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.     

Preparation of multisubstituted allenes from allylsilanes

[reaction: see text] A three-step route of converting allylsilanes to functionalized allenes was developed. Thermal decomposition of 1,1-dibromo-2-(silylmethyl)cyclopropanes, which were quantitatively prepared by treatment of allylsilane derivatives with CHBr3/KO(t)Bu, afforded substituted 2-bromo-1,3-butadienes with elimination of bromosilanes. The Pd-catalyzed reaction of the bromodienes with soft nucleophiles gave the allene derivatives. Previously inaccessible tri- and tetrasubstituted allenes can be prepared by this method as well.     

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.     

Novel one-dimensional tubelike and two-dimensional polycatenated metal-organic frameworks

Two novel metal-organic frameworks (MOFs) [Zn(TITMB)(OAc)](OH).8.5H(2)O (1) and [Ag(TITMB)N(3)].H(2)O (2) [TITMB = 1,3,5-tris(imidazol-1-ylmethyl)-2,4,6-trimethylbenzene, OAc = acetate anion] were synthesized and their structures were determined by X-ray crystallography. Complex 1 crystallizes in tetragonal space group P(-)4 with a = 23.2664(7) and c = 11.9890(3) A and Z = 8. 1 has a one-dimensional tubelike structure with large inner pore size of approximately 17 A. Complex 2 crystallizes in monoclinic space group C2 with a = 20.7193(10), b = 11.5677(8), and c = 12.2944(6) A, beta = 125.5770(10) degrees, and Z = 4. 2 consists of two-dimensional honeycomb networks that interpenetrate each other to generate a polycatenated structure. In these two complexes, both zinc(II) and silver(I) atoms are four-coordinated with the same tetrahedral coordination geometry. The topologies of 1 and 2 are predominated by the conformations of TITMB, which are cis, trans, trans in 1 and cis, cis, cis in 2, respectively.