• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.995-1004
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• 2000

In this paper we shall give a slight generalization of J. Vukman's Theorem. And show from the result that the image of a continuous linear Jordan derivation on a noncommutative Banach algebra A is contained in the radical under the condition [D(x),x]E(x) ${\in}$ rad(A) for all $x{\in}A$ . And we show some properties of the derivations on noncommutative Banach algebras.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1293-1305
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• 2009

Molodtsov [D. Molodtsov, Soft set theory First results, Comput. Math. Appl. 37 (1999) 19-31] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to the theory of BCC-algebras. The notion of (trivial, whole) soft BCC-algebras and soft BCC-subalgebras are introduced, and several examples are provided. Relations between a fuzzy subalgebra and a soft BCC-algebra are given, and the characterization of soft BCC-algebras is established.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.151-157
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• 2010

In this note, we obtain range inclusion results for left Jordan derivations on Banach algebras: (i) Let $\delta$ be a spectrally bounded left Jordan derivation on a Banach algebra A. Then $\delta$ maps A into its Jacobson radical. (ii) Let $\delta$ be a left Jordan derivation on a unital Banach algebra A with the condition sup{r$(c^{-1}\delta(c))$ : c $\in$ A invertible} < $\infty$. Then $\delta$ maps A into its Jacobson radical. Moreover, we give an exact answer to the conjecture raised by Ashraf and Ali in [2, p. 260]: every generalized left Jordan derivation on 2-torsion free semiprime rings is a generalized left derivation.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.1-12
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• 2018

Let R be a 3!-torsion free noncommutative semiprime ring, and suppose there exists a Jordan derivation $D:R{\rightarrow}R$ such that $D^2(x)[D(x),x]=0$ or $[D(x),x]D^2(x)=0$ for all $x{\in}R$. In this case we have $f(x)^5=0$ for all $x{\in}R$. Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation $D:A{\rightarrow}A$ such that $D^2(x)[D(x),x]{\in}rad(A)$ or $[D(x),x]D^2(x){\in}rad(A)$ for all $x{\in}A$. In this case, we show that $D(A){\subseteq}rad(A)$.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.183-196
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• 2011

Molodtsov [5] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to an implicative ideal of BCK-algebras. The notion of implicative soft ideals in BCK-algebras and implicative idealistic soft BCK-algebras is introduced, and related properties are investigated. Relations between implicative soft ideals and commutative (resp. positive implicative) soft ideals are discussed. Also, relations between implicative idealistic soft BCK-algebras and commutative (resp. positive implicative) idealistic soft BCK-algebras are provided.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.103-125
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• 2018

Let R be a 5!-torsion free semiprime ring, and let $D:R{\rightarrow}R$ be a Jordan derivation on a semiprime ring R. Then $[D(x),x]D(x)^2=0$ if and only if $D(x)^2[D(x), x]=0$ for every $x{\in}R$. In particular, let A be a Banach algebra with rad(A) and if D is a continuous linear Jordan derivation on A, then we show that $[D(x),x]D(x)2{\in}rad(A)$ if and only if $D(x)^2[D(x),x]{\in}rad(A)$ for all $x{\in}A$ where rad(A) is the Jacobson radical of A.

• Communications of Mathematical Education
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• v.30 no.1
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• pp.1-22
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• 2016

We had a full scale of literature survey and case survey of mathematics Flipped Learning class models. The purpose of this study is to design and adopt a Flipped Learning 'Linear Algebra' class model that fis our need. We applied our new model to 30 students at S University. Then we analyzed the activities and performance of students in this course. Our Flipped Learning 'Linear Algebra' teaching model is followed in 3 stages : The first stage involved the students viewing an online lecture as homework and participating free question-answer by themselves on Q&A before class, the second stage involved in-class learning which researcher solved the students' Q&A and highlighted the main ideas through the Point-Lecture, the third stage involved the students participating more advanced topic by themselves on Q&A and researcher (or peers) finalizing students' Q&A. According to the survey, the teaching model made a certain contribution not only to increase students' participation and interest, but also to improve their communication skill and self-directed learning skill in all classes and online. We used the Purposive Sampling from the obtained data. For the research's validity and reliability, we used the Content Validity and the Alternate-Form Method. We found several meaningful output from this analysis.

• Journal of Korean Society for Geospatial Information Science
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• v.18 no.4
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• pp.131-139
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• 2010

Recent spread of GIS and the increasing demand of spatial data have brought about the development of web GIS. In addition to sharing and mapping spatial data, web GIS is also required to provide spatial analytic functions on the web. The FOSS(free and open source software) can play an important role in developing such a system for web GIS. In this paper, we proposed a web-based system for raster data analysis using map algebra. We employed GRASS as an open source software and implemented the GRASS functionalities on the web using java methods for invocation of server-side commands. Map algebra and AHP were combined for the raster data analysis in our system. For a feasibility test, the landslide susceptibility in South Korea was calculated using rainfall, elevation, slope angle, slope aspect, and soil layers. It is anticipated that our system will be extensible to other web GIS for raster data analysis with GRASS.

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.405-417
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• 2012

We find the Hilbert function and the minimal free resolution of a star-configuration in $\mathbb{P}^n$. The conditions are provided under which the Hilbert function of a star-configuration in $\mathbb{P}^2$ is generic or non-generic We also prove that if $\mathbb{X}$ and $\mathbb{Y}$ are linear star-configurations in $\mathbb{P}^2$ of types t and s, respectively, with $s{\geq}t{\geq}3$, then the Artinian k-algebra $R/(I_{\mathbb{X}}+I_{\mathbb{Y})$ has the weak Lefschetz property.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.381-387
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• 2002

Our main goal is to show that if there Jordan derivation D, G on a noncommutative (n+1)!-torsion free prime ring R such that D($\chi$)$\chi$$^n$+$\chi$$^n$G($\chi$) $\in$ C(R) for all $\chi$ $\in$ R, then we have D=0 and G=0.