New molecular entities via intermolecular meta photocycloaddition

The intermolecular meta photocycloaddition of 1,3‐dihydroisobenzofuran and 1,3‐dihydroisoindole‐2‐carboxylic acid methyl ester with cyclopentene and 2,5‐dihydrofuran affords two new classes of photoadducts. The photoadducts were identified by the SORT&gen algorithm as New Molecular Entities in two‐dimensional scaffold space. The structures of the adducts were established by NMR spectroscopy and the stereo‐, regio‐ and chemoselectivity of the reactions is discussed.     

Clark's theorem for semi-infinite convex programs

In 1961, Clark proved that if either the feasible region of a linear program or its dual is nonempty and bounded, then the other is unbounded. Recently, Duffin has extended this result to a convex program and its Lagrangian dual. Moreover, Duffin showed that under this boundedness assumption there is no duality gap. The purpose of this paper is to extend Duffin's results to semi-infinite programs.     

Supersymmetry-breaking through D-terms

Models in which supersymmetry is broken by the Fayet-Iliopoulos mechanism are reconsidered. The possibility that scalar quark and lepton masses might arise radiatively in such theories is explored. It is shown that in several interesting cases, these masses-squared are all negative. In grand-unified versions of these models, it is shown that the scale of SU(2) × U(1) breaking tends to be much larger than the scalar quark and lepton masses, i.e. that the hierarchy is unstable.     

The synthesis of 2,5-dihydrofurans from α-allenic alcohols

α-Allenic alcohols react rapidly with PhSeCl to produce derivatives of 3-phenyl-seleno-2,5-dihydrofuran in high yields.     

Determinants of Galois automorphisms of maximal commutative rings of 2×2 matrices

The determinants of solutions X to any of the 2×2 matrix equations: (1) XAX>^?1=A^t, t denoting transpose; (2) A=XY, X, Y symmetric; (3) X=AB?BA; and (4) $\text{XAX}{}^{\mathrm{?1}}\text{=A}{}^1$, the matrix of cofactors of A transposed, are characterized over a commutative ring R as the negative of norms from the quadratic extension R[A] whenever certain elements in the Picard group Pic (R[A]) are trivial. This characterization is realized by the utilization of galois cohomology and a generalized Latimer–MacDuffee correspondence between similarity classes and the elements in Pic (R[A]). The results represent a ramification of several articles by O. Taussky on the specializations of equations (1)–(3) to either the field of rational numbers or the ring of rational integers.