• Journal for History of Mathematics
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• v.23 no.3
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• pp.91-106
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• 2010

This is the study for various methods for getting the volume of frustum of pyramid. This study will first deal with how the formula of getting the volume of frustum of pyramid has been changed in the history of Mathematics. Secondly, based on the study of 'Prasolov' this study will deal with the calculation method for the volume of frustum of pyramid which was written in the 14th question of 'Moscow Papyrus' and search for the rules of solution for frustum of pyramid in the middle school textbooks. Finally, this study will consider various solutions for the volume of frustum of pyramid and its generalization.

• Journal of the Korean School Mathematics Society
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• v.18 no.4
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• pp.371-385
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• 2015

In this paper we investigate the axioms defining area and volume so that revisit area formula for triangle, volume formula for triangular pyramid, and related contents in school mathematics from the view point of axiomatic method and Hilbert's third problem.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.19-30
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• 2008

Cavalieri is chiefly remembered for his work on the problem "indivisibles." Building on the work of Archimedes, he investigated the method of construction by which areas and volumes of curved figures could be found. Cavalieri regarded an area as made up of an indefinite number of parallel line segments and a volume of an indefinite number of parallel plane areas. He called these elements the indivisibles of area and volume. Cavalieri developed a method of the indivisibles which he used to determine areas and volumes. We call this Cavalieri's principle which states that there exists a plane such that any plane parallel to it intersects equal areas In both objects, then the volumes of the two objects are equal. Cavalieri's principle and method of the indivisibles are very important to understand of volume of a pyramid for gifted students.

• East Asian mathematical journal
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• v.33 no.2
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• pp.149-175
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• 2017

The effort to find the volume of pyramids has been done by mathematicians for a long time, and many trial-and-error calculations and proofs give various perspectives and educational material. In the early days, finding the volume of pyramids was mainly studied by calculating the volume of triangular pyramids or quadrangular pyramids by cutting and the relationship between pyramids. Thereafter, methods based on infinite, infinitesimal, limit, etc. appeared, but the research topic was still about them. The purpose of this study is to examine the four themes appearing the mathematics history in terms of methodology, and to think about its implications from the viewpoint of improving the professionalism of the teachers.

• Advances in nano research
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• v.2 no.4
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• pp.211-217
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• 2014

The self-assembled strain-induced sub-micrometric islands and nanostructures are grown from In-As-Sb-P quaternary liquid phase on InAs (100) substrates in Stranski-Krastanow growth mode. Two samples are under consideration. The first sample consists of unencapsulated islands and lens-shape quantum dots (QDs) grown from expressly inhomogeneous liquid phase. The second sample is an n-InAs/p-InAsSbP heterostructure with QDs embedded in the p-n junction interface. The morphology, size and shape of the structures are investigated by high-resolution scanning electron (SEM) and transmission electron (TEM) microscopy. It is shown that islands, as they decrease in size, undergo shape transitions. Particularly, as the volume decreases, the following succession of shape transitions are detected: sub-micrometric truncated pyramid, {111} facetted pyramid, {111} and partially {105} facetted pyramid, completely unfacetted "pre-pyramid", hemisphere, lens-shaped QD, which then evolves again to nano-pyramid. A critical size of $5{\pm}2nm$ for the shape transformation of InAsSbP-based lens-shaped QD to nano-pyramid is experimentally measured and theoretically evaluated.

• Journal of KIISE:Computer Systems and Theory
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• v.36 no.6
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• pp.511-520
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• 2009

In this paper, we present a new iso-density surface reconstruction scheme based on a hierarchy on the input volume data and the output mesh data. From the input volume data, we construct a hierarchy of volumes, called a volume pyramid, based on a 3D dilation filter. After constructing the volume pyramid, we extract a coarse base mesh from the coarsest resolution of the pyramid with the Cell-boundary representation scheme. We iteratively fit this mesh to the iso-points extracted from the volume data under O(3)-adjacency constraint. For the surface fitting, the shrinking process and the smoothing process are adopted as in the SWIS (Shrink-wrapped isosurface) algorithm[6], and we subdivide the mesh to be able to reconstruct fine detail of the isosurface. The advantage of our method is that it generates a mesh which can be utilized by several multiresolution algorithms such as compression and progressive transmission.

