• The Mathematical Education
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• v.12 no.2
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• pp.5-12
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• 1974

단위원을 가지는 하환환에 있어서의 Prime Spectrum에 관하여 다음 세가지 사실을 증명하였다. 1. X를 환 R의 prime spectrum, C(X)를 X에서 정의되는 실연적함수의 환, X를 C(X)의 maximal spectrum이라 하면 X는 C(X)의 prime spectrum의 부분공간으로서의 한 T-space로 된다. N을 환 R의 nilradical이라 하면, R/N이 regula 이면 X와 X는 위상동형이다. 2. f: R$\longrightarrow$R'을 ring homomorphism, P를 R의 한 Prime ideal, $R_{p}$, R'$_{p}$를 각각 S=R-P 및 f(S)에 관한 분수환(ring of fraction)이라 하고, k(P)를 local ring $R_{p}$의 residue' field라 할 때, R'의 prime spectrum의 부분공간인 $f^{*-1}$(P)는 k(P)(equation omitted)$_{R}$R'의 prime spectrum과 위상동형이다. 단 f*는 f*(Q)=$f^{-1}$(Q)로서 정의되는 함수 s*:Spec(R')$\longrightarrow$Spec(R)이다. 3. X를 환 S의 prime spectrum, N을 R의 nilradical이라 할 때, 다음 네가지 사실은 동치이다. (1) R/N 은 regular 이다. (2) X는 Zarski topology에 관하여 Hausdorff 공간이다. (3) X에서의 Zarski topology와 constructible topology와는 일치한다. (4) R의 임의의 원소 f에 대하여 f를 포함하지 않는 R의 prime ideal 전체의 집합 $X_{f}$는 Zarski topology에 관하여 개집합인 동시에 폐집합이다.폐집합이다....

• Journal of the Korean Geographical Society
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• v.46 no.1
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• pp.67-80
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• 2011

Choropleth mapping of population distribution is based on the assumption that people are uniformly distributed throughout each enumeration unit. Dasymetric mapping technique improves choropleth mapping by refining spatially aggregated data with residential information. Further, pycnophylactic interpolation can upgrade dasymetric mapping by considering population distribution of neighboring areas, while preserving the volumes of original units. This study proposed a combined solution of dasymetric mapping and pycnophylactic interpolation to improve the accuracy of population density distribution. Specifically, the dasymetric method accounts for the spatial distribution of population within each census unit, while pycnophylactic interpolation considers population distribution of neighboring area. This technique is demonstrated with 1990 census data of the Athens, GA. with land use land cover information derived from remotely-sensed imagery for the areal extent of populated areas. The results are evaluated by comparison between original population counts of smaller census units (census block groups) and population counts of the grid map built from larger units (census tracts) aggregated to the same areal units. The estimated populations indicate a satisfactory level of accuracy. Population distribution acquired by the suggested method can be re-aggregated to any type of geographic boundaries such as electoral boundaries, school districts, and even watershed for a variety of applications.

• Journal for History of Mathematics
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• v.25 no.4
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• pp.1-10
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• 2012

In Chinese mathematics, there have been two numeral systems, namely one in spoken language for recording and the other by counting rods for computations. They concerned with problems dealing with practical applications, numbers in them are concrete numbers except in the process of basic operations. Thus they could hardly develop a pure theory of numbers. In Song dynasty, 0 and TianYuanShu were introduced, where the coefficients were denoted by counting rods. We show that in this process, counting rods took over the role of the numeral system in spoken language and hence counting rod numeral system plays the role of that for abstract numbers together with the tool for calculations. Decimal fractions were also understood as denominate numbers but using the notions by counting rods, decimals were also admitted as abstract numbers. Noting that abacus replaced counting rods and TianYuanShu were lost in Ming dynasty, abstract numbers disappeared in Chinese mathematics. Investigating JianJie YiMing SuanFa(簡捷易明算法) written by Shen ShiGui(沈士桂) around 1704, we conclude that Shen noticed repeating decimals and their operations, and also used various rounding methods.

