• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.217-227
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• 2016

Let X be a nonempty set, and let $\mathfrak{F}=\{Y_i:i{\in}I\}$ be a family of nonempty subsets of X with the properties that $X={\bigcup}_{i{\in}I}Y_i$, and $Y_i{\cap}Y_j={\emptyset}$ for all $i,j{\in}I$ with $i{\neq}j$. Let ${\emptyset}{\neq}J{\subseteq}I$, and let $T^{(J)}_{\mathfrak{F}}(X)=\{{\alpha}{\in}T(X):{\forall}i{\in}I{\exists}_j{\in}J,Y_i{\alpha}{\subseteq}Y_j\}$. Then $T^{(J)}_{\mathfrak{F}}(X)$ is a subsemigroup of the semigroup $T(X,Y^{(J)})$ of functions on X having ranges contained in $Y^{(J)}$, where $Y^{(J)}:={\bigcup}_{i{\in}J}Y_i$. For each ${\alpha}{\in}T^{(J)}_{\mathfrak{F}}(X)$, let ${\chi}^{({\alpha})}:I{\rightarrow}J$ be defined by $i{\chi}^{({\alpha})}=j{\Leftrightarrow}Y_i{\alpha}{\subseteq}Y_j$. Next, we define two congruence relations ${\chi}$ and $\widetilde{\chi}$ on $T^{(J)}_{\mathfrak{F}}(X)$ as follows: $({\alpha},{\beta}){\in}{\chi}{\Leftrightarrow}{\chi}^{({\alpha})}={\chi}^{({\beta})}$ and $({\alpha},{\beta}){\in}\widetilde{\chi}{\Leftrightarrow}{\chi}^{({\alpha})}{\mid}_J={\chi}^{({\alpha})}{\mid}_J$. We begin this paper by studying the regularity of the quotient semigroups $T^{(J)}_{\mathfrak{F}}(X)/{\chi}$ and $T^{(J)}_{\mathfrak{F}}(X)/{\widetilde{\chi}}$, and the semigroup $T^{(J)}_{\mathfrak{F}}(X)$. For each ${\alpha}{\in}T_{\mathfrak{F}}(X):=T^{(I)}_{\mathfrak{F}}(X)$, we see that the equivalence class [${\alpha}$] of ${\alpha}$ under ${\chi}$ is a subsemigroup of $T_{\mathfrak{F}}(X)$ if and only if ${\chi}^{({\alpha})}$ is an idempotent element in the full transformation semigroup T(I). Let $I_{\mathfrak{F}}(X)$, $S_{\mathfrak{F}}(X)$ and $B_{\mathfrak{F}}(X)$ be the sets of functions in $T_{\mathfrak{F}}(X)$ such that ${\chi}^{({\alpha})}$ is injective, surjective and bijective respectively. We end this paper by investigating the regularity of the subsemigroups [${\alpha}$], $I_{\mathfrak{F}}(X)$, $S_{\mathfrak{F}}(X)$ and $B_{\mathfrak{F}}(X)$ of $T_{\mathfrak{F}}(X)$.

• Journal of the Korean Ceramic Society
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• v.40 no.11
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• pp.1106-1112
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• 2003

For the purpose of making clear the role of oxygen in the thermoelectric properties of FeSi$_2$, thermoelectric measurements and spectroscopic characterization were conducted for the oxidized specimens fabricated from ($\alpha$+$\varepsilon$)-phases and/or $\beta$-phase. Addition of oxygen to FeSi$_2$ prevented both densification during sintering and transformation from metallic phases to semiconducting phase during annealing treatment. In an specimens, electrical conductivity and thermal conductivity decreased with oxidation time. The Seebeck coefficient was positive and small for pure FeSi$_2$. And/or the oxidized specimens fabricated from ($\alpha$+$\varepsilon$)-phases. However, it was negative and showed a maximum peak at about 500 K for the oxidized FeSi$_2$ fabricated from $\beta$-phase. The value of maximum peak increased with oxidation time.

• Pediatric Gastroenterology, Hepatology & Nutrition
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• v.27 no.1
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• pp.62-70
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• 2024

Purpose: Choledochal cysts are congenital anomalies that occur as localized cystic or fusiform dilatations of the biliary tree. Reflux and stasis of pancreatic enzymes in the biliary duct may relate to the development of intestinal metaplasia which might be an important factor related to the carcinogenesis of choledochal cyst, thus the expression of beta-catenin in the metaplastic epithelium might be associated with malignant transformation of choledochal cyst epithelium. Methods: This study was conducted at a tertiary care pediatric center between October 2014 and March 2017. Forty patients were evaluated for epithelial lining, mural ulceration, fibrosis, inflammation, and metaplasia. Results: Out of 40, 12 cases (30.0%) were the infantile age group and 28 cases (70.0%) were in the classic pediatric group. Ulceration was classified as grade 0 (14 cases, 35.0%), grade 1 (17 cases, 42.5%), or grade 2 (nine cases, 22.5%). Inflammation was classified as grade 0 (2 cases, 5.0%), grade 1 (26 cases, 65.0%), or grade 2 (12 cases, 30.0%). Fibrosis was classified as grade 0 (five cases, 12.5%), grade 1 (11 cases, 27.5%), grade 2 (17 cases, 42.5%), or grade 3 (seven cases, 17.5%). Metaplasia was noted in five (12.5%) out of 40 cases. All choledochal cysts with metaplasia showed beta-catenin nuclear positivity on immunohistochemistry and were followed up. Conclusion: This study emphasizes the importance of detailed histopathological examination and documentation of metaplastic changes. Metaplasia was associated with beta-catenin nuclear positivity. These findings suggest a potential role for beta-catenin as a marker of metaplastic changes in choledochal cysts.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.631-640
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• 2017

