Fast inversion of matrices arising in image processing

In recent years, new nonlinear partial differential equation (PDE) based approaches have become popular for solving image processing problems. Although the outcome of these methods is often very promising, their actual realization is in general computationally intensive. Therefore, accurate and efficient schemes are needed. The aim of this paper is twofold. First, we will show that the three dimensional alignment problem of a histological data set of the human brain may be phrased in terms of a nonlinear PDE. Second, we will devise a fast direct solution technique for the associated structured large systems of linear equations. In addition, the potential of the derived method is demonstrated on real-life data. This revised version was published online in June 2006 with corrections to the Cover Date.     

Multifunctional,Defect‐Engineered Metal–Organic Frameworks with Ruthenium Centers: Sorption and Catalytic Properties

A mixed‐linker solid‐solution approach was employed to modify the metal sites and introduce structural defects into the mixed‐valence Ru^II/III structural analogue of the well‐known MOF family [M₃^II,II(btc)₂] (M=Cu, Mo, Cr, Ni, Zn; btc=benzene‐1,3,5‐tricarboxylate), with partly missing carboxylate ligators at the Ru₂ paddle‐wheels. Incorporation of pyridine‐3,5‐dicarboxylate (pydc), which is the same size as btc but carries lower charge, as a second, defective linker has led to the mixed‐linker isoreticular derivatives of Ru‐MOF, which display characteristics unlike those of the defect‐free framework. Along with the creation of additional coordinatively unsaturated sites, the incorporation of pydc induces the partial reduction of ruthenium. Accordingly, the modified Ru sites are responsible for the activity of the “defective” variants in the dissociative chemisorption of CO₂, the enhanced performance in CO sorption, the formation of hydride species, and the catalytic hydrogenation of olefins.     

H2S Dosimetry by CuO: Towards Stable Sensors by Unravelling the Underlying Solid-State Chemistry

The precise detection of the toxic gas H₂S requires reliable sensitivity and specificity of sensors even at minute concentrations of as low as 10 ppm, the value corresponding to typical exposure limits. CuO can be used for H₂S dosimetry, based on the formation of conductive CuS and the concomitant significant increase in conductance. In theory, at elevated temperature the reaction is reversed and CuO is formed, ideally enabling repeated and long-term use of one sensor. Yet, the performance of CuO tends to drop upon cycling. Utilizing defined CuO nanorods we thoroughly elucidated the associated detrimental chemical changes directly on the sensors, by Raman and electron microscopy analysis of each step during sensing (CuO→CuS) and regeneration (CuS→CuO) cycles. We find the decrease in the sensing performance is mainly caused by the irreversible formation of CuSO₄ during regeneration. The findings allowed us to develop strategies to reduce CuSO₄ formation and thus to substantially maintain the sensing stability even for repeated cycles. We achieved CuO-based dosimeters possessing a response time of a few minutes only, even for 10 ppm H₂S, and prolonged life-time.