• East Asian mathematical journal
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• v.16 no.1
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• pp.97-103
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• 2000

In this work, we consider a finite difference operator $L^2_N$ corresponding to $$Lu:=-(u_{xx}+u_{yy})\;in\;{\Omega},\;u=0\;on\;{\partial}{\Omega}$$, in $S_{h^2,1}$. We derive the relation between the absolute value of the bilinear form $l_{N^2}$(u, v) on $S_{h^2,1}{\times}S_{h^2,1}$ and Sobolev $H^1$ norms.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.623-630
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• 2017

For any nonzero elements x, y in a normed space X, the angular and skew-angular distance is respectively defined by ${\alpha}[x,y]={\parallel}{\frac{x}{{\parallel}x{\parallel}}}-{\frac{y}{{\parallel}y{\parallel}}}{\parallel}$ and ${\beta}[x,y]={\parallel}{\frac{x}{{\parallel}y{\parallel}}}-{\frac{y}{{\parallel}x{\parallel}}}{\parallel}$. Also inequality ${\alpha}{\leq}{\beta}$ characterizes inner product spaces. Operator version of ${\alpha}$ has been studied by $ Pe{\check{c}}ari{\acute{c}}$, $ Raji{\acute{c}}$, and Saito, Tominaga, and Zou et al. In this paper, we study the operator version of ${\beta}$ by using Douglas' lemma. We also prove that the operator version of inequality ${\alpha}{\leq}{\beta}$ holds for commutating normal operators. Some examples are presented to show essentiality of these conditions.

• Journal of the Korean Mathematical Society
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• v.41 no.4
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• pp.617-627
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• 2004

Let (equation omitted) denote the class of bounded linear Hilbert space operators with the property that $\midA^2\mid\geq\midA\mid^2$. In this paper we show that (equation omitted)-operators are finitely ascensive and that, for non-zero operators A and B, A (equation omitted) B is in (equation omitted) if and only if A and B are in (equation omitted). Also, it is shown that if A is an operator such that p(A) is in (equation omitted) for a non-trivial polynomial p, then Weyl's theorem holds for f(A), where f is a function analytic on an open neighborhood of the spectrum of A.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2010.07a
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• pp.74-76
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• 2010

Digital images or videos are used in modern digital devices. The resolution of HDTV in digital broadcasting system is higher than that of previous analog systems. Also, mobile phone with 3G can provide images as well as video streaming services in realtime. In these circumstances, the visual quality of images has become an important factor. We can make image clear by transient improvement process that reduces transient in edges. In this paper, we present an transient improvement algorithm. The proposed algorithm improves edges by making smooth edge to steep edge. Before performing transient improvement algorithm, edge detection algorithm should be operated. Laplacian operator is used in edge detection, and the absolute value of it is used to calculate gain value. Then, local maximum and minimum values are computed to discriminate current pixel value to raise up or pull down. Compensating value that gain value multiplies with the difference between maximum (or minimum) value and current pixel value adds (or subtracts) to current pixel value. That is, improved signal is generated by making the narrow transient of edge. The advantage of proposed algorithm is that it doesn't produce shooting problem like overshoot or undershoot.

• Genomics & Informatics
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• v.14 no.4
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• pp.149-159
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• 2016

With the success of the genome-wide association studies (GWASs), many candidate loci for complex human diseases have been reported in the GWAS catalog. Recently, many disease prediction models based on penalized regression or statistical learning methods were proposed using candidate causal variants from significant single-nucleotide polymorphisms of GWASs. However, there have been only a few systematic studies comparing existing methods. In this study, we first constructed risk prediction models, such as stepwise linear regression (SLR), least absolute shrinkage and selection operator (LASSO), and Elastic-Net (EN), using a GWAS chip and GWAS catalog. We then compared the prediction accuracy by calculating the mean square error (MSE) value on data from the Korea Association Resource (KARE) with body mass index. Our results show that SLR provides a smaller MSE value than the other methods, while the numbers of selected variables in each model were similar.

• Progress in Medical Physics
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• v.34 no.3
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• pp.23-32
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• 2023

Purpose: In radiomics analysis, to evaluate features, and predict genetic characteristics and survival time, the pixel values of lesions depicted in computed tomography (CT) and magnetic resonance imaging (MRI) images are used. CT and MRI offer three-dimensional images, thus producing three-dimensional features (Features_3d) as output. However, in reports, the superiority between Features_3d and two-dimensional features (Features_2d) is distinct. In this study, we aimed to investigate whether a difference exists in the prediction accuracy of radiomics analysis of lung cancer using Features_2d and Features_3d. Methods: A total of 38 cases of large cell carcinoma (LCC) and 40 cases of squamous cell carcinoma (SCC) were selected for this study. Two- and three-dimensional lesion segmentations were performed. A total of 774 features were obtained. Using least absolute shrinkage and selection operator regression, seven Features_2d and six Features_3d were obtained. Results: Linear discriminant analysis revealed that the sensitivities of Features_2d and Features_3d to LCC were 86.8% and 89.5%, respectively. The coefficients of determination through multiple regression analysis and the areas under the receiver operating characteristic curve (AUC) were 0.68 and 0.70 and 0.93 and 0.94, respectively. The P-value of the estimated AUC was 0.87. Conclusions: No difference was found in the prediction accuracy for LCC and SCC between Features_2d and Features_3d.

