• 대한수학교육학회지:학교수학
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• 제12권3호
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• pp.389-410
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• 2010

이 논문에서는 사각형의 상호 관계가 우리나라 교육과정에 어떻게 자리 잡게 되었는지를 살펴보고자 하였다. 이를 위해 1차, 2차, 3차 교육과정기에 발행된 국가수준 교육과정 문서, 교과서는 물론 당시 발간된 교사용 지도서, 교육과정 해설서, 실험용 교사용 지도서 등을 고찰하였다. 사각형의 상호 관계는 3차 교육과정에서 본격적으로 교육내용을 자리 잡았으며, 집합의 포함 관계를 지도할 수 있는 소재로서 주목을 받았다. 특히 사각형의 정의를 바탕으로 상호 관계를 이해하도록 하였는데, 이는 수학적 정의의 중요한 학문적 기능인, 범주화와 그를 통한 논증의 용이성과 관련 시킬 수 있다. 이 논문의 연구결과는, 국가수준에서 수학교육내용으로서 사각형의 상호 관계의 적정성을 판단할 때 기초적인 창조 자료가 될 것으로 기대한다.

• 대한치과교정학회지
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• 제18권1호
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• pp.235-252
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• 1988

The quadrilateral analysis is a proportional analysis which evaluates the skeletal configuration of lower face on the relations between both jaws in the horizontal as we]1 as vortical dimensions. This study was undertaken to analyse the harmony and disharmony of quadrilateral patterns in normal occlusion and malocclusion. The present study was carried out on lateral cephalograms of 530 Korean children; the subjects consisted of 135 normal occlusions (63 male and 72 female), 105 Class II division 1 malocclusions (52 male and 53 female), 109 Class III malocclusions (50 male and 59 female), 91 hypodivergent facial types (44 male and 47 female) and 90 hyperdivergent facial types (45 male and 45 female). The following conclusions were reached: 1. Means and standard deviation in each group and sex were obtained from normal occlusion and malocclusion. 2. Quadrilateral mean diagram in normal occlusion was constructed for male and female, respectively. 3. In normal occlusion, 1:1 ratio exists between the maxillary base length (A' to Ptm') and mandibular base length (B' to J'), but lower facial height is targer than above. 4. Difference is effective to estimate the degrees of Class II and Class III malocclusion, and lower facial height (LFH) and sagittal angle is effective to recognize the hypodivergent and hyperdivergent facial type. 5. Quadrilateral analysis is able to visualize the anteroposterior and vertical dysplasia of lower face, and it is helpful to recognize certain problems in malocclusion.

• 대한수학회지
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• 제53권6호
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• pp.1411-1429
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• 2016

We consider the nite volume element method for elliptic problems using isoparametric bilinear elements on quadrilateral meshes. A gradient recovery method is presented by using the patch interpolation technique. Based on some superclose estimates, we prove that the recovered gradient $R({\nabla}u_h)$ possesses the superconvergence: ${\parallel}{\nabla}u-R({\nabla}u_h){\parallel}=O(h^2){\parallel}u{\parallel}_3$. Finally, some numerical examples are provided to illustrate our theoretical analysis.

• 한국컴퓨터정보학회지
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• 제14권1호
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• pp.249-254
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• 2006

본 논문에서는 기존의 사각형을 이용한 충돌처리 기법 알고리즘에 대하여 알아보고, 문제점을 제시하며, 단순한 사각형 충돌의 단점을 보완한, 작은 사각형 단위의 충돌 체크 기법을 제안하고, 실험과 실제 구현한 게임 화면 디자인을 통하여 제안한 알고리즘이 실제 게임에서 적용할 수 있음을 보인다.

