• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.33-39
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• 2000

Well known is the directed self-avoiding walk model on the square lattice with reflecting and absorbing barriers. We consider two models, namely, a pyramid self-avoiding polygon model and a top and bottom pyramid polygon model, as subcollections of the model. We derive explicit formulas for the number of 2N-step polygons in these models.

• Journal of the Korea institute for structural maintenance and inspection
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• v.22 no.2
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• pp.83-89
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• 2018

In this study, the settlement of concrete rectangular pyramid foundation on soft ground is investigated based on a finite element analysis. considering the grounding load and the grounding area of square pyramid foundation, we compensate the insufficient design bearing capacity and investigated the effect of settlement by load. Based on this study, it is found that the rectangular pyramid foundation shows the smallest settlement of three different type of foundations. As a result of this study, it was resulted that the square pyramid foundations were more effective than the crushed stone foundations by 18%. These results show that the ground pressures of the square pyramid bases are divided into horizontal and vertical stresses, so it is analyzed that the horizontal stress builds up the rigid ground on the foundation of the structure and distributes the load widely to increase the resistance to the overhead load.

• Transactions of Materials Processing
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• v.19 no.8
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• pp.474-479
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• 2010

Newly suggested hybrid LED package can reduce the number of LED processes and enhance light efficacy in virtue of its integrated optical patterns. Square-type pyramid pattern was chosen for the integrated optical pattern in this study, and it was proved that the pattern enhances illuminance about three times and luminance about two and half times by optical simulation. Square-type pyramid patterns of 0.02mm height and 0.04mm pitch were successively machined on a copper mold which is necessary for imprinting the integrated pattern. Hybrid LED package with integrated optical pattern will be manufactured with ultra-fine machined mold in future study.

• The Journal of the Korea Contents Association
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• v.9 no.12
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• pp.582-591
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• 2009

The pyramid graph is an interconnection network topology based on regular square mesh and tree structures. In this paper, we adopt a strategy of classification into two disjoint groups of edges in regular square mesh as a base sub-graph constituting of each layer in the pyramid graph. Edge set in the mesh can be divided into two disjoint sub-sets called as NPC(represents candidate edge for neighbor-parent) and SPC(represents candidate edge for shared-parent) whether the parents vertices adjacent to two end vertices of the corresponding edge have a relation of neighbor or shared in the upper layer of pyramid graph. In addition, we also introduce a notion of shrink graph to focus only on the NPC-edges by hiding SPC-edges in the original graph within the shrunk super-vertex on the resulting graph. In this paper, we analyze that the lower and upper bound on the number of NPC-edges in a Hamiltonian cycle constructed on $2^n\times2^n$ mesh is $2^{2n-2}$ and $3*(2^{2n-2}-2^{n-1})$ respectively. By expanding this result into the pyramid graph, we also prove that the maximum number of NPC-edges containable in a Hamiltonian cycle is $4^{n-1}-3*2^{n-1}$-2n+7 in the n-dimensional pyramid.

• Journal of Korea Multimedia Society
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• v.13 no.8
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• pp.1183-1193
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• 2010

The pyramid graph is well known in parallel processing as a interconnection network topology based on regular square mesh and tree architectures. The enhanced pyramid graph is an alternative architecture by exchanging mesh into the corresponding torus on the base for upgrading performance than the pyramid. In this paper, we adopt a strategy of classification into two disjoint groups of edges in regular square torus as a basic sub-graph constituting of each layer in the enhanced pyramid graph. Edge set in the torus graph is considered as two disjoint sub-sets called NPC(represents candidate edge for neighbor-parent) and SPC(represents candidate edge for shared-parent) whether the parents vertices adjacent to two end vertices of the corresponding edge have a relation of neighbor or sharing in the upper layer of the enhanced pyramid graph. In addition, we also introduce a notion of shrink graph to focus only on the NPC-edges by hiding SPC-edges within the shrunk super-vertex on the resulting shrink graph. In this paper, we analyze that the lower and upper bounds on the number of NPC-edges in a Hamiltonian cycle constructed on $2^n{\times}2^n$ torus is $2^{2n-2}$ and $3{\cdot}2^{2n-2}$ respectively. By expanding this result into the enhanced pyramid graph, we also prove that the maximum number of NPC-edges containable in a Hamiltonian cycle is $4^{n-1}$-2n+1 in the n-dimensional enhanced pyramid.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2009.06a
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• pp.407-408
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• 2009

