Defects in oxygen-depleted titanate nanostructures

The identification of defects and their controlled generation in titanate nanostructures is a key to their successful application in photoelectronic devices. We comprehensively explored the effect of vacuum annealing on morphology and composition of Na(2)Ti(3)O(7) nanowires and protonated H(2)Ti(3)O(7) nanoscrolls using a combination of scanning electron microscopy, Auger and Fourier-transform infrared (FT-IR) spectroscopy, as well as ab initio density functional theory (DFT) calculations. The observation that H(2)Ti(3)O(7) nanoscrolls are more susceptible to electronic reduction and annealing-induced n-type doping than Na(2)Ti(3)O(7) nanowires is attributed to the position of the conduction band minimum. It is close to the vacuum level and, thus, favors the Fermi level-induced compensation of donor states by cation vacancies. In agreement with theoretical predictions that suggest similar formation energies for oxygen and sodium vacancies, we experimentally observed the annealing induced depletion of sodium from the surface of the nanowires.     

Preparation of CoNi high surface area porous foams by substrate controlled electrodeposition

We demonstrate that nanofabrication of 3D dendritic CoNi alloy foams with an open porous structure can be achieved by electrodeposition onto a single-crystalline Cu(111) substrate at ambient conditions. The very low wettability of this substrate caused by its low surface energy allows tailoring the CoNi deposit morphology. This is concluded from a comparison of polycrystalline Cu substrates with single-crystalline ones of different orientations. The advantages of the present CoNi alloy foams are low internal stresses and good mechanical stability on the substrate. In a second step, by comparing the catalytic properties of the achieved foam with those of CoNi layers obtained on polycrystalline Cu substrates, it is shown that the morphology of the CoNi layers has a decisive influence on the kinetics of the surface redox reaction. The higher reaction rate makes the open foam suitable as catalyst for oxygen evolution in electrolysers. The reversibility of the redox process provides great potential for the achieved porous layers to be used as positive material in alkaline batteries.     

Hedging lookback and partial lookback options using Malliavin calculus

The paper considers a Black and Scholes economy with constant coefficients. A contingent claim is said to be simple if the payoff at maturity is a function of the value of the underlying security at maturity. To replicate a simple contingent claim one uses so called delta-hedging, and the well-known strategy is derived from Itô calculus and the theory of partial differentiable equations. However, hedging path-dependent options require other tools since the price processes, in general, no longer have smooth stochastic differentials. It is shown how Malliavin calculus can be used to derive the hedging strategy for any kind of path-dependent options, and in particular for lookback and partial lookback options.     

On a generalization of Jentzsch’s theorem

Let E be a compact subset of with connected, regular complement and let G(z) denote Green’s function of Ω with pole at ∞. For a sequence (p_n)_nΛ of polynomials with degp_n=n, we investigate the value-distribution of p_n in a neighbourhood U of a boundary point z₀ of E if G(z) is an exact harmonic majorant of the subharmonic functions

in . The result holds for partial sums of power series, best polynomial approximations, maximally convergent polynomials and can be extended to rational functions with a bounded number of poles.     

1,3,5-Triamino-1,3,5-trideoxy-cis-inositol,a New Ligand with a Remarkable Versatility for Metal Ions. Part 2. Safe and efficient ligand preparation and structure of the free ligand and the CoIII complex

A new, convenient, and safe route to 1,3,5-triamino-1,3,5-trideoxy-cis-inositol (taci) was investigated by hydrogenation of azo-coupled derivatives of phloroglucinol. In the presence of acetic anhydride, the reduction of trisphenylazophloroglucinol (H₂/Pd(5%) on C) resulted in the formation of tri-, hexa-, and nona-acetylated derivatives of triaminophloroglucinol. All three compounds are air-stable, colorless solids. However, the succeeding hydrogenation to the cyclohexane derivative failed. Trisodiumtris(p-sulfonatophenylazo)phloroglucinol could be hydrogenated in a one-pot reaction to the desired taci· 1.5H₂SO₄ using a Pt/Rh oxide as catalyst. taci provides two distinct chair conformations with either three amino or three hydroxy groups for metal binding. The unique metal-binding properties are discussed in terms of minimal conformational changes required for coordination. Conformational analysis, based on X-ray structural data of [BiCl₆][H₃(taci)] ·2 H₂O (Pnma, a = 24.314 (5) Å, b = 10.215 (2) Å, c = 7.422 (8) Å, R = 5.8%) and [Co(taci)₂(NO₃)₃]·2H₂O (C2/c, a = 22.912 (8) Å, b = 8.942 (2) Å, c = 14.731 (3) Å, β = 128.66 (2)°, R = 4.9%) and the previously investigated [Cr(taci)₂]³⁺ revealed an almost ideal chair conformation in all three molecules.     

Permutable pairs of quasi-uniformities

We continue investigating the lattice (q(X),⊆) of quasi-uniformities on a set X. In particular in this article we start investigating permutable pairs of quasi-uniformities. Among other things, we show that the Pervin quasi-uniformity of a topological space X permutes with its conjugate if and only if X is normal and extremally disconnected.