Constituents of Withania somnifera Dun—XIII : The withanolides of chemotype III

Nine new steroidal lactones of the withanolide series (withanolides E-M) have been isolated from the leaves of Withania somnifera Dun (Solanaceae) growing in the southern coastal plane of Israel. This population of W. somnifera constitutes a new chemotype and is designated as chemotype III. The following structures have been assigned to seven of the above compounds:Withanolide G, 20α-hydroxy-1-oxo-20R,22R-witha-2,5,8(14),24-tetraenolide (1); withanolide H, 20α,27-dihydroxy-1-oxo-20R,22R-witha-2,5,8(14),24-tetraenolide (2); withanolide I, 20α-hydroxy-1-oxo-20R,22R-witha-3,5,8(14),24-tetraenolide (3); withanolide J, 17α,20α-dihydroxy-1-oxo-20S,22R-witha-2,5,8(14),24-tetraenolide (4); withanolide K, 17α,20α-dihydroxy-1-oxo-20S,22R-witha-3,5,8(14),24-tetraenolide (5); withanolide L, 17α,20α-dihydroxy-1-oxo-20S,22R-witha-2,5,14,24-tetraenolide (6); withanolide M, 17α,20α-dihydroxy-1-oxo-14α,15α-epoxy-20S,22R-witha-2,5,24-trienolide (7).     

Global systematics of the Wigner energy

Following Zeldes, double-beta decay Q   values are used as a filter for extracting symmetry energy and Wigner energy coefficients across the full range of nuclei, from A=10$A=10$ to A=246$A=246$. The symmetry coefficient extracted is found to vary smoothly with A and mass formula coefficients can be determined for the corresponding symmetry and surface symmetry terms. However, the extracted Wigner coefficient has large standard errors and fluctuates dramatically with A, even as regards its sign. Shell corrections remove most of the fluctuations and allow the determination of a reliable Wigner coefficient for the mass formula.     

Self-consistency corrections in effective-interaction calculations

Large-matrix extended-shell-model calculations are used to compute self-consistency corrections to the effective interaction and to the linked-cluster effective interaction. The corrections are found to be numerically significant and to affect the rate of convergence of the corresponding perturbation series. The influence of various partial corrections is tested. It is concluded that self-consistency is an important effect in determining the effective interaction and improving the rate of convergence.     

Non-degenerate single-particle energies in the Ginocchio model

A one-body operator expressing the breaking of the degeneracy of the single-nucleon energies is added to the pairing interaction of the Ginocchio model. This operator couples states inside the model's SD space to states outside it. The influence of this coupling on the effective interaction in the SD space and the possibility of expressing the results in terms of renormalization of parameters in the fermion hamiltonian or the IBM are investigated. The effective interaction is found to be almost diagonal in seniority, while splitting the previously-degenerate seniority multiplets. Appropriately renormalized Ginocchio and IBM hamiltonians can approximately reproduce the results, but fermion-number dependence of the hamiltonian parameters and explicit three-body interactions are needed to reproduce the computed effects exactly.     

13C NMR spectroscopy of the withanolides and other highly oxygenated C28 steroids

The ¹³C NMR spectra of 29 highly oxygenated C, steroids with the withanolide skeleton, 24 of which are naturally occurring substances or acetates thereof, were recorded and the carbon signals fully assigned. The shifts of the heavily functionalized A/B ring system can serve as a ‘fingerprint’ for the different substitution patterns. A study of the effects of hydroxyl substitution in the ring D/side chain part of the molecules leads to conformational information, including preferred rotamers around the 17—20 and 20—22 bonds. Systems with both 17α- and 17β-oriented side chains are thus analysed.     

Wild automorphisms of varieties with Kodaira dimension 0

An automorphism σ of a projective variety X is said to be wild if σ(Y) ≠ Y for every non-empty subvariety Y \subsetneq X{Y \subsetneq X} . In [1] Z. Reichstein, D. Rogalski, and J.J. Zhang conjectured that if X is an irreducible projective variety admitting a wild automorphism then X is an abelian variety, and proved this conjecture for dim(X) ≤ 2. As a step toward answering this conjecture in higher dimensions we prove a structure theorem for projective varieties of Kodaira dimension 0 admitting wild automorphisms. This essentially reduces the Kodaira dimension 0 case to a study of Calabi-Yau varieties, which we also investigate. In support of this conjecture, we show that there are no wild automorphisms of certain Calabi-Yau varieties.