• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.751-767
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• 2022

This paper deals with the Paneitz-Branson operator in compact Riemannian manifolds with negative Yamabe invariant. We start off by providing a new criterion for the positivity of the Paneitz-Branson operator when the Yamabe invariant of the manifold is negative. Another result stated in this paper is about the existence of a metric on a manifold of dimension 5 such that the Paneitz-Branson operator has multiple negative eigenvalues. Finally, we provide new inequalities related to the upper bound of the mean value of the Q-curvature.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1235-1242
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• 2013

We give area and height estimates for cmc-graphs over a bounded planar $C^{2,{\alpha}}$ domain ${\Omega}{\subset}\mathbb{R}^3$. For a constant H satisfying $H^2{\mid}{\Omega}{\mid}{\leq}9{\pi}/16$, we show that the height $h$ of H-graphs over ${\Omega}$ with vanishing boundary satisfies ${\mid}h{\mid}$ < $(\tilde{r}/2{\pi})H{\mid}{\Omega}{\mid}$, where $\tilde{r}$ is the middle zero of $(x-1)(H^2{\mid}{\Omega}{\mid}(x+2)^2-9{\pi}(x-1))$. We use this height estimate to prove the following existence result for cmc H-graphs: for a constant H satisfying $H^2{\mid}{\Omega}{\mid}$ < $(\sqrt{297}-13){\pi}/8$, there exists an H-graph with vanishing boundary.

• Proceedings of the KSME Conference
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• 2000.11b
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• pp.461-466
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• 2000

Direct numerical simulations (DNS) is carried out to study fully-developed turbulent concentric annular pipe flow with two radius ratios at $Re_{Dh}\;=\;8900$. In case of $R_1/R_2\;=\;0.5$, the present result for the mean flow is in good agreement with the previous experimental data. Because of the transverse curvature effects, the distributions of mean flow and turbulent intensities are asymmetric in contrast to those of other fully-developed flows (channel and pipe flow). From the distributions of skewness of radial velocity fluctuations, it co be identified that all of the characteristics of channel, pipe and turbulent flow on a cylinder in axial flow can be appeared in concentric annular pipe flow.

• Proceedings of the Korea Information Processing Society Conference
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• 2002.11a
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• pp.699-702
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• 2002

본 논문에서는 anisotropic diffusion 방법의 일종인 평균곡률 확산 (Mean Curvature Diffusion) 방법을 이용하여 영상에 포함된 잡음은 제거하고 동시에 에지는 보존하는 기법을 제안한다. 평균곡률 확산은 2 차원 영상의 밝기값을 3 차원 공간상의 z 좌표에 대응시켜 영상의 밝기값에 대응하는 공간 상의 곡면을 구성하고 이 곡면을 평균곡률에 비례하는 속도로 확산시킨다. 확산이 진행되면서 평균곡률이 영이 되는 에지에서는 확산이 발생하지 않고 잡음 등의 영향이 많은 에지 이외의 영역에서는 확산이 빠른 속도로 진행된다. 기존의 평균곡률 확산 방법의 성능을 개선하기 위해 최소/최대 흐름 방법을 평균곡률 확산 방법과 결합시키고 영상의 2 차 도함수를 사용하여 d얇은 에지를 보존하였다. 실험을 통해 제안한 방법이 기존의 방법보다 잡음 제거와 에지 보존 성능이 우수함을 확인할 수 있었다.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.171-184
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• 2023

In this paper, we show that a complete translating soliton Σ^m in ℝⁿ for the mean curvature flow is stable with respect to weighted volume functional if Σ satisfies that the L^m norm of the second fundamental form is smaller than an explicit constant that depends only on the dimension of Σ and the Sobolev constant provided in Michael and Simon [12]. Under the same assumption, we also prove that under this upper bound, there is no non-trivial f-harmonic 1-form of L²_f on Σ. With the additional assumption that Σ is contained in an upper half-space with respect to the translating direction then it has only one end.

