The Bounds of the General M and J Sets and the Estimations for the Hausdorff's Dimension of the General J Set

The bounds of the general M and J sets were analytically offered. Some of the bounds were optimal in certain meaning. It not only solved the primary problem of the construction of fractal sets by escape time algorithm, and followed from the conclusion, but also offered two estimations of some special Julia set’s Hausdorff’s dimension by approximate linearization method. Foundation item: the National Natural Science Foundation of China (69974008). Biography: LIX Xiang-dong (1967-), Associate Professor, Doctor     

THE BOUNDS OF THE GENERAL M AND J SETS AND THE ESTIMATIONS FOR THE HAUSDORFF'S DIMENSION OF THE GENERAL J SET

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The complex potential generated by the maximal measure for a family of rational maps

The exact complex potential generated by the maximal measure for a family of rational maps is given. The results are of analytical nature because the complex potential does not change nicely if the coordinates of a rational map are changed. There exist applications of this result to the theory of moments.     

Total synthesis of peridinin and related C37-norcarotenoid butenolides

As an extension of our synthesis of symmetrical carotenoids, the preparation of the highly functionalized C37-norcarotenoid butenolide peridinin (1), its 6'-epi- and 11'Z stereoisomers has been completed. Featuring a central dihalogenated C8 linchpin unit 6, two synthetic routes, differing in the ordering of the last three steps were explored by using the C3,C3'-bisdehydroxylated target as the model system. The first route uses the combination of a modified Z-selective Julia reaction and two sequential Stille couplings, the last one producing the isomerisation of the polyene Z double bond. The second route inverts these steps and makes the isolation of the 11'Z stereoisomers as major products possible. An efficient Z to E isomerisation of the final carotenoid skeleton simply uses the Stille reaction conditions at ambient temperature. As the reaction of bromoallene 12 with alkenylstannane 11 occurs with inversion of configuration, 6'-epi-peridinin could also be prepared by route A. The advantages and limitations of the sequential Stille cross-coupling approach to carotenoids are highlighted.     

Asymmetric Synthesis of the C（17）——C（28） Subunit of Didemnaketal B

The stereocontrolled synthesis of the C（17）--C（28） fragment 3 of didemnaketal B was accomplished in 21 steps from the natural （R）-（＋）-pulegone and （S）-（--）-citronellal. The key steps involved diastereoselective construction of two chiral carbon centers through the intramolecular chiral induction and uncommon Julia olefination of ketone forming the E-trisubstituted C（22）--C（23） double bound.     

Coupling of high temperature glass capillary columns to a mass spectrometer. GC/MS analysis of metalloporphyrins from Julia Creek oil shale samples

This paper reports on the instrumental and experimental prerequisites of the combination of high temperature gas chromatography (HTGC) with electron impact- (El) and chemical ionization (Cl) mass spectrometry (HTGC/EI/CIMS). It describes a newly developed high temperature GC/MS interface in detail and discusses the particular problems arising in HTGC/MS. The capabilities of the system are demonstrated by direct analyses of nickel- and vanadyl porphyrins, extracted from Julia Creek oil shale. The use of CI/NH₃ in the GC/MS analysis of metalloporphyrins is demonstrated for the first time.     

A formal total synthesis of crocacin C

An efficient total synthesis of a potent antifungal and moderate cytotoxic agent crocacin C is described. The synthesis involves the generation of four contiguous stereogenic centres via desymmetrization of a meso bicyclic dihydrofuran using asymmetric hydroboration.     

Synthesis and structure revision of tyroscherin, and bioactivities of its stereoisomers against IGF-1-dependent tumor cells

Synthesis of the proposed structure of tyroscherin, a growth inhibitor of IGF-1-dependent cancer cells, was succeeded by one-pot Julia coupling. However, spectral data of the synthetic compound were not identical with those of natural tyroscherin. The stereochemistry of tyroscherin is revised to be 2S,3R,8R,10R by syntheses of stereoisomers. Synthetic tyroscherin showed more potent activity than its stereoisomers against IGF-1-dependent cancer cells.