Real function reconstruction from sparse Fourier samples

In this paper we use the Prony method to reconstruct structured, real-valued functions from the smallest possible number of equidistantly distributed Fourier samples. In particular, we consider characteristic functions in whose supports are unit-height polygons in the plane with N vertices. We show that these functions can be recovered by 3N Fourier samples. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The stable set of associated prime ideals of a polymatroidal ideal

The associated prime ideals of powers of polymatroidal ideals are studied, including the stable set of associated prime ideals of this class of ideals. It is shown that polymatroidal ideals have the persistence property and for transversal polymatroids and polymatroidal ideals of Veronese type the index of stability and the stable set of associated ideals is determined explicitly.     

Continuous‐wave optical parametric oscillator based infrared spectroscopy for sensitive molecular gas sensing

Over the past 10 years, with the advent of new crystals designs and a new generation of pump lasers, continuous‐wave (cw) optical parametric oscillators (OPOs) have developed into mature monochromatic light sources. Nowadays, cw OPOs can fulfill a wide variety of criteria for sensitive molecular gas sensing. It can access the mid‐infrared wavelength region, where many molecules have their fundamental rotational‐vibrational transitions, with high power. This high power combined with wide wavelength tuning and narrow linewidth creates excellent conditions for sensitive, high‐resolution spectroscopy. OPOs combined with robust methods, such as photoacoustic spectroscopy and cavity‐enhanced spectroscopy, are well suited for field measurements and remote‐sensing applications. The wide tunability of cw OPOs allows detection of larger molecules with broad absorption band structures, and its fast scanning capabilities allow rapid detection of trace gases, the latter is a demand for life‐science applications. After a short introduction about the physical principle of cw OPOs, with its most recent physical developments, this review focuses on sensitive molecular gas sensing with a variety of spectroscopic applications in atmospheric and life sciences.     

A Riemann–Hilbert approach to Painlevé IV

The methods of [vdP-Sa, vdP1, vdP2] are applied to the fourth Painlevé equation. One obtains a Riemann–Hilbert correspondence between moduli spaces of rank two connections on ?¹ and moduli spaces for the monodromy data. The moduli spaces for these connections are identified with Okamoto–Painlevé varieties and the Painlevé property follows. For an explicit computation of the full group of Bäcklund transformations, rank three connections on ?¹ are introduced, inspired by the symmetric form for PIV, studied by M. Noumi and Y. Yamada.     

Accordion‐Like Motion in Electrochemically Switchable Crown Ether/Ammonium Oligorotaxanes

Reversible oxidation reactions in electrochemically switchable oligorotaxanes with tetrathiafulvalene (TTF) decorated 24‐crown‐8 ether wheels generate intramolecular mixed‐valence and radical‐cation interactions between the wheels. This induces shuttling of the wheels and a contraction of inter‐wheel distances. Further oxidation generates repulsive forces between the TTFs and maximizes the inter‐wheel distances instead. These interactions and co‐conformational changes were not observed for structurally similar controls in which acetyl groups along the axle prevent translational motion of the wheels. This operation mode of oligorotaxanes, which is reminiscent of an accordion‐like motion, is promising for functional materials and nanodevices such as piston‐type rotaxane motors.     

Performance of Pleurotus ostreatus Mushrooms and Spent Substrate for the Biosorption of Cd(II) From Aqueous Solution

The capacities of Pleurotus ostreatus mushroom and spent substrate were evaluated for the biosorption of cadmium (II) from aqueous solution in order to select the most efficient material for bioremediation. The optimum sorption conditions were optimized, including the pH of the aqueous solution, contact time, biomass dosage, initial metal concentration, and temperature. The sorption of cadmium on both biosorbents was also evaluated by several kinetic, equilibrium, and thermodynamic models. The possible heavy metal biosorption mechanisms were evaluated through point of zero charge (pH_pzc), Fourier-transform infrared (FTIR) spectroscopy and scanning electron microscopy coupled with energy dispersive X-ray microanalysis (SEM-EDX). Based on the results of column studies, the effectiveness of the P. ostreatus spent substrate was confirmed as a biosorbent for Cd(II) removal from aqueous solutions.     

Decomposition of Picolyl Radicals at High Temperature: A Mass Selective Threshold Photoelectron Spectroscopy Study

The reaction products of the picolyl radicals at high temperature were characterized by mass-selective threshold photoelectron spectroscopy in the gas phase. Aminomethylpyridines were pyrolyzed to initially produce picolyl radicals (m/z=92). At higher temperatures further thermal reaction products are generated in the pyrolysis reactor. All compounds were identified by mass-selected threshold photoelectron spectroscopy and several hitherto unexplored reactive molecules were characterized. The mechanism for several dissociation pathways was outlined in computations. The spectrum of m/z=91, resulting from hydrogen loss of picolyl, shows four isomers, two ethynyl pyrroles with adiabatic ionization energies (IE_ad) of 7.99 eV (2-ethynyl-1H-pyrrole) and 8.12 eV (3-ethynyl-1H-pyrrole), and two cyclopentadiene carbonitriles with IE′s of 9.14 eV (cyclopenta-1,3-diene-1-carbonitrile) and 9.25 eV (cyclopenta-1,4-diene-1-carbonitrile). A second consecutive hydrogen loss forms the cyanocyclopentadienyl radical with IE′s of 9.07 eV (T₀) and 9.21 eV (S₁). This compound dissociates further to acetylene and the cyanopropynyl radical (IE=9.35 eV). Furthermore, the cyclopentadienyl radical, penta-1,3-diyne, cyclopentadiene and propargyl were identified in the spectra. Computations indicate that dissociation of picolyl proceeds initially via a resonance-stabilized seven-membered ring.     

Brown HT

Journal of Thermal Analysis and Calorimetry - Thermal behavior of Brown HT food dye was studied in correlation with the physical and biological antioxidant properties. Brown HT’s structure...     

Preparation and Characterization of a π-Conjugated Donor–Acceptor System Containing the Strongly Electron-Accepting Tetraphenylborolyl Unit

A novel thiophene-bridged donor–acceptor system was synthesized with a carbazole as donor and a borole as acceptor unit. The borole group was successfully installed via the tin–boron exchange reaction of 1,1-dimethyl-2,3,4,5-tetraphenylstannole with 9-(5-(dibromoboryl)thiophen-2-yl)carbazole. The effect of the borole on the optoelectronic properties of the donor–acceptor system was explored by spectroscopic (UV/Vis and fluorescence spectroscopy), electrochemical (cyclic voltammetry) and theoretical (TD-DFT) methods as well as by modifying its structure. The corresponding donor–acceptor compound bearing the widely employed dimesitylboryl acceptor group was also synthesized for comparison.