• East Asian mathematical journal
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• v.17 no.2
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• pp.275-286
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• 2001

In this paper, a skew polynomial ring $R[x;\alpha]$ of a ring R with a monomorphism $\alpha$ are investigated as follows: For a reduced ring R, assume that $\alpha(P){\subseteq}P$ for any minimal prime ideal P in R. Then (i) $R[x;\alpha]$ is a reduced ring, (ii) a ring R is Baer(resp. quasi-Baer, p.q.-Baer, a p.p.-ring) if and only if the skew polynomial ring $R[x;\alpha]$ is Baer(resp. quasi-Baer, p.q.-Baer, a p.p.-ring).

• YAKHAK HOEJI
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• v.39 no.4
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• pp.433-437
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• 1995

Optically pure(-)-and (+)-$\alpha$-hydroxy-$\alpha$-(p-chlorobiphenyl)acetic acids were prepared. The racemate was synthesized through three steps. By condensation of p-cnorobiphenyl with diethyl ketomalonate in the presence of SnCl$_{4}$, diethyl $\alpha$-hydroxy-$\alpha$-(p-chlorobiphenyl)malonate (1) was formed and subsequently ($\pm$)-$\alpha$-hydroxy-$\alpha$-(p-chlorobiphenyl)acetic acid (3) was obtained through hydrolysis and decarboxylation. For the separation of the racemate the classical resolution method, derivatization of a racemate by reaction with an optically pure compound was employed. In this case the optically pure compound were [R]-(+)-$\alpha$-methylbenzylamine and [S]-(-)-$\alpha$-methylbenzylamine. Diastereomeric salts between acids and bases could be easily separated by crystallization in absolute ethanol.

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.255-263
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• 2009

For an endomorphism ${\alpha}$ of R, in [1], a module $M_R$ is called ${\alpha}$-compatible if, for any $m{\in}M$ and $a{\in}R$, ma = 0 iff $m{\alpha}(a)$ = 0, which are a generalization of ${\alpha}$-reduced modules. We study on the relationship between the quasi-Baerness and p.q.-Baer property of a module MR and those of the polynomial extensions (including formal skew power series, skew Laurent polynomials and skew Laurent series). As a consequence we obtain a generalization of [2] and some results in [9]. In particular, we show: for an ${\alpha}$-compatible module $M_R$ (1) $M_R$ is p.q.-Baer module iff $M[x;{\alpha}]_{R[x;{\alpha}]}$ is p.q.-Baer module. (2) for an automorphism ${\alpha}$ of R, $M_R$ is p.q.-Baer module iff $M[x,x^{-1};{\alpha}]_{R[x,x^{-1};{\alpha}]}$ is p.q.-Baer module.

• East Asian mathematical journal
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• v.19 no.1
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• pp.73-80
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• 2003

Let D be a bounded domain in $\mathbb{C}^n$ with $C^2$ boundary. In this paper, we prove the following inequality $${\parallel}u{\parallel}_{p_2,{\alpha}_2}{\lesssim}{\parallel}u{\parallel}_{p_1,{\alpha}_1}+{\parallel}\bar{\partial}u{\parallel}_{p_1,{\alpha}_1+p_1}/2$$, where $1{\leq}p_1{\leq}p_2<\infty,\;{\alpha}_j>0,(n+{\alpha}_1)/p_1=(n+{\alpha}_1)/p_1=(n+{\alpha}_2)/p_2$, and $1/p_2{\geq}1/p_1-1/2n$.

• Kyungpook Mathematical Journal
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• v.28 no.2
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• pp.129-139
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• 1988

Let $T^{\alpha}_{\lambda}$(p, A, B) denote the class of functions $$f(z)=z^p-{\sum\limits^{\infty}_{k=1}}{\mid}a_{p+k}{\mid}z^{p+k}$$ which are regular and p valent in the unit disc U = {z: |z| <1} and satisfying the condition $\left|{\frac{{e^{ia}}\{{\frac{f^{\prime}(z)}{z^{p-1}}-p}\}}{(A-B){\lambda}p{\cos}{\alpha}-Be^{i{\alpha}}\{\frac{f^{\prime}(z)}{z^{p-1}}-p\}}}\right|$<1, $z{\in}U$, where 0<${\lambda}{\leq}1$, $-\frac{\pi}{2}$<${\alpha}$<$\frac{\pi}{2}$, $-1{\leq}A$<$B{\leq}1$, 0<$B{\leq}1$ and $p{\in}N=\{1,2,3,{\cdots}\}$. In this paper, we obtain sharp results concerning coefficient estimates, distortion theorem and radius of convexity for the class $T^{\alpha}_{\lambda}$(p, A, B). It is further shown that the class $T^{\alpha}_{\lambda}$(p, A, B) is closed under "arithmetic mean" and "convex linear combinations". We also obtain class preserving integral operators of the form $F(z)=\frac{p+c}{z^c}{\int^z_0t^{c-1}}f(t)dt$, c>-p, for the class $T^{\alpha}_{\lambda}$(p, A, B). Conversely when $F(z){\in}T^{\alpha}_{\lambda}$(p, A, B), radius of p valence of f(z) has also determined.

