• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.697-707
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• 2022

It is well known that the continued fraction expansion of ${\sqrt{d}}$ has the form $[{\alpha}_0,\;{\bar{{\alpha}_1,\;{\ldots},\;{\alpha}_{l-1},\;2_{{\alpha}_0}}]$ and ${\alpha}_1,\;{\ldots},\;{\alpha}_{l-1}$ is a palindromic sequence of positive integers. For a given positive integer l and a palindromic sequence of positive integers ${\alpha}_1,\;{\ldots},\;{\alpha}_{l-1},$ we define the set $S(l;{\alpha}_1,\;{\ldots},\;{\alpha}_{l-1})\;:=\;\{d{\in}{\mathbb{Z}}{\mid}d>0,\;{\sqrt{d}}=[{\alpha}_0,\;{\bar{{\alpha}_1,\;{\ldots},\;{\alpha}_{l-1},\;2_{{\alpha}_0}}],\;where\;{\alpha}_0={\lfloor}{\sqrt{d}}{\rfloor}\}.$ In this paper, we completely determine when $S(l;{\alpha}_1,\;{\ldots},\;{\alpha}_{l-1})$ is not empty in the case that l is 4, 5, 6, or 7. We also give similar results for $(1+{\sqrt{d}})/2.$ For the case that l is 4, 5, or 6, we explicitly describe the fundamental units of the real quadratic field ${\mathbb{Q}}({\sqrt{d}}).$ Finally, we apply our results to the Mordell conjecture for the fundamental units of ${\mathbb{Q}}({\sqrt{d}}).$

• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.123-131
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• 2000

Let {X(t) : t $\geq$B 0} be a Symmetric $\alpha$ Stable and H-Self-similar process with stationary increments. We examine a.s. Holder unboundedness of S$\alpha$S H-sssi Chentsov processes and H-sssi Chentsov fields for order ${\gamma}$>H. Finally, we prove a.s. Holder continuity of S$\alpha$S H-sssi processes with ergodic seating transformations for the case of H>1/$\alpha$.

• Journal of Microbiology and Biotechnology
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• v.12 no.4
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• pp.610-616
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• 2002

The growth-inhibiting effects of Pinus densiflpora leaf-derived materials on nine human intestinal bacteria were investigated using the impregnated paper disk method, and their activities were compared with those of 13 commercially available terpenes. The biologically active constituent of the extract of P densiflora leaf was characterized as the monoterpene (1R)-(+)-$\alpha$-pinene by various spectroscopic analyses. Responses varied according to bacterial strain, chemicals, and dose. At 10 mg/disk, limonene and (1R)-(+)-$\alpha$-pinene strongly inhibited the growth of Clostridium perfringens, Staphylococcus aureus, and Escherichia coli, without adverse effects on the growth of five lactic acid-bacteria (Bifidobacterium adolescentis, B. bifidum, B. longum, Lactobacillus acidophilus, and L. casei). Little or no inhibition against seven bacteria was observed with anethole, borneol, camphor, caryophyllene, 1,8-cineole, estragole, linalool, and $\alpha$-terpineol. Structure-activity relationship revealed that (1R)-(+)-$\alpha$-pinene had more growth-inhibiting activity against C. perfringens than (1R)-(+)-$\beta$-, (1S-(-)-$\alpha$-, and (1S-(-)-$\beta$-pinenes. Furthermore, the growth-inhibition against L. casei was much more pronounced in (1R)-(+)-$\beta$- and (In-(-)-$\beta$-pinenes than (1R)-(+)-$\alpha$- and (1S)-(-)-$\alpha$-pinenes. These results indicate that the (+)-$\alpha$ form seems to be required against C. perfringens and $\beta$ form against L. casei for growth-inhibiting activity. Morphologically, most strains of C. perfringens were damaged and disappeared at 5 and 2 mg/disk of (1R)-(+)-$\alpha$-pinene. Morphological study revealed that (1R)-(+)-$\alpha$-pinene had more growth-inhibiting activity against C. perfringens than (1R)-(+)-$\beta$-, (1S)-(-)-$\alpha$-, and (1S)-(-)-$\beta$-pinenes. As naturally occurring growth-inhibiting agents, the Pinus leaf-derived materials described above could be useful preventive agents against diseases caused by harmful intestinal bacteria such as clostridia.

