Tate–Vogel Completions of Half-Exact Functors

We provide a general method to construct the Tate–Vogel homology theory for a general half-exact functor with one variable, aiming at a good generalization of Cohen–Macaulay approximations of modules over commutative Gorenstein rings. For a half exact functor F, using the left and right satellites (S _n and S ⁿ ), we define F (X)=lim S _n S ⁿ F(X) and F (X)=lim S _n S ⁿ F(X), and call F and F the Tate–Vogel completions of F. We provide several properties of F and F , and their relations with the G-dimension and the projective dimension of the functor F. A comparison theorem of Tate–Vogel completions with ordinary Tate–Vogel homologies is proved. If F is a half exact functor over the category of R-modules, where R is a commutative Noetherian local ring inspired by Martsinkovsky's works, we can define the invariants (F) and (F) of F. If F=Ext _R ⁱ (M, ), then they coincide with Martsinkovsky's -invariants and Auslander's delta invariants. Our advantage is that we can consider these invariants for any half exact functors. We also compute these invariants for the local cohomology functors.     

Synthesis of a new class of furan-fused tetracyclic compounds using o-quinodimethane chemistry and investigation of their antiviral Activity

The synthesis and evaluation of antiviral activity of new furan-fused tetracyclic compounds are described. The syntheses were satisfactorily achieved on the basis of o-quinodimethane chemistry, using furan-containing benzocyclobutene derivatives as a substrate, in high generality and stereoselectivity. The various derivatives thus synthesized were examined on their inhibitory activity on virus growth using a hemagglutinin (HA) method, leading to a discovery of promising candidates for new antiviral drugs having high activity and good therapeutic index.     

Diastereoselective aldol reaction of N,N-dibenzyl-alpha-amino aldehydes with ketones catalyzed by proline

[reaction: see text] L-proline-catalyzed direct aldol reaction of L-amino acid-derived N,N-dibenzyl amino aldehydes with acetone, cyclopentanone, or hydroxyacetone provides gamma-amino-beta-hydroxy- or gamma-amino-alpha,beta-dihydroxy-ketones with moderate to excellent yields and diastereoselectivities.     

The intramolecular thermal ene reaction route to (+)-9(O)-methano-Δ6(9α) -PGI1

(+)-9(O)-Methano-Δ^6(9α)-PGI₁, a more potent carbon analog than carbacyclin, has been synthesized from the Corey lactone by utilizing the intramolecular thermal ene reaction as a key step.