• Honam Mathematical Journal
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• v.30 no.4
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• pp.589-602
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• 2008

As a survey-type article, the paper reviews various digital topological utilities from digital covering theory. Digital covering theory has strongly contributed to the calculation of the digital k-fundamental group of both a digital space(a set with k-adjacency or digital k-graph) and a digital product. Furthermore, it has been used in classifying digital spaces, establishing almost Van Kampen theory which is the digital version of van Kampen theorem in algebrate topology, developing the generalized universal covering property, and so forth. Finally, we remark on the digital k-surface structure of a Cartesian product of two simple closed $k_i$-curves in ${\mathbf{Z}}^n$, $i{\in}{1,2}$.

• Honam Mathematical Journal
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• v.26 no.1
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• pp.107-117
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• 2004

The aim of this paper is to introduce a digital $({\kappa}_0,\;{\kappa}_1)$-covering map and a local $({\kappa}_0,\;{\kappa}_1)$-homeomorphism. And further, we show that a digital $({\kappa}_0,\;{\kappa}_1)$-covering map is a local $({\kappa}_0,\;{\kappa}_1)$-homeomorphism and the converse does not hold. Finally, some property of a digital covering map is investigated with relation to some restriction map. Furthermore, we raise an open problem with relation to the product covering map.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.537-545
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• 2005

The aim of this paper is to solve the open problem on product properties of digital covering maps raised from [5]. Namely, let us consider the digital images $X_1 {\subset}Z^{n_{0}}$ with $k_0-adjacency$, $Y_1{\subset}Z^{n_{1}}$ with $k_3-adjacency$, $X_2{\subset}Z^{n_{2}}$ with $k_2-adjacency$ and $Y_2{\subset}Z^{n_{3}}$ with $k_3-adjacency$. Then the reasonable $k_4-adjacency$ of the product image $X_1{\times}X_2$ is determined by the $k_0-$ and $k_2-adjacency$ and the suitable k_5-adjacency$ is assumed on $Y_1{\times}Y_2$ via the $k_1-$ and $k_3-adjacency$ [3] such that each of the projection maps is a digitally continuous map, e.g., $p_1\;:\;X_1{\times}X_2{\rightarrow}X_1$ is a digitally ($k_4,\;k_1$)-continuous map and so on. Let us assume $h_1\;:\;X_1{\rightarrow}Y_1$ to be a digital $(k_0, k_1)$-covering map and $h_2\;:\;X_2{\rightarrow}Y_2$ to be a digital $(k_2,\;k_3)$-covering map. Then we show that the product map $h_1{\times}h_2\;:\;X_1{\times}X_2{\rightarrow}Y_1{\times}Y_2$ need not be a digital $(k_4,k_5)$-covering map.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.207-217
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• 2008

Digital geometry has strongly contributed to the study of a discrete topological space $X{\subset}{\mathbf{Z}}^n$ with k-adjacency of ${\mathbf{Z}}^n$. As a survey-type article, we review various utilities of digital geometry.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1479-1503
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• 2007

In this paper, we study a strong k-deformation retract derived from a relative k-homotopy and investigate its properties in relation to both a k-homotopic thinning and the k-fundamental group. Moreover, we show that the k-fundamental group of a wedge product of closed k-curves not k-contractible is a free group by the use of some properties of both a strong k-deformation retract and a digital covering. Finally, we write an algorithm for calculating the k-fundamental group of a dosed k-curve by the use of a k-homotopic thinning.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.411-421
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• 2004

A digital $(k_0,\;k_1)$-homotopy is induced from digital $(k_0,\;k_1)$-continuity with the n kinds of $k_i$-adjacency relations in ${\mathbb{Z}}^n$, $i{\in}\{0,\;1\}$. The k-fundamental group, ${\pi}^k_1(X,\;x_0)$, is derived from the pointed digital k-homotopy, $k{\in}\{3^n-1(n{\geq}2),\;3^n-{\sum}^{r-2}_{k=0}C^n_k2^{n-k}-1(2{\leq}r{\leq}n-1(n{\geq}3)),\;2n(n{\geq}1)\}$. In this paper two kinds of digital 8-pseudotori stemmed from the minimal simple closed 4-curve and the minimal simple closed 8-curve with 8-contractibility or without 8-contractibility, e.g., $DT_8$ and $DT^{\prime}_8$, are introduced and their digital topological properties are studied by the calculation of the k-fundamental groups, $k{\in}\{8,\;32,\;64,\;80\}$.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.707-716
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• 2013

