• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.1
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• pp.41-53
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• 2008

Polynomials are one of most important and widely used numerical tools in dealing with a smooth function on a bounded domain and trigonometric functions work for smooth periodic functions. However, they are not the best choice if a function has a bounded support in space and in frequency domain. The Prolate Spheroidal wave function (PSWF) of order zero has been known as a best candidate as a basis for band-limited functions. In this paper, we review some basic properties of PSWFs defined as eigenfunctions of bounded Fourier transformation. We also propose numerical inversion schemes based on PSWF and present some numerical examples to show their feasibilities as signal processing tools.

• School Mathematics
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• v.14 no.4
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• pp.531-552
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• 2012

In December of 2009, General Guidelines of Curriculum Revised in 2009 was announced and research on corresponding mathematics curriculum revision has been initiated from that period. Finally, in August 2011, Mathematics Curriculum Revised in 2009 was announced. Based on the examination the backgrounds and the basic directions of revision newly reformed mathematics curriculum should be applied in math class effectively and efficiently. According to this purpose, this paper first of all finds out what are the major points or difficulties to be caused by managing 'Mathematics Curriculum Revised in 2009' according to the change of 'General Guidelines of Curriculum Revised in 2009'. They are i) the implementation of grade band system, ii) management of differentiated class, and iii) increasing or decreasing of 20% in math class hour. According to those three points to be changed and reinforced newly in new curriculum, this paper investigates the alternatives and policy of dealing with smoothly and efficiently those issues while solving the difficulties.

• Journal of the Korean Association of Geographic Information Studies
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• v.13 no.1
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• pp.155-163
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• 2010

The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) on-board the NASA's Terra spacecraft provides along-track digital stereo image data at 15m resolution with a base-height ratio 0.6. Automated stereocorrelation procedure was implemented using the ENVI 4.1 software to derive DEMs with $15m{\times}15m$ in 43km long and 50km wide area using the ASTER stereo images. The accuracy of DEMs was analyzed in comparison with those which were obtained from digital topographic maps of 1:25,000 scale. Results indicate that RMSE in elevation between ${\pm}7$ and ${\pm}20m$ could be achieved. Excluding cloud, water and building areas as the factors which make RMSE value exceeding 10m, the accuracy of DEMs showed RMSE of ${\pm}5.789m$. Therefore for the purpose of elevating accuracy of topographic information, we intended to detect the cloud areas and shadow areas by a landcover classification method, remove those areas on the ASTER DEM and then replace with those areas detached from the cartographic DEM by band math.

• Journal for History of Mathematics
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• v.32 no.4
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• pp.159-173
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• 2019

In this paper, we examine the brief history of the ring of four almonds regarding Mesopotamian mathematics, and present reasons why the Omar Khayyam's triangle, a special right triangle in a ring of four almonds, was essential for artisans due to its unique pattern. We presume that the ring of four almonds originated from a point symmetry figure given two concentric squares used in the proto-Sumerian Jemdet Nasr period (approximately 3000 B.C.) and a square halfway between two given concentric squares used during the time of the Old Akkadian period (2340-2200 B.C.) and the Old Babylonian age (2000-1600 B.C.). Artisans tried to create a new intricate pattern as almonds and 6-pointed stars by subdividing right triangles in the pattern of the popular altered Old Akkadian square band at the time. Therefore, artisans needed the Omar Khayyam's triangle, whose hypotenuse equals the sum of the short side and the perpendicular to the hypotenuse. We presume that artisans asked mathematicians how to construct the Omar Khayyam's triangle at a meeting between artisans and mathematicians in Isfahan. The construction of Omar Khayyam's triangle requires solving an irreducible cubic polynomial. Omar Khayyam was the first to classify equations of integer polynomials of degree up to three and then proceeded to solve all types of cubic equations by means of intersections of conic sections. Omar Khayyam's triangle gave practical meaning to the type of cubic equation $x^3+bx=cx^2+a$. The work of Omar Khayyam was completed by Descartes in the 17th century.

