• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2008.06a
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• pp.118-118
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• 2008

The oxide CMP has been applied to interlayer dielectric(ILD) and shallow trench isolation (STI) in chip fabrication. Recently the slurry used in oxide CMP being changed from silica slurry to ceria (cerium dioxide) slurry particularly in STI CMP, because the material selectivity of ceria slurry is better than material selectivity of silica slurry. Moreover, the ceria slurry has good a planarization efficiency, compared with silica slurry. However ceria abrasives make a material removal rate too high at the region of wafer center. Then we focuses on why profile of material removal rate is convex. The material removal rate sharply increased to 3216 $\AA$/min by $4^{th}$ run without conditioning. After $4^{th}$ run, material removal rate converged. Furthermore, profile became more convex during 12 run. And average material removal rate decreased when conditioning process is added to end of CMP process. This is due to polishing mechanism of ceria. Then the ceria abrasive remains at the pad, in particular remains more at wafer center contacted region of pad. The field emission scanning electron microscopy (FE-SEM) images showed that the pad sample in the wafer center region has a more ceria abrasive than in wafer outer region. The energy dispersive X-ray spectrometer (EDX) verified the result that ceria abrasive is deposited and more at the region of wafer center. Therefore, this result may be expected as ceria abrasives on pad surface causing the convex profile of material removal rate.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.407-417
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• 2022

Archimedes proved that for a point P on a parabola X and a chord AB of X parallel to the tangent of X at P, the area of the region bounded by the parabola X and the chord AB is four thirds of the area of the triangle ∆ABP. This property was proved to be a characteristic of parabolas, so called the Archimedean characterization of parabolas. In this article, we study strictly convex curves in the plane ℝ². As a result, first using a functional equation we establish a characterization theorem for quadrics. With the help of this characterization we give another proof of the Archimedean characterization of parabolas. Finally, we present two related conditions which are necessary and sufficient for a strictly convex curve in the plane to be an open arc of a parabola.

• Journal of the Society of Naval Architects of Korea
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• v.52 no.1
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• pp.70-76
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• 2015

The ship hull is accomplished by assembling various curved surfaces. There are numerous existing methods for ship hull processing, which need certain appropriate processing methods to enable it to be more efficient. The curved hull plates can be divided into convex region and saddle region. It is common to use line heating method to form a saddle region, when it comes to a convex region, it will be triangle heating method to be utilized. A precise analysis for curvature domain is required for the application of proper processing method. There exist various problems on existing calculation methods of curvature domain. Therefore, a more powerful method is demanded to it more accurately. In this study, a method called Dual Contouring is applied to extract curved surfaces, which is able to improve accuracy of extracted area. Based on all above, a best-suited heat processing method should be selected.

• International Journal of Contents
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• v.1 no.1
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• pp.40-44
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• 2005

This paper introduces region partitioning method of non-perfect nested loops with non-uniform dependences. This kind of loop normally can't be parallelized by existing parallelizing compilers and transformations. Even when parallelized in rare instances, the performance is very poor. Based on the Convex Hull theory which has adequate information to handle non-uniform dependences, this paper proposes an enhanced region partitioning method which divides the iteration space into minimum parallel regions where all the iterations inside each parallel region can be executed in parallel by using variable renaming after copying.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.583-595
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• 2016

Archimedes showed that for a point P on a parabola X and a chord AB of X parallel to the tangent of X at P, the area S of the region bounded by the parabola X and chord AB is four thirds of the area T of triangle ${\Delta}ABP$. It is well known that the area U formed by three tangents to a parabola is half of the area T of the triangle formed by joining their points of contact. Recently, the first and third authors of the present paper and others proved that among strictly locally convex curves in the plane ${\mathbb{R}}^2$, these two properties are characteristic ones of parabolas. In this article, in order to generalize the above mentioned property $S={\frac{4}{3}}T$ for parabolas we study strictly locally convex curves in the plane ${\mathbb{R}}^2$ satisfying $S={\lambda}T+{\nu}U$, where ${\lambda}$ and ${\nu}$ are some functions on the curves. As a result, we present two conditions which are necessary and sufficient for a strictly locally convex curve in the plane to be an open arc of a parabola.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.283-290
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• 2003

Andras Bezdek proved that if a convex n-gon and n points are given, then the points and the sides of the polygon can be renumbered so that at least[${\frac{n}{3}}$] triangles spanned by the ith point and the ith side (i = 1,2,...n) are mutually non-overlapping. In this paper, we show that at least [${\frac{n}{2}}$] mutually non-overlapping triangles can be constructed. This lower bound is best possible.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.1-23
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• 2005

The decentralized static output feedback design problem is considered. A constrained trust region method is developed that solves this optimal control problem when a complete set of state variables is not available. The considered problem is interpreted as a non-linear (non-convex) constrained matrix optimization problem. Then, a decentralized constrained trust region method is developed for this problem class exploiting the diagonal structure of the problem and using inexact computations. Finally, numerical results are given for the proposed method.

• Management Science and Financial Engineering
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• v.12 no.1
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• pp.113-125
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• 2006

Bilevel programming problem is a two-stage optimization problem where the constraint region of the first level problem is implicitly determined by another optimization problem. In this paper we consider the bilevel quadratic/linear fractional programming problem in which the objective function of the first level is quasiconcave, the objective function of the second level is linear fractional and the feasible region is a convex polyhedron. Considering the relationship between feasible solutions to the problem and bases of the coefficient submatrix associated to variables of the second level, an enumerative algorithm is proposed which finds a global optimum to the problem.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.34D no.7
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• pp.88-96
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• 1997

As the need of automatized system has been increased recently together with the development of industrial and military technologies, the adaptive real-time target detection technologies that can be embedded on vehicles, planes, ships, robots and so on, are hgihly demanded. Accordingly, this paper proposes a novel approach to detect and segment the moving targets using the binary phase extraction joint transform correlator (BPEJTC), the advanced image subtraction filter and convex hull processing. The BPEJTC which was used as a target detection unit mainly for target tracking compensating the camera movement. The target region has been detected by processing the successful three frames using the advanced image subtraction filter, and has become more accurate by applying the developed convex hull filter. As shown by some experimental results, it is expected that the proposed approaches for compensation of the camera movement and segmentationof of target region, can be used for th emissile guiddance, aero surveillance, automatic inspectin system as well as the target detection unit of automatic target recognition system that request adaptive real-time processing.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.39 no.2
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• pp.69-78
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• 2002

This paper addresses a method to automatically detect out a person's face from a given image that consists of a hair and face view of the person and a complex background scene. Out method involves an effective detection algorithm that exploits the spatial distribution characteristics of human skin color via an adaptive fuzzy color classifier (AFCC), The universal skin-color map is derived on the chrominance component of human skin color in Cb, Cr and their corresponding luminance. The desired fuzzy system is applied to decide the skin color regions and those that are not. We use RGB model for extracting the hair color regions because the hair regions often show low brightness and chromaticity estimation of low brightness color is not stable. After some preprocessing, we apply convex-hull to each region. Consequent face detection is made from the relationship between a face's convex-hull and a head's convex-hull. The algorithm using the convex-hull shows better performance than the algorithm using pattern method. The performance of the proposed algorithm is shown by experiment. Experimental results show that the proposed algorithm successfully and efficiently detects the faces without constrained input conditions in color images.