• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.387-401
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• 2001

If the distance between two vertices becomes longer after the removal of a vertex u, then u is called a hinge vertex. In this paper, a linear time sequential algorithm is presented to find all hinge vertices of an interval graph. Also, a parallel algorithm is presented which takes O(n/P + log n) time using P processors on an EREW PRAM.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.9
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• pp.1081-1090
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• 1988

A series of procedures using image processing techniques is presented for extracting layout information fast and automatically from chip images. CIF (caltech intermediate form) is chosen for representing such information. First, line-edges are extracted using a line-edge detector. Then, thinning and noise removal procedures follow. Subsequent procedures are vertex extraction and vertex grouping. Finally, CIF is extracted from the coordinates of the grouped vertices. In this paper, the final process is applied to only metal layer. In experiments, this processing scheme is shown to be very effective in extracting CIF.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.745-754
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• 2016

In a graph G = (V, E), a non-empty set $S{\subseteq}V$ is said to be an open packing set if no two vertices of S have a common neighbour in G. The maximum cardinality of an open packing set is called the open packing number and is denoted by ${\rho}^{\circ}$. In this paper, we examine the effect of ${\rho}^{\circ}$ when G is modified by deleting a vertex.

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.77-83
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• 2024

Chung defined a pebbling move on a graph G as the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The monophonic pebbling number guarantees that a pebble can be shifted in the chordless and the longest path possible if there are any hurdles in the process of the supply chain. For a connected graph G a monophonic path between any two vertices x and y contains no chords. The monophonic pebbling number, µ(G), is the least positive integer n such that for any distribution of µ(G) pebbles it is possible to move on G allowing one pebble to be carried to any specified but arbitrary vertex using monophonic a path by a sequence of pebbling operations. The aim of this study is to find out the monophonic pebbling numbers of the sun graphs, (C_n × P₂) + K₁ graph, the spherical graph, the anti-prism graphs, and an n-crossed prism graph.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.163-176
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• 2019

Given a distribution of pebbles on the vertices of a connected graph G, a pebbling move is defined as the removal of two pebbles from some vertex and the placement of one of those pebbles at an adjacent vertex. The t-pebbling number, $f_t(G)$, of a connected graph G, is the smallest positive integer such that from every placement of $f_t(G)$ pebbles, t pebbles can be moved to any specified vertex by a sequence of pebbling moves. A graph G has the 2t-pebbling property if for any distribution with more than $2f_t(G)$ - q pebbles, where q is the number of vertices with at least one pebble, it is possible, using the sequence of pebbling moves, to put 2t pebbles on any vertex. In this paper, we determine the t-pebbling number for the middle graph of a complete binary tree $M(B_h)$ and we show that the middle graph of a complete binary tree $M(B_h)$ satisfies the 2t-pebbling property.

• The Journal of Korean Academy of Prosthodontics
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• v.39 no.6
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• pp.709-734
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• 2001

