On Analytical Results for the Optimal Control of the quasi-stationary Radiative Heat Transfer System

We state an optimal control problem of the coupled quasi-stationary radiative heat equations consisting of the radiative transfer equation and the instationary heat transfer equation that model radiative-conductive heat transfer. We give an existence and uniqueness result for the state equations and the adjoint equations of the quasi-stationary radiative heat transfer system. For the optimal control problem the existence of a minimizer is proven. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nodal Solutions of a p-Laplacian Equation

We prove that the p-Laplacian problem –_p u = f(x, u),with u on a bounded domain R^N, with p > 1 arbitrary, has a nodal solution providedthat f : x R R is subcritical, and f(x, t) / |t|^p –² is superlinear. Infinitely many nodal solutions are obtainedif, in addition, f(x, –t) = –f(x, t). 2000 MathematicsSubject Classification 35J20, 35J65, 58E05.     

A New Supramolecular Assembly Formed by Melamine and Sulfuric Acid

Polymeric melaminium sulfate [(LH₂)₂(SO₄)₂]_n has been synthesized by reaction of melamine L with sulfuric acid in aqueous solution. The compound was characterized by elemental analysis, ¹H NMR, ESI MS and a single crystal X‐ray diffraction analysis. The architecture of the assembly formed is based on hydrogen bonded dimers of diprotonated melaminium cations (LH₂)²⁺ which are linked by a hydrogen bonded network with sulfate ions forming 2D sheets. A 3D polymeric structure results from the presence of mutual hydrogen bonds between sulfate ions and melaminium cations in different sheets. Significant π‐π stacking is also present between the aromatic cations in this supramolecular arrangement.     

Surface morphology of Ge‐modified 3C‐SiC/Si films

The influence of Ge deposition prior to carbon interaction with 3° off‐axis Si(111) substrates on the structural and morphological properties of the formed silicon carbide (SiC) layer is studied. In situ reflection high‐energy electron diffraction (RHEED) and X‐ray diffraction (XRD) revealed the formation of the cubic silicon carbide (3C‐SiC) modification. In situ spectroscopic ellipsometry measurements revealed a decreasing 3C‐SiC thickness with increasing Ge predeposition. Atomic force microscopy (AFM) studies revealed that the surface overlayer morphology is mainly formed by periodic step arrangements whose relevant geometric parameters, i.e. lateral separation, height and terrace width, depend on the Ge content. Besides the changes of the step morphology, the surface roughness and the grain size and the strain of the formed 3C‐SiC decreases with increasing germanium precoverage. Copyright © 2008 John Wiley & Sons, Ltd.