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2007.05a
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• pp.266-267
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• 2007

Sandwich sheet with inner structure is expected to find many applications because of high stiffness to mass ratio. In order to simulate forming of sandwich sheet with pyramid core, an effective simulation method is required. Compared to the expensive model using solid elements, cost effective model using simplified elements such as shells and beams is developed. By comparing two models in terms of the cost and accuracy for unit cell deformation, a developed model shows some advantages over the model using solid elements. Evolution of two kind of forming limits, face buckling and core buckling are successfully expressed by developed model. Developed model is also applied in the simulation of square cup drawing and L-type bending. The corresponding experiments are carried out. Deformation shape and wrinkling behavior are compared and discussed. It is found that simulation results using a developed model are in good agreement with experiments.

• Journal of Powder Materials
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• v.22 no.3
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• pp.169-174
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• 2015

The optical film for light luminance improvement of BLU that is used in LCD/LED and retro-reflective film is used as luminous sign consist of square and triangular pyramid structure pattern based on V-shape micro prism pattern. In this study, we analyzed machining characteristics of Cu-plated flat mold by shaping with diamond tool. First, cutting conditions were optimizing as V-groove machining for the experiment of micro prism structure mold machining with prism pattern shape, cutting force and roughness. Second, the micro prism structure such as square and triangular pyramid pattern were machined by cross machining method with optimizing cutting conditions. Burr and chip shape were discussed with material properties and machining method.

• Journal of the Korean Chemical Society
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• v.29 no.1
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• pp.38-44
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• 1985

Photoreaction path for the monocyanochromium (Ⅲ) ion was inferred from the experimentally observed product ratio and theoretical analysis. The angular overlap model was used to analyze the d-orbital of various intermediates along a selected reaction coordinate and to determine quartet state energy level. A loss of equatorial ammine leads to pentacoordinated square pyramid with CN- ligand in an equatorial position. The SP(CNeq) intermediate undergoes a rearrangement by the N-Cr-CN bending. This process leads to a trigonal bipyramidal intermediate in which the CN- ligand is located in equatorial position. The subsequent association with a solvent molecule should probably proceed by lateral attack an one edge of the equatorial triangle. The assumption adopted above was consistent with experimental results.

• The Korea Journal of Herbology
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• v.37 no.5
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• pp.75-81
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• 2022

Objectives : In 『Treatise on Cold Damage Diseases』, the volume of preparation dosage measured in Hap was 6.5mL. This study aimed to confirm that a square-inch-spoon, which measures powder preparation dosage, was 1/3 Hap, and that Jeon-bi was 1/8 square-inch-spoon. Based on these values, this study also aimed to adjust the diameter of Firmiana-Seed-sized pill preparation, currently known as 6.5mm, so that one square-inch-spoon of powder preparation creates 16 pills. Methods : Calculated the ratio between the floor areas of square-inch-spoon and Jeon-bi and measured the ratio of volume; assumed that powder preparations were stacked as much as possible in the shape of a square pyramid when scooped comfortably, then calculated the slopes of 1/3 Hap and 1/4 Hap; measured the volumes of powdered Oryeongsan and Lijungwhan in square-inch-spoon and Jeon-bi; created the powders into Firmiana-Seed-sized pill preparation; adjusted the diameter of Firmiana Seed so that 16 pills could be created. Results : Inferring from the floor areas, the volume of square-inch-spoon is 9.2 times that of Jeon-bi; one square-inch-spoon should be 1/3 Hap for the powder to reach its maximum slope of 47° and, according to actual measurement of powder preparations, reach its maximum volume; when created into Firmiana-Seed-sized pill preparations, one square-inch-spoon should be 1/3 Hap so that approximately 16 pills were created. Conclusions : One square-inch-spoon of powder preparation was 1/3 Hap(2.17mL), Jeon-bi was 1/8 square-inch-spoon(0.27mL), and the diameter of Firmiana-Seed-sized pill preparation was 5.5mm.