• 대한수학회보
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• 제47권1호
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• pp.211-219
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• 2010

Let P be a Jacobian polynomial such as deg P = $deg_y$ P. Suppose the Jacobian polynomial P satisfies the intersection condition satisfying $dim_C$ C[x, y]/$P_y$> = deg P - 1, we can prove that the Keller map which has P as one of coordinate polynomial always has its inverse.

• 대한수학회지
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• 제58권6호
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• pp.1485-1500
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• 2021

A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are geodesics on hypercones. We later use this association to characterize rectifying curves that are also slant helices in three-dimensional space as geodesics of circular cones. In addition, we consider curves that lie on a moving hyperplane normal to (i) one of the normal vector fields of the Frenet frame and to (ii) a rotation minimizing vector field along the curve. The former class is characterized in terms of the constancy of a certain vector field normal to the curve, while the latter contains spherical and plane curves. Finally, we establish a formal mapping between rectifying curves in an (m + 2)-dimensional space and spherical curves in an (m + 1)-dimensional space.

• 대한수학회보
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• 제60권6호
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• pp.1477-1496
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• 2023

A class of normalized univalent functions f defined in an open unit disk of the complex plane is introduced and studied such that the values of the quantity zf'(z)/f(z) lies inside the evolute of a nephroid curve. The inclusion relations of the newly defined class with other subclasses of starlike functions and radius problems concerning the second partial sums are investigated. All the obtained results are sharp.

• Journal of Oral Medicine and Pain
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• 제25권2호
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• pp.205-214
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• 2000

This study was performed to investigate the relationship between mandibular midline shift and anteroposterior first molar occlusal relation, and their effects on the mandibular height and the occlusal plane angle. For this study, 49 patients with temporomandibular disorders were selected. They did not show facial asymmetry and their facial midline coincide with maxillary dental midline. Upper and lower mandibular impression were taken and the casts were fabricated. Amount and direction of the mandibular midline shift and the anteroposterior shift between the two occluding first molars were measured on the casts. Several items related to height such as mandibular height from top of the articular surface of the condyle to curve changing point between antegonial notch and mandibular angle, condylar height which was the vertical distance from the articular surface to retroepicondyle of the condyle, and sigmoid height from the deepest point of sigmoid notch to the curve changing point and the occlusal plane angle were also measured on the panoramic and on the transcranial radiographs. Correlation between midline shift and anteroposterior first molar relation and comparison between right and left mandibular height by the midline shift and the first molar relation were analysed by SPSS windows program. The results of this study were as follows : 1. Mean amount of midline shift in the subjects with midline shift were 2.0mm for both side, respectively. The first molar relation of the ipsilateral side of midline shift showed Angle class II tendency and the contralateral side showed Angle class III tendency, which meant drift of the dentition to the side of the midline shift. 2. The occlusal plane angle on the panoramic radiograph were $13.0^{\circ}$ in right, and $12.5^{\circ}$ in left side, and their were no correlation between occlusal plane angle and mandibular midline shift and the first molar occlusal relation. 3. Angle's classification for both sides of the first molar relation were same in about half of all the subjects. Amount of deviation from class I first molar relation, however, were decreased in the contralateral side of observed side. 4. Mandibular height of the ipsilateral side to which mandibular midline shift showed tendency of lower than that of the contralateral side, and there was a tendency that the height was higher in class III subjects, then class II subjects, and lower in class I subjects. However, condylar height did not show any difference in the subjects with midline shift and also show no difference by the first molar occlusal relation.

• 대한치과교정학회지
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• 제30권5호
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• pp.521-533
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• 2000

본 연구의 목적은 피개교합 양상에 따른 성인 I급 부정교합자의 골격적 특징과 수직부조화를 야기하는 치성 및 골격성 요인들을 분석하기 위한 것이다. 서울대학교 치과대학 교정학교실에 소장되어 있는 정상교합군 표본 중 40명을 정상교합군, 서울대학교병원 교정과에 내원하여 I급 부정교합으로 진단받은 성인 환자중 전치부 수직피개량이 -0.1mm 이하인 40명을 개방교합군, 4.0mm 이상인 40명을 과개교합군으로 선정하여 측모 두부 X-선 계측사진을 촬영하였다. 46개의 계측항목을 선정하고 SPSS program을 이용하여 각 군별 ANOVA, 판별분석, 다중회귀분석을 시행하여 다음과 같은 결론을 얻었다. 1. 주로 하악골 형태와 하안면부의 치성, 골격성 요인이 수직부조화의 양상에 많은 영향을 끼쳤다. 2. 개방교합군의 수직부조화 양상은 하안면부에서 두드러지게 나타났으며 하악골 형태와 하악하연평면 경사도와 관련이 있었고, 판별분석 결과 골격적 요인의 기여도가 높았다. 3. 과개교합자의 수직부조화에는 주로 curve of Spee, 상악구치의 수직고경 등 치성 요인들의 기여도가 높았으며, 골격적 요인으로는 articular angle의 기여도가 높았다. 4. 다중회귀분석 결과 I급 구치관계를 갖는 성인에서 overbite의 결정요인에는 주로 하악전치와 교합평면각, curve of Spee, 절치간 각도 등의 치성요인이 기여하였다.

