• 대한수학회논문집
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• 제39권2호
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• pp.303-311
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• 2024

In this paper, our focus lies in exploring the concept of Cohen-Macaulay dimension within the category of homologically finite complexes. We prove that over a local ring (R, 𝔪), any homologically finite complex X with a finite Cohen-Macaulay dimension possesses a finite CM-resolution. This means that there exists a bounded complex G of finitely generated R-modules, such that G is isomorphic to X and each nonzero G_i within the complex G has zero Cohen-Macaulay dimension.

• 천문학회지
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• 제37권4호
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• pp.137-141
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• 2004

We have estimated the fractal dimension of the molecular clouds in the Antigalactic Center based on the $^{12}CO$ (J = 1- 0) and $^{13}CO$ (J = 1- 0) database obtained using the 14m telescope at Taeduk Radio Astronomy Observatory. Using a developed code within IRAF, we were able to identify slice-clouds, and determined the dispersions of two spatial coordinates as well as perimeters and areas. The fractal dimension of the target region was estimated to be D = 1.34 for low resolution $^{12}CO$ (J = 1 - 0) database, and D = 1.4 for higher resolution $^{12}CO$ (J = 1 - 0) and $^{13}CO$ (J = 1 - 0) database, where $P {\propto} A^{D/2}$. The sampling rate (spatial resolution) of observed data must be an important parameter when estimating fractal dimension. Our database with higher resolution of 1 arcminute, which is corresponding to 0.2 pc at a distance of 1.1 kpc, gives us the same estimate of fractal dimension to that of local dark clouds. Fractal dimension is apparently invariant when varying the threshold temperatures applied to cloud identification. According to the dispersion pattern of longitudes and latitudes of identified slice-clouds, there is no preference of elongation direction.

• Imaging Science in Dentistry
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• 제32권2호
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• pp.75-79
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• 2002

Purpose : To evaluate the effect of exposure time and image resolution on fractal dimension calculations for determining the optimal range of these two variances. Materials and Methods : Thirty-one radiographs of the mandibular angle area of sixteen human dry mandibles were taken at different exposure times (0.01, 0.08, 0.16, 0.25, 0.40, 0.64, and 0.80 s). Each radiograph was digitized at 1200 dpi, 8 bit, 256 gray level using a film scanner. We selected an Region of Interest (ROI) that corresponded to the same region as in each radiograph, but the resolution of ROI was degraded to 1000, 800, 600, 500, 400, 300, 200, and 100 dpi. The fractal dimension was calculated by using the tile-counting method for each image, and the calculated values were then compared statistically. Results: As the exposure time and the image resolution increased, the mean value of the fractal dimension decreased, except the case where exposure time was set at 0.01 seconds (α = 0.05). The exposure time and image resolution affected the fractal dimension by interaction (p<0.001). When the exposure time was set to either 0.64 seconds or 0.80 seconds, the resulting fractal dimensions were lower, irrespective of image resolution, than at shorter exposure times (α = 0.05). The optimal range for exposure time and resolution was determined to be 0.08- 0.40 seconds and from 400-1000 dpi, respectively. Conclusion : Adequate exposure time and image resolution is essential for acquiring the fractal dimension using tile-counting method for evaluation of the mandible.

• 한국CDE학회논문집
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• 제11권3호
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• pp.172-182
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• 2006

This paper presents a method to convert 3D CAD model to an appropriate analysis model using wrap-around, smooth-out and thinning operators that have been originally developed to realize the multi-resolution modeling. Wrap-around and smooth-out operators are used to simplify 3D model, and thinning operator is to reduce the dimension of a target object with simultaneously decomposing the simplified 3D model to 1D or 2D shapes. By using the simplification and dimension-reduction operations in an appropriate way, the user can generate an analysis model that matches specific applications. The advantage of this method is that the user can create optimized analysis models of various simplification levels by selecting appropriate number of detailed features and removing them.