The aims of this experiment were to investigate the strain and temperature changes simultaneously within autopolymerzing acrylic resin specimens. A computerized data acquisition system with an electrical resistance strain gauge and a thermocouple was used over time periods up to 180 minutes. The overall strain kinetics, the effects of stress relaxation and additional heat supply during the polymerization were evaluated. Stone mold replicas with an inner butt-joint rectangular cavity ($40.0{\times}25.0mm$, 5.0mm in depth) were duplicated from a brass master mold. A strain gauge (AE-11-S50N-120-EC, CAS Inc., Korea) and a thermocouple were installed within the cavity, which had been connected to a personal computer and a precision signal conditioning amplifier (DA1600 Dynamic Strain Amplifier, CAS Inc., Korea) so that real-time recordings of both polymerization-induced strain and temperature changes were performed. After each of fresh resin mixture was poured into the mold replica, data recording was done up to 180 minutes with three-second interval. Each of two poly(methyl methacrylate) products (Duralay, Vertex) and a vinyl ethyl methacrylate product (Snap) was examined repeatedly ten times. Additionally, removal procedures were done after 15, 30 and 60 minutes from the start of mixing to evaluate the effect of stress relaxation after deflasking. Six specimens for each of nine conditions were examined. After removal from the mold, the specimen continued bench-curing up to 180 minutes. Using a waterbath (Hanau Junior Curing Unit, Model No.76-0, Teledyne Hanau, New York, U.S.A.) with its temperature control maintained at $50^{\circ}C$, heat-soaking procedures with two different durations (15 and 45 minutes) were done to evaluate the effect of additional heat supply on the strain and temperature changes within the specimen during the polymerization. Five specimens for each of six conditions were examined. Within the parameters of this study the following results were drawn: 1. The mean shrinkage strains reached $-3095{\mu}{\epsilon},\;-1796{\mu}{\epsilon}$ and $-2959{\mu}{\epsilon}$ for Duralay, Snap and Vertex, respectively. The mean maximum temperature rise reached $56.7^{\circ}C,\;41.3^{\circ}C$ and $56.1^{\circ}C$ for Duralay, Snap, and Vertex, respectively. A vinyl ethyl methacrylate product (Snap) showed significantly less polymerization shrinkage strain (p<0.01) and significantly lower maximum temperature rise (p<0.01) than the other two poly(methyl methacrylate) products (Duralay, Vertex). 2. Mean maximum shrinkage rate for each resin was calculated to $-31.8{\mu}{\epsilon}/sec,\;-15.9{\mu}{\epsilon}/sec$ and $-31.8{\mu}{\epsilon}/sec$ for Duralay, Snap and Vertex, respectively. Snap showed significantly lower maximum shrinkage rate than Duralay and Vertex (p<0.01). 3. From the second experiment, some expansion was observed immediately after removal of specimen from the mold, and the amount of expansion increased as the removal time was delayed. For each removal time, Snap showed significantly less strain changes than the other two poly(methyl methacrylate) products (p<0.05). 4. During the external heat supply for the resins, higher maximum temperature rises were found. Meanwhile, the maximum shrinkage rates were not different from those of room temperature polymerizations. 5. From the third experiment, the external heat supply for the resins during polymerization could temporarily decrease or even reverse shrinkage strains of each material. But, shrinkage re-occurred in the linear nature after completion of heat supply. 6. Linear thermal expansion coefficients obtained from the end of heat supply continuing for an additional 5 minutes, showed that Snap exhibited significantly lower values than the other two poly(methyl methacrylate) products (p<0.01). Moreover, little difference was found between the mean linear thermal expansion coefficients obtained from two different heating durations (p>0.05).

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1213-1231
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• 2007

The domination number ${\gamma}(G)$ of a graph G=(V,E) is the minimum cardinality of a subset of V such that every vertex is either in the set or is adjacent to some vertex in the set. The bondage number of b(G) of a graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater than ${\gamma}(G)$. In this paper, we calculate the bondage number of the Cartesian product of cycles $C_3\;and\;C_n$ for all n.

• Proceedings of the Korea Society for Simulation Conference
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• 2001.10a
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• pp.248-254
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• 2001

This paper presents a progressive algorithm for reconstructing a 3D structure from a given 2D sketch drawing (edge-vertex graph without hidden line removal) according to the user's sketch order. While previous methods reconstruct a 3D structure at once, the proposed method progressively calculate a 3D structure by optimizing the coordinates of vertices of an object according to the sketch order. The progressive method reconstructs the most plausible 3D object quickly by applying 3D constraints that are derived from the relationship between the object and the sketch drawing in the optimization process. The progressive reconstruction algorithm is discussed, and examples from a working implementation are given.

• Journal of Korea Game Society
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• v.2 no.2
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• pp.28-36
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• 2002

In general, triangular meshes have been used for modeling geometric objects such as virtual game characters. The dense meshes give us considerable advantages in representing complex, highly detailed objects, while they are more expensive for storing, transmitting and rendering the objects. Therefore, several researches have been performed for producing a high quality approximation in place of detailed objects, that is, a simplification of triangular meshes. In this paper, we propose a new measure with respect to edges and vertices, which is called an approximate mean curvature and is used as criteria to simplify an original mesh. An edge mean curvature is computed by considering its neighboring edges, and a vertex mean curvature is defined as an average of its incident edges' mean curvatures. And we apply the proposed measure to simplify the models such as a bunny, dragon and teeth. As a result, we can see that the mean curvatures can be used as good criteria for providing much better approximation of models.

• The KIPS Transactions:PartA
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• v.9A no.4
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• pp.581-588
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• 2002

In implementing interactive multimedia systems, real-time visualization plays an important role. This paper presents efficient data structures and algorithms for real-time terrain navigation. Terrain data set is usually too huge to display as is. Therefore LOD (levels of detail) methods and view frustum culling are essential tools. This paper describes in detail compact hierarchical data structures, fast view frustum culling, and efficient LOD construction/rendering algorithms. Unlike previous works, we use a precise screen-space error metric for vertex removal and a strict error threshold allowing sub-pixel -sized errors only. Nevertheless, we can achieve 22 fps on average in a PC platform. The methods presented in this paper also satisfy almost all of the requirements for interactive real-time terrain Visualization.