• Communications of the Korean Mathematical Society
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• v.39 no.2
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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.

• Journal of The Korean Astronomical Society
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• v.37 no.4
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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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• v.32 no.2
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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.

• Korean Journal of Computational Design and Engineering
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• v.11 no.3
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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.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.1
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• pp.145-149
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• 2023

High-resolution images of surfaces provide detailed information on pores or shapes with specific sizes ranging from nano sizes to micrometers. However, it is not yet clear to determine an efficient association for pores or shapes from high-resolution images of surfaces. For the efficient association of pores and shapes, the surface characteristics of the device were considered as fractal dimensions by taking SEM photographs and binarizing the images. The fractal program was directly coded for surface analysis of the device. The device surface characteristics and electrical characteristics are thought to be related to the fractal dimension. The fractal dimension decreased with an increase in internal pores. The density and grain boundary of particles, which are structural characteristics of the device surface, were related to the fractal dimension. The particle size decreased with an increase in the fractal dimension and was uniformly formed. When the particles were uniformly formed, fewer pores were present and the fractal dimension increased.

• Journal of the Korean Mathematical Society
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• v.59 no.4
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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.

• Journal of The Korean Astronomical Society
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• v.49 no.6
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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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• v.2 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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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.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2012.05a
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• pp.681-682
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• 2012