• The Journal of Engineering Geology
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• v.24 no.3
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• pp.411-421
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• 2014

The purpose of this study is to analyze the key factors that contribute to landslide causes through swelling clay minerals and terrain analysis in landslide sites taken place of in Yongin city, Gyeonggi-do, 2011. The study was conducted based on field survey by XRD (X-ray Diffraction), XRF (X-ray fluorescence), spectroscopic analysis on soil samples obtained from landslide sites and ASTER satellite image. Illite shows absorption features; $Fe^{2+}$ and $Fe^{3+}$ at 0.9 and $1.0{\mu}m$, broad water absorption features near 1.4 and $1.9{\mu}m$, and additional Al-hydroxyl features at 2.2, 2.3 and $2.4{\mu}m$, respectively. These absorption features are consistent with the bands 5, 6, and 7 of ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) satellite image. Illite image was extracted using band math of $SWIR_{Illite}$. From these results, we confirmed the applicability of ASTER satellite image using identification of swelling clay minerals to landslide study.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.867-872
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• 2002

A high intensity acoustic test facility is constructed at Korea Aerospace Research Institute (KARI) by 2003. The reverberant chamber of the facility has a volume of 1,228 cubic meters and shall provide an acoustic environment of 152 dB over the frequency range of 25 Hz to 10,000 Hz. The facility consists of a large scaled reverberant chamber, acoustic power generation systems, gases nitrogen supply systems, and acoustic control systems. This paper describes how the basic parameters of a chamber and power generation systems are controlled to meet the requirement of the test. The volume of a reverberant chamber is controlled by the size of test objects and the reverberant characteristics of a chamber. The capacity of acoustic power generation systems is determined by the energy absorption of a chamber and the efficiency of acoustic modulators. Simple math is employed to calculate the required power of acoustic modulators. Moreover, the paper explains how the distribution of sound pressure level at low frequency is checked by analytical and numerical methods.

• Korean Journal of Remote Sensing
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• v.36 no.4
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• pp.535-544
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• 2020

In synthetic aperture radar (SAR) based ship detection application, false alarms frequently occur due to various noises caused by the radar imaging process. Among them, radio frequency interference (RFI) and azimuth smearing produce substantial false alarms; the latter also yields longer length estimation of ships than the true length. These two noises are prominent at cross-polarization and relatively weak at co-polarization. However, in general, the cross-polarization data are suitable for ship detection, because the radar backscatter from background sea surface is much less in comparison with the co-polarization backscatter, i.e., higher ship-sea image contrast. In order to improve the ship detection accuracy further, the RFI and azimuth smearing need to be mitigated. In the present letter, Sentinel-1 VV- and VH-polarization intensity data are used to show a novel technique of removing these noises. In this method, median image intensities of noises and background sea surface are calculated to yield arithmetic tendency. A band-math formula is then designed to replace the intensities of noise pixels in VH-polarization with adjusted VV-polarization intensity pixels that are less affected by the noises. To verify the proposed method, the adaptive threshold method (ATM) with a sliding window was used for ship detection, and the results showed that the 74.39% of RFI false alarms are removed and 92.27% false alarms of azimuth smearing are removed.

• Education of Primary School Mathematics
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• v.25 no.4
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• pp.395-410
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• 2022

Nominalization is one of the grammatical metaphors, and it is the representation of verbal meaning through noun equivalent phrases. In mathematical word problems, texts using nominalization have both the advantage of clarifying the object to be noted in the mathematization stage, and the disadvantage of complicating sentence structure, making it difficult to understand the sentences and hindering the experience of the full steps in mathematical modelling. The purpose of this study is to analyze word problems in the textbooks from the perspective of nominalization, a linguistic element, and to derive implications in relation to students' difficulties during solving the word problems. To this end, the types of nominalization of 341 word problems from the content domain of 'Numbers and Operations' of elementary math textbooks according to the 2015 revised national curriculum were analyzed in four aspects: grade-band group, main class and unit assessment, specialized class, and mathematical expression required word problems. Based on the analysis results, didactical implications related to the linguistic expression of the mathematical word problems were derived.

• Journal of Cadastre & Land InformatiX
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• v.47 no.1
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• pp.15-26
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• 2017

The decrease of green space according to the urbanization has caused many environmental problems as the destruction of habitat, air pollution, heat island effect. With interest growing in natural view recently, proper management of evergreen tree which is lived even the winter season has been on the rise importantly. This study analyzed the distribution area of evergreen tree using vegetation index based on unmanned aerial vehicle (UAV). Firstly, RGB and NIR+RG camera were loaded in fixed-wing UAV and image mosaic was achieved using GCPs based on Pix4d SW. And normalized differences vegetation index (NDVI) and soil adjusted vegetation index (SAVI) was calculated by band math function from acquired ortho mosaic image. validation points were applied to evaluate accuracy of the distribution of evergreen tree for each range value and analysis showed that kappa coefficient marked the highest as 0.822 and 0.816 respectively in "NDVI > 0.5" and "SAVI > 0.7". The area of evergreen tree in "NDVI > 0.5" and "SAVI > 0.7" was $11,824m^2$ and $15,648m^2$ respectively, that was ratio of 4.8% and 6.3% compared to total area. It was judged that UAV could supply the latest and high resolution information to vegetation works as urban environment, air pollution, climate change, and heat island effect.