Algebraic properties of number theories

Among other things we prove the following. (A) A number theory is convex if and only if it is inductive. (B) No r.e. number theory has JEP. (C) No number theory has AP. We also give some information about the hard cores of number theories.     

First-principles modelling of scanning tunneling microscopy using non-equilibrium Green’s functions

The investigation of electron transport processes in nano-scale architectures plays a crucial role in the development of surface chemistry and nano-technology. Experimentally, an important driving force within this research area has been the concurrent refinements of scanning tunneling microscopy (STM) techniques. The theoretical treatment of the STM operation has traditionally been based on the Bardeen and Tersoff-Hamann methods which take as input the single-particle wave functions and eigenvalues obtained from finite cluster or slabs models of the surface-tip interface. Here, we present a novel STM simulation scheme based on non-equilibrium Green’s functions (NEGF) and Wannier functions which is both accurate and very efficient. The main novelty of the scheme compared to the Bardeen and Tersoff-Hamann approaches is that the coupling to the infinite (macroscopic) electrodes is taken into account. As an illustrating example we apply the NEGF-STM method to the Si(001)-(2×1):H surface with sub-surface P doping and discuss the results in comparison to the Bardeen and Tersoff-Hamann methods.     

First observation of F

We measured the excitation function for ¹³O + p elastic scattering to obtain data on the unknown ¹⁴F nucleus. The ground state and several low-lying excited states in ¹⁴F were observed and spin/parity assignments were made. ¹⁴F appears to be much less unstable than was predicted. We compare theoretical predictions for the ¹⁴F level scheme with the experimental results.     

Ga(III)-catalyzed cycloisomerization strategy for the synthesis of icetexane diterpenoids: total synthesis of (+/-)-salviasperanol

[reaction: see text] A general approach to the tricyclic core of the icetexane natural products via the cycloisomerization of alkynyl indenes using GaCl(3) is presented. This strategy provides an efficient synthesis of the natural product salviasperanol and sets the stage for access to other members of this family of diterpenoids.     

Stereocontrolled synthesis of trisubstituted cyclopropanes: expedient, atom-economical, asymmetric syntheses of (+)-Bicifadine and DOV21947

[reaction: see text] An expedient, atom-economical, asymmetric synthesis of 1-aryl-3-azabicyclo[3.1.0]hexanes, including (+)-Bicifadine and DOV21947, in a single-stage through process without isolation of any intermediates has been developed. The key of this synthesis is the in-depth mechanistic understanding of the complicated epoxy nitrile coupling at each reaction stage. Therefore, the desired trisubstituted cyclopropane can be prepared in high ee and yield by controlling the reaction pathway through manipulating the nitrile anion aggregation state.     

The effect of non-linear delay costs on workforce mix

This paper formulates a simple model to examine the appropriate mix of dedicated and flexible maintenance technicians (servers) required when total delay cost is a non-linear function of mean delay time. The primary decision variable is the number of flexible servers needed to minimize system-related costs. Non-linear delay costs appear to significantly increase the level of cross-training required compared with previous research using a linear cost function, which showed that a small proportion of flexible servers was sufficient. This has important implications for service system designers in regard to the amount of cross-training that might be appropriate.     

Anticrossing of spin-split subbands in quasi-one-dimensional wires

In quantum Hall systems, both anticrossings and magnetic phase transitions can occur when opposite-spin Landau levels coincide. Our results indicate that both processes are also possible in quasi-1D quantum wires in an in-plane B field, Bparallel. Crossings of opposite-spin 1D subbands resemble magnetic phase transitions at zero dc source-drain bias, but display anticrossings at high dc bias. Our data also imply that the well-known 0.7 structure may evolve into a spin-hybridized state in finite dc bias.