The aim of this paper is to introduce the binomial sequence spaces $b_0^{r,s}(\nabla)$, $b_c^{r,s}(\nabla)$ and $b_{\infty}^{r,s}(\nabla)$ by combining the binomial transformation and difference operator. We prove that these spaces are linearly isomorphic to the spaces $c_0$, c and ${\ell}_{\infty}$, respectively. Furthermore, we compute the Schauder bases and the ${\alpha}-$, ${\beta}-$ and ${\gamma}-duals$ of these sequence spaces.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1557-1569
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• 2011

In this paper, we consider the oscillation of the following certain second order nonlinear differential equations $(r(t)(x^{\prime}(t))^{\alpha})^{\prime}+q(t)x^{\beta}(t)=0$>, where ${\alpha}$ and ${\beta}$ are ratios of positive odd integers. New oscillation theorems are established, which are based on a class of new functions ${\Phi}={\Phi}(t,s,l)$ defined in the sequel. Also, we establish some interval oscillation criteria for this equation.

• Journal of Integrative Natural Science
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• v.1 no.3
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• pp.192-194
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• 2008

A series of non-free hydride reducing systems containing boron or aluminum atom, which possess no metal-hydride bond but an available hydrogen at a branched ${\beta}$-position, has been applied to the selective reduction (chemo--, regio-, and stereoselective reduction) of organic compounds. The systems, comprised of diisopinocampheylborane and diisobutylalane derivatives, exhibited almost perfect selectivities in the reduction of aldehydes and ketones. The characteristics features of this systems leading to a perfect transformation have been depicted in this report, especially in the 1) Reduction of ${\alpha}$,${\beta}$-Unsaturated Carbonyl Compounds to Allylic Alcohols via 1,2-Reduction, 2) Chemoselective Reduction between Structurally Different Carbonyl Compounds, and 3) Stereoselective Reduction of Cyclic Ketones.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.4
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• pp.280-286
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• 1987

A new method is presented for obtaining redced-order model for time-invariant systems. This method does not require the calculation of the reciprocal transformation, the alpha table, the beta-table and the alpha-beta expansion which should be calculated in Routh approximation method, hence it is computationally very attractive better than Routh approximation method, furthemore the stability of the reduced-order model is guaranted if the original system is stable. This method starts with the continued fraction espansion of auxiliary denominator polynomial give for the denominator polynomial of the reduced-order model. The coefficients of the numerator polynomial are then obtained by equating moment of the original and the reduced-order medel.

• Proceedings of the Korean Society for Emotion and Sensibility Conference
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• 2001.11a
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• pp.255-259
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• 2001

본 연구에서는 긍/부정 판단 과제 시 연령간 뇌파 반응의 차이를 밝히고자 한다. 실험 대상의 연령은 10명(20대 5명, 60대 5명)이었으며, 모두 오른손잡이였다. 실험과제는 의미과제와 일화과제로 구분되며 각각 12문항으로 구성된다. 의미기억과제 덧셈문제를, 일화기억 과제는 도형을 이용하였으며, 마우스 버튼을 눌러 긍/부정 판단 반응을 하도록 하였다. 뇌파는 PE1, PF2, F3, F4, O1, O2에서 단극유도법으로 측정되었으며, EOG를 측정하여 뇌파분석 시에 눈 깜박임으로 인하 noise를 제거하도록 하였다. 뇌파 분석은 원자료를 FFT(Fast Fourier Transformation)를 수행하여 각 대역의 상대적인 power를 구하는 방법으로 이루어졌다. 분석 결과, 반응 시간은 긍/부정판단간의 차이는 없었으나, 두 과제 모두에서 연령별로 유의미한 차이가 있었다. 긍/부정판단간의 따른 뇌파 반응은 명확한 차이가 나타나지 않았다. 연령에 따른 뇌파반응은 theta파, slow beta, fast beta에서 유의한 차이가 나타났다.

• Journal of the Korean Ceramic Society
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• v.50 no.6
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• pp.429-433
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• 2013

Silicon, carbon, and B4C powders were used as raw materials for the fabrication of porous SiC. ${\beta}$-SiC was synthesized at $1500^{\circ}C$ in an Ar atmosphere from a silicon and carbon mixture. The synthesized powders were pressed into disk shapes and then heated at $2100^{\circ}C$. ${\beta}$-SiC particles transformed to ${\alpha}$-SiC at over $1900^{\circ}C$, and rapid grain growth of ${\alpha}$-SiC subsequently occurred and a porous structure with elongated plate-type grains was formed. The mechanism of this rapid grain growth is thought to be an evaporation-condensation reaction. The mechanical properties of the fabricated porous SiC were investigated and discussed.

• Journal of the Korean Chemical Society
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• v.28 no.5
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• pp.323-327
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• 1984

Nicotine was reacted with an equimolar amount of ozone in methylene chloride and distilled water. The reaction mixture was separated by column chromatography or thin layer chromatography and then purified by vacuum distillation. The six compounds obtained from this reaction were characterized by NMR, IR and Mass spectrometry. These were identified as unchanged nicotine, nornicotine, anabasine, ${\beta}$-nicotyrine, cotinine and nicotine-N-oxide. From these results, reaction mechanism for the ozonolysis ofon nicotine was proposed; the pyrrolidine ring is attacked by ozone at the 1'-position followed by further transformation.