The Atiyah-Singer index theorem as passage to the classical limit in quantum mechanics

A new approach to the Atiyah-Singer index theorem is described, using the technique of continuous fields ofC ^*-algebras. The proof is given in the case of elliptic pseudodifferential operators on ℝ ⁿ .     

The Heisenberg group andK-theory

A simple proof of Bott periodicity, and at the same time of the Connes isomorphism theorem for one-parameter crossed products, is given using continuous fields ofC*-algebras.     

Oily drug carriers in cancer chemotherapy. II. Preparation of viscous ethyl oleate for intraarterial infusion therapy and its disposition in rats and hamsters.

Viscous ethyl oleate (VEO) was prepared as an oil drug carrier by the addition of aluminum stearate or ethyl cellulose. Since the rate of shear of VEO containing aluminum stearate was greatly and nonlinearly changed against the shearing stress compared to that containing ethyl cellulose, the latter was used for subsequent microvascular and organ distribution experiments in rats and hamsters. For infusion into the carotid artery in hamsters, neat ethyl oleate (EO, 4cP) or VEOs of various apparent viscosities (40, 80, 120 cP-VEOs) embolized the vascular system in the cheek pouch, although arrival time to the site where the embolization was observed and the embolization period differed depending on the type of oily drug carrier. For infusion into the hepatic artery in rats, however, only 120 cP-VEO embolized the vascular system in the liver. After infusion of the oily drug carrier containing 3H-oleic acid into the artery of hamster cheek pouch and rat liver, 30-50% of the radioactivity was gradually eliminated within 48 h, whereas about 80% of the dose was rapidly eliminated after infusion to rat stomach and kidney. In addition, the amount of 120 cP-VEO remaining in each organ 48 h after infusion was higher than those of EO and 40 and 80 cP-VEOs. Histological observation after infusion in rat liver revealed that 120 cP-VEO slowly migrated from the artery or arteriole to the sinusoidal capillary region. These results suggest that 120 cP-VEO can be used as a drug carrier because of its function of vascular embolization and high retention in a targeted tissue.     

Preparation of benzene, furan, and thiophene analogs of duocarmycin SA employing a newly-devised phenol-forming reaction

Five A-ring analogs of duocarmycin SA 9a-e were synthesized in racemic form modifying our second synthetic route toward duocarmycin SA. The problem encountered at the crucial phenol forming step to secure 17a, b from 16a, b under the conventionally used Kuwajima conditions was overcome by devising a more convenient method: simple heating of 16a-c in benzene in the presence of bis(triphenylphosphine)palladium(II) chloride (10 mol%), cesium carbonate (3 eq), and triphenylphosphine (0.3 eq) gave 17a-c in high yields of 86-91%. The intermediates 17a-e were readily led to the A-ring analogs (+/-)-9a-e almost according to the reported route.