• Journal of Institute of Control, Robotics and Systems
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• v.22 no.8
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• pp.597-602
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• 2016

In image guided surgery, a patient registration process is a critical process for the successful operation, which is required to use pre-operative images such as CT and MRI during operation. Though several patient registration methods have been studied, we concentrate on one method that utilizes 3D surface measurement data in this paper. First, a hand-held 3D surface measurement device measures the surface of the patient, and secondly this data is matched with CT or MRI data using optimization algorithms. However, generally used ICP algorithm is very slow without a proper initial location and also suffers from local minimum problem. Usually, this problem is solved by manually providing the proper initial location before performing ICP. But, it has a disadvantage that an experience user has to perform the method and also takes a long time. In this paper, we propose a method that can accurately find the proper initial location automatically. The proposed method finds the proper initial location for ICP by converting 3D data to 2D curvature images and performing image matching. Curvature features are robust to the rotation, translation, and even some deformation. Also, the proposed method is faster than traditional methods because it performs 2D image matching instead of 3D point cloud matching.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.737-767
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• 2016

This paper concerns closed hypersurfaces of dimension $n{\geq}2$ in the hyperbolic space ${\mathbb{H}}_{\kappa}^{n+1}$ of constant sectional curvature evolving in direction of its normal vector, where the speed equals a power ${\beta}{\geq}1$ of the mean curvature. The main result is that if the initial closed, weakly h-convex hypersurface satisfies that the ratio of the biggest and smallest principal curvature at everywhere is close enough to 1, depending only on n and ${\beta}$, then under the flow this is maintained, there exists a unique, smooth solution of the flow which converges to a single point in ${\mathbb{H}}_{\kappa}^{n+1}$ in a maximal finite time, and when rescaling appropriately, the evolving hypersurfaces exponential convergence to a unit geodesic sphere of ${\mathbb{H}}_{\kappa}^{n+1}$.

• Restorative Dentistry and Endodontics
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• v.22 no.1
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• pp.388-395
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• 1997

Maintaining the original canal path during instrumentation is a challenge in narrow curved canals. This study compared the maintenance of the original canal path of curved root canals during instrumentation with two kinds of stainless steel K-files(Brassler USA & Mani Japan), K-flexofiles(Maillefer Swiss) and Ni-Ti files(Brassler USA, Savannah, GA) using circumferential filing technique to # 40 MAF on 60 extracted human molars. Buccal and mesial canals with minimal initial curvature of 20 degrees were used. The maximal initial curvature was 41.5 degrees. Sixty curved canals divided into four groups according to file type(Group 1 : Ni-Ti file, Group 2 : K-flexofile, Group 3: K-file(Brassler), Group 4 : K-file(Mani)). Radiographs of canals were obtained before and after canal shaping. And postoperative radiographs were compared with preoperative radiographs using superimposition method. Data analysis was performed using Covariance analysis and paired-comparison test. The results observed were as follow ; 1. The angle of curvature was better maintained with Ni-Ti file than with stainless steel files. (p<0.01) 2. There was no significant difference in maintaining canal curvature between K-flexofile, Brassler$^{(R)}$ K-file and Mani$^{(R)}$ K-file, although there was some differences in mean values of postoperative canal curvature. 3. Paired-comparison t test revealed significant differences within each of the three stainless steel file types when comparing the mean differences before and after instrumentation, but no significant differences were observed within Ni-Ti file group.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2001.10a
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• pp.163-169
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• 2001

The solution of two-dimensional deflection of circular wavy reinforcing fiber elastics was obtained for one end clamped boundary under concentrated load condition. The fiber was regarded as a linear elastic material. Wavy shape was described as a combination of half-circular arc smoothly connected each other with constant curvature of all the same magnitude and alternative sign. Also load direction was taken into account. As a result, the solution was expressed in terms of a series of elliptic integrals. These elliptic integrals had two different transformed parameters involved with load value and initial radius of curvature. While we found the exact solutions and expressed them in terms of elliptic integrals, the recursive ignition formulae about the displacement and arc length at each segment of circular section were obtained. Algorithm of determining unknown parameters was established and the profile curve of deflected beam was shown in comparison with initial shape.

