whereas, the psychological aspect was negatively related to attitudes toward women's role. 3) Conformity-individuality in clothing was related positively to attitudes toward women's role and education. 4) Modesty in clothing was related negatively to attitudes toward women's role and education, conformity individuality, and was related positively to age. 5) In 1945 most of the subjects over 51 -year-old wore Korean clothing always or most of time, whereas, about 1/3 of them wore the same in 1976 , Only 4% of the total participants regardless of their ages wore Korean clothing for everyday life in 1976. 6) In general , highly positive attitudes toward Korean clothing were found on psychological aspect, whereas, highly negative attitudes toward Korean clothing were found on practical aspect.

• The Korean Journal of Applied Statistics
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• v.23 no.1
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• pp.151-165
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• 2010

Images are often corrupted by impulse noise due to a noise sensor or channel transmission errors. The filter based on SVM(Support Vector Machine) and the improved adaptive median filtering is proposed to preserve image details while suppressing impulse noise for image restoration. Our approach uses an SVM impulse detector to judge whether the input pixel is noise. If a pixel is detected as a noisy pixel, the improved adaptive median filter is used to replace it. To demonstrate the performance of the proposed filter, extensive simulation experiments have been conducted under both salt-and-pepper and random-valued impulse noise models to compare our method with many other well known filters in the qualitative measure and quantitative measures such as PSNR and MAE. Experimental results indicate that the proposed filter performs significantly better than many other existing filters.

• Journal of the Korean Association of Geographic Information Studies
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• v.13 no.3
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• pp.64-73
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• 2010

This study aims to analyse the spatial characteristics and to draw the declining areas from the whole area of Chung-Cheong Province. For this purpose, the temporal and spatial conditions by the urban decline diagnosis indexes are utilized. Additionally, the spatial autocorrelation method was applied for extraction of those areas. The spatial autocorrelation method is one of the methods on exploring spatial characteristics and considering the spatial factors. We also adopted the concepts of economics and then discovered the characteristics of deprivation areas. In applying this method, the positively valued areas were classified as the complementary areas, and the negatively valued areas as the substitutional areas. The findings show the declining areas and the growing areas caused by the growth of periphery. This study supports the regeneration plan of Chung-Cheong Province in extracting depressed or activated areas and explaining the characteristics of those areas.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.43 no.3
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• pp.191-203
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• 2020

This study aims to present the differentiating factors of B2B salesperson competency through comparing the suppliers and buyers in Korean steel industry in their perception on the importance and priority of B2B salesperson competency. Based on previous studies, analysis on B2B salesperson competency has been analyzed using the B2B salesperson performance competency measure factors and appropriately reorganizing them for better application to the steel industry. The required performance competencies of B2B salesperson can be categorized into 3 different types, namely social exchange competency, advisory sales competency, and skill & knowledge competency. AHP analysis was performed for analyzing the relative importance of B2B salesperson competency based on the factors of previous studies, in which categorization of the aforementioned types had been done. As the result, first, it has been confirmed that there is a difference in 1st layer main factors between the supplier group and buyer group. The supplier group valued the advisory sales competency, while the buyer group valued skill & knowledge competency. Second, it has been proved that there is same result of relative importance in 2nd detailed factors between the supplier group and buyer group. Both group confirmed that customer member, identify customer needs and communication skill are very important factors. Third, as the result of analysis on the gap between B2B salesperson competency of the suppliers and buyers, the gap in the product knowledge and sales team member need improvement for buyer's satisfaction according to overall results of relative importance and priority. The steel supplier was able to develop B2B salesperson competency according to the buyers' needs based on the result of this study, and furthermore it is expected that this study will be able to contribute to increase in buyer competitiveness through differentiation in B2B salesperson competency.

• Journal of Environmental Science International
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• v.21 no.8
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• pp.965-975
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• 2012

Loading of NPS pollutant was valued through simulation by using BASINS/HSPF model which can simulate runoff volume in rainfall by time. For the verification of the model, it was analyzed the scatter diagram of the simulation value and measure value of water quality and runoff volume in Dongcheon estuary. Using the built model, a study on the time-variant characteristics of runoff and water quality was simulated by being classified into four cases. The result showed the simulation value was nearly same as that of the measured runoff. In the result of fit level test for measured value and simulated value, correlation of runoff volume was computed high by average 0.86 and in the water quality items, fit level of simulation and measurements was high by BOD 0.82, T-N 0.85 and T-P 0.79.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.655-672
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• 2011

Let $C^r$[0,t] be the function space of the vector-valued continuous paths x : [0,t] ${\rightarrow}$ $R^r$ and define $X_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{(n+1)r}$ and $Y_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{nr}$ by $X_t(x)$ = (x($t_0$), x($t_1$), ..., x($t_{n-1}$), x($t_n$)) and $Y_t$(x) = (x($t_0$), x($t_1$), ..., x($t_{n-1}$)), respectively, where 0 = $t_0$ < $t_1$ < ... < $t_n$ = t. In the present paper, with the conditioning functions $X_t$ and $Y_t$, we introduce two simple formulas for the conditional expectations over $C^r$[0,t], an analogue of the r-dimensional Wiener space. We establish evaluation formulas for the analogues of the analytic Wiener and Feynman integrals for the function $G(x)=\exp{{\int}_0^t{\theta}(s,x(s))d{\eta}(s)}{\psi}(x(t))$, where ${\theta}(s,{\cdot})$ and are the Fourier-Stieltjes transforms of the complex Borel measures on ${\mathbb{R}}^r$. Using the simple formulas, we evaluate the analogues of the conditional analytic Wiener and Feynman integrals of the functional G.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.7C
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• pp.937-945
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• 2004

A binary decision model which is used to denoising has demerits to measure the precise ratio of signal to noise because of only a binary classification. To supplement these demerits, complex statistical model and undecimated wavelet transform are generally exploited. In this paper, we propose a noise reduction method using a multi-level decision model for measuring the ratio of noise in noisy image. The propose method achieves good denoising performance with orthogonal wavelet transform because the ratio of signal to noise can be calculated to multi-valued form. In simulation results, the proposed denoising method outperforms 0.1dB in the PSNR sense than the state of art denoising algorithms using orthogonal wavelet transform.