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Choi, Ki Seong
- Journal of the Chungcheong Mathematical Society
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- v.26 no.2
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- pp.393-402
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- 2013
For 0 < $p$ < ${\infty}$, ${\alpha}$ > -1 and 0 < $r$ < 1, we show that if $f$ is in the space of Dirichlet type $\mathfrak{D}^p_{p-1}$, then ${\int}_{1}^{0}M_{p}^{p}(r,f^{\prime})(1-r)^{p-1}rdr$ < ${\infty}$ and ${\int}_{1}^{0}M_{(2+{\alpha})p}^{(2+{\alpha})p}(r,f^{\prime})(1-r)^{(2+{\alpha})p+{\alpha}}rdr$ < ${\infty}$ where $M_p(r,f)=\[\frac{1}{2{\pi}}{\int}_{0}^{2{\pi}}{\mid}f(re^{it}){\mid}^pdt\]^{1/p}$. For 1 < $p$ < $q$ < ${\infty}$ and ${\alpha}+1$ < $p$, we show that if there exists some positive constant $c$ such that ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathfrak{D}^p_{\alpha}}$ for all $f{\in}\mathfrak{D}^p_{\alpha}$, then ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathcal{B}_p(q)}$ where $\mathcal{B}_p(q)$ is the weighted Besov space. We also find the condition of measure ${\mu}$ such that ${\sup}_{a{\in}D}{\int}_D(k_a(z)(1-{\mid}a{\mid}^2)^{(p-a-1)})^{q/p}d{\mu}(z)$ < ${\infty}$.
https://doi.org/10.14403/jcms.2013.26.2.393 인용 PDF KSCI

Kim, Chung-Sook;Park, Myoung-Ho
- Journal of Technologic Dentistry
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- v.23 no.1
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- pp.107-114
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- 2001
R.P.D fabrication can be made if the skills already is properly used in the manufacturing press. You may feel extremely comfortable to wear it. The material used has high elasticity that it can endure the hole process of Acetal Wax pattern casting without any deformation moreover its adaptability is not bad. Because of the poor financial condition of patterns and health insurance, Acetal R.P.D Framework can be one of the best alternatives used for setting clasp partial denture cheaply. R.P.D Framework is aesthetically excellent. The color caused by saliva is so similar to that of the rest of teeth that even dentists as well as patients can not recognize clasp arm. Clasp also helps to secure prosthesis ideally without damaging teeth due to its deep position downward. Since dentists and patients have a good reaction to clasp so far, we are encouraged to apply it to other technical fields.
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Chang, Gyu-Whan
- Bulletin of the Korean Mathematical Society
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- v.47 no.5
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- pp.907-913
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- 2010
Let D be an integrally closed domain with quotient field K, * be a star operation on D, X, Y be indeterminates over D, $N_*\;=\;\{f\;{\in}\;D[X]|\;(c_D(f))^*\;=\;D\}$ and $R\;=\;D[X]_{N_*}$. Let b be the b-operation on R, and let $*_c$ be the star operation on D defined by $I^{*_c}\;=\;(ID[X]_{N_*})^b\;{\cap}\;K$. Finally, let Kr(R, b) (resp., Kr(D, $*_c$)) be the Kronecker function ring of R (resp., D) with respect to Y (resp., X, Y). In this paper, we show that Kr(R, b) $\subseteq$ Kr(D, $*_c$) and Kr(R, b) is a kfr with respect to K(Y) and X in the notion of [2]. We also prove that Kr(R, b) = Kr(D, $*_c$) if and only if D is a $P{\ast}MD$. As a corollary, we have that if D is not a $P{\ast}MD$, then Kr(R, b) is an example of a kfr with respect to K(Y) and X but not a Kronecker function ring with respect to K(Y) and X.
https://doi.org/10.4134/BKMS.2010.47.5.907 인용 PDF KSCI