• 대한치과교정학회지
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• 제48권4호
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• pp.236-244
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• 2018

Objective: The aim of this study is to compare the adaptation of a straight wire between brackets positioned at the mid-lingual surface and those placed gingivally by using a three-dimensional simulation software. Methods: This cross-sectional study was performed using OrthoAid, an in-house software. The subjects were 36 adolescents with normal Class I occlusion. For each dental cast, two bracket positioning approaches, namely the middle and gingival, were examined. In the middle group, the reference points were placed on the mid-lingual surface of each tooth, while in the gingival group, the reference points were positioned lingually on the anterior teeth. A 4th degree polynomial was adopted, and the in-plane and off-plane root mean squares (RMSs) of the distances between the reference points and the fitted polynomial curve were calculated using the software. Statistical analysis was performed using the paired-samples t-test (${\alpha}=0.05$). Results: The mean in-plane RMS of the polynomial curve to the bracket distance in the gingival group was significantly lower than that in the middle group (p < 0.001). The off-plane RMS was higher in the gingivally positioned brackets in the maxilla than in the middle group (p < 0.001). However, the off-plane RMS in mandible was not statistically significantly different between the two groups (p = 0.274). Conclusions: The results demonstrated that the gingival placement of lingual brackets on the anterior teeth could decrease the distance between a tooth and the straight wire.

• 대한수학회지
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• 제43권2호
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• pp.413-424
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• 2006

Let $\Gamma$ be a bounded rotation (BR) curve without cusps in the complex plane $\mathbb{C}$ and let G := int $\Gamma$. We prove that the rate of convergence of the interpolating polynomials based on the zeros of the Faber polynomials $F_n\;for\;\bar G$ to the function of the reflexive Smirnov-Orlicz class $E_M (G)$ is equivalent to the best approximating polynomial rate in $E_M (G)$.

• 대한치과교정학회지
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• 제25권2호
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• pp.153-163
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• 1995

본 연구는 III급 부정 교합을 판별하는데 있어, 수평 부조화의 진단에 이용되는 여러 진단 항목들의 진단학적 효율과 타당성을 ROC analysis로 비교하는데 그 목적이 있다. ROC(Receiver Operating Characteristic) analysis는 연속적으로 변하는 cut-off value에서의 sensitivity와 1-specificity에 의해 그려지는 곡선으로서 진단 방법의 타당성을 결정하고, 여러 진단 방법들을 비교하는 분석법으로 알려져 있다. 부정교합자 496명을 대상으로 측모 두부 X-선 계측사진과 진단모형을 이용하여, 진단모형 계측을 통해 부정교합군을 분류하였으며, 이중 III급 부정 교합자는 245명이었다. 측모 두부 X-선계측사진에서 16개의 계측항목을 선정하였으며, 이 계측항목들과 III급 부정교합의 관계를 알아보고자 각도 계측항목에서는 $1^{\circ}$ 간격으로, 선계측항목에서는 1mm의 간격으로 sensitivity와 specificity를 구해 ROC curve를 그렸다. 그리고, 이 계측항목들의 직접적인 비교를 위해 ROC curve 아래의 면적을 계산해냈다. 결과는 다음과 같다. 1. III급 부정교합을 판별하는데 있어, "Wits" appraisal이 다른 계측 항목에 비해 더 나은 진단 효율을 보였다. 2. AB plane angle, ANB angle, App-Bpp distance, AF-BF distance, APDI, N perpendicular to A 와 Pog to N perpendicular의 차이, maxillomandibular differential도 높은 진단 가치를 보였다. 3. 하악골의 위치를 평가하는 계측항목은 중정도의 진단 효율을 보였다. 4. 상악골에 대한 계측항목은 III급 부정교합의 판별에 대한 진단 가치가 낮았다.

• 대한수학회보
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• 제51권1호
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• pp.29-41
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• 2014

In this paper, we prove that infinite-dimensional vector spaces of -dense curves are generated by means of the functional equations f(x)+f(2x)+${\cdots}$+f(nx) = 0, with $n{\geq}2$, which are related to the partial sums of the Riemann zeta function. These curves ${\alpha}$-densify a large class of compact sets of the plane for arbitrary small ${\alpha}$, extending the known result that this holds for the cases n = 2, 3. Finally, we prove the existence of a family of solutions of such functional equation which has the property of quadrature in the compact that densifies, that is, the product of the length of the curve by the $n^{th}$ power of the density approaches the Jordan content of the compact set which the curve densifies.

• 한국태양에너지학회:학술대회논문집
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• 한국태양에너지학회 2012년도 춘계학술발표대회 논문집
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• pp.457-462
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• 2012

Daylighting software is an important component to predict the performance of daylighting system in advance of a field demonstration study with installing them in buildings. PHOTOPIA is a powerful software to generate a candela distribution curve(CDC) of an active daylighting system like a tracking dish concentrator. With PHOTOPIA, a set of candela distribution curves was generated under clear sky conditions and different solar altitude angles. The candela distribution curves were then imported to RADIANCE for rendering and analysis on the daylighting performance of a tracking dish concentrator when it installed in a actual class room without windows. As a result, the daylight collection efficiency of the dish concentrator was 68.4% when we assumed that there was no tracking error. It was found that candela(cd) and total lumens(lm) increased with solar altitude rising, whereas the distribution angle was fixed. The illuminance uniformity on the work plane in the class room was relatively low, 0.12, while the illuminance uniformity on the area of $2.7m^2$ to which the light was illuminated was considerably high, 0.60. The maximum illuminance was 1,340lux with a solar altitude angle of 80 degrees.