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Localizing virtual fundamental cycles for semi-perfect obstruction theories
World Scientific 2018 International Journal of Mathematics Vol.29 No.4
<P>Recently, Chang and Li generalized the theory of virtual fundamental class to the setting of semi-perfect obstruction theory. A semi-perfect obstruction theory requires only the local existence of a perfect obstruction theory with compatibility conditions. In this paper, we generalize the torus localization of Graber-Pandharipande [T. Graber and R. Pandharipande, Localization of virtual cycles, <I>Invent. Math.</I><B>135</B>(2) (1999) 487-518], the cosection localization [Y.-H. Kiem and J. Li, Localizing virtual cycles by cosections, <I>J. Amer. Math. Soc.</I><B>26</B>(4) (2013) 1025-1050] and their combination [H.-L. Chang, Y.-H. Kiem and J. Li, Torus localization and wall crossing for cosection localized virtual cycles, <I>Adv. Math.</I><B>308</B> (2017) 964-986], to the setting of semi-perfect obstruction theory. As an application, we show that the Jiang-Thomas theory [Y. Jiang and R. Thomas, Virtual signed Euler characteristics, preprint (2014), arXiv:1408.2541] of virtual signed Euler characteristic works without the technical quasi-smoothness assumption from derived algebraic geometry.</P>
A New 24-Nor-Lupane-Glycoside of Acanthopanax trifoliatus
Kiem, Phan-Van,Minh, Chau-Van,Cai, Xing-Fu,Lee, Jung-Joon,Kim, Young-Ho The Pharmaceutical Society of Korea 2003 Archives of Pharmacal Research Vol.26 No.9
A new 24-nor-lupaneglycoside was isolated from the leaves of Acanthopanax trifoliatus. Based on spectroscopic data its chemical structure was determined as 24-nor-11$\alpha$-hydroxy-3-oxo-lup-20(29)-en-28-oic acid 28-Ο-$\alpha$-L-rhamnopyranosyl-(1$\rightarrow4)-\beta-D-glucopyranosyl-(1\rightarrow6)-\beta$-D-glucopyranosyl ester.
Chemical Constituents of Acanthus ilicifolius L. and Effect on Osteoblastic MC3T3E1 Cells
Kiem, Phan Van,Quang, Tran Hong,Huong, Tran Thu,Nhung, Le Thi Hong,Cuong, Nguyen Xuan,Minh, Chau Van,Choi, Eun-Mi,Kim, Young-Ho 대한약학회 2008 Archives of Pharmacal Research Vol.31 No.7
A new coumaric acid derivative called acancifoliuside (1) and six known compounds as acteoside (2), isoacteoside (3), acanthaminoside (4), (+)-lyoniresinol 3a-O-$\beta$-glucopyranoside (5), (-)-lyoniresinol (6), and $\alpha$-amyrin (7), were isolated from the methanolic extract of the leaves of Acanthus ilicifolius L. (Acanthaceae). Their structures were determined by spectroscopic methods and a comparison with the spectral data reported in the literature. The effects of the compounds on the function of osteoblastic MC3T3-E1 cells were tested. Compounds 2, 3, and 5 ($30\;{\mu}M$) increased the growth and differentiation of osteoblasts significantly (P<0.05), indicating that A. ilicifolius leaves may help prevent osteoporosis.
Phenolic Constituents with Inhibitory Activity against NFAT Transcription from Desmos chinensis
Kiem Phan Van,Minh Chau Van,Huang Hoang Thanh,Lee Jung Joon,Lee Im Seon,Kim Young Ho The Pharmaceutical Society of Korea 2005 Archives of Pharmacal Research Vol.28 No.12
Six phenolic constituents, 2-methoxybenzyl benzoate (1), negletein (2), 2',3'-dihydroxy-4',6'dimethoxydihydrochalcone (3), 5,6-dihydroxy-7-methoxy-dihydroflavone (4), astilbin (5), and quercitrin (6) were isolated from the methanol extract of the dried leaves of Desmos chinensis. Their structures were elucidated from spectral and chemical data. Of these constituents, compounds 2 ($IC_{50}$: 3.89 $\pm$ 0.39 $\mu$M) and 3 ($IC_{50}$: 9.77 $\pm$ 0.26 $\mu$M) exhibited potent inhibitory activity against nuclear factor of activated T cells (NFAT) transcription factor, and compound 1 ($IC_{50}$: 28.4 $\pm$ 2.62 $\mu$M) exhibited moderate inhibitory activity.
