• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1247-1263
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• 2019

In ordered trees, two randomly chosen vertices are said to be dependent if one lies under the other. If not, we say that they are independent. We consider several classes of ordered trees with uniform updegree requirements and find the generating functions for the trees with two marked dependent/independent vertices. As a result, we compute the probability for two vertices being dependent/independent. We also count such trees by the distance between two independent vertices.

• The Mathematical Education
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• v.43 no.2
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• pp.177-186
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• 2004

In this paper, we introduce new functional definitions for school geometry based on DGS (dynamic geometry system) teaching-learning environment. For the vertices forming a geometric figure, we first consider the relationship between the independent vertices and dependent vertices, and using this relationship and educational considerations in DGS, we introduce functional definitions for the geometric figures in terms of its independent vertices. For this purpose, we design a new DGS called JavaMAL MicroWorld. Based on the needs of new definitions in DGS environment for the student's construction activities in learning geometry, we also design a new DGS based geometry curriculum in which the definitions of the school geometry are newly defined and reconnected in a new way. Using these funct onal definitions, we have taught the new geometry contents emphasizing the sequential expressions for the student's geometric activities.

• Korean Journal of Computational Design and Engineering
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• v.19 no.1
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• pp.61-67
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• 2014

This paper proposes a procedure enabling the extraction of view-dependent triangular approximations from a height map. In general, procedures to approximate a height map use tree hierarchies. These methods, however, have a limitation in terms of accuracy, because they depend on tree hierarchy than terrain features. To overcome the difficult, we apply the simplification method for triangular meshes to a height map. The proposed procedure maintains full decimation procedure to support multiresolution. The maintenance of decimation procedure results in creation of the groups (trees), each of which consists of vertices that can be merged into one vertex (root node). As the groups have tolerance which is determined by some tests, they support the generation of view-dependent arbitrary triangular meshes.

• The Journal of Korean Association of Computer Education
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• v.9 no.1
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• pp.89-95
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• 2006

The local geometric properties such as curvatures and normal vectors play important roles for analyzing the local shape of objects in the fields of computer graphics and computer vision. The result of the geometric operations such as mesh simplification and mesh smoothing is dependent on how to compute the curvatures of meshes because there is no exact mathematical definition of curvature at vertices on 3D meshes. Therefore, In this paper, we indicate the fatal error in computing the sectional curvatures of the most previous discrete curvature estimations. Moreover, we present a discrete curvature estimation to overcome the error, which is based on the parabola interpolation and the geometric properties of Bezier curves. Therefore, We can well distinguish between the sharp vertices and the flat ones, so our method may be applied to a variety of geometric operations.

• Journal of the Korean Operations Research and Management Science Society
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• v.14 no.1
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• pp.88-96
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• 1989

General measure in the reliability is the k-terminal reliability, which is the probability that the specified vertices are connected by the working edges. To compute the k-terminal reliability components are usually assumed to be statistically independent. In this study the modeling and analysis of the k-terminal reliability are investigated when dependency among components is considered. As the size of the network increases, the number of the joint probability parameter to represent the dependency among components is increasing exponentially. To avoid such a difficulty the structured-event-based-reliability model (SERM) is presented. This model uses the combination of the network topology (physical representation) and reliability block diagram (logical representation). This enables us to represent the dependency among components in a network form. Computational algorithms for the k-terminal reliability in SERM are based on the factoring algorithm Two features of the ractoring algorithm are the reliability preserving reduction and the privoting edge selection strategy. The pivoting edge selction strategy is modified by two different ways to tackle the replicated edges occuring in SERM. Two algorithms are presented according to each modified pivoting strategy and illustrated by numerical example.

• The Transactions of the Korea Information Processing Society
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• v.3 no.7
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• pp.1894-1905
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• 1996

Delauuany triangulation which is the dual of Dirichlet tessellation is not affine invariant. In other words, the triangulation is dependent upon the choice of the coordinate axes used to represent the vertices. In the same reason, Delahanty tetrahedrization does not have an affine iveariant transformation property. In this paper, we present a new type of tetrahedrization of spacial points sets which is unaffected by translations, scalings, shearings and rotations. An affine invariant tetrahedrization is discussed as a means of affine invariant 2 -D triangulation extended to three-dimensional tetrahedrization. A new associate norm between two points in 3-D space is defined. The visualization of the structure of tetrahedrization can discriminate between Delaunay tetrahedrization and affine invariant tetrahedrization.

• Journal of the Korea Computer Graphics Society
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• v.4 no.1
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• pp.1-10
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• 1998

The idea of level-of-detail based on multiresolution model is gaining popularity as a natural means of handling the complexity regarding the realtime rendering of virtual environments. To generate an effective multiresolution model, we should capture the prominent visual features in the process of simplifying original complex model. In this paper, we incorporate view dependent features such as silhouette features and backface features, to the generation process of multiresolution model. To capture the view directional parameter, we propose multiresolution view sphere. View sphere maps the directional relationship between object surface and the view. Using the view sphere, coherence in the directional space is mapped into spatial coherence in the view sphere. View sphere is generated in multiresolution fashion to simplify the object. To access multiresolution view sphere efficiently, we devise quad tree for the view sphere. We also devise a mechanism for realtime simplification process using proposed view sphere. Using proposed mechanism, regenerating simplified model in realtime is effectively done in the order of number of rendered vertices.

• Proceedings of the Korean Vacuum Society Conference
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• 2011.02a
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• pp.47-47
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• 2011

There have been numerous efforts to enhance the efficiency of light-emitting diodes (LEDs) by using low dimensional structures such as quantum dots (QDs), wire (QWRs), and wells (QWs). We demonstrate QD/QWR/QW hybrid structured LEDs by using nano-scaled pyramid structures of GaN with ~260 nm height. Photoluminescence (PL) showed three multi-peak spectra centered at around 535 nm, 600 nm, 665 nm for QWs, QWRs, and QDs, respectively. The QD emission survived at room temperature due to carrier localization, whereas the QW emission diminished from 10 K to 300 K. We confirmed that hybrid LEDs had zero-, one-, and two-dimensional behavior from a temperature-dependent time-resolved PL study. The radiative lifetime of the QDs was nearly constant over the temperature, while that of the QWs increased with increasing temperature, due to low dimensional behavior. Cathodoluminescence revealed spatial distributions of InGaN QDs, QWRs, and QWs on the vertices, edges, and sidewalls, respectively. We investigated the blue-shifted electroluminescence with increasing current due to the band-filling effect. The hybrid LEDs provided broad-band spectra with high internal quantum efficiency, and color-tunability for visible light-emitting sources.