• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.787-798
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• 2018

For $1{\leq}p{\leq}{\infty}$, let $H^p$ be the usual Hardy space on the unit circle. When ${\alpha}$ and ${\beta}$ are bounded functions, a singular integral operator $S_{{\alpha},{\beta}}$ is defined as the following: $S_{{\alpha},{\beta}}(f+{\bar{g}})={\alpha}f+{\beta}{\bar{g}}(f{\in}H^p,\;g{\in}zH^p)$. When p = 2, we study the hyponormality of $S_{{\alpha},{\beta}}$ when ${\alpha}$ and ${\beta}$ are some special functions.

• East Asian mathematical journal
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• v.38 no.1
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• pp.129-141
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• 2022

We obtain interior regularity estimates in the weighted Orlicz spaces for viscosity solutions of fully nonlinear uniformly parabolic equations u_t - F(D² u, x, t) = f(x, t) in Q₁ under relaxed structure conditions on the nonlinear operator F.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.543-552
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• 2012

In this paper, we will show that if ${\mu}$ is a Borel measure on the unit disk D such that ${\int}_{D}\frac{d{\mu}(z)}{(1-\left|z\right|^2)^{p\alpha}}$ < ${\infty}$ where 0 < ${\alpha},{\rho}$ < ${\infty}$, then a bounded sequence of functions {$f_n$} in the $\alpha$-Bloch space $\mathcal{B}{\alpha}$ has a convergent subsequence in the space $D_p({\mu})$ of analytic functions f on D satisfying $f^{\prime}\;{\in}\;L^p(D,{\mu})$. Also, we will find some conditions such that ${\int}_D\frac{d\mu(z)}{(1-\left|z\right|^2)^p$.

• Journal of Korean society of Dental Hygiene
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• v.10 no.4
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• pp.757-764
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• 2010

Objectives : The fluoride coating for caries prevention and strengthen enamel use NaF(sodium fluoride, Junsei Chemical Co., Ltd, Japan) 2% gel, SnF2(stannous fluoride, SIGMA-ALDRICH Gmbh, USA)8% gel and APF(acidulated phosphate fluoride, Sultan health care, USA) 1.23% gel. Methods : After put the enamel piece in these fluoride compound gel, we observed density level. And after measuring the vickers hardness, Got the following conclusions. Results : 1. After settling in the APF 1.23% during 6 days, we observed high density level of enamel surface using 250 magnification scanning microscope. The vacuum of surface packed (in) like sardines. 2. After settling in the APF 1.23% during 6 days, we observed reducing the space between the cluster of enamel surface using 50,000 magnification scanning microscope. 3. The vickers hardness change was very much on the all kinds of fluoride compound gel[2% NaF(sodium fluoride)gel, 8% SnF2(stannous fluoride) gel, 1.23% APF(acidulated phosphate fluoride)gel]. It's all because of reducing the space between the cluster of enamel surface(p<0.001). Conclusions : The vickers hardness change was very much on the all kinds of fluoride compound. It's all because of reducing the space between the cluster of enamel surface.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.537-543
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• 2010

Let X be a regular $T_1$-space such that each single point set is a $G_{\delta}$ set. Denot 'hereditarily closure-preserving' by 'HCP'. To consider a question of closed maps of S. Lin in [6], we improve some results of Foged in [1], and prove the following propositions. Proposition 1. $D\;=\;\{x{\in}X\;:\;\mid\{F{\in}\cal{F}:x{\in}F\}\mid{\geq}{\aleph}_0\}$ is discrete and closed if $\cal{F}$ is a collection of HCP. Proposition 2. $\cal{H}\;=\;\{{\cup}\cal{F}'\;:\;F'$ is an fininte subcolletion of $\cal{F}_n\}$ is HCP if $\cal{F}$ is a collection of HCP. Proposition 3. Let (X,$\tau$) have a $\sigma$-HCP k-network. Then (X,$\tau$) has a $\sigma$-HCP k-network F = ${\cup}_n\cal{F}_n$ such that such tat: (i) $\cal{F}_n\;\subset\;\cal{F}_{n+1}$, (ii) $D_n\;=\;\{x{\in}X\;:\;\mid\{F{\in}\cal{F}_n\;:\;x{\in}F\}\mid\;{\geq}\;{\aleph}_0\}$ is a discrete closed set and (iii) each $\cal{F}_n$ is closed to finite intersections.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.233-246
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• 2008

