• Communications of the Korean Mathematical Society
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• v.38 no.3
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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.

• Honam Mathematical Journal
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• v.41 no.3
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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 $Q({\Gamma})$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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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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• v.18 no.3
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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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• v.42
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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.

• The korean journal of orthodontics
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• v.30 no.5 s.82
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• pp.535-542
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• 2000

The purpose of this study was to find the characteristics of the frontal natural head position(NHP) of patients with facial asymmetry, and to contribute to the diagnosis of facial asymmetry in the clinical examination of orthodontic patients. Twenty adult patients who had apparent facial asymmetry and no severe sagittal skeletal discrepancy were selected as the asymmetry group, and 21 young adults who had symmetric faces were selected as the symmetry group. Frontal cephalograms were obtained in the state of NHP using a pivot-mounted fluid level device. The degree of the menton deviation was defined as the angle between the line drawn through crista galli and anterior nasal spine and the line drawn through crista galli and menton. The following angles were measured and each of them was compared with the degree of the menton deviation one is the angle between the true vertical line and the supra-orbital line which is a tangent line to the extreme cranial point on the supra-orbital margin, and the other is the angle between the true vertical line and the cervical line drawn through the midpoint of atlas and the 4th cervical vertebra. Through the statistical analysis, following results were obtained. 1. The angle between the supra-orbital line and the true vertical line was much mote deviated from the right angle in the asymmetry group than in the symmetry group. 2. The angle between the cervical line and the true vertical line in the asymmetry group showed greater tendency than in the symmetry group, but the difference was not statistically significant. 3. In the asymmetry group, the degree of the menton deviation was positively correlated with the angle between the supraorbital line and the true vertical line. The above results suggest that racial asymmetry patients show the tendency to have the tilted NHP to compensate the deviation of menton position.

• Archives of Plastic Surgery
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• v.36 no.5
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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.

• Korean Journal of Optics and Photonics
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• v.17 no.5
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• pp.420-429
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• 2006

In the zoom lens of digital still cameras with the variation of the image plane generated by various symmetric error factors such as curvature, thickness and refractive index error of each lens surface about the optic axis, we induce a theoretical condition to fix constantly the image plane by translating the compensator group of the zoom lens by using the Gaussian bracket. We confirm the validity of this condition by using three examples of general zoom lens types with 3, 4, and 5 groups, respectively. When these error factors are randomly changed within the range of tolerance according to the Monte Carlo method, we verify that the distributions of the degree of moving of the compensator are normal distributions at three zoom lens types. From capability analysis using these results, we theoretically propose the method estimating the standard deviation, that is, sigma-level, as a function of the maximum movement of the compensator.

• Journal of Veterinary Science
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• v.21 no.4
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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.