• Advances in nano research
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• v.5 no.2
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• pp.179-192
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• 2017

The transverse vibration of double walled carbon nanotube (DWCNT) embedded in elastic medium with an initial imperfection is considered. In this paper, Timoshenko beam theory is employed. However the nonlocal theory is used for modeling the nano scale of nanotube. In addition, the governing Equations of motion are obtained utilizing the Hamilton's principle and simply-simply boundary conditions are assumed. Furthermore, the Navier method is used for determining the natural frequencies of DWCNT. Hence, some parameters such as nonlocality, curvature amplitude, Winkler and Pasternak elastic foundations and length of the curved DWCNT are analyzed and discussed. The results show that, the curvature amplitude causes to increase natural frequency. However, nonlocal coefficient and elastic foundations have important role in vibration behavior of DWCNT with imperfection.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.749-761
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• 2018

Here, we calculate the evolution equation of the reduced hh-curvature and the Ricci scalar along the Finslerian Ricci flow. We prove that Finsler Ricci flow preserves positivity of the reduced hh-curvature on finite time. Next, it is shown that evolution of Ricci scalar is a parabolic-type equation and moreover if the initial Finsler metric is of positive flag curvature, then the flag curvature, as well as the Ricci scalar, remain positive as long as the solution exists. Finally, we present a lower bound for Ricci scalar along Ricci flow.

• Communications of the Korean Institute of Information Scientists and Engineers
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• v.1 no.1
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• pp.72-74
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• 1983

Traditionally, polynomials have been used to approximte functions with prescribed values at a number of points(called the knots) on a given interal on the real line. The method of splines recently developed is more flexible. It approximates a function in a piece-wise fashion, by means of a different polynomial in each subinterval. The cubic spline gas ets origins in beam theory. It possessed continuous first and second deriatives at the knots and is characterised by a minimum curvature property which es rdlated to the physical feature of minimum potential energy of the supported beam. Translated into mathematical terms, this means that between successive knots the approximation yields a third-order polynomial sith its first derivatives continuous at the knots. The minimum curvature property holds good for each subinterval as well as for the whole region of approximation This means that the integral of the square of the second derivative over the entire interval, and also over each subinterval, es to be minimized. Thus, the task of determining the spline lffers itself as a textbook problem in discrete computer programming, since the integral of ghe square of the second derivative can be obviously recognized as the criterion function whicg gas to be minimized. Starting with the initial value of the function and assuming an initial solpe of the curve, the minimum norm property of the curvature makes sequential decision of the slope at successive knots (points) feasible. It is the aim of this paper to derive the cubic spline by the methods of computer programming and show that the results which is computed the all the alues in each subinterval of the spline approximations.

• Structural Engineering and Mechanics
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• v.54 no.1
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• pp.121-133
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• 2015

The aluminum dome has been widely used in natatorium, oil storage tank, power plant, coal, as well as other industrial buildings and structures. However, few research has focused on the structural behavior and design method of this dome. At present, most designs of aluminum alloy domes have referred to theories and methods of steel spatial structures. However, aluminum domes and steel domes have many differences, such as elasticity moduli, roof structures, and joint rigidities, which make the design and analysis method of steel spatial structures not fully suitable for aluminum alloy dome structures. In this study, a stability analysis method, which can consider structural imperfection, member initial curvature, semi-rigid joint, and skin effect, was presented and used to study the stability behavior of aluminum dome structures. In addition, some meaningful conclusions were obtained, which could be used in future designs and analyses of aluminum domes.

• Journal of Korean Institute of Industrial Engineers
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• v.19 no.4
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• pp.105-114
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• 1993

In this article, a planar geodesic (2-dimensional minimum length curve between two points) on which the maximum curvature is constrained and with prescribed initial and terminal directions is studied. A generic problem is formulated by the minimum-time optimal control problem in free terminal time. It is shown that the optimal path ($G^2$) may contain a singular arc or not and that the general types of $G^2$ can he classified into the 3 classes of control sequences. Finally, the explicit form of $G^2$ is derived geometrically as well as algebraically form the main theorem of this article.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.3
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• pp.834-845
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• 1995

An experimental study is made in a nearly two-dimensional 90.deg. curved duct to investigate the effects of interaction between streamline curvature and mean strain on turbulence. The initial shear at the entrance to the curved duct is varied by an upstream shear generator to produce five different shear conditions ; a uniform flow (UF), a positive weak shear (PW), a positive strong shear(PS), a negative weak shear (NW) and a negative strong shear(NS). With the mean field data of the case UF, variations of the momentum thickness, the shape factor and the skin friction over the convex(inner) surface and the concave (outer) surface are scrutinized quantitatively in-depth. It is found that, while the pressure loss due to curvature is insensitive to the inlet shear rates, the distributions of wall static pressure along both convex and concave surfaces are much influenced by the inlet shear rates.