CRITICAL VIRTUAL MANIFOLDS AND PERVERSE SHEAVES
Kiem, Young-Hoon,Li, Jun Korean Mathematical Society 2018 대한수학회지 Vol.55 No.3
In Donaldson-Thomas theory, moduli spaces are locally the critical locus of a holomorphic function defined on a complex manifold. In this paper, we develop a theory of critical virtual manifolds which are the gluing of critical loci of holomorphic functions. We show that a critical virtual manifold X admits a natural semi-perfect obstruction theory and a virtual fundamental class $[X]^{vir}$ whose degree $DT(X)=deg[X]^{vir}$ is the Euler characteristic ${\chi}_{\nu}$(X) weighted by the Behrend function ${\nu}$. We prove that when the critical virtual manifold is orientable, the local perverse sheaves of vanishing cycles glue to a perverse sheaf P whose hypercohomology has Euler characteristic equal to the Donaldson-Thomas type invariant DT(X). In the companion paper, we proved that a moduli space X of simple sheaves on a Calabi-Yau 3-fold Y is a critical virtual manifold whose perverse sheaf categorifies the Donaldson-Thomas invariant of Y and also gives us a mathematical theory of Gopakumar-Vafa invariants.
Chemical Constituents of the Ficus elastica Leaves and Their Antioxidant Activities
Kiem, Phan Van,Minh, Chau Van,Nhiem, Nguyen Xuan,Tai, Bui Huu,Quang, Tran Hong,Anh, Hoang Le Tuan,Cuong, Nguyen Xuan,Hai, Truong Nam,Kim, Seung-Hyun,Kim, Jin-Kyoung,Jang, Hae-Dong,Kim, Young-Ho Korean Chemical Society 2012 Bulletin of the Korean Chemical Society Vol.33 No.10
Two New Phenylpropanoid Glycosides from the Stem Bark of Acanthopanax trifoliatus
Kiem, Phan-Van,Minh, Chau-Van,Dat, Nguyen-Tien,Cai, Xing-Fu,Lee, Jung-Joon,Kim, Young-Ho The Pharmaceutical Society of Korea 2003 Archives of Pharmacal Research Vol.26 No.12
Two new phenylpropanoid glycosides, 1-$\beta$-D-glucopyranosyl-2,6-dimethoxy-4-propenylphenol (1) and 1-[$\beta$-D-glucopyranosyl-(1$\rightarrow6)-\beta$-D-glucopyranosyl]-2,6-dimethoxy-4-propenylphenol (2) were isolated from the stem bark of Acanthopanax trifoliatus along with four known compounds (3∼6). Their structures were established on the basis of spectral and chemical evidences.
New Cytotoxic Benzopyrans from the Leaves of Mallotus apelta
Kiem Phan Van,Dang Nguyen Hai,Bao Ha Viet,Huong Hoang Thanh,Minh Chau Van,Huong Le Mai,Lee Jung Joon,Kim Young Ho The Pharmaceutical Society of Korea 2005 Archives of Pharmacal Research Vol.28 No.10
Two new benzopyrans 6-[1'-oxo-3'(R)-hydroxy-butyl]-5,7 -dimethoxy-2,2-dimethyl-2H-1-ben-zopyran (1) and 6-[1'-oxo-3'(R)-methoxy-butyl]-5,7 -dimethoxy-2,2-dimethyl-2H-1-benzopyran (2) were isolated from the leaves of Mallotus apelta Muell.-Arg., (Euphorbiaceae). Their chemical structures were elucidated by spectroscopic analyses, especially by 1D-, 2D-NMR and MS spectra. Compound 1 was found to have strong cytotoxic effect against two human cancer cell lines as human hepatocellular carcinoma (Hep-2, $IC_{50}\;:\;0.49\;{\mu}g/mL$) and rhabdosarcoma (RD, $IC_{50}\;:\;0.54\;{\mu}g/mL$), while compound 2 showed moderate activity against Hep-2 cell line ($IC_{50}\;:\;4.22\;{\mu}g/mL$) by in vitro assay.