Kernel polynomials for the solution of indefinite and ill-posed problems

We introduce a new family of semiiterative schemes for the solution of ill-posed linear equations with selfadjoint and indefinite operators. These schemes avoid the normal equation system and thus benefit directly from the structure of the problem. As input our method requires an enclosing interval of the spectrum of the indefinite operator, based on some a priori knowledge. In particular, for positive operators the schemes are mathematically equivalent to the so-called -methods of Brakhage. In a way, they can therefore be seen as appropriate extensions of the -methods to the indefinite case. This extension is achieved by substituting the orthogonal polynomials employed by Brakhage in the definition of the -methods by appropriate kernel polynomials. We determine the rate of convergence of the new methods and establish their regularizing properties.     

Inverse relation between photocurrent and absorption layer thickness in polymer solar cells

Organic solar cells based on polymer–fullerene bulk heterojunctions were optimised with respect to the short circuit photocurrent by means of optical modelling. Due to interference effects present in the thin film multilayer device, an inverse relation between active layer thickness and photocurrent was predicted and experimentally verified. Optimised photovoltaic devices yield power conversion efficiencies of 4%. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Correlation of charge transport with structural order in highly ordered melt‐crystallized poly(3‐hexylthiophene) thin films

A series of well‐defined poly(3‐hexylthiophene)s (P3HT) of different molecular weight (MW) and high regioregularity was investigated for charge transport properties in as‐cast and melt‐crystallized films. The semicrystalline structure of the P3HT was characterized by X‐ray scattering and Atomic force microscopy. Crystallization by cooling from the melt led to a substantial increase in crystallinity and a stronger alignment of the crystals in comparison to as‐cast films. The increase in crystallinity went along with an increase in hole mobility of up to an order of magnitude as measured by the space charge limited current method. Additionally, the hole mobility depended on the long period of P3HT lamellae and consequently on the MW. In compliance with the long period, the charge carrier mobility first increased with the MW before decreasing again at the onset of chain folding. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013 , 51, 943–951     

On the correlation of pseudorandom numbers generated by inversive methods

We introduce two new types of inversive generators for pseudorandom numbers. These new methods offer several advantages over the conventional inversive generator. For instance, we establish good correlation properties of our generators that cannot be obtained for the conventional inversive generator with current methods. A new bound on character sums for finite fields is the essential technical tool for this work. Authors’ addresses: Harald Niederreiter, Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Republic of Singapore; Jo?l Rivat, Institut de Mathématiques de Luminy, Université de la Méditerranée, CNRS-UMR 6206, 163 avenue de Luminy, Case 907, 13288 Marseille Cedex 9, France