In this paper, we obtain the general solution of the following cubic type functional equation and establish the stability of this equation (0.1) $kf({{\sum}\limits^{n-1}_{j=1}}x_j+kx_n)+kf({{\sum}\limits^{n-1}_{j=1}}x_j-kx_n)+2{{\sum}\limits^{n-1}_{j=1}}f(kx_j)+(k^3-1)(n-1)[f(x_1)+f(-x_1)]=2kf({\sum\limits^{n-1}_{j=1}}x_j)=K^3{\sum\limits^{n-1}_{j=1}[f(x_j+x_n)+f(x_j-x_n)]$ for any integers k and n with k ${\geq}$ 2 and n ${\geq}$ 3.

• Honam Mathematical Journal
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• v.33 no.1
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• pp.73-84
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• 2011

Let f, g, h, k : $\mathbb{R}^n{\rightarrow}\mathbb{C}$ be locally integrable functions. We deal with the $L^{\infty}$-version of the Hyers-Ulam stability of the quadratic functional inequality and the Pexiderized quadratic functional inequality $${\parallel}f(x + y) + f(x - y) -2f(x) - 2f(y){\parallel}_{L^{\infty}(\mathbb{R}^n)}\leq\varepsilon$$ $${\parallel}f(x + y) + g(x - y) -2h(x) - 2f(y){\parallel}_{L^{\infty}(\mathbb{R}^n)}\leq\varepsilon$$ based on the concept of linear functionals on the space of smooth functions with compact support.

• Speech Sciences
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• v.14 no.4
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• pp.203-212
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• 2007

This study was to compare some acoustic characteristics of vowels produced by children with cochlear implant (CI) and the children with normal hearing. 20 subjects under ten years old were further classified into two groups (one group of CI children under four years old and the other group of CI children over four years old). For the normal hearing group, 20 subjects are participated in the experiment. Some acoustic parameters including fundamental frequency (F0) and formant frequencies (F1, F2) were measured in the two groups according to the age of cochlear implant operation. For the CI group, three comer vowels (/a/, /i/, /u/) were recorded five times in isolation and analyzed with Multi-Speech (Kay Elemetrics, model 3700), and two independent t-tests on their formant data were conducted using SPSS 11.5. The result showed that the implanted group over four years had a significant difference in F0 and F1 comparing with the implanted group under four years of age as well as the normal hearing group. Those values of the children with the implanted group under four years old were closer to those of the children with the normal hearing. As to the F2, there was no significant difference among implanted groups. However, it was shown that the vowel space for the implanted groups regardless the operation age indicated much smaller than that for the normal hearing children. This acoustic results suggest that CI surgery would be much more effective if it is done under the age of four years old.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.223-245
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• 2011

In this paper, we de ne an $L_p$ analytic generalized Fourier Feynman transform and a convolution product of functionals in a Ba-nach algebra $\cal{F}$($C_{a,b}$[0, T]) which is called the Fresnel type class, and in more general class $\cal{F}_{A_1;A_2}$ of functionals de ned on general functio space $C_{a,b}$[0, T] rather than on classical Wiener space. Also we obtain some relationships between the $L_p$ analytic generalized Fourier-Feynman transform and convolution product for functionals in $\cal{F}$($C_{a,b}$[0, T]) and in $\cal{F}_{A_1,A_2}$.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.437-445
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• 2008

We show the existence of at least four nontrivial critical points of the $C^{1,1}$ functional f on the Hilbert space $H=X_0{\oplus}X_1{\oplus}X_2{\oplus}X_3{\oplus}X_4$, $X_i$, i = 0, 1, 2, 3 are finite dimensional, with f(0) = 0 when two sublevel subsets, torus with three holes and sphere, of f link, the functional f satisfies sup-inf variatinal linking inequality on the linking subspaces, the functional f satisfies $(P.S.)_c$ condition, and $f{\mid}_{X_0{\oplus}X_4}$ has no critical point with level c. We use the deformation lemma, the relative category theory and the critical point theory for the proof of main result.