• Title/Summary/Keyword: quotient structure

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Hong Gil Ju(洪吉周)'s Algebra (홍길주(洪吉周)의 대수학(代數學))

  • Hong, Sung-Sa;Hong, Young-Hee
    • Journal for History of Mathematics
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    • v.21 no.4
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    • pp.1-10
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    • 2008
  • In this paper, we investigate the part dealing with algebra in Hong Gil Ju's GiHaSinSul to analyze his algebraic structure. The book consists of three parts. In the first part SangChuEokSan, he just renames Die jie hu zheng(疊借互徵) in Shu li jing yun to SangChuEokSan and adds a few examples. In the second part GaeBangMongGu, he obtains the following identities: $$n^2=n(n-1)+n=2S_{n-1}^1+S_n^0;\;n^3=n(n-1)(n+1)+n=6S_{n-1}^2+S_n^0$$; $$n^4=(n-1)n^2(n+1)+n(n-1)+n=12T_{n-1}^2+2S_{n-1}^1+S_n^0$$; $$n^5=2\sum_{k=1}^{n-1}5S_k^1(1+S_k^1)+S_n^0$$ where $S_n^0=n,\;S_n^{m+1}={\sum}_{k=1}^nS_k^m,\;T_n^1={\sum}_{k=1}^nk^2,\;and\;T_n^2={\sum}_{k=1}^nT_k^1$, and then applies these identities to find the nth roots $(2{\leq}n{\leq}5)$. Finally in JabSwoeSuCho, he introduces the quotient ring Z/(9) of the ring Z of integers to solve a system of congruence equations and also establishes a geometric procedure to obtain golden sections from a given one.

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An Analysis of Small Area Variations of Hospital Services Utilization in Korea (지역간 입원 이용 변이에 관한 연구)

  • Cho, Woo-Hyun;Lee, Sun-Hee;Park, Eun-Cheol;Sohn, Myong-Sei;Kim, Se-Ra
    • Journal of Preventive Medicine and Public Health
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    • v.27 no.3 s.47
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    • pp.609-626
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    • 1994
  • This study was conducted to investigate whether variations in hospital services utilization across small geographic areas in Korea existed, and if so, what factors are responsible for the variation. The claims data of the fiscal year 1992 obtained from the regional health insurance societies were used for the study. Main findings of the research can be summarized as follows: 1 Extremal Quotients (EQ) of hospital expenditure per capita and hospital days per capita were 2.69 and 2.73, and Coefficient of Variation (CV) were 0.14, both, respectively. The EQ and the CV of admission rate were also 2.71, 0.15. The EQ and the CV of expenditure per admission were 1.73, 0.10 and those of hospital days per admission were 1.29, 0.06. All these statistics were statistically significant and this result provides strong evidence for the existence of small area variations. 2. Comparing patterns of variation among areas, the area which showed higher utilization amounts is Chansungp'o. Koje area, whereas the areas which showed lower utilization amounts are Yongju, Changhung, Miryang, Mokp'o, Koch'ang area. 3. Multivariate analytic methods were used to examine factors related to the variation across areas. In terms of the health resource availability variables, beds per capita or physicians per capita were positively associated with all utilization indices. As for the health service market structure variables, the proportion of health care institutions operating for less than f years was positively related to the expenditure per capita, hospital days per capita and expenditure per admission. In addition the proportion of the private health care institutions also had a negative relationship with total utilization amount and admission rate and the proportion of physicians under age 40 was negatively associated with expenditure per capita and expenditure per admission. With regard to the socio-demographic characteristics, proportion of medicaid population was positively related to hospital days per capita, and percentage of paved road was positively related to hospital days per admission. As a conclusion, wide variations existed across small areas in Korea and supply factors were found to be important in explaining the variation.

