• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.527-540
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• 2010

We characterize the boundedness and compactness of the weighted composition operator on the logarithmic Bloch space $\mathcal{L}\ss=\{f{\in}H(D):sup_D(1-|z|^2)ln(\frac{2}{1-|z|})|f'(z)|$<+$\infty$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$. The results generalize the known corresponding results on the composition operator and the pointwise multiplier on the logarithmic Bloch space ${\mathcal{L}\ss$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.977-991
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• 2008

We characterize the boundedness and compactness of the weighted composition operator $uC_{\psi}$ from the general function space F(p, q, s) into the logarithmic Bloch space ${\beta}_L$ on the unit disk. Some necessary and sufficient conditions are given for which $uC_{\psi}$ is a bounded or a compact operator from F(p,q,s), $F_0$(p,q,s) into ${\beta}_L$, ${\beta}_L^0$ respectively.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.187-198
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• 2017

We obtain some necessary and sufficient conditions for the boundedness of the composition operators between weighted Bergman spaces of logarithmic weights. In terms of the conditions for the boundedness, we compute the essential norm of the composition operators.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.321-338
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• 2020

In this paper, we investigate the viscoelastic plate equation with a constant delay term and logarithmic nonlinearities. Under some conditions, we will prove the global existence. Furthermore, we use weighted spaces to establish a general decay rate of solution.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.423-435
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• 2014

In this paper, the fractional Hardy-type operator of variable order ${\beta}(x)$ is shown to be bounded from the Herz-Morrey spaces $M\dot{K}^{{\alpha},{\lambda}}_{p_1,q_1({\cdot})}(\mathbb{R}^n)$ with variable exponent $q_1(x)$ into the weighted space $M\dot{K}^{{\alpha},{\lambda}}_{p_2,q_2({\cdot})}(\mathbb{R}^n,{\omega})$, where ${\omega}=(1+|x|)^{-{\gamma}(x)}$ with some ${\gamma}(x)$ > 0 and $1/q_1(x)-1/q_2(x)={\beta}(x)/n$ when $q_1(x)$ is not necessarily constant at infinity. It is assumed that the exponent $q_1(x)$ satisfies the logarithmic continuity condition both locally and at infinity that 1 < $q_1({\infty}){\leq}q_1(x){\leq}(q_1)+$ < ${\infty}(x{\in}\mathbb{R}^n)$.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.145-169
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• 2020

Let k be a field of characteristic 0. Let ${\mathfrak{C}}=Spec(k[x,y]/{\langle}f{\rangle})$ be a weighted homogeneous plane curve singularity with tangent space ${\pi}_{\mathfrak{C}}:T_{{\mathfrak{C}}/k}{\rightarrow}{\mathfrak{C}$. In this article, we study, from a computational point of view, the Zariski closure ${\mathfrak{G}}({\mathfrak{C}})$ of the set of the 1-jets on ${\mathfrak{C}}$ which define formal solutions (in F[[t]]² for field extensions F of k) of the equation f = 0. We produce Groebner bases of the ideal ${\mathcal{N}}_1({\mathfrak{C}})$ defining ${\mathfrak{G}}({\mathfrak{C}})$ as a reduced closed subscheme of $T_{{\mathfrak{C}}/k}$ and obtain applications in terms of logarithmic differential operators (in the plane) along ${\mathfrak{C}}$.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.8
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• pp.3873-3887
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• 2018

In this paper, we propose a novel method to recover images corrupted by impulse noise. The proposed method uses two stages: noise detection and filtering. In the first stage, we use pixel values, rank-ordered logarithmic difference values, and median values to train a neural-network-based impulse noise detector. After training, we apply the network to detect noisy pixels in images. In the next stage, we use group-based weighted couple sparse representation to filter the noisy pixels. During this second stage, conventional methods generally use only clean pixels to recover corrupted pixels, which can yield unsuccessful dictionary learning if the noise density is high and the number of useful clean pixels is inadequate. Therefore, we use reconstructed pixels to balance the deficiency. Experimental results show that the proposed noise detector has better performance than the conventional noise detectors. Also, with the information of noisy pixel location, the proposed impulse-noise removal method performs better than the conventional methods, through the recovered images resulting in better quality.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.35 no.1
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• pp.31-39
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• 2017

The goal of this study was to efficiently analyze the relationships of the number of thefts with related factors, considering the spatial patterns of theft crimes. Theft crime data for a 5-year period (2009-2013) were collected from Haeundae Police Station. A logarithmic transformation was performed to ensure an effective statistical analysis and the number of theft crimes was used as the dependent variable. Related factors were selected through a literature review and divided into social, environmental, and defensive factors. Seven factors, were selected as independent variables: the numbers of foreigners, aged persons, single households, companies, entertainment venues, community security centers, and CCTV (Closed-Circuit Television) systems. OLS (Ordinary Least Squares) and GWR (Geographically Weighted Regression) were used to analyze the relationship between the dependent variable and independent variables. In the GWR results, each independent variable had regression coefficients that differed by location over the study area. The GWR model calculated local values for, and could explain the relationships between, variables more efficiently than the OLS model. Additionally, the adjusted R square value of the GWR model was 10% higher than that of the OLS model, and the GWR model produced a AICc (Corrected Akaike Information Criterion) value that was lower by 230, as well as lower Moran's I values. From these results, it was concluded that the GWR model was more robust in explaining the relationship between the number of thefts and the factors related to theft crime.

• Proceedings of the KIEE Conference
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• 2003.11b
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• pp.75-78
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• 2003

In this paper, a second-order 3-bit DSM using DWA(Data Weighted Averaging) algorithm is designed for bluetooth Zero-IF Receiver. The designed circuit has two integrators using a designed OTA, nonoverlapping two-phase clerk generator, 3-bit A/D converter, DWA algorithm and 3-bit D/A converter An ideal model of second-order lowpass DSM with a 3-bit quantizer was configured by using MATLAB, and each coefficients and design specification of each blocks were determined to have 10-bit resolution in 1MHz channel bandwidth. The designed second-order 3-blt lowpass DSM has maximum SNR of 74dB and power consumption is 50mW at 3.3V.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.11C
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• pp.1098-1110
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• 2003

In this paper, we propose a homomorphic wavelet-based MMSE filter with edge detection to restore images degraded by speckle noise. In the proposed method, a noisy image is first transformed into logarithmic domain. Each pixel in the transformed image is then classified into flat and edge regions by applying DIP operator to the image restored by homomorphic directional MMSE filter. Each pixel in flat region is restored by homomorphic wavelet-based MMSE filter. Each pixel in edge region is restored by the weighted sum of the output of homomorphic wavelet-based MMSE filtering and that of homomorphic directional MMSE filtering. The restored image in spatial domain is finally obtained by applying the exponential function to the restored image in logarithmic domain. Experimental results show that the restored images by the proposed method have ISNR improvement of 3.3-4.0 ㏈ and ${\beta}$, a measurement parameter on edge preservation, improvement of 0.0103-0.0126 and superior subjective image quality over those by conventional methods.