Nested Cantor sets

We give sufficient conditions for two Cantor sets of the line to be nested for a positive set of translation parameters. This problem occurs in diophantine approximations. It also occurs as a toy model of the parameter selection for non-uniformly hyperbolic attractors of the plane. For natural Cantors sets, we show that this condition is optimal.     

Testing an alternative search algorithm for compound identification with the ‘Wiley Registry of Tandem Mass Spectral Data,MSforID’

A tandem mass spectral database system consists of a library of reference spectra and a search program. State‐of‐the‐art search programs show a high tolerance for variability in compound‐specific fragmentation patterns produced by collision‐induced decomposition and enable sensitive and specific ‘identity search’. In this communication, performance characteristics of two search algorithms combined with the ‘Wiley Registry of Tandem Mass Spectral Data, MSforID’ (Wiley Registry MSMS, John Wiley and Sons, Hoboken, NJ, USA) were evaluated. The search algorithms tested were the MSMS search algorithm implemented in the NIST MS Search program 2.0g (NIST, Gaithersburg, MD, USA) and the MSforID algorithm (John Wiley and Sons, Hoboken, NJ, USA). Sample spectra were acquired on different instruments and, thus, covered a broad range of possible experimental conditions or were generated in silico. For each algorithm, more than 30 000 matches were performed. Statistical evaluation of the library search results revealed that principally both search algorithms can be combined with the Wiley Registry MSMS to create a reliable identification tool. It appears, however, that a higher degree of spectral similarity is necessary to obtain a correct match with the NIST MS Search program. This characteristic of the NIST MS Search program has a positive effect on specificity as it helps to avoid false positive matches (type I errors), but reduces sensitivity. Thus, particularly with sample spectra acquired on instruments differing in their setup from tandem‐in‐space type fragmentation, a comparably higher number of false negative matches (type II errors) were observed by searching the Wiley Registry MSMS. Copyright © 2013 John Wiley & Sons, Ltd.     

Surface Properties of Anatase TiO2 Nanowire Films Grown from a Fluoride‐Containing Solution

Controlling the surface chemistry of nucleating seeds during wet‐chemical synthesis allows for the preparation of morphologically well‐defined nanostructures. Synthesis conditions play a key role in the surface properties, which directly affect the functional properties of the material. Therefore, it is important to establish post‐synthesis treatments to facilitate the optimization of surface properties with respect to a specific application, without losing the morphological peculiarity of the nanostructure. We studied the surface properties of highly crystalline and porous anatase TiO₂ nanowire (NW) electrodes, grown by chemical‐bath deposition in fluoride‐containing solutions, using a combined electrochemical and spectroscopic approach. As‐deposited films showed low capacity for catechol adsorption and a poor photoelectrocatalytic activity for water oxidation. Mild thermal annealing at 200 °C resulted in a significant improvement of the electrode photoelectrocatalytic activity, whereas the bulk properties of the NWs (crystal structure, band‐gap energy) remained unchanged. Enhancement of the functional properties of the material is discussed on the basis of adsorption capacity and electronic properties. The temperature‐induced decrease of recombination centers, along with the concomitant increase of adsorption and reaction sites upon thermal annealing are called to be responsible for such improved performance.     

Separation of 9 Sulfonamide Drugs in ≈4 Min by Ultra-High Performance Supercritical Fluid Chromatography (UHPSFC): with a Feasibility Study for Detection in Milk

Nine widely used veterinary sulfonamide drugs were baseline separated (R _s ≥1.5) in just over 4 min using a 3 × 100 mm, 1.8 μm RX-Sil column, with 9.2 % methanol in carbon dioxide, at 110 bar and 30 °C, with direct UV detection at 260 nm using a 3 mm, 2 μL tapered flow cell. Pressure drop was only 172 bar. Optimization was difficult due to the similarity in structures. Small changes in modifier concentration, temperature and pressure, each tended to improve the resolution of some peak pairs but degraded the resolution of others. There were four critical pairs, each responding differently to changes in conditions. Optimization was performed by plotting resolution between pairs as a function of modifier concentration first, temperature second, and outlet pressure third. Retention time was then minimized by changing flow rate. The estimated limit of quantitation (LOQ, S/N >10), for direct injections, was ≈200–400 ng/g of each, inadequate for regulatory requirements. Solid phase extraction (SPE) attempted to pre-concentrate samples spiked with sulfamethazine by ≈20:1. From water, the limit of detection (LOD) was ≈2.7 ng/mL with LOQ ≈9 ng/mL using UV at 260 nm. The LOD for milk was 6.2 ng/mL, and LOQ was 20.1 ng/mL. A better pre-concentration step or a more sensitive detector such as MS–MS is required. Even with these inadequacies, SFC was shown to be a feasible, faster, “greener” alternative to HPLC for the separation of these drugs.     

An Anionic Amido-Substituted Seven-Vertex Siliconoid Cluster

The silanide [Si₄{N(SiMe₃)Dipp}₃]⁻ ( 1 ) transforms into the anionic siliconoid cluster [Si₇{N(SiMe₃)Dipp}₃]⁻ ( 2 ) with four unsubstituted silicon atoms as a contact ion pair with [K([18]crown-6)] in C₆D₆ at room temperature within five weeks. Anion 2 was investigated by natural population analysis and visualization of intrinsic atomic orbitals. Magnetically induced current-density calculations of 2 revealed two distinct strong diatropic vortices that sum up in one direction and create a strongly shielded apical silicon atom in 2 .     

Para-Fluorination of Anilides Using Electrochemically Generated Hypervalent Iodoarenes

The para-selective fluorination reaction of anilides using electrochemically generated hypervalent ArIF₂ is reported, with Et₃N ⋅ 5HF serving as fluoride source and as supporting electrolyte. This electrochemical reaction is characterized by a simple set-up, easy scalability and affords a broad variety of fluorinated anilides from easily accessible anilides in good yields up to 86 %.     

Enantioselective Synthesis of Acyclic Orthogonally Functionalized Compounds Bearing a Quaternary Stereocenter Using Chiral Ammonium Salt Catalysis

We herein report an asymmetric protocol to access a series of orthogonally functionalized acyclic chiral target molecules containing a quaternary stereogenic center by carrying out the enantioselective α-alkylation of novel orthogonally functionalized dioxolane-containing cyanoacetates under chiral ammonium salt catalysis. By using just 1 mol % of Maruoka's spirocyclic ammonium salt catalysts enantioselectivities up to e.r.=97.5 : 2.5 could be achieved and further functional group manipulations of the products were carried out as well.     

Spin precession and avalanches

In many magnetic materials, spin dynamics at short times are dominated by precessional motion as damping is relatively small. We describe how avalanches evolve under these conditions. The growth front is spread out over a large region and consists of rapidly fluctuating spins often above the ferromagnetic transition temperature. In the limit of no damping the system will transition to an ergodic state if the initial instability is large enough, but otherwise can die out. This dynamic nucleation phenomenon is analyzed theoretically and the implications for real materials are discussed.