ON THE ESSENTIAL SPECTRUM OF PSEUDODIFFERENTIAL OPERATORS （Ⅱ）

This paper coutinues the studies of the essential spectrum of nonsemi-bounded pseudodifferential operators. The author improves the results in [5] in some sense. For the relativistic Schrodinger operator,√(-Δ+m^2)+v(x),complete results are obtained.     

Synthesis of 4-acetylisocoumarin: first total syntheses of AGI-7 and sescandelin

A practical synthetic route to 4-acetylisocoumarins and the first total synthesis of AGI-7 (5) and sescandelin (4) are described. The readily available homophthalate 8 was transformed to the vinylogous amide ester 13 in high overall yield. Upon treatment of 13 with refluxing aqueous formic acid, the desired 4-acetylisocoumarin (5) and its regioisomer 3-methyl-4-formylisocoumarin (17) were produced in a 3:1 ratio. After separation of the desired product (5) from the unwanted minor isomer, the enantioselective reduction of AGI-7 by borane in the presence of Corey's (S)-oxazaborolidine reagent afforded (+)-sescandelin (4) with a 93% ee.