• Microbiology and Biotechnology Letters
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• v.26 no.1
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• pp.68-75
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• 1998

The overproduction and high level secretion of Glucose Oxidase (GOD) from A. niger in S. cerevisiae was carried out by cloning GOD gene. For this purpose, using two different strong promoters (ADH1 promoter, GAL10 promoter) and signal sequences (${alpha}$-MF signal sequence of S. cerevisiae and ${alpha}$-amylase signal sequence of A. oryzae) and GAL7- and GOD terminator, four expression vectors were constructed. All the expression vectors were transformed in S. cerevisiae 2805 using auxotroph method. By the flask culture, transformants of pGAL expression vector series containing GAL 10 promotor showed much higher GOD productivity than transformants of pADH expression vector series containing ADH1 promoter Transformants of pGALGO2 containing GAL10 promotor and ${alpha}$-amylase signal sequence has shown the best productivity of GOD ($GOD_{total}$: 10.3 unit/mL, $GOD_{ex}$: 8.7 unit/mL) at 115 hr. This value was three fold higher than that of pGALGO1 containing GAL 10 promotor and ${alpha}$-MF signal sequence, even if the same promotor was involved. Through the ${alpha}$-amylase signal sequence of A. oryzae, GOD was secreted much more than the case of ${alpha}$-MF signal sequence from S. cerevisiae. These results suggest that signal sequence may play a important roles in not only the secretion but also the overproduction of foreign protein. Secretion rate of GOD in pGALGO1 and pGALGO2 was 89% and 84%, respectively, Because of the overglycosylation in S. cerevisiae the molecular weight of recombinant GOD in S. cerevisiae was much larger (250 kDa) than that of nature GOD in A. niger (170 kDa).

• The Zoological Society Korea : Newsletter
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• v.18 no.2
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• pp.38-44
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• 2001

전위활성화 칼슘통로를 통한 칼슘이온의 세포 내 유입은 근육수축, 시냅스 전달, 호르몬 분비, 효소의 활성도 및 유전자 발현을 조절한다. 이와 같이 중요한 생리적 기능을 조절하기 때문에 칼슘통로를 대상으로 한 다방면의 연구가 과거 20년간 활발히 진행되어 왔다 칼슘통로는 $\alpha$1, $\alpha$2-$\delta$, $\beta$로 구성되어 있으며, 이 중 $\alpha$1은 칼슘통로의 일반적 특성을 나타내는 기본 구조체이며, $\alpha$2-$\delta$와 $\beta$는 $\alpha$1을 조절하는 보조 기능을 한다. 지금까지 10개의 $\alpha$1 subunits(L-형: $\alpha$1S, $\alpha$1C, $\alpha$1D, $\alpha$1F; non-L-형: $\alpha$1A, a1B, $\alpha$1E; T-형: $\alpha$1G, $\alpha$1H, $\alpha$1I), 4종류의 $\beta$ subunits, 3 종류의 $\alpha$2-$\delta$ subunits가 클로닝되었으며, 이들 클론을 이용한 분자 수준에서의 연구가 활발히 이루어지고 있다. 본 논단에서는 칼슘통로의 구조, 기능 및 조절에 대한 연구가 전기생리학적, 분자생물학적 및 약리학적 방법을 사용하여 어떻게 수행되어왔는지 살펴보고, 최근 연구성과에 대해서도 소개하고자 한다.

• Journal of Life Science
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• v.27 no.12
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• pp.1403-1409
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• 2017

In this study, the xylitol dehydrogenase (XYL2) gene was expressed in Saccharomyces cerevisiae as a host cell for ease of use in the degradation of lignocellulosic biomass (xylose). To select suitable expression systems for the S.XYL2 gene from S. cerevisiae and the P.XYL2 gene from Pichia stipitis, $pGMF{\alpha}-S.XYL2$, $pGMF{\alpha}-P.XYL2$, $pAMF{\alpha}-S.XYL2$ and $pAMF{\alpha}-P.XYL2$ plasmids with the GAL10 promoter and ADH1 promoter, respectively, were constructed. The mating factor ${\alpha}$ ($MF{\alpha}$) signal sequence was also connected to each promoter to allow secretion. Each plasmid was transformed into S. cerevisiae $SEY2102{\Delta}trp1$ strain and the xylitol dehydrogenase activity was investigated. The GAL10 promoter proved more suitable than the ADH1 promoter for expression of the XYL2 gene, and the xylitol dehydrogenase activity from P. stipitis was twice that from S. cerevisiae. The xylitol dehydrogenase showed $NAD^+$-dependent activity and about 77% of the recombinant xylitol dehydrogenase was secreted into the periplasmic space of the $SEY2102{\Delta}trp1/pGMF{\alpha}-P.XYL2$ strain. The xylitol dehydrogenase activity was increased by up to 41% when a glucose/xylose mixture was supplied as a carbon source, rather than glucose alone. The expression system and culture conditions optimized in this study resulted in large amounts of xylitol dehydrogenase using S. cerevisiae as the host strain, indicating the potential of this expression system for use in bioethanol production and industrial applications.