• The Journal of Advanced Prosthodontics
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• v.2 no.3
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• pp.92-96
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• 2010

PURPOSE. The aim of this study was to evaluate the thickness of buccal and palatal alveolar bone and buccal bony curvature below root apex in maxillary anterior teeth of Korean adults using Cone-beam CT images. MATERIALS AND METHODS. The 3D image was reconstructed with dicom file obtained through CBCT from 20 - 39 year old Korean subjects (n = 20). The thickness of buccal and palatal plate, root diameter, the buccal bony curvature angle below root apex and the distance from root apex to the deepest point of buccal bony curvature were measured on maxillary anterior teeth area using OnDemand3D program. RESULTS. Mean thickness of buccal plate 3 mm below CEJ was $0.68{\pm}0.29\;mm$ at central incisor, $0.76{\pm}0.59\;mm$ at lateral incisor, and $1.07{\pm}0.80\;mm$ at canine. Mean thickness of palatal plate 3 mm below CEJ was $1.53{\pm}0.55\;mm$ of central incisor, $1.18{\pm}0.66\;mm$ of lateral incisor, $1.42{\pm}0.77\;mm$ of canine. Bucco-lingual diameter 3 mm below CEJ was $5.13{\pm}0.37\;mm$ of central incisor, $4.58{\pm}0.46\;mm$ of lateral incisor, and $5.93{\pm}0.47\;mm$ of canine. Buccal bony curvature angle below root apex was $134.7{\pm}17.5^{\circ}$ at central incisor, $151.0{\pm}13.9^{\circ}$ at lateral incisor, $153.0{\pm}9.5^{\circ}$ at canine. Distance between root apex and the deepest point of buccal bony curvature of central incisor was $3.67{\pm}1.28\;mm$ at central incisor, $3.90{\pm}1.51\;mm$ at lateral incisor, and $5.13{\pm}1.70\;mm$ at canine. CONCLUSION. Within the limitation of this study in Korean adults, the thickness of maxillary anterior buccal plate was very thin within 1mm and the thickness of palatal plate was thick, relatively. The buccal bony curvature below root apex of maxillary central incisor was higher than that of lateral incisor and canine and it seems that the buccal bony plate below root apex of central incisor is most curved.

• Journal of Korean Medicine Rehabilitation
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• v.15 no.2
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• pp.105-105
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• 2005

Objectives : The purpose of this study was to investigate the correlation between cervical spine curvature and thermography on neck pain patients. Methods : The cervical spine curvature was assessed on lateral view of plain radiograph by three measurements(Depth of cervical curve, Method of Jochumsen, Angle of cervical curve), then the neck pain patients were divided into straight curvature group(Straight group), normal curvature group(Control I), and no neck pain group(Control II) was selected by random sampling. I measured temperature of the both side Pungji(風池, G20), Kyonjong(肩井, G21), Chonjong(天宗, SI11) by thermography examination on Experimental group(Straight group) and control group(Control I, II), then analyzed the temperature statically with student's t-test, ANOVA. Results : The temperature of six point on Straigt group was lower than that of Control I, but had no significant difference(p>0.05). The temperature of six point on Straigt group was lower than that of Control II. The descent of temperature on Lt. Pungji(風池, G20), Lt. Kyonjong(肩井, G21), Rt. Chonjong(天宗, SI11) had significance(p<0.05). There is no corelation between onset period and mean temperature of six points. Conclusions : Thermography represnets the presence of neck pain, but has no correlation with straight of cervical curvature.

• Communications of the Korean Mathematical Society
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• v.6 no.1
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• pp.119-133
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• 1991

• Journal of the Korean Mathematical Society
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• v.30 no.2
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• pp.299-313
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• 1993

• The korean journal of orthodontics
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• v.51 no.3
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• pp.145-156
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• 2021

Objective: The aim of this retrospective study was to assess the midfacial soft tissue changes following maxillary expansion using micro-implant-supported maxillary skeletal expanders (MSEs) in young adults by cone-beam computerized tomography (CBCT) and to evaluate the correlations between hard and soft tissue changes after MSE usage. Methods: Twenty patients (mean age, 22.4 years; range, 17.6-27.1) with maxillary transverse deficiency treated with MSEs were selected. Mean expansion amount was 6.5 mm. CBCT images taken before and after expansion were superimposed to measure the changes in soft and hard tissue landmarks. Statistical analyses were performed using paired t-test and Pearson's correlation analysis on the basis of the normality of data. Results: Average lateral movement of the cheek points was 1.35 mm (right) and 1.08 mm (left), and that of the alar curvature points was 1.03 mm (right) and 1.02 mm (left). Average forward displacement of the cheek points was 0.59 mm (right) and 0.44 mm (left), and that of the alar curvature points was 0.61 mm (right) and 0.77 mm (left) (p < 0.05). Anterior nasal spine (ANS), posterior nasal spine (PNS), and alveolar bone width showed significant increments (p < 0.05). Changes in the cheek and alar curvature points on both sides significantly correlated with hard tissue changes (p < 0.05). Conclusions: Maxillary expansion using MSEs resulted in significant lateral and forward movements of the soft tissues of cheek and alar curvature points on both sides in young adults and correlated with the maxillary suture opening at the ANS and PNS.