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ON A GENERALIZATION OF HIRZEBRUCH'S THEOREM TO BOTT TOWERS

  • Kim, Jin Hong
    • Journal of the Korean Mathematical Society
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    • v.53 no.2
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    • pp.331-346
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    • 2016
  • The primary aim of this paper is to generalize a theorem of Hirzebruch for the complex 2-dimensional Bott manifolds, usually called Hirzebruch surfaces, to more general Bott towers of height n. To do so, we first show that all complex vector bundles of rank 2 over a Bott manifold are classified by their total Chern classes. As a consequence, in this paper we show that two Bott manifolds $B_n({\alpha}_1,{\ldots},{\alpha}_{n-1},{\alpha}_n)$ and $B_n({\alpha}_1,{\ldots},{\alpha}_{n-1},{\alpha}_n^{\prime})$ are isomorphic to each other, as Bott towers if and only if both ${\alpha}_n{\equiv}{\alpha}_n^{\prime}$ mod 2 and ${\alpha}_n^2=({\alpha}_n^{\prime})^2$ hold in the cohomology ring of $B_{n-1}({\alpha}_1,{\ldots},{\alpha}_{n-1})$ over integer coefficients. This result will complete a circle of ideas initiated in [11] by Ishida. We also give some partial affirmative remarks toward the assertion that under certain condition our main result still holds to be true for two Bott manifolds just diffeomorphic, but not necessarily isomorphic, to each other.

THE SHARP BOUND OF THE THIRD HANKEL DETERMINANT FOR SOME CLASSES OF ANALYTIC FUNCTIONS

  • Kowalczyk, Bogumila;Lecko, Adam;Lecko, Millenia;Sim, Young Jae
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.6
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    • pp.1859-1868
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    • 2018
  • In the present paper, we have proved the sharp inequality ${\mid}H_{3,1}(f){\mid}{\leq}4$ and ${\mid}H_{3,1}(f){\mid}{\leq}1$ for analytic functions f with $a_n:=f^{(n)}(0)/n!$, $n{\in}{\mathbb{N}},$, such that $$Re\frac{f(z)}{z}>{\alpha},\;z{\in}{\mathbb{D}}:=\{z{\in}{\mathbb{C}}:{\mid}z{\mid}<1\}$$ for ${\alpha}=0$ and ${\alpha}=1/2$, respectively, where $$H_{3,1}(f):=\left|{\array{{\alpha}_1&{\alpha}_2&{\alpha}_3\\{\alpha}_2&{\alpha}_3&{\alpha}_4\\{\alpha}_3&{\alpha}_4&{\alpha}_5}}\right|$$ is the third Hankel determinant.

Molecular Cloning of ${\alpha}$-Amylase Gene from Schwanniomyces CBS 2863 (Schwanniomyces castellii CBS 2863으로부터 ${\alpha}$-Amylase 유전자 Cloning)

  • Park, Jong-Chun;Bai, Suk;Chun, Bai-CHun
    • Korean Journal of Microbiology
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    • v.32 no.1
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    • pp.34-39
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    • 1994
  • The gene encoding ${\alpha}$-amylase of Schwanniomyces castellii was cloned in Saccharomyces cerevisiae. The 5.0-kilobase insert was shown to direct the synthesis of ${\alpha}$-amylase. Southern blot analysis confirmed that this ${\alpha}$-amylase gene was derived from the genomic DNA of Sch. castellii. Immunoblot analysis showed that ${\alpha}$-amylase production from S. cerevisiae transformant was less than that of donor strain. The ${\alpha}$-amylase secreted from S. cerevisiae transformant was shown to be indistinguishable from that of Sch. castellii on the basis of molecular weight and enzyme properties.

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The Glucoamylase Signal Sequence Directs the Efficient Secretion of Human $\alpha$1-Antitrypsin in Yeast Cells (효모에서 Glucoamylase 신호서열에 의한 인체 $\alpha$1-Antitrypsin의 분비 효율 향상)