• Communications for Statistical Applications and Methods
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• v.30 no.3
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• pp.273-289
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• 2023

In this paper, we develop a new time series model for predicting IPO (initial public offering) data with non-negative integer value. The proposed model is based on integer-valued autoregressive (INAR) model with a Poisson thinning operator. Just as the heterogeneous autoregressive (HAR) model with daily, weekly and monthly averages in a form of cascade, the integer-valued heterogeneous autoregressive (INHAR) model is considered to reflect efficiently the long memory. The parameters of the INHAR model are estimated using the conditional least squares estimate and Yule-Walker estimate. Through simulations, bias and standard error are calculated to compare the performance of the estimates. Effects of model fitting to the Korea's IPO are evaluated using performance measures such as mean square error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE) etc. The results show that INHAR model provides better performance than traditional INAR model. The empirical analysis of the Korea's IPO indicates that our proposed model is efficient in forecasting monthly IPO volumes.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.37 no.4
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• pp.20-28
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• 2000

The error diffusion algorithm is good for reproducing continuous image to binary image. However the reproduction of edge characteristic is weak in power spectrum analysts of display error. In this paper, an error diffusion method which include pre-filter algorithm for edge characteristic enhancement is proposed Pre-filter algorithm is organized horizontal and vertical directional differential value and weighting function of pre-filter First, it is obtained the horizontal and vertical differential value from the peripheral pixels in original image using $3{\times}3$ Sobel operator Secondly weighting function of pre-filter is composed by function including absolute value and sign of differential value The improved Error diffusion algorithm using pre-filter, present a good result visually which edge characteristic is enhanced. The difference between orignal image and halftoning image is compared with edge-enhanced error diffusion algorithm by measuring the radially averaged power spectrum density.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.32 no.3
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• pp.235-240
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• 1996

Forecasts of monthly landings of walleye pollock, Theragra chalcogramma, in Korea were carried out by the seasonal Autoregressive Integrated Moving Average(ARlMA) model. The Box - Cox transformation on the walleye pollock catch data handles nonstationary variance. The equation of Box - Cox transformation was Y'=($Y^0.31$_ 1)/0.31. The model identification was determined by minimum AIC(Akaike Information Criteria). And the seasonal ARlMA model is presented (1- O.583B)(1- $B^1$)(l- $B^12$)$Z_t$ =(l- O.912B)(1- O.732$B^12$)et where: $Z_t$=value at month t ; $B^p$ is a backward shift operator, that is, $B^p$$Z_t$=$Z_t$-P; and et= error term at month t, which is to forecast 24 months ahead the walleye pollock landings in Korea. Monthly forecasts of the walleye pollock landings for 1993~ 1994, which were compared with the actual landings, had an absolute percentage error(APE) range of 20.2-226.1 %. Thtal observed annual landings in 1993 and 1994 were 16, 61OM/T and 1O, 748M/T respectively, while the model predicted 10, 7 48M/T and 8, 203M/T(APE 37.0% and 23.7%, respectively).

• Proceedings of the Korea Water Resources Association Conference
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• 2023.05a
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• pp.47-47
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• 2023

Drought occurs due to lack of water resources over an extended period and its intensity has been magnified globally by climate change. In recent years, drought over South Korea has also been intensed, and the prediction was inevitable for the water resource management and water industry. Therefore, drought forecasting over South Korea was performed in the current study with the following procedure. First, accumulated spring precipitation(ASP) driven by the 93 weather stations in South Korea was taken with their median. Then, correlation analysis was followed between ASP and Df4m, the differences of two pair of the global winter MSLP. The 37 Df4m variables with high correlations over 0.55 was chosen and sorted into three regions. The selected Df4m variables in the same region showed high similarity, leading the multicollinearity problem. To avoid this problem, a model that performs variable selection and model fitting at once, least absolute shrinkage and selection operator(LASSO) was applied. The LASSO model selected 5 variables which showed a good agreement of the predicted with the observed value, R²=0.72. Other models such as multiple linear regression model and ElasticNet were also performed, but did not present a performance as good as LASSO. Therefore, LASSO model can be an appropriate model to forecast spring drought over South Korea and can be used to mange water resources efficiently.