• School Mathematics
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• v.10 no.4
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• pp.603-623
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• 2008

The purpose of this research was to gain a better understanding of the characteristics of students' mathematical representations using additive strategy in ratio and proportion tasks. The additive strategy is the erroneous one used most often among the strategies reported in solving ratio and proportion tasks. It is a problem solving strategy that preserves the difference from one ratio to another. Students' additive strategies were categorized into four parts: subtracting without considering units of quantities, comparing the numbers that represent the whole subtracted from the part and same part, adding the difference, and subtracting the difference. In order to change from additive strategy to multiplicative strategy, the researcher asked to find out the unit quantity and found the characteristics of students' mathematical notations in the following: Firstly, the students made the number which they wanted by multiplying and adding same numbers. Secondly, they represented the mid-points between natural numbers. Thirdly, they related $a{\div}b$ to decimal number, not $\frac{a}{b}$. Fourthly, they were inclined to divide the larger number with the smaller number without understanding the context of the problem. These results are interpreted as showing that lower level of performance in the dividing operation with the notations of fraction hinders the transformation from additive strategy to multiplicative strategy.

• Korean Journal of Remote Sensing
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• v.39 no.6_2
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• pp.1605-1613
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• 2023

The physical properties of the ocean interior are determined by temperature and salinity. To observe them, we rely on satellite observations for broad regions of oceans. However, the satellite for salinity measurement, Soil Moisture Active Passive (SMAP), has low temporal and spatial resolutions; thus, more is needed to resolve the fast-changing coastal environment. To overcome these limitations, the algorithm to use the Geostationary Ocean Color Imager-II (GOCI-II) of the Geo-Kompsat-2B (GK-2B) was developed as the inputs for a Multi-layer Perceptron Neural Network (MPNN). The result shows that coefficient of determination (R²), root mean square error (RMSE), and relative root mean square error (RRMSE) between GOCI-II based sea surface salinity (SSS) (GOCI-II SSS) and SMAP was 0.94, 0.58 psu, and 1.87%, respectively. Furthermore, the spatial variation of GOCI-II SSS was also very uniform, with over 0.8 of R² and less than 1 psu of RMSE. In addition, GOCI-II SSS was also compared with SSS of Ieodo Ocean Research Station (I-ORS), suggesting that the result was slightly low, which was further analyzed for the following reasons. We further illustrated the valuable information of high spatial and temporal variation of GOCI-II SSS to analyze SSS variation by the 11th typhoon, Hinnamnor, in 2022. We used the mean and standard deviation (STD) of one day of GOCI-II SSS, revealing the high spatial and temporal changes. Thus, this study will shed light on the research for monitoring the highly changing marine environment.

• Korean Journal of Heritage: History & Science
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• v.53 no.3
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• pp.80-109
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• 2020

The Sacheonwangsa Temple in Silla is an esoteric temple that was founded provisionally in 670, and was completed in 679. This study attempted to elucidate the planning method of the Sacheonwangsa Temple based on the results of research on excavations and investigations into its construction processes and construction measures thereof. The research results are as follows. (1) In the site construction, assuming the size of one Bang (坊) on the south of Nangsan Mountain, after dividing the north-south width into three equal parts, there is a possibility that two of these parts were set to the flat portion. (2) In the 'Jochang (祖創, 670)', it is estimated that an area of 300 cheoks by 300 cheoks was postulated on the flat surface, and, as an initial conception, the mandala's plane design of the outer square 2 hasta (3 cheoks) and inner square 1 hasta (1.5 cheoks) was originally devised for the setting of 'Mudra (神印)', and an area 100 times greater has been set as the basis in the scale and layout planning of the central block. (3) During 'Gaechang (攺刱, ~679)', it is judged that because of the narrowness of the distance between the Pagoda and Geumdang Hall, which occurs when the center of the Geumdang Hall coincides with the center of 'the first stage of the foundation (先築基壇)', the scale and layout planning were adjusted from the initial conception. (4) The arrangement of the building was determined by dividing the fixed size of the central block (280 cheoks by 320 cheoks). Specifically, the east-west direction is set on the quartile's line of the east-west width of the central block, and in contrast, the north-south direction is based on the structural characteristics of the central block. It is presumed that the position of the transept was determined through the division and adjustment of the column spacing of the east-west corridor, then the Geumdang Hall and Altar were based on this. (5) The scale of the Geumdang Hall and Pagoda is determined by the petition of the division by the unit fraction starting from the quartile's line of the central block's east-west width. This planning is understood to be based on the self-similarity, which is rooted in the mandala's plane design as the model.