Spanning trees with many leaves

We show that if G is a simple connected graph with and , then G has a spanning tree with > t leaves, and this is best possible. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 189–197, 2001     

Numerical indefinite integration of functions with singularities

We derive an indefinite quadrature formula, based on a theorem of Ganelius, for functions, for 1$">, over the interval . The main factor in the error of our indefinite quadrature formula is , with nodes and . The convergence rate of our formula is better than that of the Stenger-type formulas by a factor of in the constant of the exponential. We conjecture that our formula has the best possible value for that constant. The results of numerical examples show that our indefinite quadrature formula is better than Haber's indefinite quadrature formula for -functions.

     

Toward the peri‐Pentacene Framework

Based on modern pyrene chemistry, a new route toward the synthesis of the peri‐pentacene framework was developed. Firstly, the tetraketo form as stable precursor was targeted, because the fully aromatic peri‐pentacene is predicted to suffer from high instability and reactivity. Therefore, a recently developed 4,5,9,10‐tetrafunctionalization of pyrene was utilized to build up a planar and a dragonfly‐shaped derivative in five steps, which only differ in the two outer bonds between the peripheral benzene rings. The planar tetraketone could only be dissolved in strong acids upon protonation, which limited the use of analytical methods. In contrast, the dragonfly‐shaped form showed excellent organosolubility. In‐depth investigation by NMR spectroscopy revealed co‐existence of atropo‐isomers in solution. The optical and electronic properties were analyzed by UV/Vis spectroscopy and cyclic voltammetry. To approach aromatic conjugation, stepwise reduction in solution by using tetrabutylammonium borohydride was carried out. Reduced species were studied by ESR and UV/Vis spectroscopy, as well as by MALDI‐TOF MS, confirming the formation of the radical anion.     

The evolution of a finite rate periodic oscillation

Finite rate oscillations of a gas in a closed tube arise when the amplitude of the applied periodic piston velocity is small while its acceleration is unrestricted. The asymptotic form of the periodic motion for large acceleration is given. The evolution to the final periodic motion from the initial state of rest is constructed for a finite rate oscillation. Exact results for a piecewise linear piston velocity are used to illustrate the solutions.     

Work function increase of transparent conductive electrodes by solution processed electron acceptor molecular monolayers

We show how the work function of transparent conductive oxide surfaces can be increased by more than 1 eV by solution-depositing strong electron acceptor monolayers comprising tetrafluoro-tetracyanoquinodimethane (F4TCNQ) or hexaazatriphenylene-hexacarbonitrile (HATCN). The effects of ambient atmosphere on the work function are investigated by comparing Kelvin probe measurements in air and ultraviolet photoelectron spectroscopy in ultrahigh vacuum. In this way, important technological issues related to the influence of ambient moisture on electrode properties are elucidated.