• Title/Summary/Keyword: Positive linear maps

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BOUNDARIES OF THE CONE OF POSITIVE LINEAR MAPS AND ITS SUBCONES IN MATRIX ALGEBRAS

  • Kye, Seung-Hyeok
    • Journal of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.669-677
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    • 1996
  • Let $M_n$ be the $C^*$-algebra of all $n \times n$ matrices over the complex field, and $P[M_m, M_n]$ the convex cone of all positive linear maps from $M_m$ into $M_n$ that is, the maps which send the set of positive semidefinite matrices in $M_m$ into the set of positive semi-definite matrices in $M_n$. The convex structures of $P[M_m, M_n]$ are highly complicated even in low dimensions, and several authors [CL, KK, LW, O, R, S, W]have considered the possibility of decomposition of $P[M_m, M_n] into subcones.

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INTERSECTIONS OF MAXIMAL FACES IN THE CONVEX SET OF POSITIVE LINEAR MAPS BETWEEN MATRIX ALGEBRAS

  • Kye, Seung-Hyeok;Lee, Sa-Ge
    • Communications of the Korean Mathematical Society
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    • v.10 no.4
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    • pp.917-924
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    • 1995
  • Let $P_I$ be the convex compact set of all unital positive linear maps between the $n \times n$ matrix algebra over the complex field. We find a necessary and sufficient condition for which two maximal faces of $\cap P_I$ intersect. In particular, we show that any pair of maximal faces of $P_I$ has the nonempty intersection, whenever $n \geq 3$.

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The Linear Discrepancy of a Fuzzy Poset

  • Cheong, Min-Seok;Chae, Gab-Byung;Kim, Sang-Mok
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.11 no.1
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    • pp.59-64
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    • 2011
  • In 2001, the notion of a fuzzy poset defined on a set X via a triplet (L, G, I) of functions with domain X ${\times}$ X and range [0, 1] satisfying a special condition L+G+I = 1 is introduced by J. Negger and Hee Sik Kim, where L is the 'less than' function, G is the 'greater than' function, and I is the 'incomparable to' function. Using this approach, we are able to define a special class of fuzzy posets, and define the 'skeleton' of a fuzzy poset in view of major relation. In this sense, we define the linear discrepancy of a fuzzy poset of size n as the minimum value of all maximum of I(x, y)${\mid}$f(x)-f(y)${\mid}$ for f ${\in}$ F and x, y ${\in}$ X with I(x, y) > $\frac{1}{2}$, where F is the set of all injective order-preserving maps from the fuzzy poset to the set of positive integers. We first show that the definition is well-defined. Then, it is shown that the optimality appears at the same injective order-preserving maps in both cases of a fuzzy poset and its skeleton if the linear discrepancy of a skeleton of a fuzzy poset is 1.

Factors Influencing Self-esteem Changes in Multicultural Adolescents: Using a Linear Mixed Model (다문화 청소년의 자아존중감 변화에 영향을 미치는 요인: 선형혼합모형을 활용하여)

  • Seo, Jiyeong;Park, Min Ah;Han, Myeunghee
    • Research in Community and Public Health Nursing
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    • v.33 no.3
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    • pp.290-298
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    • 2022
  • Purpose: This study was conducted to determine factors influencing changes in the self-esteem of multicultural adolescents over time. Methods: A longitudinal design was adopted to analyze secondary data. This study used the 2nd, 4th, and 6th year data of Multicultural Adolescents Panel Study (MAPS) collected by the Korea Youth Policy Institute. The linear mixed model was utilized to analyze self-esteem changes over time. Results: The factors of sex and age of the students, the mother's Korean writing ability, and the Filipino or Japanese mothers had a significant effect on the self-esteem change of multi-cultural adolescents over time. Specifically, it was found that female students' self-esteem was decreased by 0.04 (t=-2.39, p=.017) more than male students over time. As the subject's age and mother's Korean writing ability increased, self-esteem was decreased by 0.01 (t=-2.53, p=.011) and 0.03 (t=-2.52, p=.012) over time. In addition, compared to that of those who had mothers from Korea, self-esteem of those who had Filipino or Japanese mothers was decreased by 0.04 significantly. Conclusion: Therefore, when developing a self-esteem promotion program, it is necessary to develop content by reflecting the characteristics of mothers as well as the gender and age of students. Furthermore, the significance of this study is in that it established a foundation for a positive self-identity of multicultural adolescents whose number is increasing recently by identifying factors affecting their self-esteem.