• East Asian mathematical journal
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• v.26 no.4
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• pp.535-551
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• 2010

In this paper, we investigate the methodology to calculate the volume of the pyramid and frustum of the pyramid that is found in Gu Jang Sel Hae and San Hak Jeong Ui(The first volume)text. Comparing and analyzing content in Korean and Chinese mathematics education textbooks that uses as a foundation the aforementioned methodology, it is proposed that in future development of mathematics education curriculum the area of solid geometry be taught in greater depth in basic study guides.

• ETRI Journal
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• v.44 no.6
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• pp.1034-1046
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• 2022

The learning-based multiview stereo (MVS) methods for three-dimensional (3D) reconstruction generally use 3D volumes for depth inference. The quality of the reconstructed depth maps and the corresponding point clouds is directly influenced by the spatial resolution of the 3D volume. Consequently, these methods produce point clouds with sparse local regions because of the lack of the memory required to encode a high volume of information. Here, we apply the atrous spatial pyramid pooling (ASPP) module in MVS methods to obtain dense feature maps with multiscale, long-range, contextual information using high receptive fields. For a given 3D volume with the same spatial resolution as that in the MVS methods, the dense feature maps from the ASPP module encoded with superior information can produce dense point clouds without a high memory footprint. Furthermore, we propose a 3D loss for training the MVS networks, which improves the predicted depth values by 24.44%. The ASPP module provides state-of-the-art qualitative results by constructing relatively dense point clouds, which improves the DTU MVS dataset benchmarks by 2.25% compared with those achieved in the previous MVS methods.

• Journal of Korean Society for Geospatial Information Science
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• v.4 no.1 s.6
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• pp.67-73
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• 1996

The objective of this research is to investigate the behavior of the $F\"{o}rstner$ interest operator, which has been widely used for detecting distinct points in the field of digital photogrammetry and computer vision, in scale space. Considering the hugh volume of digital image utilized in digital photogrammetry, the scale space (image pyramid) approach which appears to be a solution for enhancing image processing, began to gain its attention. The investigation of the $F\"{o}rstner$ interest operator in scale space generated by the Gaussian kernel shows its behavior and feasibility for being used in practice.

• Proceedings of the Korean Vacuum Society Conference
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• 2012.08a
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• pp.184-184
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• 2012

Recently, InGaN/GaN multi-quantum well grown on GaN pyramid structures have attracted much attention due to their hybrid characteristics of quantum well, quantum wire, and quantum dot. This gives us broad band emission which will be useful for phosphor-free white light emitting diode. On the other hand, by using quantum dot emission on top of the pyramid, site selective single photon source could be realized. However, these structures still have several limitations for the single photon source. For instance, the quantum efficiency of quantum dot emission should be improved further. As detection systems have limited numerical aperture, collection efficiency is also important issue. It has been known that micro-cavities can be utilized to modify the radiative decay rate and to control the radiation pattern of quantum dot. Researchers have also been interested in nano-cavities using localized surface plasmon. Although the plasmonic cavities have small quality factor due to high loss of metal, it could have small mode volume because plasmonic wavelength is much smaller than the wavelength in the dielectric cavities. In this work, we used localized surface plasmon to improve efficiency of InGaN qunatum dot as a single photon emitter. We could easily get the localized surface plasmon mode after deposit the metal thin film because lnGaN/GaN multi quantum well has the pyramidal geometry. With numerical simulation (i.e., Finite Difference Time Domain method), we observed highly enhanced decay rate and modified radiation pattern. To confirm these localized surface plasmon effect experimentally, we deposited metal thin films on InGaN/GaN pyramid structures using e-beam deposition. Then, photoluminescence and time-resolved photoluminescence were carried out to measure the improvement of radiative decay rate (Purcell factor). By carrying out cathodoluminescence (CL) experiments, spatial-resolved CL images could also be obtained. As we mentioned before, collection efficiency is also important issue to make an efficient single photon emitter. To confirm the radiation pattern of quantum dot, Fourier optics system was used to capture the angular property of emission. We believe that highly focused localized surface plasmon around site-selective InGaN quantum dot could be a feasible single photon emitter.