• 대한수학회논문집
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• 제38권3호
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• pp.913-924
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• 2023

We consider the number of colors for colorings of links by the symmetric group S₃ of degree 3. For knots, such a coloring corresponds to a Fox 3-coloring, and thus the number of colors must be 1 or 3. However, for links, there are colorings by S₃ with 4 or 5 colors. In this paper, we show that if a 2-bridge link admits a coloring by S₃ with 5 colors, then the link also admits such a coloring with only 4 colors.

• 호남수학학술지
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• 제41권3호
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• pp.595-607
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• 2019

We consider quasigroups $Q({\Gamma})$ obtained as certain double covers of the symmetric group $S_3$ of degree 3, for directed graphs ${\Gamma}$ on the vertex set $S_3$. We completely characterize the strong compatibility of elements of $Q({\Gamma})$ for any quasigroup nonuniform homogeneous space of degree 4. For such homogeneous spaces, we classify all the strong and weak compatibility graphs of $Q({\Gamma})$.

• 대한수학회보
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• 제50권2호
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• pp.667-674
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• 2013

Considering a special double-cover Q of the symmetric group of degree 3, we show that a proper non-regular approximate symmetry occurs from its quasigroup homogeneous space. The weak compatibility of any two elements of Q is completely characterized in any such quasigroup homogeneous space of degree 4.

• Journal of the Optical Society of Korea
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• 제18권3호
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• pp.207-216
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• 2014

In this work, we report detailed numerical analysis of the near-elliptic core index-guiding triangular-lattice and square-lattice photonic crystal fiber (PCFs); where we numerically characterize the birefringence, single mode, cut-off behavior and group velocity dispersion and effective area properties. By varying geometry and examining the modal field profile we find that for the same relative values of $d/{\Lambda}$, triangular-lattice PCFs show higher birefringence whereas the square-lattice PCFs show a wider range of single-mode operation. Square-lattice PCF was found to be endlessly single-mode for higher air-filling fraction ($d/{\Lambda}$). Dispersion comparison between the two structures reveal that we need smaller lengths of triangular-lattice PCF for dispersion compensation whereas PCFs with square-lattice with nearer relative dispersion slope (RDS) can better compensate the broadband dispersion. Square-lattice PCFs show zero dispersion wavelength (ZDW) red-shifted, making it preferable for mid-IR supercontinuum generation (SCG) with highly non-linear chalcogenide material. Square-lattice PCFs show higher dispersion slope that leads to compression of the broadband, thus accumulating more power in the pulse. On the other hand, triangular-lattice PCF with flat dispersion profile can generate broader SCG. Square-lattice PCF with low Group Velocity Dispersion (GVD) at the anomalous dispersion corresponds to higher dispersion length ($L_D$) and higher degree of solitonic interaction. The effective area of square-lattice PCF is always greater than its triangular-lattice counterpart making it better suited for high power applications. We have also performed a comparison of the dispersion properties of between the symmetric-core and asymmetric-core triangular-lattice PCF. While we need smaller length of symmetric-core PCF for dispersion compensation, broadband dispersion compensation can be performed with asymmetric-core PCF. Mid-Infrared (IR) SCG can be better performed with asymmetric core PCF with compressed and high power pulse, while wider range of SCG can be performed with symmetric core PCF. Thus, this study will be extremely useful for designing/realizing fiber towards a custom application around these characteristics.

• Maxillofacial Plastic and Reconstructive Surgery
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• 제42권
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• pp.17.1-17.11
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• 2020

Background: To evaluate the facial asymmetry, three-dimensional computed tomography (3D-CT) has been used widely. This study proposed a method to quantify facial asymmetry based on 3D-CT. Methods: The normal standard group consisted of twenty-five male subjects who had a balanced face and normal occlusion. Five anatomical landmarks were selected as reference points and ten anatomical landmarks were selected as measurement points to evaluate facial asymmetry. The formula of facial asymmetry index was designed by using the distances between the landmarks. The index value on a specific landmark indicated zero when the landmarks were located on the three-dimensional symmetric position. As the asymmetry of landmarks increased, the value of facial asymmetry index increased. For ten anatomical landmarks, the mean value of facial asymmetry index on each landmark was obtained in the normal standard group. Facial asymmetry index was applied to the patients who had undergone orthognathic surgery. Preoperative facial asymmetry and postoperative improvement were evaluated. Results: The reference facial asymmetry index on each landmark in the normal standard group was from 1.77 to 3.38. A polygonal chart was drawn to visualize the degree of asymmetry. In three patients who had undergone orthognathic surgery, it was checked that the method of facial asymmetry index showed the preoperative facial asymmetry and the postoperative improvement well. Conclusions: The current new facial asymmetry index could efficiently quantify the degree of facial asymmetry from 3D-CT. This method could be used as an evaluation standard for facial asymmetry analysis.

