Composing and Factoring Generalized Green's Operators and Ordinary Boundary Problems

We consider solution operators of linear ordinary boundary problems with "too many" boundary conditions, which are not always solvable. These generalized Green's operators are a certain kind of generalized inverses of differential operators. We answer the question when the product of two generalized Green's operators is again a generalized Green's operator for the product of the corresponding differential operators and which boundary problem it solves. Moreover, we show that---provided a factorization of the underlying differential operator---a generalized boundary problem can be factored into lower order problems corresponding to a factorization of the respective Green's operators. We illustrate our results by examples using the Maple package IntDiffOp, where the presented algorithms are implemented.Comment: 19 page

Ab initio calculations of edge-functionalized armchair graphene nanoribbons: Structural, electronic, and vibrational effects

We present a theoretical study on narrow armchair graphene nanoribbons (AGNRs) with hydroxyl functionalized edges. Although this kind of passivation strongly affects the structure of the ribbon, a high degree of edge functionalization proves to be particularly stable. An important consequence of the geometric deviations is a severe reduction of the band-gap of the investigated 7-AGNR. This shift follows a linear dependence on the number of added hydroxyl groups per unit cell and thus offers the prospect of a tunable band-gap by edge functionalization. We furthermore cover the behavior of characteristic phonons for the ribbon itself as well as fingerprint modes of the hydroxyl groups. A large down-shift of prominent Raman active modes allows the experimental determination of the degree of edge functionalization.Comment: 6 pages, 9 figure

Scattering and bound states in two-dimensional anisotropic potentials

We propose a framework for calculating scattering and bound state properties in anisotropic two-dimensional potentials. Using our method, we derive systematic approximations of partial wave phase shifts and binding energies. Moreover, the method is suitable for efficient numerical computations. We calculate the s-wave phase shift and binding energy of polar molecules in two layers polarized by an external field along an arbitrary direction. We find that scattering depends strongly on their polarization direction and that absolute interlayer binding energies are larger than thermal energies at typical ultracold temperatures.Comment: 5 pages, 2 figure

Spectroscopic evidence for temperature-dependent convergence of light and heavy hole valence bands of PbQ (Q=Te, Se, S)

We have conducted temperature dependent Angle Resolved Photoemission Spectroscopy (ARPES) study of the electronic structures of PbTe, PbSe and PbS. Our ARPES data provide direct evidence for the \emph{light} hole upper valence bands (UVBs) and hitherto undetected \emph{heavy} hole lower valence bands (LVBs) in these materials. An unusual temperature dependent relative movement between these bands leads to a monotonic decrease in the energy separation between their maxima with increasing temperature, which is referred as band convergence and has long been believed to be the driving factor behind extraordinary thermoelectric performances of these compounds at elevated temperatures.Comment: 6 pages, 4 figures. arXiv admin note: text overlap with arXiv:1404.180

Clinical pharmacology becomes a specialty in South Africa

South Africa recently became the first African country where clinical pharmacology has been approved as a specialty. This article outlines the need for clinical pharmacologists, their role in advancing public health, the potential benefits to the country, and recommendations for ensuring a healthy future for the discipline