A stereoselective 3-endo-alkyl-5,6-dehydroisoquinuclidine synthesis.

Cycloaddition of N-carbethoxy-2-alkyl-1,2-dihydropyridines $\text{4}$ with phenylvinylsulfone $\text{5}$ provides adducts $\text{6}$, which upon desulfonylation afford stereoselectively N-carbethoxy-3-$\text{endo}$- alkyl-5,6-dehydroisoquinuclidines $\text{1}$.     

Projective repesentations of the Hilbert Lie group U (H)2 via quasifree statres on the CAR algebra

The group $\text{U}$ (H)₂ of unitary operators (on a Hilbert space H) which differ from the identity by a Hilbert-Schmidt operator may be imbedded in the group of Bogoliubov automorphisms of the CAR algebra over H in such a way as to be weakly inner in any gauge-invariant quasifree representation. Consequently each such quasifree representation determines a projective representation of $\text{U}$ (H)₂. If 0 ? A ? I is the operator on H determining the quasifree representation π_A and ?_A denotes the cyclic projective representation of $\text{U}$ (H)₂ generated from the G.N.S. cyclic vector $\text{Ω}{}_{\mathrm{A}}\text{for}\text{π}{}_{\mathrm{A}}$, then the 2-cocycle in $\text{U}$ (H)₂ determined by ?_A can be given explicitly. We prove that this 2-cocycle is a coboundary if any only if A or 1 ? A is Hilbert-Schmidt. The representations ?_A, on restriction to the group $\text{U}$ (H)₁ consisting of unitaries which differ from the identity by a trace class operator, always determine 2-cocycles which are coboundaries. These representations of $\text{U}$ (H)₁ have already been investigated by 21., 22., 87–110). Thus the Stratila-Voiculescu representations of $\text{U}$ (H)₁ always extend to projective representations of $\text{U}$ (H)₂ and to ordinary representations when A or 1 ? A is Hilbert-Schmidt. This fact enables exploitation of the type analysis of Stratila and Voiculescu to determine the type of the von Neumann algebra ρ_A($\text{U}$(H)₂)″. In the special case where 0 and 1 are not eigenvalues of $\text{A, Ω}{}_{\mathrm{A}}$ is cyclic and separating for ρ_A($\text{U}$(H)₂)″ and hence determines a K.M.S. state on this algebra. It is shown that for special choices of A, type III_λ (0 < λ ? 1) factors ρ_A($\text{U}$(H)₂)″ may be constructed.     

Spectrophotofluorometric determination of terbium and europium in potassium carbonate solution

The conditions for the spectrophotofluorometric determination of terbium and europium, in solutions of potassium carbonate, have been established. The apparent excitation and fluorescence wavelengths used, respectively, are 245 mmu and 550 mmu for terbium and 400 mmu and 620 mmu for europium. The fluorescence varies linearly with the concentration of terbium and europium in the range 0.3-70 mug, of terbium/ml and 4-800 mug of europium/ml. Large amounts of gadolinium, lutetium and yttrium do not interfere. Cerium(IV) interferes seriously.     

A note on the boson-fermion correspondence and infinite dimensional groups

We show how to construct irreducible projective representations of the infinite dimensional Lie group Map (S ¹, ), by embedding it into the group of Bogoliubov automorphisms of the CAR. Using techniques of G. Segal for extending certain representations of Map (S ¹, SU(2)) we show that our representations extend to give representations of a certain infinite dimensional superalgebra. We relate our work to the well known boson-fermion correspondence which exists in 1+1 dimensions.