• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.617-630
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• 2011

Let X, Y be vector spaces, and let r be 2 or 4. It is shown that if an odd mapping $f:X{\rightarrow}Y$ satisfies the functional equation $${\hspace{50}}rf(\frac{\sum_{j=1}^{d}\;x_j} {r})+\;{\sum\limits_{\iota(j)=0,1 \atop {\sum_{j=1}^{d}}\;{\iota}(j)=l}}\;rf(\frac{\sum_{j=1}^{d}{(-1)^{\iota(j)}x_j}}{r}) \\({\ddag}){\hspace{160}}=(_{d-1}C_l-_{d-1}C_{l-1}+1)\;{\sum\limits_{j=1}^{d}\;f(x_j)}$$ then the odd mapping $f:X{\rightarrow}Y$ is additive, and we prove the Cauchy-Rassias stability of the functional equation in Banach modules over a unital $C^*$-algebra. As an application, we show that every almost linear bijection $h:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ of a unital $C^*$-algebra ${\mathcal{A}}$ onto a unital $C^*$-algebra ${\mathcal{B}}$ is a $C^*$-algebra isomorphism when $h(2^nuy)=h(2^nu)h(y)$ for all unitaries $u{\in}{\mathcal{A}}$, all $y{\in}{\mathcal{A}}$, and $n=0,1,2,{\cdots}$.

• Journal of the Korean Institute of Traditional Landscape Architecture
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• v.33 no.2
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• pp.89-102
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• 2015

This study contemplates the tendency of the examination questions for History of Korean Landscape Architecture. The study targets the questions of 'Landscape Architecture History' which has been set in the written test for National Qualification Test of a landscape engineer for recent 10 years from 2005 to 2014 and derives analyzable items based on the guidelines of question-setting presented by Human Resources Development Service of Korea. The results of the study are drawn as follows. First, among 5 areas composing Landscape History, the proportion of Korean Landscape questions is getting increased while that of Western ones is decreasing. Second, about 30 traditional trees and 11 types of traditional landscape elements including traditional facilities were shown in Korean Landscape questions. Besides, history, geographic, practical science, horticulture, anthology books and the 25 tradition landscape-related historic documents categorized as the garden painting data were found. And the kings from ancient era to Choseon Dynasty who were associated with the time of palace garden building, the builders or owners of the villas, the authors of the document and Chinese scholars also appeared. Third, there were no the questions of prehistoric times and Balhae Kingdom, whereas those of Choseon Dynasty were dominantly focused. Among the traditional sites of Choseon Dynasty, Byeolseo(villas) were set most, followed by Dosung or Gung-gweol(castle towns or palaces), houses, Nu Jeong Dea(pavilions) and Seowon(local schools) in order. Nak-an eupseong and Yong-ju sa were the only cases for a castle town and a temple each. Fourth, being associated with tradition spaces, the questions asked for understanding the detailed contents of time of sites' construction, builders, location features, building structures, ground plan types and the components s of garden. In addition, as a result of checking whether traditional landscape sites were shown in the set questions in 9 Korean Landscape textbooks, Dongchundang, Pungamjeonsa, Simgogseowon did not appeared. As a result of reviewing the tendency of the examination questions for History of Korean Landscape Architecture, the questions which ask minor facts without generality and which include difficult information and site uncomprehended in the textbook should be reconsidered.