The present paper consists of two parts. Since the recent paper [4] proved that an Alexandroff $T_0$-space is a semi-$T_{\frac{1}{2}}$-space, the first part studies semi-open and semi-closed structures of the Khalimsky nD space. The second one focuses on the study of a relation between the LS-property of ($SC^{n_1,l_1}_{k_1}{\times}SC^{n_2,l_2}_{k_2}$, k) relative to the simple closed $k_i$-curves $SC^{n_i,l_i}_{k_i}$, $i{\in}\{1,2\}$ and its normal k-adjacency. In addition, the present paper points out that the main theorems of Boxer and Karaca's paper [3] such as Theorems 4.4 and 4.7 of [3] cannot be new assertions. Indeed, instead they should be attributed to Theorems 4.3 and 4.5, and Example 4.6 of [10].

• Bulletin of the Korean Chemical Society
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• v.26 no.6
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• pp.966-970
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• 2005

To measure the thickness of liquid films from 10 to 60 ${\mu}m$, we used photochromic dye activation. And we used silicone oil with 10 centi-Stokes and commercial photochromic dyes. To make films with exact and known thicknesses, we used two glass wafers. A film formed between two wafers after placing a drop of liquid of known volume on one wafer and covering the other. The film thickness could be estimated from the diameter of wafer and the dropped liquid volume. To quantitatively evaluate the result, captured the images using digital camera then analyzed the images using the image tool. The gray scale intensity using the captured images of activated dye with these thicknesses showed the repeatability below ${\pm}$ 1.0% when measured with a silicone oil solution containing 0.1% SO and SO-ANTH dyes. And we showed that photochromic dye activation method could be used to measure our liquid film thickness ranges.

• Korean Journal of Digital Imaging in Medicine
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• v.11 no.2
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• pp.85-92
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• 2009

This study, "The study about performance evaluations of mobile cover for X-ray's diffusion and distribution in mobile radiation" is based on the rules of mobile defense apparatus for radiation producer in 2006. To use the mobile cover for X-ray for diagnosis has been compulsory in common wards except operation rooms, emergency rooms and intensive care units. we have confirmed the effect in arbitrary shielding material after Qualitiy Control was carried out for accuracy in an experiment of mobile photographing equipment. The performance evaluation was conducted with the fabrics of selenium, 0.2 mmPb, 0.1 mmPb and aluminiums. Considering the result, we choosed 0.1 mmPb and attached cover to mobile photographing equipment. We have finished making the cover after drew up the draft to attach cover to mobile photographing equipment through the modeling and the structural analysis. the process of the study is that we assembled the manufactured structures and carried out the practical experiment to take the photograph after attaching the fabric of 0.1 mmPb to mobile photographing equipment. It is need of additional thesises hereafter that we compare the result between the part to improve for safety besides convenience in photographic experiment about clinical radiation and the effect of covering the diffusion in condition attached the cover.

• Journal of information and communication convergence engineering
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• v.14 no.4
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• pp.222-226
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• 2016

A design method for a compact square loop antenna fed by a microstrip (MS) line for indoor digital television (DTV) applications is proposed. The proposed antenna consists of a square loop, circular sectors, and an MS line. The square loop combined with circular sectors is printed on one side of a substrate, and a $75-{\Omega}$ MS line is printed on the other side. The circular sectors are used as a wideband balun or transition to connect the MS line and the square loop. A prototype of the proposed square loop antenna operating in the DTV band (470-806 MHz) is designed and fabricated on an FR4 substrate. Experimental results show that the proposed antenna has the desired impedance characteristics in the frequency band of 464-1,220 MHz (89.8%) for a voltage standing wave ratio (VSWR) of <2 covering the DTV band, and a broadside gain of 0.8-3.3 dBi in the DTV band.