Univalence criteria for lifts of harmonic mappings to minimal surfaces

A general criterion in terms of the Schwarzian derivative is given for global univalence of the Weierstrass-Enneper lift of a planar harmonic mapping. Results on distortion and boundary regularity are also deduced. Examples are given to show that the criterion is sharp. The analysis depends on a generalized Schwarzian defined for conformai metrics and on a Schwarzian introduced by Ahlfors for curves. Convexity plays a central role.     

Platinum-catalyzed hydroformylation of terminal and internal octenes

A brief historic overview of Pt/Sn-catalyzed hydroformylation as well as recent advances in the hydroformylation of internal alkenes is provided. This serves as background for the results obtained with the [Pt(Sixantphos)Cl(2)] system, for which the molecular structure and the spectroscopic data are described. Insitu UV/Vis-spectroscopic studies have revealed rapid formation of the corresponding Pt-stannate complex upon reaction with SnCl(2), whereas high-pressure insitu IR-spectroscopy showed formation of a Pt-CO species and a short-lived Pt-H species under syngas, as well as rapid evolution of aldehyde product upon addition of 1-octene to the preformed catalyst in the IR autoclave. The hydroformylation of 1-octene and the i-octenes has been performed. For the internal alkenes, selective tandem isomerization/hydroformylation towards n-nonanal is observed with this catalyst system.     

Sparse hyperspectral unmixing using an approximate L0 norm

Sparse unmixing aims at finding an optimal subset of spectral signatures in a large spectral library to effectively model each pixel in the hyperspectral image and compute their fractional abundances. In most previous work concerned with the sparse unmixing, L₂ norm is used to measure the error tolerance and the L₁ norm is added as the sparsity regularization. However, in some applications, using L₁ norm to measure the error tolerance has significant robustness advantages over the L₂ norm. Besides, in some cases, using a smooth function to approximate the L₀ norm can obtain more accurate results than the L₁ norm in the field of sparse regression. Thus, in this paper, we consider the two alternative choices for sparse unmixing. A reweighted iteration algorithm is also proposed so that the unconvex regularizer (smoothed L₀ norm) can be efficiently solved through transforming it into a series of weighted L₁ regularizer problems. Experimental results on both synthetic and real hyperspectral data demonstrate the efficacy of the new models.     

The growth of a single crystal of Sr3CuIrO6 and its magnetic behavior compared to polycrystals

We have grown single crystals of the psuedo-one-dimensional compound Sr₃CuIrO₆, a K₄CdCl₆-derived monoclinic structure with Cu-Ir chains along the [101] direction. We present the ac and dc magnetization behavior of the single crystals in comparison with that of the polycrystalline form reported earlier. There is a distinct evidence for at least two magnetic transitions, at 5 K (T ₁) and 19 K (T ₂), with different relative magnitudes in the single and polycrystals. The low temperature magnetic relaxation behavior of both the forms is found to be widely different, exhibiting unexpected time dependence.     

Finite unions of interpolation sequences

A unified and relatively simple proof is given for some well-known results involving finite unions of uniformly separated sequences.