• Journal of Educational Research in Mathematics
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• v.13 no.1
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• pp.57-75
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• 2003

The goal of this paper is to offer material which make mathematising Fruedenthal(1991) proposed be experienced through the process of teaching and learning mathematics. In this paper, the number of unit squares a diagonal passes through for an m$\times$n lattice rectangle is studied and its generalization is discussed. Through this discussion, the adaptability of this material Is analysed. Especially, beyond inductional conjecture, the number of unit squares is studied by more complete way, and generalization in 3-dimension and 4-dimension are tried. In school mathematics, it is enough to generalize in 3-dimension. This material is basically appropriate for teaching and learning mathematising in math classroom. In studying the number of unit squares and unit cubes, some kinds of mathematising are accompanied. Enough time are allowed for students to study unit squares and unit cubes to make them experience mathematising really. To do so, it is desirable to give students that problem as a task, and make them challenge that problem for enough long time by their own ways. This material can be connected to advanced mathematics naturally in that it is possible to generalize this problem in n-dimension. So, it is appropriate for making in-service mathematics teachers realize them as a real material connecting school mathematics and advanced mathematics.

• Journal of KIISE:Computer Systems and Theory
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• v.29 no.2
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• pp.94-104
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• 2002

As a part of scientific data visualization automatic generation algorithms for a contour map have been investigated mainly on data which are defined at every lattice point. But in actual situation like weather data measurement. it is impossible to get data defined at every lattice point This is because the exact value on every lattice point can not be obtained due to characteristics in sampling devices or sampling methods. In order to define data on every lattice point where data were not sampled an interpolation method. was applied to the sample data to assign approximate values for some lattice type data but by using the non-lattice type of sample data sets. A triangle data link was defined by using non lattice points directly based on actually sample data set, not by using the pre-processed rectangle lattice points. The suggested algorithm generates a contour map a contour map only by using sample data set which are much smaller than old one without data interpolation and there is no skew on data any more since it does not need any interpolation to get the values of the defined lattice points.

• Proceedings of the Korean Vacuum Society Conference
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• 2010.02a
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• pp.362-362
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• 2010

Today, vast attention has been paid to periodic arrays of nanostructures due to their potential for applications such as memory with huge storage density. Such application requires large-scale fabrication of well ordered nano-sized structures. One of the most widely used methods for the ordered nanostructures is lithography. This top-down process, however, has the limit to reduce size. Here the promising alternative is the self-organization of ordered nano-sized structures such as large scale 2d carbon-induced reconstructions on W(110). In the present study, we report on the first well-resolved atomic resolution STM studies of the well-known R($15{\times}3$) and R($15{\times}12$) carbon induced reconstruction of the W(110). From the atomic image of R($15{\times}3$) for different values of tunneling gap resistance, we can tell there are no missing atoms in unit cells of R($15{\times}3$) and some atomic displacements are substantial from the clean W(110), even though not all the imaged position of atoms correspond to tungsten, but may include those of carbon. We are considering two cases; First case is related to lattice deformation, or top layer of W(110) is deformed in the process of relief of strain caused by random inserting of carbon atoms possibly in the interstitial position. In the second case, R($15{\times}3$) unit cell results from a coincidence lattice between clean W(110) substrate and tungsten carbide overlayer which has rectangular atomic arrangement and giving R($15{\times}3$) coincidence lattice. beta-W2C showing rectangular unit cell should be a candidate. Further, we report on new reconstructions. Unlike the well-known R($15{\times}12$) consisting of two parts, two inner structures between two "Backbone" structures. The new reconstruction, which we found for the first time, contains more parts between the "Backbone"s. Sometimes we can observe the reconstruction consists of only inner parts without "Backbone" parts. Thus, the observed reconstruction can be built by constructing of two types of "Lego"-like block. Moreover, the rectangle shape of "Backbone" transform to parallelogram-like shape over time, the so-called wavy-R($15{\times}12$). Adsorption of hydrogen can be the reason for this transformation.

• Journal of Korea Water Resources Association
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• v.40 no.6 s.179
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• pp.469-483
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• 2007

Nitrate and chloride are the most common contaminants in groundwater and their concentrations increase easily due to fertilizer consumption and urbanization. The number of time series data for groundwater quality at a single site was not sufficient to analyze trends on Jeju Island. Therefore rectangle grids were drawn for the whole island and single grid was determined to be $500m{\times}500m$ after considering similar stream density, homogeneous hydraulic coefficients, geologic features of volcanic rock and low topographic slopes. All data within each lattice were collected and arranged in time series order and analyzed using Sen's method. 10.6 % of the total lattices for chloride and 22.4% for nitrate showed upward trends from the early 1990's to the early 2000's. Especially, upward trends for nitrate concentration are distinct in the low mid-mountainous areas of western and southern watersheds. Many septic tanks and much domestic waste from the urbanization of the low mid-mountainous area have produced this upward trend. Additionally, the agricultural region has dramatically increased since the 1990's and this has led to an increase of fertilizer consumption and, as a result, nitrate concentration. Therefore, the target of any management plan for groundwater quality on Jeiu Island needs to be focused on careful land use decisions in the mid-mountainous areas which are near Halla Mountain.

