Class numbers with many prime factors

Here, we construct infinitely many number fields of any given degree d>1 whose class numbers have many prime factors.     

High-sensitivity microchip electrophoresis determination of inorganic anions and oxalate in atmospheric aerosols with adjustable selectivity and conductivity detection

A sensitive and selective separation of common anionic constituents of atmospheric aerosols, sulfate, nitrate, chloride, and oxalate, is presented using microchip electrophoresis. The optimized separation is achieved in under 1 min and at low background electrolyte ionic strength (2.9 mM) by combining a metal-binding electrolyte anion (17 mM picolinic acid), a sulfate-binding electrolyte cation (19 mM HEPBS), a zwitterionic surfactant with affinity towards weakly solvated anions (19 mM N-tetradecyl,N,N-dimethyl-3-ammonio-1-propansulfonate), and operation in counter-electroosmotic flow (EOF) mode. The separation is performed at pH 4.7, permitting pH manipulation of oxalate's mobility. The majority of low-concentration organic acids are not observed at these conditions, allowing for rapid subsequent injections without the presence of interfering peaks. Because the mobilities of sulfate, nitrate, and oxalate are independently controlled, other minor constituents of aerosols can be analyzed, including nitrite, fluoride, and formate if desired using similar separation conditions. Contact conductivity detection is utilized, and the limit of detection for oxalate (S/N = 3) is 180 nM without stacking. Sensitivity can be increased with field-amplified sample stacking by injecting from dilute electrolyte with a detection limit of 19 nM achieved. The high-sensitivity, counter-EOF operation, and short analysis time make this separation well-suited to continuous online monitoring of aerosol composition.     

Über die Einwirkung der salpetrigen Säure auf die Amide der Malonsäure und ihrer Homologen

Ohne Zusammenfassung     

Novel ring-cleaving reaction of 4-nitro-1,1,2,2,9,9,10,10-octafluoro[2.2]paracyclophane with nucleophiles

When 4-nitro-AF4 is treated with nucleophiles such as alkoxides and cyanide, a novel ring opening, cyclophane destroying reaction is observed whereby, via an S_NAr mechanism, the nucleophile attacks the bridgehead aryl carbon vicinal to the nitro group with subsequent aryl-CF₂ bond cleavage.     

Adjoint sensitivity analysis of kinetic,thermochemical, and transport data of nitrogen and ammonia chemistry

Many studies apply sensitivity analysis to explore the impact of reaction kinetic parameters on model predictions. The importance of thermochemical and transport data is often assumed to be relatively low. While this is true for specific combustion properties of hydrocarbons, the role of thermochemical and transport data in combustion processes of nitrogen-containing molecules remains to be investigated. Thus, this work applies adjoint sensitivity analysis to the complete set of parameters in combustion models, i.e., kinetics, thermodynamics, and transport data. This integral approach increases the number of parameters considered in the sensitivity analysis drastically. Compared to forward sensitivity analysis, the adjoint approach is very efficient for a large number of parameters, and analysis with several thousand parameters can be performed in seconds. Nitrogen oxide formation in methane/air flames and laminar burning velocities of ammonia/air flames are considered as prediction targets. Sensitivity analysis results for kinetic, thermochemical, and transport data are compared by jointly considering all appearing parameter uncertainties. The comparison reveals that, due to their importance for the equilibrium constants of elementary reactions, the optimization potential of thermodynamic properties is often similarly high as that of the kinetics parameters. Transport parameters are found to be of the lowest priority for the model development due to their low uncertainties, even though high sensitivities are determined for several of them. More specifically, the analysis for the laminar burning velocities of ammonia/air flames reveals a high optimization potential for parameters in the N₂-amine chemistry, including the molar heat capacities of N₂H₂, N₂H₃, and NH. Interestingly, analyses with different mechanisms reveal strongly diverging results, especially regarding the importance of reactions with OH, which is uncommon when considering the combustion of hydrocarbons.     

Imines in the Titanium Coordination Sphere – Transformation of Imidoyl Chlorides to Nitrilium Ions

In the reaction of TiCl₄ in benzene as solvent with the imidoyl chloride p‐Tolyl(Cl)C=NPh ( 1 ) the abstraction of the chloride substituent is observed, leading to the nitrilium salt [p‐Tolyl–C≡N–Ph]⁺[Ti₂Cl₉]^– ( 2 ) in quantitative yield. The highly electrophilic salt 2 is characterized by IR‐ and NMR spectroscopy. The observed band for the C≡N stretching mode of 2 clearly indicates the formation of a nitrilium ion. Especially a characteristic line broadening of the ¹³C{¹H}‐NMR signals related to carbon atoms next to the nitrogen is observed. By ¹⁵N,¹H‐HMBC NMR experiments it is shown that the nitrogen signal of 2 is significantly shifted to high‐field in relation to nitriles and imines. The molecular structure of 2 was confirmed by single‐crystal X‐ray diffraction. The C≡N bond length and the linearity of the C–C≡N–C unit in 2 confirm the triple bond character of this bond.     

Correlation between Dynamic Heterogeneity and Local Structure in a Room‐Temperature Ionic Liquid: A Molecular Dynamics Study of [bmim][PF6]

The complex dynamics of a room‐temperature ionic liquid, 1‐n‐butyl‐3‐methylimidazolium hexafluorophosphate ([bmim][PF₆]), is studied using equilibrium classical molecular dynamics simulations in the temperature range of 250–450 K. The activation energies for the self‐diffusion of ions are around 30–34 kJ mol^?1, with that of the anion a little higher than that for the cation. The electrical conductivity of the liquid is calculated and good agreement with experiments is obtained. Structural relaxation is studied through the decay of coherent (total density–density correlation) and incoherent (self part of density–density correlation) intermediate scattering functions over a range of temperatures and wave vectors relevant to the system. The relaxation data are used to identify and characterize two processes, α and β. The dependence of the two relaxation times on temperature and wave vector is obtained. The dynamical heterogeneity of the ions determined through the non‐Gaussian parameter indicates the motion of the cation to be more heterogeneous than that of the anion. The faster ones among the cations are coordinated to faster anions, while slower cations are surrounded predominantly by slower anions. Thus, the dynamical heterogeneity in this ionic liquid is shown to have structural signatures.     

Mean-field pairing theory for the charge-stripe phase of high-temperature cuprate superconductors

Striped high-T(c) superconductors such as La(2-y-x)Nd(y)Sr(x)CuO(4) and La(2-x)Ba(x)CuO(4) near x = 1/8 show a fascinating competition between spin and charge order and superconductivity. A theory for these systems therefore has to capture both the spin correlations of an antiferromagnet and the pair correlations of a superconductor. For this purpose we present here an effective Hartree-Fock theory incorporating both electron pairing with finite center-of-mass momentum and antiferromagnetism. We show that this theory reproduces the key experimental features such as the formation of the antiferromagnetic stripe patterns at 7/8 band filling or the quasi-one-dimensional electronic structure observed by photoemission spectroscopy.