• 한국인터넷방송통신학회논문지
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• 제23권1호
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• pp.145-149
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• 2023

표면의 고해상도 이미지는 나노(nano)사이즈 부터 마이크로미터까지 특정한 크기를 갖는 기공이나 형상에 대한 자세한 정보를 제공한다. 그러나 표면의 고해상도 이미지로 부터 기공이나 형상에 대한 효율적인 연관성을 결정하는 것은 아직 확실하지 않다. 기공이나 형상의 효율적 연관성을 위하여 소자의 표면특성은 SEM 사진을 촬영하고 이미지를 이진화하여 프랙탈 차원으로 고찰하였다. 소자의 표면 분석을 위하여 프랙탈 프로그램은 직접 코딩하였다. 소자 표면 특성과 전기적 특성은 프랙탈 차원과 연관성이 있을 것으로 생각된다. 프랙탈 차원은 내부 기공의 증가와 더불어 감소하였다. 소자 표면의 구조적 특성인 입자의 밀도와 입계는 프랙탈 차원과 연관이 있었다. 입자의 크기는 프랙탈 차원의 증가와 더불어 감소하였으며 균일하게 형성되었다. 입자가 균일하게 형성되면 기공이 적게 존재하여 프랙탈 차원이 증가하였다.

• 대한수학회지
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• 제59권4호
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• pp.733-756
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• 2022

In this paper, we introduce the notion of Gorenstein quasiresolving subcategories (denoted by 𝒢𝒬𝓡_𝒳 (𝓐)) in term of quasi-resolving subcategory 𝒳. We define a resolution dimension relative to the Gorenstein quasi-resolving categories 𝒢𝒬𝓡_𝒳 (𝓐). In addition, we study the stability of 𝒢𝒬𝓡_𝒳 (𝓐) and apply the obtained properties to special subcategories and in particular to modules categories. Finally, we use the restricted flat dimension of right B-module M to characterize the finitistic dimension of the endomorphism algebra B of a 𝒢𝒬_𝒳-projective A-module M.

• 천문학회지
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• 제49권6호
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• pp.255-259
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• 2016

We estimate the fractal dimension of the ${\rho}$ Ophiuchus Molecular Cloud Complex, associated with star forming regions. We selected a cube (${\upsilon}$, l, b) database, obtained with J = 1-0 transition lines of $^{12}CO$ and $^{13}CO$ at a resolution of 22" using a multibeam receiver system on the 14-m telescope of the Five College Radio Astronomy Observatory. Using a code developed within IRAF, we identified slice-clouds with two threshold temperatures to estimate the fractal dimension. With threshold temperatures of 2.25 K ($3{\sigma}$) and 3.75 K ($5{\sigma}$), the fractal dimension of the target cloud is estimated to be D = 1.52-1.54, where $P{\propto}A^{D/2}$, which is larger than previous results. We suggest that the sampling rate (spatial resolution) of observed data must be an important parameter when estimating the fractal dimension, and that narrower or wider dispersion around an arbitrary fit line and the intercepts at NP = 100 should be checked whether they relate to firms noise level or characteristic structure of the target cloud. This issue could be investigated by analysing several high resolution databases with different quality (low or moderate sensitivity).

• Current Optics and Photonics
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• 제2권2호
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• pp.153-164
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• 2018

In semiconductor manufacturing, critical dimensions indicate the features of patterns formed by the semiconductor process. The purpose of measuring critical dimensions is to confirm whether patterns are made as intended. The deposition process for an organic light emitting diode (OLED) forms a luminous organic layer on the thin-film transistor electrode. The position of this organic layer greatly affects the luminescent performance of an OLED. Thus, a system for measuring the position of the organic layer from outside of the vacuum chamber in real-time is desired for monitoring the deposition process. Typically, imaging from large stand-off distances results in low spatial resolution because of diffraction blur, and it is difficult to attain an adequate industrial-level measurement. The proposed method offers a new superresolution single-image using a conversion formula between two different optical systems obtained by a deep learning technique. This formula converts an image measured at long distance and with low-resolution optics into one image as if it were measured with high-resolution optics. The performance of this method is evaluated with various samples in terms of spatial resolution and measurement performance.

• 대한수학회지
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• 제56권4호
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• pp.1031-1048
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• 2019

In this paper we study recollements of abelian categories and balanced pairs. The main results are: recollements induce new balanced pairs from the middle category; the resolution dimensions are bounded under certain conditions. As an application, the resolution dimensions with respect to cotilting objects of abelian categories involved in recollements are recovered.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2012년도 춘계학술대회 논문집
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• pp.681-682
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• 2012