• Korean Journal of Heritage: History & Science
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• v.45 no.2
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• pp.20-37
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• 2012

After withdrawal of military troops of Chinese Tang dynasty in the 18th year of King Moon-moo's reign(678), the Silla Kingdom had actually unified the Korean peninsula and had divided the territory into 9 states benchmarking the China's local administrations adjustment system. He had established local administrative units by deploying secondary capitals, counties and prefectures in the nine states. The so-called "9 Provinces and 5 Secondary capitals" are what constitutes the local administrations system. The provinces can be compared to current provinces of the Republic of Korea(hereinafter Korea), and secondary capitals to megalopolises. According to a chapter of the Samkuksaki(三?史記) which had recorded the achievements of king Kyoungdeok in December in his 16th year on the throne(757), the local administrative units had amounted to 5 secondary capitals, 117 counties and 293 prefectures. There are still lots of ambiguous points since there have never been any consultation on locations of provinces and secondary capitals' castles, and on structures of cities because the researches for local cities inside the 9 Provinces and 5 Secondary capitals in the Unified Silla Kingdom has been conducted centering on the historic literatures only. The research for restoring structures of cities seen from an archeological perspective are limited to the studies of Taewoo Park("A study on the local cities in the Unified Kingdom Age" 1987) and that of the author("A study on the restoration of planned cities for the Unified Silla Kingdom in terms of the structures and realities of the castles in the 9 Provinces and 5 Secondary capitals" 2009). The Gangneung city of Gangwon province was originally called Haseoryang(河西良) of the Gogureo Kingdom as an ancient nation of Ye(濊). According to "Samkuksaki", it had evolved from Haseoju(河西州) to a secondary capitals in the 8th year of King Seonduk(639). Afterwards, it had been renamed as Myeongju(溟洲) in the 16th year of King Kyoungduk(757), and then several other names were given to it after Goryo dynasty. Taewoo Park claims that it is being defined as a sanctuary remaining in Myoungjudong because of the vestige of bare castle, and this cannot be ascertained due to the on-going urbanization processes. Also, the Kwandong university authority is suggesting an opinion of regarding Myeongju mountain castle located 3 Kms southwest of the center of Gangwon city as commanding post for the pertinent state. The author has restored the pertinent area into a city composed of villages within a lattice framework like Silla Keumkyoung and many other cities. The structure is depicted next. The downtown of Gangneung is situated on a flat terrain at the west bank of Namdaecheon stream flowing southwest to northeast along the inner area of the city. Though there isn't any hill comparatively higher than others in the vicinity, hills are continuously linked east to west along the northern area of the downtown, and the maximum width of flat terrain is about 1 Km and is not so large. Currently, urbanization is being proceeded into the inner portion of Gangneung city, the lands in all directions from the hub of Gangneung station have been readjusted, and thus previous land-zoning program is almost nullified. However, referring to the topographic chart drawn at the time of Japanese colonial rule, it can be validated that land-zoning program to accord the lattice framework with the length of its one side equaling to 190m leaves its vestige about 0.8Km northwest to southeast and about 1.7Km northeast to southwest of the vicinity of Okcheondong, Imdangdong, Geumhakdong, Myeongjudong, and etcetera which comprize the hub of the downtown. The land-zoning vestige within the lattice framework, compared to other cases related with the '9 states and 5 secondary capitals', is very much likely to be that of the Unified Silla Kingdom. That the length of a side of a lattice framework is 190m as opposed to that of Silla Geumkyoung and other cities with their 140m or 160m long sides is a single survey item in the future. The baseline direction for zoning the lands is tilting approximately 37.5 degrees west of northwest to southeast axis in accordance with the topographic features. It seems that this phenomenon takes place because of the direction of Namdaecheon and the geographic constraints of the hills in the north. Reviewing minimally, a rectangular size of zoned land by 4 Pangs(坊) on the northwest to southeast side multiplied by 7 Pangs(坊) on the northeast to southwest side had been restored within a lattice framework. Otherwise, considering the extent of expansion of the existing zoned lands in the lattice framework and one more Pang(坊) being added to each side, it is likely that the size could have been with 5 Pangs(坊) on the northwest to southeast side multiplied by 8 Pangs(坊) on the northeast to southwest side(950 M on the northwest to southeast side multiplied by 1,520m on the northeast to southwest side). The overall shape is rectangle, but land-zoning programs reminiscent of rebuilt roads(red phoenix road) like Jang-an castle(長安城) of Chinese Tang dynasty or Pyoungseong castle(平城城) in Japan is not to be validated. There are some historic items among the roof tiles and earthen wares excavated at local administrative office sites or Gangneung's town castle in Joseon dynasty inside the area assumed to be containing municipal vestiges even though archeological survey for the vestige of Myeongju has not been made yet, and these items deserve dating back to the Unified Silla Kingdom age. Also, all of the construction sites at local administrative authorities of the Joseon dynasty are showing large degrees of slant in the azimuth. This is a circumstantial evidence indicating the fact that the inherited land-zoning programs to be seen in Gangneung in terms of the lattice framework had ever existed in the past. Also, the author does not decline that Myeongju mountain castle had once been the commanding post when reviewing the roof tiles at the edge of eaves in this stronghold. The ancient municipal castles in the Korean peninsula are composed of castles on the flat terrain as well as hilly areas and the cluster of strongholds like Myounghwal, Namhan, Seohyoung mountain castles built around municipal castle of Geumkyoung based on a lattice framework program. Considering that mountain castles are spread in the vicinity of municipal vestiges in other cities other than the 9 states and 5 secondary capitals, it is estimated that Myeongju was assuming the function of commanding post incorporating cities on the flat terrain and castles on the hills.