• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.87-95
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• 1994

Relationships between the prime ideals of a ring R and of a normalizing extension S have been studied by several authors. Relationships between the prime ideals of a ring R and of an intermediate normalizing extension T also have studied by several authors where $R{\subset}T{\subset}S$. In this note, some relationships between prime ideals of T and S are studied.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.281-286
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• 2008

In this note we prove that if A and $B^*$ are subnormal operators and is a bounded linear operator such that AX - XB is a Hilbert-Schmidt operator, then f(A)X - Xf(B) is also a Hilbert-Schmidt operator and $${\parallel}f(A)X\;-\;Xf(B){\parallel}_2\;\leq\;L{\parallel}AX\;-\;XB{\parallel}_2$$, for f belonging to a certain class of functions. Furthermore, we investigate the similar problem in the case that S, T are hyponormal operators and $X\;{\in}\;\cal{L}(\cal{H})$ is such that SX - XT belongs to a norm ideal (J, ${\parallel}\;{\cdot}\;{\parallel}_J$) and prove that f(S)X - Xf(T) $\in$ J and ${\parallel}f(S)X\;-\;Xf(T){\parallel}_J\;\leq\;C{\parallel}SX\;-\;XT{\parallel}_J$, for f in a certain class of functions.

• The Pure and Applied Mathematics
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• v.2 no.2
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• pp.91-95
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• 1995

Let H be an arbitrary complex Hilbert space and let (equation omitted)(H) be the *-algebra of all bounded linear operators on H. An operator T in (equation omitted)(H) is called normal if T$\^$＊/T = TT$\^$＊/, hyponormal if T$\^$＊/T $\geq$ TT$\^$＊/, and quasi-hyponormal if T$\^$＊/(T$\^$＊/T － TT$\^$＊/)A $\geq$ 0, or equivalently ∥T$\^$＊/T$\chi$∥ $\leq$ ∥TT$\chi$∥ for all $\chi$ in H.(omitted)

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.1003-1008
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• 2010

In allelic model $X\;=\;(x_1,\;x_2,\;\cdots,\;x_d)$, $$M_f(t)\;=\;f(p(t))\;-\;\int_0^t\;Lf(p(t))ds$$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we define $T_tf\;=\;E_{p_0}^{p^*}\;[f((P(t))]$ for $t\;{\geq}\;0$ for using a new diffusion operator $L^*$ and we show the diffusion relations between $T_t$ and diffusion operator $L^*$.

• Bulletin of the Korean Mathematical Society
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• v.20 no.2
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• pp.69-70
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• 1983

• Kyungpook Mathematical Journal
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• v.6 no.1
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• pp.21-26
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• 1964

• The Mathematical Education
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• v.22 no.1
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• pp.89-90
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• 1983

• Journal of Digital Convergence
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• v.20 no.2
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• pp.573-583
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• 2022

This study was attempted to analyze the effect of a note-taking strategy applied to blended learning adult nursing education. Data were collected from September 17 to October 15, 2021, and analyzed using the SPSS/WIN 26.0 program with a single group pre/post design targeting 33 nursing students. As a main result, learning motivation rose from 3.27 before class to 3.40 after class, but there was no significant difference(t=-1.501, p=.143), and class participation significantly increased from 2.95 before class to 3.27 after class(t=-2.669, p=.012). Motivation for learning before class was pre-class participation(r=.838, p<.001), learning motivation after class(r=.545, p=.001), and class participation after class(r=.462, p=.007) and each showed a significant positive correlation. Learning motivation and class participation according to gender(Wilks'𝛌=.866), class interest(Wilks'𝛌=.632), and class satisfaction(Wilks'𝛌=.822) were all higher than the significance level of .05, so they were no significant difference. Based on these results, applying a note-taking strategy to blended learning adult nursing education was effective in improving class participation. In a future study, it is necessary to verify the effectiveness by applying a note-taking strategy customized according to academic achievement.

• East Asian mathematical journal
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• v.17 no.1
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• pp.87-92
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• 2001

In this paper, we have the extended result of Bunce's theorem. And we show that if T is an irreducible p-hyponormal operator such that T*T-TT* is compact, then ${\sigma}_{ap}(T)={\sigma}_e(T)$ and ${\sigma}_p({\phi}(T))={\sigma}_e({\phi}(T))$.

• Korean Journal of Mathematics
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• v.20 no.2
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• pp.177-184
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• 2012

In this paper, we study the four different types of relations, $\mathcal{P}(X,T)$, $\mathcal{R}(X,T)$, $\mathcal{L}(X,T)$, and $\mathcal{S}(X,T)$ in a transformation (X,T), and obtain some of their properties. In particular, we give a relationship between $\mathcal{R}(X,T)$ and $\mathcal{S}(X,T)$.