Total Synthesis of Crenulatan Diterpenes: Strategy and stereocontrolled construction of a bicyclic keto-lactone building block

The bicyclic keto lactone 26 was synthesized for the purpose of developing a viable route to marine diterpenes of the crenulatan type. Following the efficient conversion of (S)-citronellol ( 5 ) to the allylated alcohol 9a (Scheme 2), the αβ-unsaturated lactone 12 was efficiently accessed in preparation for stereocontrolled conjugate addition. The hydroxymethyl equivalent most suited to this task was (i-PrO)Me₂SiCH₂MgCl, which gave 13 predominantly in the presence of CuI and Me₃SiCl. Once the OH group was deprotected (→ 14 ), it proved an easy matter to implement acid-catalyzed isomerization to lactone 15 , oxidation of which gave the pivotal aldehyde 16 . Condensation of 16 with PhSeCH₂Li led via 21 to 22 (Scheme 3). Once the OH group was protected (→ 22b ), it proved possible to effect aldolization with crotonaldehyde (→ 23 ). Exposure of 23 to acid gave the sub-target compound 25 . Its subsequent oxidation and thermal activation resulted in sequential selenoxide elimination with Claisen rearrangement (→ 26 ). The structural features of 26 require that a chair-like transition state be adopted during the [3.3]sigmatropic event. With the clarification of these issues, a highly serviceable and more advanced assault on the crenulatans should prove capable of being mounted.     

Reliability bounds in DFRA class with known mean and variance

ＲＥＬＩＡＢＩＬＩＴＹＢＯＵＮＤＳＩＮＤＦＲＡＣＬＡＳＳＷＩＴＨＫＮＯＷＮＭＥＡＮ　ＡＮＤ　ＶＡＲＩＡＮＣＥＣＨＥＮＧＫＡＮ（程侃）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ,ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅ,Ｂ...     

Rigidity of circle domains whose boundary hasσ-finite linear measure

Summary Let be a circle domain in the Riemann sphere whose boundary has -finite linear measure. We show that is rigid in the sense that any conformal homeomorphism of onto any other circle domain is equal to the restriction of a Möbius transformation. Previously, Kaufman and Bishop have independently found examples of non-rigid circle, domains whose boundary is a Cantor set of (Hausdorff) dimension one.Oblatum 19-VI-1992 & 2-IV-1993Supported by NSF and Sloan Foundation     

NLS-tupe equations in 2+1 dimensions: New type of solutions and non-isospectral problems

Integrable systems of NLS type in 2+1 dimensions are studied in three ways: their special solutions by Lie point symmetries, breaking-solutions by the ISM, as well as the non-isospectral problems.Department of Mathematics, Statistics and Computing Science, University of New England, Armidale N.S.W. 2351, Australia. E-mail: zhuhan@neumann.une.edu.au, xhe@metz.une.edu.au Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 3, pp. 382–389, June, 1994.