• 대한치과교정학회지
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• 제30권5호
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• pp.535-542
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• 2000

본 연구는 안면비대칭 환자의 natural head position(NHP)시 정면에서의 두부 또는 경추의 경사 정도를 알아봄으로써 교정환자의 임상검사시 비대칭의 진단에 도움이 되고자 시행되었다. 두드러진 전후방 골격 이상은 없으나 뚜렷한 좌우 안면비대칭을 보이는 성인 20명을 비대칭군으로, 좌우 대칭적인 외모와 비교적 정상교합을 보이는 성인 21명 을 대칭군으로 선정 한 다음 물방울 수평계를 이용하여 NHP 상태의 정모두부방사선사진을 촬영하고 투사도를 작성하였다. Crista galli와 anterior nasal spine을 연결한 선과 crista galli와 menton을 연결한 선이 이루는 각을 menton의 변위 정도로 정하고, 좌우 supra-orbital margin의 최상방점을 지나는 supra-orbital line과, 제1경추와 제4경추의 중심을 연결한 cervical line이 각각 true vertical line과 이루는 각을 계측한 다음 이들간의 상관관계를 비교 분석하여 다음과 같은 결과를 얻었다. 1. Supra-orbital line이 true vortical line과 이루는 각이 직각에서 벗어난 정도가 대칭군에 비하여 비대칭군에서 통계적으로 유의하게 크게 나타났다. 2. Cervical line이 true vertical line과 이루는 각은 통계적 유의차는 없었으나 비대칭군에서 더 큰 경향을 보였다. 3. 비대칭군에서 supra-orbital line이 true vortical line과 이루는 각이 직각에서 벗어난 정도는 menton의 변위 정도와 통계적으로 유의한 순상관관계를 보였다. 이상의 결과로 안면비대칭 환자는 menton의 변위를 보상하려는 방향으로 기울어진 NHP를 가지는 경향이 있음을 알 수 있었다.

• Archives of Plastic Surgery
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• 제36권5호
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• pp.637-641
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• 2009

Purpose: Most unilateral secondary cleft lip nose deformities have depressed nostril base and sill on the cleft side. To obtain a symmetric nose, correction of the recession on nostril is critical. The authors have worked out effective methods to elevate the nostril of the cleft side according to the extent of the depression. Methods: A total of 115 unilateral secondary cleft lip nose deformity patients with nostril depression were evaluated. Data were acquired from patients' charts and photography with special reference to the height difference of the nostrils between the cleft side and the non - cleft side. Patients were divided into three groups based on the difference and operated with various techniques : (1) mild degree(< 1 mm) with graft, (2) moderate degree(1 ~ 3 mm) with C - flap or suspension suture of septal cartilage (3) severe degree(> 3 mm) with graft, C - flap and suspension suture. Follow - up period averaged 21.3 months. Results: Forty - six patients(40 percent) were in mild group, and forty - two(37 percent) were in moderate. In twenty - seven patients(23 percent), nostril recession was more than 3 mm. The elevated nostril base and sill were maintained without height alteration during follow - up. Conclusion: The symmetry of the nostril base, especially projection of nostril sill influences successful correction of unilateral cleft lip nose deformity. Our tolerable techniques can be applied to most deformities with nostril depression and can present a new guideline.

• 한국광학회지
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• 제17권5호
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• pp.420-429
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• 2006

곡률, 두께, 굴절률 오차와 같은 광축대칭 오차요인들 때문에 상면이 이동하는 디지털 카메라용 줌렌즈 광학계에서 보상자를 이동시켜서 상면을 고정시키는 조건을 가우스 괄호법을 이용하여 유도하였다. 그리고 줌렌즈 광학계의 일반적인 세 가지 형태(3군, 4군, 5군 줌렌즈)를 사용하여 이 조건의 타당성을 검증하였다. 이러한 줌렌즈 형태에서 각 면의 곡률, 두께, 굴절률 등을 공차 내에서 Monte Carlo 방법에 따라 임의로 변화시켰을 때, 보상자의 이동량의 분포가 정규분포를 이루는 것을 확인하였다. 그리고 이로부터 공정능력을 계산하여 보상자의 최대 이동량에서 이에 따른 불량률을 이론적으로 예측하는 방법을 제시하였다.

• Journal of Veterinary Science
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• 제21권4호
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• pp.58.1-58.11
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• 2020

Background: Quantitative evaluation of renal cortical echogenicity (RCE) has been tried and developed in human and veterinary medicine. Objectives: The objective of this study was to propose a method for evaluating RCE quantitatively and intuitively, and to determine associations between ultrasonographic renal structural distinction and estimated glomerular filtration rate (eGFR) in canine chronic kidney disease (CKD). Methods: Data were collected on 63 dogs, including 27 with normal kidney function and 36 CKD patients. Symmetric dimethylarginine and creatinine concentrations were measured for calculating eGFR. RCE was evaluated as 3 grades on ultrasonography images according to the distinction between the renal cortex and outer medulla. The RCE grade of each kidney was measured. Results: There was a significant difference in eGFR between the group normal and CKD (p < 0.001). As mean of RCE grades (the mean values of each right and left kidney's RCE grade) increases, the proportion of group CKD among the patients in each grade increases (p < 0.001). Also, severity of RCE (classified as "high" if any right or left kidney evaluated as RCE grade 3, "low" otherwise) and eGFR is good indicator for predicting group CKD (p < 0.001). Conclusions: The degree of distinction between the renal cortex and the outer medulla is closely related to renal function including eGFR and the RCE grade defined in this study can be used as a method of objectively evaluating RCE.