• Title, Summary, Keyword: commuting map

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COMPOUND-COMMUTING ADDITIVE MAPS ON MATRIX SPACES

  • Chooi, Wai Leong
    • Journal of the Korean Mathematical Society
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    • v.48 no.1
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    • pp.83-104
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    • 2011
  • In this note, compound-commuting additive maps on matrix spaces are studied. We show that compound-commuting additive maps send rank one matrices to matrices of rank less than or equal to one. By using the structural results of rank-one nonincreasing additive maps, we characterize compound-commuting additive maps on four types of matrices: triangular matrices, square matrices, symmetric matrices and Hermitian matrices.

TRIVIALITY OF A TRACE ON THE SPACE OF COMMUTING TRACE-CLASS SELF-ADJOINT OPERATORS

  • Myung, Sung
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.6
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    • pp.1205-1211
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    • 2010
  • In the present article, we investigate the possibility of a real-valued map on the space of tuples of commuting trace-class self-adjoint operators, which behaves like the usual trace map on the space of trace-class linear operators. It turns out that such maps are related with continuous group homomorphisms from the Milnor's K-group of the real numbers into the additive group of real numbers. Using this connection, it is shown that any such trace map must be trivial, but it is proposed that the target group of a nontrivial trace should be a linearized version of Milnor's K-theory as with the case of universal determinant for commuting tuples of matrices rather than just the field of constants.

ON 4-PERMUTING 4-DERIVATIONS IN PRIME AND SEMIPRIME RINGS

  • Park, Kyoo-Hong
    • The Pure and Applied Mathematics
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    • v.14 no.4
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    • pp.271-278
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    • 2007
  • Let R be a 2-torsion free semiprime ring. Suppose that there exists a 4-permuting 4-derivation ${\Delta}:R{\times}R{\times}R{\times}R{\rightarrow}R$ such that the trace is centralizing on R. Then the trace of ${\Delta}$ is commuting on R. In particular, if R is a 3!-torsion free prime ring and ${\Delta}$ is nonzero under the same condition, then R is commutative.

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ON PRIME AND SEMIPRIME RINGS WITH SYMMETRIC n-DERIVATIONS

  • Park, Kyoo-Hong
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.3
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    • pp.451-458
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    • 2009
  • Let $n{\geq}2$ be a fixed positive integer and let R be a noncommutative n!-torsion free semiprime ring. Suppose that there exists a symmetric n-derivation $\Delta$ : $R^{n}{\rightarrow}R$ such that the trace of $\Delta$ is centralizing on R. Then the trace is commuting on R. If R is a n!-torsion free prime ring and $\Delta{\neq}0$ under the same condition. Then R is commutative.

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ON PRIME AND SEMIPRIME RINGS WITH PERMUTING 3-DERIVATIONS

  • Jung, Yong-Soo;Park, Kyoo-Hong
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.4
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    • pp.789-794
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    • 2007
  • Let R be a 3-torsion free semiprime ring and let I be a nonzero two-sided ideal of R. Suppose that there exists a permuting 3-derivation ${\Delta}:R{\times}R{\times}R{\rightarrow}R$ such that the trace is centralizing on I. Then the trace of ${\Delta}$ is commuting on I. In particular, if R is a 3!-torsion free prime ring and ${\Delta}$ is nonzero under the same condition, then R is commutative.

An improvement strategy of metropolitan commuter railways according to the reformation of bus system on a metropolitan area (대도시권 버스개편추세에 따른 통근전철의 대응 전략)

  • Han Woo-jin
    • Proceedings of the KSR Conference
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    • pp.1601-1606
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    • 2004
  • Nowadays, the bus system of a metropolitan area is improving very fast. According to the bus, commuter railways increase their competitive power. For this, trains get the mobility increasing, effective transferring system and unified information service. For the mobility increasing, commuting railway must be faster by flexible train diagram and facilities improvement. And finally, optimal commuter train, 'Liner' is needful. And for effective transferring system, it is necessary that railway station and transferring center of a city be merged. And it is needful that direct management bus by railway company and unification fare system on metropolitan region. Next, for information service system improving, the commuting railway station must be regional transportation hub at first. And it is needful that unified line map of trunk line transportation systems and regionally collective transportation system information book. Therefore, metropolitan commuting railways compete with trunk line bus and cooperate with feeder line bus, and can make optimal metropolitan public transportation systems.

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SEMI-COMPATIBILITY, COMPATIBILITY AND FIXED POINT THEOREMS IN FUZZY METRIC SPACE

  • Singh, Bijendra;Jain, Shishir
    • Journal of the Chungcheong Mathematical Society
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    • v.18 no.1
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    • pp.1-22
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    • 2005
  • The object of this paper is to introduce the concept of a pair of semi-compatible self-maps in a fuzzy metric space to establish a fixed point theorem for four self-maps. It offers an extension of Vasuki [10] to four self-maps under the assumption of semi-compatibility and compatibility, repsectively. At the same time, these results give the alternate results of Grebiec [5] and Vasuki [9] as well.

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A study on the actual state of learning competences in students at a college (J 대학교 재학생의 학습역량 실태조사)

  • Song, Kyoung-hee
    • Journal of Korean Dental Hygiene Science
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    • v.1 no.2
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    • pp.21-39
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    • 2018
  • The purpose of this study was to examine the learning competencies of students at a college from September 1 to November 30, 2017, in an effort to provide some information on how to foster learning competencies in college years, which lay the foundation for work and social lives. 1. The learning competencies of the subjects consisted of academic vision, student identity, cognitive regulation, emotional regulation, learning management and creating learning environments. Out of five points, they scored the highest in academic vision and student identity with 3.34, followed by learning management with 3.20, creating learning environments with 3.18, emotional regulation with 3.16 and cognitive regulation with 3.14. 2. There were statistically significant differences in academic vision according to age, the area of major, the academic credential of their fathers, commuting time, military service experience and career plans. 3. There were statistically significant differences in student identity and cognitive regulation according to gender, age, the area of major, the academic credential of their fathers, commuting time, military service experience and career plans. 4. There were statistically significant differences in emotional regulation according to age, the area of major, the academic credential of their fathers, commuting time, career plans and daily mean study hours. 5. There were statistically significant differences in learning management according to gender, age, the area of major, grade point average, the academic credential of their fathers, career plans and daily mean study hours. 6. There were statistically significant differences in creating learning environments according to gender, age, the area of major, the academic credential of fathers, commuting time, career plans and daily mean study hours. As they were poorest at the cognitive regulation area among the areas of learning competencies, self-directed learning programs that deal with how to study, learning process, how to take notes and arrange them, how to link different pieces of acquired knowledge and how to map out study plans should be developed to give support to students.

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