The Subgroups of Direct Products of Surface Groups

A subgroup of a product of n surface groups is of type FP _n if and only if it contains a subgroup of finite index that is itself a product of (at most n) surface groups.     

Triple asymmetric synthesis for fragment assembly: Validity of approximate multiplicativity of the three diastereofacial selectivities

A strategy of triple asymmetric synthesis is illustrated to be effective for stereochemical control in fragment assembly, a task often encountered in convergent natural product synthesis. The stereochemical outcome of aldol reactions involving three chiral components supports a rule of approximate multiplicativity of facial selectivities intrinsic to the chiral reactants involved in each reaction.     

Small cancellation theory and automatic groups

Oblatum V-1989 &; 31-I-1990     

Synthesis and interconversion of 6-aroyl-4-oxohexanoie acids and 5-aryl-2-furanpropionic acids. Antiinflammatory agents

A series of 6-aroyl-4-oxohexanoic acids ( 2 ) was prepared for intermediate use by acid-catalyzed solvolysis of substituted 3-(2-furyl)acrylophenones ( 1 ). This reaction occasionally gave 5-aryl-2-furanpropionic acids ( 3 ) instead of, or in addition to, the desired diketones ( 2 ). Equilibrium between 2 and 3 was observed in the case where Ar is m-nitrophenyl. A rationalization for the formation of 3 is offered, and published reports with which our results differ are discussed. Diketones ( 2 ) were cyclized to furans ( 3 ) and antiinflammatory screening data are reported for the latter.     

Synthesis of 5-aryl-2-oxazolepropionic acids and analogs. Antiinflammatory agents

Condensation of 2-bromoacetophenones with sodium succinimide gave N-phenacylsuccinimides ( 1 ) which were opened with sodium hydroxide to N-phenacylsuccinamic acids ( 2 ). The latter were cyclized to 5-aryl-2-oxazolepropionic acids ( 3 ) in sulfuric acid. Similar cyclization of N-phenacylphthalamic acid ( 5 ) and succinic acid 2-benzoylhydrazide ( 7 ) gave o-(5-phenyl-2-oxazolyl)benzoic acid ( 6 ) and 5-phenyl-1,3,4-oxadiazole-2-propionic acid ( 8 ). The succinamic acids 2 and the phthalamic acid 5 were observed to recyclize to the corresponding imides ( 1 and 4 ) on heating, and the succinic acid hydrazide 7 was similarly cyclized to N-benzamidosuccinimide ( 9 ) with acetic anhydride. Antiinflammatory screening data are reported for 3 , 6 and 8 .     

Structural and Magnetic Chemistry of NdBaCo2O5+δ

The crystallographic and magnetic structures of the oxygen-deficient perovskites NdBaCo₂O_5+δ (δ=0, 0.38, 0.5, 0.69) have been studied as a function of temperature by neutron powder diffraction. Long-range G-type antiferromagnetic order is realized for all samples apart from that with δ=0.5. The lack of magnetic order for δ=0.5 can be understood on the basis of a crystal-field-induced spin-state ordering between low-spin and high-spin Co³⁺. Contrary to studies of similar materials with smaller lanthanides, the δ=0 material exhibits no evidence of long-range charge ordering. No evidence of a spin-state transition as observed in YBaCo₂O₅ is found for any of our samples.