  • Song, Moo-Young;Kwon, Ki-Sun;Kang, Dae-Ook;Yu, Myeong-Hee;Park, Hee-Moon;Kim, Jinmi
    • Korean Journal of Microbiology
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    • v.31 no.3
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    • pp.203-207
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    • 1993
  • Five different secretion vectors were constructed by varying the signal sequences and .alpha.-antitrypsin (.alpha.1-AT) a numan secretory protein, was produced from yeast cells. The signal sequences used are those of acid phosphatase (PH05) and .alpha.-factor (M f.alphal1) of Saccharomyces cerevisiae, glucoamylase (STA1) of Saccharomyces diastaticus, and human .alpha.1-AT. Four vectors directed the efficient secretion of .alpha.1-AT ito the culture media. The secretion vector carrying the glucoamylase signal sequence (pGAT11) showed the highest efficiency of secretion. About 70% of .alpha.1-AT produce dwere secreted into the media. The endo H treatment of partially purified .alpha.1-AT indicates that the secreted .alpha.1-AT appeared to be glycosylated. This glycosylation pattern was altered when amino acid substitution mutations were introduced at the three glycosylation sites of .alpha.-AT.

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Dust-scattered H${\alpha}$ halos around H II regions: On the origins of the diffuse H${\alpha}$ emission

  • Seon, Kwang-Il
    • The Bulletin of The Korean Astronomical Society
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    • v.37 no.1
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    • pp.74.1-74.1
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    • 2012
  • It is known that the diffuse H${\alpha}$ halos around bright H II regions are more extended than the dust-scattered halos around point sources and the line ratios [S II] ${\lambda}$6716/H${\alpha}$ and [N II] ${\lambda}$6583/H${\alpha}$ observed outside of bright H II regions are generally higher than those in H II regions. These observational facts have been regarded as evidence against the dust-scattering origin of the diffuse H${\alpha}$ emission and the effect of dust-scattering has been neglected in studying the diffuse H${\alpha}$ emission. In this paper, we find, however, that dust-scattered halos of H II regions should be more extended than those of point sources and is in good agreement with the observed H${\alpha}$ profiles around H II regions. We also found that the observed line ratios [S II]/H${\alpha}$, [N II]/H${\alpha}$, and He I ${\lambda}$5876/H${\alpha}$ in the diffuse regions can be well reproduced with the dust-scattered halos around H II regions which are photoionized by late O- and/or early B-type stars in the interstellar medium with the abundances close to those of the warm neutral medium. Therefore, we conclude that the diffuse H${\alpha}$ emission may originate mostly from the dust-scattering.

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The Ability of Anti-$TNF-{\alpha}$ Antibodies Produced in Sheep Colostrums

  • Yun, Sung-Seob
    • Journal of Dairy Science and Biotechnology
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    • v.25 no.2
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    • pp.1-4
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    • 2007
  • The present study was performed to elucidate the ability of anti-$TNF-{\alpha}$ antibodies produced in sheep colostrums to neutralise $TNF-{\alpha}$ action in a cell-based bioassay and in a small animal model of intestinal inflammation. Colostrums from sheep immunized against $TNF-{\alpha}$ significantly inhibited $TNF-{\alpha}$ bioactivity in the cell based assay. The higher than anticipated variability in the two animal models precluded assessment of the ability of antibody to prevent $TNF-{\alpha}$ induced intestinal damage in the intact animal.

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Increased Association of ${\alpha}$-synuclein to Perturbed Cellular Membranes

  • Kim, Yoon-Suk;Lee, Seung-Jae
    • Biomedical Science Letters
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    • v.17 no.2
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    • pp.167-171
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    • 2011
  • [ ${\alpha}$ ]synuclein (${\alpha}$-syn) is implicated in the pathogenesis of Parkinson's disease (PD) and other related diseases. We have previously reported that ${\alpha}$-syn binds to the cell membranes in a transient and reversible manner. However, little is known about the physiologic function and/or consequence of this association. Here, we examined whether chemically induced perturbations to the cellular membranes enhance the binding of ${\alpha}$-syn, based on hypothesis that ${\alpha}$-syn may play a role in maintenance of membrane integrity or repair. We induced membrane perturbations or alterations in ${\alpha}$-syn-overexpressing human neuroblastoma cells (SH-SY5Y) by treating the cells with hydrogen peroxide ($H_2O_2$) or oleic acid. In addition, membranes fractionated from these cells were perturbed by treating them with proteinase K or chloroform. Dynamic interaction of ${\alpha}$-syn to the membranes was analyzed by the chemical cross-linking assay that we developed in the previous study. We found that membrane interaction of ${\alpha}$-syn was increased upon treatment with membrane-perturbing reagents in a dose and time dependent manner. These results suggest that perturbations in the cellular membranes cause increased binding of ${\alpha}$-syn, and this may have significant implication in the physiological function of ${\alpha}$-syn in cells.