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A Study on the Location of Retail Trade in Kwangju-si and Its Inhabitants와 Effcient Utilization (광주시 소매업의 입지와 주민의 효율적 이용에 관한 연구)

  • ;Jeon, Kyung-sook
    • Journal of the Korean Geographical Society
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    • v.30 no.1
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    • pp.68-92
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    • 1995
  • Recentry the structure of the retail trade have been chanaed with its environmantal changes. Some studies may be necessary on the changing process of environment and fundamental structure analyses of the retail trade. This study analyzes the location of retail trades, inhabitants' behavior in retail tredes and their desirable utilization scheme of them in Kwangju-si. Some study methods, contents and coming-out results are as follows: 1. Retail trades can be classified into independent stores, chain-stores (supermarket, voluntary chain and frenchiise system and convenience store), department stores, cooperative associations, traditional, markets mail-order marketing, automatic vending and others by service levels, selling-items, prices, managements, methods of retailing and store or nonstore type. 2. In Kwangju, the environment of retail trades is related to the consumers of population structure: chanes in consumers pattern, trends toward agings and nuclear family, increase of leisur: time and female advances to society. Rapid structural shift in retail trade has also been occurred due to these social changes. Traditionl and premodern markets until 1970s altere to supermarkets or department stores in 1980s, and various types, large enterprises and foreign capitals came into being in 1990s. 3. The locational characteristics of retail trades are resulted from the spatial analysis of the total population distribution, and from the calculation of segregation index in the light of potential demand. The densely-populated areas occurs in newly-built apartment housing complex which is distributed with a ring-shaped pattern around the old urban core. The numbers and rates of the aged over sixty in Kwangsan-gu and the circumference area of Mt.Moodeung, are larger and higher where rural elements are remarkable. A relation between population distribution and retail trade are analysed by the index of population per shop. The index of the population number per shop is lower in urban center, as a whole, being more convenient for consumers. In newly-formed apartment complex areas, on the other, the index more than 1,000 per shop, meeting not the demands for consumers. Because both the younger and the aged are numerous in these areas, the retail trade pattern pertinent to both are needed. Urban fringes including Kwangsan-gu and the vicinity of Mt.Moodeung have some problems owing to the most of population number per shop (more than 1, 500) and the most extensive as well. 4. The regional characteristic of retail trade is analyzed through the location quotient of shops by locational patterns and centerality index. Chungkum-dong is the highest-order central place in CBD. It is the core of retail trades, which has higher-ordered specialty store including three big department stores, supermarkets and large stores. Taegum-dong, Chungsu-dong, Taeui-dong, and Numun-dong that are neiahbored to Chungkum-dong fall on the second group. They have a central commercial section where large chain stores, specialty shopping streets, narrow-line retailing shops (furniture, amusement service, and gallary), supermarkets and daily markets are located. The third group is formed on the axis of state roads linking to Naju-kun, Changseong-kun, Tamyang-kun, Hwasun-kun and forme-Songjeong-eup. It is related to newly, rising apartment housing complex along a trunk road, and characterized by markets and specialty stores. The fourth group has neibourhood-shopping centers including older residential area and Songjeong-eup area with independent stores and supermarkets as main retailing functions. The last group contains inner residential area and outer part of a city including Songjeong-eup. Outer part of miscellaneous shops being occasionally found is rural rather than urban (Fig. 7). 5. The residents' behaviors using retail trade are analyzed by factors of goods and facilities. Department stores are very high level in preference for higher-order shopping-goods such as clothes for full dress in view of both diversity and quality of goods(28.9%). But they have severe traffic congestions, and high competitions for market ranges caused by their sma . 64.0% of respondents make combined purpose trips together with banking and shopping. 6. For more efficiency of retail-trading, it is necessary to induce spatial distribution policy with regard to opportunity frequency of goods selection by central place, frontier regions and age groups. Also we must consider to analyze competition among different types of retail trade and analyze the consumption behaviors of working females and younger-aged groups, in aspects of time and space. Service improvement and the rationalization of management should be accomplished in such as cooperative location (situation) must be under consideration in relations to other functions such as finance, leisure & sports, and culture centers. Various service systems such as installment, credit card and peremium ticket, new used by enterprises, must also be carried service improvement. The rationalization and professionalization in for the commercial goods are bsically requested.

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