• Bulletin of the Korean Mathematical Society
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• v.24 no.1
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• pp.13-17
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• 1987

Let S denote the class of nivalent functions normalized so that f(0)=f'(0)-1=0 in vertical bar z vertical bar <1. Let $S_{\alpha}$$^{*}$, -.pi./2<.alpha.<.pi./2, denote the subclass of S that satisfies Re $e^{i{\alpha}}$zf'(z)/f(z).geq.0 in vertical bar z vertical bar <1; then f is called .alpha.-spiral-like and the case .alpha.=0 is the class of normalized starlike functions [6, pp.52]. Let T denote the class of functions f normalized as above and satisfying Im z[Im f(z)]..geq.0 in vertical bar z vertical bar <1; then f is called typically real and T contains those functions of S whose coefficients are real [6, pp.55]. Also, in view of [6, pp.231], let B(.lambda.) be the class of function normalized as above and map vertical bar z vertical bar <1 onto the complement of an arc with radial angle .lambda.(0<.lambda.<.pi./2). The radial angle is meant to be the angle between the tangent and radial vectors to the arc. This note includes a sharp version for Corollary 1 of [2] when f.mem. $S_{\alpha}$$^{*}$ as well as a logarithmic coefficient estimate.nt estimate.

• East Asian mathematical journal
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• v.5 no.1
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• pp.35-47
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• 1989

Let $S_o*({\alpha},{\beta},{\mu})$ denote the class of functions $f(z)=a_1z-{\sum}{\limit}^{\infty}_{n=2}\;a_nz^n$ analytic in the unit disc $U=\{z:{\mid}z{\mid}<1\}$ and satisfying the condition $${\mid}\frac{\frac{zf'(z)}{f(z)}-1}{(1+\mu)\;\beta(\frac{zf'(z)}{f(z)}-\alpha)-(\frac{zf'(z)}{f(z)}-1)}\mid<1$$ for some $\alpha(0{\leq}{\alpha}<1),\;{\beta}(0<{\beta}{\leq}1),\;{\mu}(0{\leq}{\mu}{\leq}1)$ and for all $z{\in}U$. And it is the purpose of this paper to show a necessary and sufficient condition for the class $S_o*({\alpha},{\beta},{\mu})$, some results for the Hadamard products of two functions f(z) and g(z) in the class $S_o*({\alpha},{\beta},{\mu})$, the distortion theorem and the distortion theorems for the fractional calculus.

• Asian-Australasian Journal of Animal Sciences
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• v.6 no.4
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• pp.541-547
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• 1993

A phage clone containing the partial ${\alpha}_{S1}$-casein gene was isolated from a bovine genomic library by using mixed probes of ovine ${\alpha}_{S1}$-, ${\beta}$- and ${\kappa}$-casein cDNAs. Restriction enzyme mapping analysis for 14.6 kb revealed that the map was in conflict with the report of Meade et al. (1990), especially in the 3'-end fragment. Sequence analysis of 12.6 kb revealed a high AT/GC ratio (1.64); we have identified eight exon sequences according to the bovine ${\alpha}_{S1}$-casein cDNA sequence. The same exon/intron splice junction sequence was observed between these exons. We suggest that the bovine ${\alpha}_{S1}$-casein gene night contain a minimum of 18 exons and the full length is approximately 18-19 kb.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1643-1653
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• 2019

This paper shows that if $1<p<{\infty}$, ${\alpha}{\geq}-n-2$, ${\alpha}>-1-{\frac{p}{2}}$ and f is holomorphic on the unit ball ${\mathbb{B}}_n$, then $${\int_{{\mathbb{B}}_n}}{\mid}Rf(z){\mid}^p(1-{\mid}z{\mid}^2)^{p+{\alpha}}dv_{\alpha}(z)<{\infty}$$ if and only if $${\int_{{\mathbb{B}}_n}}{\int_{{\mathbb{B}}_n}}{\frac{{\mid}f(z)-F({\omega}){\mid}^p}{{\mid}1-(z,{\omega}){\mid}^{n+1+s+t-{\alpha}}}}(1-{\mid}{\omega}{\mid}^2)^s(1-{\mid}z{\mid}^2)^tdv(z)dv({\omega})<{\infty}$$ where s, t > -1 with $min(s,t)>{\alpha}$.