A Study on Cost Reduction Effect of Drone Implementation in Traffic Survey (교통조사부문 드론 활용시 비용절감효과 분석 연구)

  • Kim, Dongjun;Ahn, Hyosub;Kim, Jin-tae
    • International Journal of Highway Engineering
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    • v.20 no.4
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    • pp.73-84
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    • 2018
  • PURPOSES : Most of the traffic surveys are carried out by an inspection method by the manpower. In some cases, the video equipment is used only in some regions when the traffic volume is surveyed. In this case, there is environmental restriction that the road equipment to fix the video equipment should exist. Also, in areas where information such as digital maps and satellite photographs is old or not provided, they are forced to rely on manpower research, but it is difficult to put huge amounts of time and money into the research in places where labor supply and demand is difficult. This difficulty is particularly pronounced in overseas business. METHODS : The purpose of this study is to improve the efficiency of business by using the drones in the traffic investigation through analysis of the cost reduction effect between the existing method and the proposed method in the overseas business traffic survey. The scope of the research is limited to the scope of research, and based on the case of overseas projects, the method of using drone for each research sector is suggested. RESULTS : In the traffic condition survey section, we propose the use of drone for traffic survey and queue length survey, and it is confirmed that there is a cost saving effect of 16% ~ 27% compared with the existing method. In the road condition survey, we propose the use of drones for road surface linear survey, geometry survey, and obstacle survey, and it was confirmed that the cost reduction effect is 39% ~ 93% compared to the existing method. CONCLUSIONS : In addition to overseas business, it is expected that it will have a positive effect on research time and cost reduction by using drone in traffic survey in domestic area where labor supply is not easy or basic data is insufficient.

Site Selection Model for Wetland Restoration and Creation for the Circulation of Water in a Newly-built Community (신도시 물순환체계 구축을 위한 습지조성 입지선정에 관한 연구)

  • Choi, Hee-Sun;Kim, Kwi-Gon
    • Journal of the Korean Institute of Landscape Architecture
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    • v.36 no.6
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    • pp.43-54
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    • 2009
  • This study attempted to develop a model for selecting sites for ecologically effective, multi-functional wetlands during the environmental and ecological planning stage, prior to land use Planning. This model was developed with an emphasis upon the creation of a water circulation system for a newly-created city, dispersing and retaining the run-off that is increased due to urbanization and securing spaces to create wetlands that can promote urban biodiversity. A series of Precesses for selecting sites for wetland restoration and creation - watershed analysis, selection of evaluation items, calculation of weights, reparation of thematic maps and synthesis - were incorporated into the model. Its potentials and limitations were examined by applying it to the recently-planned WiRae New Community Development Area, which is located in the Seoul metropolitan region. At the watershed analysis stage, the site was divided into 13 sub-catchment areas. Inflow to watersheds including the area was $3,020,765m^3$ Run-off before and after development is estimated as $1,901,969m^3$ and $1,970,735{\sim}2,039,502m^3$, respectively. The total storage capacity required in the development area amounts to $68,766{\sim}137,533m^3$. When thematic maps were overlapped during the selection stage for wetland sites, 13 sub-catchment areas were prioritized for wetland restoration and creation. The locations and areas for retaining run-off showed that various types of wetlands, including retaining wetlands (area wetlands), riverine wetlands (linear wetlands) and pond wetlands (point wetlands), can be created and that they can be systematically connected. By providing a basic framework for the water circulation system plan of an entire city, it may be used effectively in the space planning stage, such as planning an urban eco-network through integration with greet areas. In order to estimate reasonable run-off and create an adequate water circulation system however, a feedback process following land use planning is required. This study strived to promote urban changes in a positive direction while minimizing urban changes in negative forms.