A Short,Affordable, One-Pot Synthesis of a Camphor-Derived Amino Alcohol

The commercially available α-ketoxime of camphorquinone (1) was reduced to the corresponding exo,exo-amino alcohol (2) in a two-step, one-pot procedure using sodium borohydride and nickel(II) chloride hexahydrate.     

A New Reaction Involving the Formation of Unsaturated Carbenes

Treatment of 5,5-dialkyl-N-nitrosooxazolidones (1) with Lithium ethoxide (and other bases) under certain conditions yields reaction products the formation of which seems best explained by assuming that unsaturated carbenes [A] are involved.^3–5     

Assortative mixing in networks

A network is said to show assortative mixing if the nodes in the network that have many connections tend to be connected to other nodes with many connections. Here we measure mixing patterns in a variety of networks and find that social networks are mostly assortatively mixed, but that technological and biological networks tend to be disassortative. We propose a model of an assortatively mixed network, which we study both analytically and numerically. Within this model we find that networks percolate more easily if they are assortative and that they are also more robust to vertex removal.     

A note on growing binary trees

The class ? of binary search trees is studied. A leaf is a vertex of degree 0; ?_n is the subset of ? consisting of trees with n leaves. We grow trees in ?_n from ?_n ? 1 thereby inducing a probability measure on ?_n. We will show that the expected value of the average leaf distance of t ∈ ?_n is asymptotic to log₂n as n → ∞.     

Quasi-localized representation of electronic band structures in cubic crystals

Tabulated results and formulae are given for the parametrization of electronic band structures in simple cubic, body-centered cubic and face-centred cubic systems. This technique is based on the decoupling transformation and does not involve least squares fitting.A band labelling scheme is introduced which allows the decoupling transformation to be used to define the energy matrix of Wannier states in copper. This approach is used to re-examine the significance of the tight binding approximation for the d-states and to relate Fermi surface parameters directly to calculated band energies.     

On the calculation of charge densities in crystals

A general method is given for determining the spatial charge distribution of a filled electronic band using Bloch state charge distributions determined at very few k points. Formulae are given for several important cases.