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One hundered years ago exactly, in 1906, Hartogs published a celebrated extension phenomenon (birth of Several Complex Variables),
whose global counterpart was understood later: Holomorphic functions in a connected neighborhood V(∂Ω) of a connected boundary
∂Ω ⋐ℂn ≥ 2) do extend holomorphically and uniquely to the domain ό. Martinelli, in the early 1940’s, and Ehrenpreis in 1961 obtained
a rigorous proof, using a new multidimensional integral kernel or a short
argument, but it remained unclear how to derive a proof using only analytic discs, as did Hurwitz (1897), Hartogs (1906),
and E. E. Levi (1911) in some special, model cases. In fact, known attempts (e.g., Osgood, 1929, Brown, 1936) struggled for
monodromy against multivaluations, but failed to get the general global theorem.
Moreover, quite unexpectedly, in 1998, Fornœss exhibited a topologically strange (nonpseudoconvex) domain όF ⊂ ℂ2 that cannot befitted in by holomorphic discs, when one makes the additional requirement that discs must all lie entirely
inside όF. However, one should point out that the standard, unrestricted disc method usually allows discs to go outside the domain
(just think of Levi pseudoconcavity).
Using the method of analytic discs for local extensional steps and Morse-theoretical tools for the global topological control
of monodromy, we show that the Hartogs extension theorem can be established in such a way. 相似文献
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Liposoluble camptothecin derivative, research name TQ-B3203, is a recently developed investigational antiproliferative agent by our group. The structure of TQ-B3203 is 2-(hexadecyloxycarbonyl)-2,5,7,8-tetramethylchroman-6-yl 7-ethyl-camptothecin-10-yl succinate, containing an SN-38 component, a trolox component, a succinic acid linker, and a hexadecanol chain. In this study, the process-related impurities of bulk TQ-B3203 were identified, characterized, and synthesized. Seven major impurities were revealed based on the mass spectrum (MS) and nuclear magnetic resonance (NMR) spectral data. They were characterized as SN-38 (IMP-I), trolox (IMP-II), 2-(dodecyloxycarbonyl)-2,5,7,8-tetramethylchroman-6-yl 7-ethyl-camptothecin-10-yl succinate (IMP-III), hexadecyl 7-ethyl-camptothecin-10-yl succinate (IMP-IV), 2-(tetradecyloxycarbonyl)-2,5,7,8-tetramethylchroman-6-yl 7-ethyl-camptothecin-10-yl succinate (IMP-V), 4-(2-(hexadecyloxycarbonyl)-2,5,7,8-tetramethylchroman-6-yloxy)-4-oxobutanoic acid (IMP-VI), and 4-(2-(octodecyloxycarbonyl)-2,5,7,8-tetramethylchroman-6-yloxy)-4-oxobutanoic acid (IMP-VII). The probable origin of the impurities from the preparation process of TQ-B3203 was discussed. 相似文献
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