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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>
New Phenylpropanoid Esters of Sucrose from Polygonum hydropiper and Their Antioxidant Activity
Kiem, Phan Van,Nhiem, Nguyen Xuan,Cuong, Nguyen Xuan,Hoa, Tran Quynh,Huong, Hoang Thanh,Huong, Le Mai,Minh, Chau Van,Kim, Young-Ho 대한약학회 2008 Archives of Pharmacal Research Vol.31 No.11
By various chromatographic methods, two new phenylpropanoid esters of sucrose named hidropiperosides A (1) and B (2), and three known compounds as vanicosides A (3), B (4), and E (5) were isolated from the methanolic extract of the whole plant of Polygonum hydropiper L. (Polygonaceae). Their structures were elucidated by extensive spectroscopic methods including 1D- and 2D-NMR experiments, as well as ESI-MS analysis. All the isolated compounds were tested for their antioxidant activity in the 1,1-diphenyl-2-picrylhydrazyl (DPPH) radical scavenging assay system. Among them, compounds 2 and 3 showed significant antioxidant activity with their $SC_{50}$ values of 23.4 and $26.7{\mu}g/mL$, respectively.
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
Lupane-Triterpenes from the Leaves of Brassaiopsis glomerulata
Kiem, Phan-Van,Dat, Nguyen-Tien,Minh, Chau-Van,Lee, Jung-Joon,Kim, Young-Ho The Pharmaceutical Society of Korea 2003 Archives of Pharmacal Research Vol.26 No.8
Three known lupane-triterpenes, 3a-hydroxy-lup-20(29)-en-23,28-dioic acid (1), 3$\alpha$-hydroxylup-20(29)-en-23,28-dioic acid 28-Ο-$\alpha$-L-rhamnopyranosyl-(1$\rightarrow4)-\beta-D-glucopyranosyl-(1\rightarow6)-\beta$-D-glucopyranosyl ester (acankoreoside A, 2) and $3\alpha$, $11\alpha$-dihydroxy-23-oxo-lup-20(29)-en-28-oic acid (3) were isolated from the leaves of Brassaiopsis glomerulata (Blume) Regel, a species of Araliaceae family growing in Vietnam. Their structures were determined on the basis of spectroscopic data.
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.
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.
Pentacyclic Triterpenoids from Mallotus apelta
Kiem, Phan-Van,Minh, Chau-Van,Huong, Hoang-Thanh,Nam, Nguyen-Hoai,Lee, Jung-Joon,Kim, Young-Ho The Pharmaceutical Society of Korea 2004 Archives of Pharmacal Research Vol.27 No.11
A new triterpene (1) and six known pentacyclic terpenoids (2-7) were isolated from the methanol extract of the dried leaves from Mallotus apelta. Based on the spectral and chemical evidence, their structures were determined to be 3$\alpha$-hydroxyhop-22(29)-ene (1), hennadiol (2), friedelin (3), friedelanol (4), epifriedelanol (5), taraxerone (6), and epitaraxerol (7).
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.
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.