• East Asian mathematical journal
• /
• 제17권2호
• /
• pp.275-286
• /
• 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).

• 약학회지
• /
• 제39권4호
• /
• pp.433-437
• /
• 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
• /
• 제49권2호
• /
• pp.255-263
• /
• 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
• /
• 제19권1호
• /
• pp.73-80
• /
• 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
• /
• 제28권2호
• /
• pp.129-139
• /
• 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.

• 충청수학회지
• /
• 제26권2호
• /
• pp.393-402
• /
• 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 ${\sup}_{a{\in}D}{\int}_D(k_a(z)(1-{\mid}a{\mid}^2)^{(p-a-1)})^{q/p}d{\mu}(z)$ < ${\infty}$.

• 대한수학회보
• /
• 제46권6호
• /
• pp.1041-1050
• /
• 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
• /
• 제27권9호
• /
• pp.1586-1592
• /
• 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
• /
• 제28권6호
• /
• pp.477-483
• /
• 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.

• 한국발생생물학회지:발생과생식
• /
• 제12권1호
• /
• pp.107-112
• /
• 2008

점망둑의 난모세포 성숙과정에서 생성되는 주요 성 스테로이드 호르몬, $C_{21}$-스테로이드를 분석하고자 전구물질 $^3H-17{\alpha}hydroxyprogesterone$ ($^3H-17{\alpha}OHP$)를 성숙기 난모세포(난경 $0.74{\sim}0.97\;mm$) 배양초기에 첨가하여 24시간 배양하였다. 스테로이드 대사물질 분석과 동정은 thin layer chromatography와 gaschromatography-mass spectrometry로 이루어졌다. $^3H-17{\alpha}20{\alpha}P$로부터 생성된 주요 성 스테로이드 대사물질은 $17{\alpha}$-hydroxy, $20{\alpha}$-dihydroprogesterone ($17{\alpha}20{\alpha}P$)와 $17{\alpha}$-hydroxy, $20{\beta}$-dihydroprogesterone ($17{\alpha}20{\beta}P$)로 확인되었다. 이들 대사물질은 난경 0.80 mm 이상에서 관찰되었으며, GVBD (germinal vesicle breakdown) 유도 효능 테스트에서 점망둑의 난모세포는 $17{\alpha}20{\beta}P$에 더 민감하게 반응하였다. 이러한 결과는 점망둑의 난소성숙 과정에 $17{\alpha}20{\alpha}P$와 $17{\alpha}20{\beta}P$이 모두 관여하나, MIS (maturation inducing steroid)로서의 가능성은 $17{\alpha}20{\beta}P$이 더 큰 것으로 관찰되었다.