• 한국CDE학회논문집
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• 제4권2호
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• pp.153-161
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• 1999

An atomatic mesh generation scheme with unstructured quadrilateral elements on trimmed surfaces has been developed. Trimmed surfaces are often encountered in modeling of structures with complex shapes such as aircrafts, automobile structures, pressure vessels and etc. For unstructured mesh generation with quadrilateral elements, a domain decomposition algorithm employing loop operators has been used. Mesh generation on trimmed surface is performed in three steps. First, trimmed surfaces with holes or cuts are transformed to th largest projection planes in which the meshes are constructed. The constructed meshes are transformed to the u-v parametric plane and then finally to the original 3D surfaces. Th exact locations of holes or cuts in projection planes are determined by the Newton-Raphson method. Sample meshes are constructed to demonstrate the effectiveness of the proposed algorithm.

• 대한기계학회논문집A
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• 제27권10호
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• pp.1762-1771
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• 2003

In part of mechanical design analysis, quadrilateral mesh is usually used because it provides less approximate errors than triangular mesh. Over the decades, Paving method has been considered as the most robust method among existing automatic quadrilateral element mesh generation methods. However, it also has some problems such as unpredictable node projection and relatively large element generation. In this study, the aforementioned problems are corrected by updating the Paving method. In so doing, a part of node projection process is modified by classifying nodes based on the interior angles. The closure check process is also modified by adding more nodes while generating elements. The result shows well shaped element distribution in the final mesh without any aforementioned problems.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.377-387
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• 2014

Let G be a (p, q) graph. Let f be a map from V (G) to {1, 2, ${\ldots}$, p}. For each edge uv, assign the label ${\mid}f(u)-f(\nu){\mid}$. f is called a difference cordial labeling if f is a one to one map and ${\mid}e_f(0)-e_f(1){\mid}{\leq}1$ where $e_f(1)$ and $e_f(0)$ denote the number of edges labeled with 1 and not labeled with 1 respectively. A graph with admits a difference cordial labeling is called a difference cordial graph. In this paper, we investigate the difference cordial labeling behavior of triangular snake, Quadrilateral snake, double triangular snake, double quadrilateral snake and alternate snakes.

• 한국자동차공학회논문집
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• 제3권6호
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• pp.145-153
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• 1995

An algorithm for the automatic generation of quadrilateral shell elements on three-dimensional sculptured surfaces has been developed, which is one of the key issues in the finite element analysis of structures with complex shapes such as automobile structures. Mesh generation on sculptured surfaces is performed in three steps. First a sculptured surface is transformed to a projection plane, on which the loops are subdivided into subloops by using the best split lines, and with the use of 6-node/8-node loop operators and a layer operator, quadrilateral finite elements are constructed on this plane. Finally, the constructed mesh is transformed back to the original sculptured surfaces. The proposed mesh generation scheme is suited for the generation of non-uniform meshes so that it can be effectively used when the desired mesh density is available. Sample meshes are presented to demonstrate the versatility of the algorithm.

• 한국CDE학회논문집
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• 제14권3호
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• pp.197-206
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• 2009

In a finite element analysis of the metal forming processes having large plastic deformation, largely distorted elements are unstable and hence they influence upon the result toward negative way so that adaptive remeshing is required to avoid a failure in the numerical computation. Therefore automatic mesh generation and regeneration is very important to avoid a numerical failure in a finite element analysis. In case of generating quadrilateral mesh, the automation is more difficult than that of triangular mesh because of its geometric complexity. However its demand is very high due to the precision of analysis. Thus, in this study, an automatic quadrilateral mesh generation and regeneration method using grid-based approach is developed. The developed method contains decision of grid size to generate initial mesh inside a two dimensional domain, classification of boundary angles and inner boundary nodes to improve element qualities in case of concave domains, and boundary projection to construct the final mesh.

• International Journal of CAD/CAM
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• 제11권1호
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• pp.11-17
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• 2011

A new method has been developed in this paper for automatic quadrilateral mesh generation for a two-dimensional domain. The method is named 'centering method' because it centers a point at the domain and then divides it into sub-domains using cutting lines from the center point. Each of the cutting lines is selected based on the criterion using the angles between the boundary of the domain and the cutting line. The decomposition of the domain into sub-domains is repeated until every subdomain has four or six nodes. Pre-defined splitters are used to divide six-node domains into quadrilateral elements depending on their configuration and presence on the boundary of the initial domain. Arbitrary domains are meshed as examples to verify the robustness of the new method.