Preparation of cis-5-methoxy-and-7-methoxy-1-acetoxy-1,2,3,4,4a,10a- hexahydro-9(10H)-phenanthrenone. An epoxide-arene reaction involving a selective 1,2-alkyl shift rearrangement.

The preparation of cis-1-acetoxy-7-methoxy-1,2,3,4,4a,10a-hexahydro-9(10H)- phenanthrenone 5 was accomplished starting from 6-methoxy-1-tetralone. Reduction of 7-methoxy-1,2,3, 4,9,10-hexahydro-1-oxo-phenanthrene 8, acetylation and subsequent oxidation delivered 5. Application of an analogus procedure to the preparation of cis-1β-acetoxy-5-methoxy-1,2,3,4,,4a,10a-hexahydro-9(10H)- phenanthrenone 6 was not feasible. A more elaborate route was developed for the synthesis of compound 6, where an epoxide-arene reaction involving a 1,2-alkyl shift rearrangement, constituted a highly selective key transformation.     

The Hume–Rothery Compound Mn8Ga27.4Zn13.6: Separated Zn13‐Clusters Interspersed in a Primitive Cubic Host Lattice

Separated Zn ₁₃ cluster entities unexpectedly occur in the solid‐state structure of Mn₈Ga_27.4Zn_13.6 (the central building block is shown). They correspond to centered cuboctahedra, that is, small volumes of face‐centered cubic metal. The intriguing segregation of Ga and Zn atoms in Mn₈Ga_27.4Zn_13.6 was verfied by Rietveld refinement of neutron powder diffraction data.     

Semiflexible chain molecules with nonuniform curvature, 2. . Brownian dynamics simulations of electric dichroism orientation dynamics

The hydrodynamically induced orientation dynamics of charged polymer molecules during electric dichroism has been studied by Brownian dynamics simulations. The effect of a locally changed flexibility or bending angle has been of special interest. The results show that simultaneously changing the bending angles and the corresponding force constants so as to keep the persistence length constant does not produce any large changes in the orientation dynamics or molecular shape although, quantitatively, a larger number of kinks in the chain will give a smaller steady-state orientation. Releasing the constraint of a fixed persistence length when randomly increasing or decreasing the flexibility at different positions in the molecule drastically changes the dynamics, and the corresponding results are discussed and also compared with the orientation obtained when introducing the inhomogeneities in a cooperative manner.     

Functions on discrete sets holomorphic in the sense of isaacs,or monodiffric functions of the first kind

We study discrete analogues of holomorphic functions of one and two variables, especially those that were called monodiffric functions of the first kind by Rufus Isaacs. Discrete analogues of the Cauchy-Riemann operators, domains of holomorphy in one discrete variable, and the Hartogs phenomenon in two discrete variables are investigated.     

Refined Asymptotic Costs for Renewal Reward Processes

A common criteria function for the selection of decision variables in renewal reward processes is the leading term in the asymptotic expansion of the expected cost per unit time, namely the ratio of expected cost per cycle to expected cycle length. The general implications of refining this criteria function by adopting the first two terms in the asymptotic expansion as an objective function are discussed. An analysis for both an age based and a cumulative damage based renewal reward process is presented.