• 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 ${\sup}_{a{\in}D}{\int}_D(k_a(z)(1-{\mid}a{\mid}^2)^{(p-a-1)})^{q/p}d{\mu}(z)$ < ${\infty}$.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1041-1050
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• 2009

Let R be a ring and ${\alpha}$ a monomorphism of R. We study the skew Laurent polynomial rings R[x, x$^{-1}$; ${\alpha}$] over an ${\alpha}$-skew Armendariz ring R. We show that, if R is an ${\alpha}$-skew Armendariz ring, then R is a Baer (resp. p.p.-)ring if and only if R[x, x$^{-1}$; ${\alpha}$] is a Baer (resp. p.p.-) ring. Consequently, if R is an Armendariz ring, then R is a Baer (resp. p.p.-)ring if and only if R[x, x$^{-1}$] is a Baer (resp. p.p.-)ring.

• Journal of Microbiology and Biotechnology
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• v.27 no.9
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• pp.1586-1592
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• 2017

Some promoters were isolated and characterized from the genome of Leuconostoc mesenteroides SY2, an isolate from kimchi, a Korean traditional fermented vegetable. Chromosomal DNA of L. mesenteroides SY2 was digested with Sau3AI and ligated with BamHI-cut pBV5030, a promoter screening vector containing a promoterless cat-86. Among E. coli transformants (TFs) resistant against Cm (chloramphenicol), 17 were able to grow in the presence of $1,000{\mu}g/ml$ Cm and their inserts were sequenced. Transcription start sites were examined for three putative promoters (P04C, P25C, and P33C) by primer extension. Four putative promoters were inserted upstream of a promoterless ${\alpha}$-amylase reporter gene in $pJY15{\alpha}$. ${\alpha}$-Amylase activities of E. coli TFs containing $pJY15{\alpha}$ (control, no promoter), $pJY03{\alpha}$ ($pJY15{\alpha}$ with P03C), $pJY04{\alpha}$ (with P04C), $pJY25{\alpha}$ (with P25C), and $pJY33{\alpha}$ (with P33C) were 66.9, 78.7, 122.1, 70.8, and 99.3 U, respectively. Cells harboring $pJY04{\alpha}$ showed 1.8 times higher activity than the control. Some promoters characterized in this study might be useful for construction of food-grade expression vectors for Leuconostoc sp. and related lactic acid bacteria.

• BMB Reports
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• v.28 no.6
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• pp.477-483
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• 1995

The recombinant human interferon alpha 2a ($rhIFN-{\alpha}2a$), expressed in Saccharomyces cerevtsiae, was purified from insoluble aggregates. The inclusion body of $rhIFN-{\alpha}$ was solubilized by guanidine salt in the presence of disulfide reducing agent. The refolding of denatured $rhIFN-{\alpha}2a$ was achieved by simple dilution. The authentic interferon alpha, which has two correctly matched disulfide bonds, was seperated from incompletely oxidized $IFN-{\alpha}$ and dimeric $IFN-{\alpha}$ by use of a CM-Sepharose column, followed by size exclusion columns at two different pH conditions. The purified protein has been subjected to detailed physicochemical characterization including sequence determination. Unlike other $rhIFN-{\alpha}2a$ from E. coli reported, the $rhIFN-{\alpha}2a$ from S. cerevisiae has no methionine residue at its N-terminus originating from the start codon, ATG. The pI of the protein was determined to be 6.05 with a single band in the pI gel, which demonstrated that the purified $rhIFN-{\alpha}$ was homogeneous. The structural study using circular dichroism showed that the protein retains its three dimensional structure in the wide range of pH conditions between pH 3 and 9, and only minor strucural deformation was observed at pH 1.0.

• Development and Reproduction
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• v.12 no.1
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• pp.107-112
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• 2008

To investigate the $C_{21}$-steroids produced from maturating oocytes in the longchin goby, Chasmichthys dolichognathus, the oocytes ($0.74{\sim}0.97\;mm$) were incubated with radiolabeled $17{\alpha}$-hydroxyprogesterone ($^3H-17{\alpha}OHP$) for 24 hours. The resulting metabolites were analyzed by thin layer chromatography and identified by gas chromatography-mass spectrometry. Two $C_{21}$-steroids, $17{\alpha}$-hydroxy, $20{\alpha}$-dihydroprogesterone ($17{\alpha}20{\alpha}P$) and $17{\alpha}$-hydroxy, $20{\beta}$-dihydroprogesterone ($17{\alpha}20{\beta}P$), were converted from $^3H-17{\alpha}OHP$ in the maturing oocytes. These two main metabolites were detected at 0.80 mm diameter oocytes or greater. In addition, the effects of these metabolites on in vitro germinal vesicle breakdown (GVBD) were tested. The sensitivity of oocytes to the induction of GVBD was greater at $17{\alpha}20{\beta}P$ than $17{\alpha}20{\alpha}P$. This result showed that $17{\alpha}20{\beta}P$ is a major maturation inducing steroid (MIS) in longchin goby, suggesting $17{\alpha}20{\alpha}P$ may play a role in regulating the oocyte maturation process.