Peroxisome proliferator-activated receptor $\alpha$(PPAR$\alpha$) and its clinical significance

  • 윤미정
    • The Zoological Society Korea : Newsletter
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    • v.18 no.2
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    • pp.6-11
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    • 2001
  • Peroxisome proliferator-activated receptor $\alpha$ (PPAR$\alpha$)에 대한 본격적인 연구는 고지혈증 치료제인 fibrate류의 약물들이 PPAR$\alpha$ activator로 작용한다는 사실이 밝혀짐으로써 크게 증대되었다. PPAR$\alpha$는 fibrate를 포함한 다양한 종류의 peroxisome proiferator (PP)에 의해 활성화되는데 이들을 쥐에 단기간 투여할 경우 간의 peroxisome수와 지 방산 산화효소의 유전자발현이 증가되고 장기간 투여 할 경우 간암을 발생시키지만, fibrate류의 약물들을 고지혈증 환자에게 투여 할 경우 간암을 발생시키지 않으므로써 PP에 대한 반응성에 있어서 species difference를 나타낸다 PPAR$\alpha$는 핵에 존재하는 orphan receptor로서 PP에 의해 활성화되어 9-cis-retinoic acid receptor(RXR)와 heterodimer를 이룬 후 target gene들의 upstream에 있는 peroxisome proliferator response element (PPRE)에 결합하여 target gene들의 발현을 조절한다. 지금까지 연구된 PPAR$\alpha$의 target gene들은 모두 lipid와 lipoprotein 대사를 조절하는 것으로 알려져 있으며, 이러 한 결과들을 기초로 lipid 대사 및 energy balance와 관련된 질병들 - 동맥경화증, 관상동맥질환, 비만, 제 2형 당뇨병 등에서 PPAR$\alpha$의 역할이 집중적으로 연구되고 있다. PPAR$\alpha$가 활성화되면 lipoprotein lipase와 HDL이 증가되고 apo C-III가 감소됨으로써 동맥경화증에 대한 예방적 기능을 나타내고, 몸무게를 감소시킴으로써 비만을 방지할 수 있으며, 인슐린 감수성을 증가시켜 제 2형 당뇨병의 치료효과를 가지는 것으로 보인다. 그러나 PPAR$\alpha$-null mouse에서는 이러한 효과들이 나타나지 않는 것으로 보아 이들 질병에서 PPAR$\alpha$가 중요한 역할을 하는 것으로 생각된다.

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Inhibition of Platelet Activation by Marine Sterols from Octocorals (팔방산호충류에서 분리한 해양 스테롤 화합물의 혈소판 응집 억제작용)

  • Park, Young-Hyun;Chang, Sung-Keun;Seo, Young-Wan;Shin, Jong-Heon
    • YAKHAK HOEJI
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    • v.41 no.5
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    • pp.547-553
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    • 1997
  • The purpose of this investigation was to determine the inhibition on $Na^+,\;K^+$-ATPase, cyclic AMP phosphodiesterase and platelet activation by marine sterols isolated from octocorals. Three marine polyhydroxysterols, 7${\alpha},\;8{\alpha}-epoxy-3b{\beta},\;5{\alpha},\;6{\alpha}-trihydroxycholestane (1),\;24-methyl-7{\alpha},\;8{\alpha}-epoxy-3{\beta},\;5{\alpha},\;6{\alpha}-trihydroxycholest-22-ene (2),\;and\;7{\alpha},\;8{\alpha}-epoxy-3{\beta},\;5{\alpha},\;6{\alpha}-trihydroxycholest-22-ene (3)$, were isolated from the Gorgonian Acabaria undulata. Five marine sterols(compound 4, 5, 6, 7, 8) were isolated from the soft coral Alcyonium gracillimum. Three marine polyhydroxysterols (1, 2, 3) and pregna-1. 20-diene-3-one (8) exhibit a potent inhibitory effect on rabbit platelet aggregation induced by collagen and thrombin. Those polyhydroxysterols also exhibit a potent inhibitory effect on cyclic AMP phosphodiesterase. Compound 6 with an unusual cyclic enolether exhibit a inhibitory effect on $Na^+,\;K^+$-ATPase.

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Purification and Characterization of Recombinant Human Interferon Alpha 2a Produced from Saccharomyces cerevisiae

  • Rae, Tae-Ok;Chang, Ho-Jin;Kim, Jung-Ho;Park, Soon-Jae
    • 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.

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