• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.247-257
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• 1997

It was the turning point in the "fixed point arena" when the notion of weak commutativity was introduced by Sessa [9] as a sharper tool to obtain common fixed points of mappings. As a result, all the results on fixed point theorems for commuting mappings were easily transformed in the setting of the new notion of weak commutativity of mappings. It gives a new impetus to the studying of common fixed points of mappings satisfying some contractive type conditions and a number of interesting results have been found by various authors. A bulk of results were produced and it was the centre of vigorous research activity in "Fixed Point Theory and its Application in various other Branches of Mathematical Sciences" in last two decades. A major break through was done by Jungck [3] when he proclaimed the new notion what he called "compatibility" of mapping and its usefulness for obtaining common fixed points of mappings was shown by him. There-after a flood of common fixed point theorems was produced by various researchers by using the improved notion of compatibility of mappings. of compatibility of mappings.

• Journal of Advanced Navigation Technology
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• v.24 no.5
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• pp.358-367
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• 2020

With the increases of average commuting time of office workers in the Seoul metropolitan area and the cost of traffic congestion on roads, the need for new transportation is increasing and urban air mobility (UAM) is emerging as an alternative. Therefore, in this paper, the vertiport locations were selected and routes were established using population, traffic and commuting data of Seoul and Gyeonggi Province. Vector thrust type and multicopter type of eVTOL compatible for UAM were selected by analyzing the types of eVTOLand time required for selected routes was calculated. In addition, the time required when we utilize other transportations was compared with UAM. Finally, it was verified that the commuting time can be sharply reduced when we use UAM.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1145-1153
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• 2014

Let G be a finite group and X be a union of conjugacy classes of G. Define C(G,X) to be the graph with vertex set X and $x,y{\in}X$ ($x{\neq}y$) joined by an edge whenever they commute. In the case that X = G, this graph is named commuting graph of G, denoted by ${\Delta}(G)$. The aim of this paper is to study the automorphism group of the commuting graph. It is proved that Aut(${\Delta}(G)$) is abelian if and only if ${\mid}G{\mid}{\leq}2$; ${\mid}Aut({\Delta}(G)){\mid}$ is of prime power if and only if ${\mid}G{\mid}{\leq}2$, and ${\mid}Aut({\Delta}(G)){\mid}$ is square-free if and only if ${\mid}G{\mid}{\leq}3$. Some new graphs that are useful in studying the automorphism group of ${\Delta}(G)$ are presented and their main properties are investigated.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.57-68
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• 2012

The commuting graph of an arbitrary ring R, denoted by ${\Gamma}(R)$, is a graph whose vertices are all non-central elements of R, and two distinct vertices a and b are adjacent if and only if ab = ba. In this paper, we investigate the connectivity, the diameter, the maximum degree and the minimum degree of the commuting graph of group ring $Z_nQ_8$. The main result is that $\Gamma(Z_nQ_8)$ is connected if and only if n is not a prime. If $\Gamma(Z_nQ_8)$ is connected, then diam($Z_nQ_8$)= 3, while $\Gamma(Z_nQ_8)$ is disconnected then every connected component of $\Gamma(Z_nQ_8)$ must be a complete graph with a same size. Further, we obtain the degree of every vertex in $\Gamma(Z_nQ_8)$, the maximum degree and the minimum degree of $\Gamma(Z_nQ_8)$.

• Asia Pacific Journal of Business Review
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• v.6 no.1
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• pp.21-48
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• 2021

Promoting low carbon transportation adoption is important for energy saving. Some prior studies have discussed on environmental values affect low carbon transportation commuting is inconclusive. This study has constructed the environmental values, utility value, and social influence-based low-carbon transportation adoption model through the theory of the technology acceptance model and VBN model and the IS success model. Through the SEM model and stepwise regression analysis, we have found that environmental values positively affect utility value, and utility value also positively affects the behavior adoption of low carbon transportation. The utility value as mediating effect in the relationship between environmental values and low carbon transportation commuting behavior. Besides, we also have found that social influence positively impacts the behavior adoption of low carbon transportation. It better enhances the level of household residents' environmental values and utility values, and social influence for promoting the adoption of low carbon transportation. This present research provides theoretical guidance and suggestions for promoting the development of low-carbon transportation innovation.

• 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.

• Journal of the Korean Geographical Society
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• v.44 no.3
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• pp.339-354
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• 2009

The purposes of this study are to identify many implications of commuting regional type according to the features of foreigner commuting. Research on the pattern of distribution of foreigners has been very simple and limited because foreigners usually lived together in a specific area, and their workplace often tended to be their residence. However they currently live dispersed more Widely, and their job and housing increasingly tend to be mismatched. This study divided areas inhabited by foreigners into general one characterized by job-housing match and exceptional one characterized by job-housing mismatch, and then examined the features of foreigner commuting. General commute type showed a high rate of intra area commute and foreign workers' universal features. Inflow commute type showing high E/R ratio. In these areas, outflow commuters had a short journey to work while inflow commuters had relatively a long journey to work, and professionals accounted for a high proportion of employees. Outflow commute type showing low E/R ratio. In these areas, outflow commuters had a long journey to work while inflow commuters had a relatively short journey to work. The composition ratio of three commute types was different according to nationality and visa type.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.117-123
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• 2013

Let G be a finite non-abelian group. We define the non-commuting graph ${\nabla}(G)$ of G as follows: the vertex set of ${\nabla}(G)$ is G-Z(G) and two vertices x and y are adjacent if and only if $xy{\neq}yx$. In this paper we prove that if G is a finite group with $${\nabla}(G){\simeq_-}{\nabla}(\mathbb{A}_{22})$$, then $$G{\simeq_-}\mathbb{A}_{22}$$where $\mathbb{A}_{22}$ is the alternating group of degree 22.

• Korean Journal of Mathematics
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• v.16 no.1
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• pp.115-122
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• 2008

In the present article, we give a set of axioms for determinants and traces of the l-tuples of commuting operators on a fixed finite dimensional vector space over a field when $l{\geq}2$. We describe them with or without a coherence assumption especially when k is the field of real numbers. Under the coherence assumption, it turns out that there are only a trivial determinant and trace over arbitrary field k. This leads us to formulate a more appropriate definition of the determinants. In this case, the set of determinants can be described in terms of the Milnor's K-theory. As for the traces, it is not clear to us how to correctly formulate a definition except for certain cases.

• Journal of the Economic Geographical Society of Korea
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• v.11 no.4
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• pp.661-667
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• 2008

We examine the major factors governing the travel time for commuters in the Seoul metropolitan area. To identify the determinants of the commuting time for residents with jobs in the city centre, a multiple regression analysis is performed using household survey data. The results reveal that commuters in Seoul place higher value on time than on living space. Thus, we may conclude that recent trends in income segregation in Seoul are not the result of increased housing demand but of dispersed jobs and better amenities offered in the suburbs.