• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.213-228
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• 2010

A weighted version of the geometric mean of k ($\geq\;3$) positive invertible operators is given. For operators $A_1,{\ldots},A_k$ and for nonnegative numbers ${\alpha}_1,\ldots,{\alpha}_k$ such that $\sum_\limits_{i=1}^k\;\alpha_i=1$, we define weighted geometric means of two types, the first type by a direct construction through symmetrization procedure, and the second type by an indirect construction through the non-weighted (or uniformly weighted) geometric mean. Both of them reduce to $A_1^{\alpha_1}{\cdots}A_k^{{\alpha}_k}$ if $A_1,{\ldots},A_k$ commute with each other. The first type does not have the property of permutation invariance, but satisfies a weaker one with respect to permutation invariance. The second type has the property of permutation invariance. We also show a reverse inequality for the arithmetic-geometric mean inequality of the weighted version.

• Journal of the Korean Regional Science Association
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• v.36 no.2
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• pp.3-12
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• 2020

Recently, metropolitanization and suburbization have been occurring mainly in large cities, and spatial miss-match between residential and employment areas has increased. Spatial miss-match is different in the metropolitan cities and other metropolitan cities in Korea. Seoul and other metropolitan cities have grown to become centers of business functions, while other metropolitan cities have been transformed into residential function centers. Accordingly, The reverse commuting phenomenon is occurring in the rural metropolitan. The reverse commuting phenomenon limits the employment opportunities of specific classes among urban residents, and cause various problems such as environmental pollution and traffic congestion. Therefore, many studies on spatial mismatch and reverse commuting have been conducted, but a number of studies have been conducted on the Seoul metropolitan area, and research on other metropolitan areas is insufficient. The purpose of this study is to analyze the cause of the commuting phenomenon in the metropolitan area of the non-metropolitan area by considering spatial mismatch and understanding the reverse commutation situation in the local metropolitan area. This study is analyzed by a multi-level model and suggests the need for management of industrial location and expansion of residence in suburban.

• Korea journal of population studies
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• v.24 no.1
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• pp.5-40
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• 2001

We have approached this study on the basis of population and family changes. We have selected two suburban and two general rural areas for this research. The suburban rural areas are located next to Chungju City, which is the biggest city in Chungbuk Province, and the residents are able to commute to Chungju. The general rural areas are located in Boeun Gun, which is a typical agricultural county in Chungbuk Province. We have conducted two round surveys at the research areas: 1995-1996 for the first round and 1999-2000 for the second round surveys. Since the surveys were completed ones interviewed by enumerators, we have used the survey data directly for the analysis by year and region. The population structure by age and sex in general rural areas is shaped as a reverse triangle, which is becoming more serious because of the continuing emigration of young generation. Most of the young generation moves to the urban areas and their old parents only are left in their hometown, rural areas. When the parents become old and die, the number of households in the areas decreases rapidly. If there are no more new family formations, therefore, the rural society itself would cease to exist in near future. However, the situation of suburban rural areas was a different case. Although the rural young generation has moved to urban areas, other young age groups have moved into the areas with their small enterprises and for the low living costs. The original residents become older and the young age groups are replaced with the new immigrants continuously. Therefore, the traditional agricultural society will be replaced with a non-agricultural society, which will have more characteristics of urban areas.

• Journal of the Korean association of regional geographers
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• v.3 no.1
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• pp.13-34
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• 1997

The impact of a central place on daily living over wide outlying territory has been one of traditional subjects in the field of urban geography. The flow of rural population toward the central city of Chinju characterizes the population movement in Western Kyungnam, where the spillover of urban population into outlying areas, an especially prominent phenomenon in American society, does not occur. The central city of Chinju is supposed to be the most favored settlement area in Western Kyungnam. More than two thousands of teachers. who live in Chinju, cross the city boundary each morning to do their jobs in Western Kyungnam. But only ninety teachers living outside Chinju commute to the workplace in the city. The teachers willingly spend hours commuting each day to enjoy better quality of life in the central city. In fact, the central city of Chinju functions as bedroom communities for many middle-class workers in Western Kyungnam. On the basis of teachers' commuting behavior, four levels of Chinju's urban spheres are identified in Western Kyungnam. As Table-6 and Figure-2 show, the first-order level of Chinju's sphere includes most Myuns of Sanchung/Hadong Guns and some Myuns of Sachun/Gosung Guns. The second-order level comprises Sanchung/Sachun Eubs and many Myuns of Sachun /Gosung Guns. The third-order level is made up of Samchunpo, Hadong/Gosung/Eryung/Namhae/Habchun/Hamyang Eups, and many Myuns of Eryung/Namhae/Habchun Guns. And all of Guchang Gun and most Myuns of Hamyang Gun belong to the fourth-order level of Chinju's sphere. The influence sphere of Metropolitan Chinju is extended farther in the direction of less competition with other metropolises. Such a situation occurs to the west and south of Chinju. Daily commuting, defined as the journeys to and from work, is an excellent indicator for delimiting urban spheres of influence.