GIRSANOV'S THEOREM ON ABSTRACT WIENER SPACES

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On the absolute matrix summability of Fourier series and some associated series

The object of the paper is to study the absolute matrix summability problem of Fourier series, conjugate series and some associated series under a new set of conditions on matrix methods, generalising many known results in the literature.     

On inclusion theorems for absolute matrix summability methods, corrections: [J. Math. Anal. Appl. 238 (1999) 82-90]

We modify some of the conditions of the theorem to make it more applicable.     

Total synthesis and absolute stereochemistry of (9R,10S)-epoxyheptadecan-4,6-diyn-3-one, a diacylglycerol acyltransferase inhibitor from Panax ginseng

Asymmetric synthesis of four possible stereoisomers of (9,10)-epoxyheptadecan-4,6-diyn-3-one was accomplished, and the absolute configuration of the naturally occurring (9R,10S)-epoxyheptadecan-4,6-diyn-3-one (1) was elucidated.     

Synthesis of (+)-zeylenone from shikimic acid

Starting from shikimic acid, the total synthesis of zeylenone was studied. The product was proved to be the (+)antipode of zeylenone through analysis and comparison of their respective spectra (including NMR, MS, IR and CD) and optical data. The absolute configuration of the natural product was thus determined to be (1S,2S,3R).     

Synthesis of cordiaquinone J and K via B-alkyl Suzuki-Miyaura coupling as a key step and determination of the absolute configuration of natural products

A versatile methodology for the synthesis of various terpenoids via B-alkyl Suzuki-Miyaura coupling as a key step is established. Synthesis of cordiaquinone J and K, new antifungal and larvicidal meroterpenoids, was achieved by using this methodology. The absolute configurations of cordiaquinone J and K were confirmed by the synthesis.     

Conformational studies by dynamic NMR spectroscopy. Part 96: Stereomutations of highly hindered naphthylphenyl atropisomers in solution and in the solids

When a benzene ring bears two 2-methyl-1-naphthyl moieties in the para, meta or ortho positions as in 1,4-bis(2-methyl-1-naphthyl)benzene, 1, 1,3-bis(2-methyl-1-naphthyl)benzene, 2 and 1,2-bis(2-methyl-1-naphthyl)benzene 3, two rotational isomers (atropisomers) are generated, with the two naphthyl substituents in a syn or anti relationship. In the case of the para and meta derivatives (1 and 2, respectively) these atropisomers could not be separated but were detected by NMR spectroscopy, that also allowed the determination of their syn-anti interconversion barriers in solution (19.5 and 20.4 kcal mol⁻¹, respectively) and, in the case of 2, also in the solid state (26.7 kcal mol⁻¹). In the more hindered ortho derivative 3, the syn (meso) and anti (racemic) atropisomers interconvert in solution with a barrier (31.2 kcal mol⁻¹) sufficiently high to allow their physical separation. The racemic form could also be separated (by enantioselective HPLC) into the PP and MM enantiomers. Analysis of the corresponding CD spectra allowed the assignment of the absolute configuration. When three such naphthyl substituents are bonded to the phenyl in a meta relationship, two atropisomers in statistical proportions were observed: the anti (C_s symmetry) and the syn (C_3v symmetry) display a 3:1 ratio at the equilibrium in solution. This ratio is different in the solid state, as is the interconversion barrier (22.1 and 32.1 kcal mol⁻¹ in solution and in the solid, respectively).     

Total Syntheses of Cystobactamids and Structural Confirmation of Cystobactamid 919‐2

The cystobactamids are a family of antibacterial natural products with unprecedented chemical scaffolds that are active against both Gram‐positive and Gram‐negative pathogens. Herein, we describe the first total synthesis of cystobactamid 919‐2 from three fragments. Our convergent synthesis enabled both the confirmation of the correct structure and the determination of the absolute configuration of cystobactamid 919‐2.     

Irreducibility and the distribution of some exponential sums

We relate the distribution of the absolute value of some generalized Gauss sums to the absolute irreducibility of some polynomials in two variables in characteristic 0 and p.