On the order of a derivation

In this note we provide the solution to a problem posed by the first author in a previous paper. In particular, we prove a result relating the number of nonzero coefficients of a certain functional equation to the order of any derivation satisfying that equation.     

Fluorescence Nanoscopy with Optical Sectioning by Two‐Photon Induced Molecular Switching using Continuous‐Wave Lasers

During the last decade far‐field fluorescence microscopy methods have evolved that have resolution far below the wavelength of light. To outperform the limiting role of diffraction, all these methods, in one way or another, switch the ability of a molecule to emit fluorescence. Here we present a novel rhodamine amide that can be photoswitched from a nonfluorescent to a fluorescent state by absorption of one or two photons from a continuous‐wave laser beam. This bright marker enables strict control of on/off switching and provides single‐molecule localization precision down to 15 nm in the focal plane. Two‐photon induced nonlinear photoswitching of this marker with continuous‐wave illumination offers optical sectioning with simple laser equipment. Future synthesis of similar compounds holds great promise for cost‐effective fluorescence nanoscopy with noninvasive optical sectioning.     

Synthetic, structural, electrochemical and solvent extraction studies of neutral trinuclear Co(II), Ni(II), Cu(II) and Zn(II) metallocycles and tetrahedral tetranuclear Fe(III) species incorporating 1,4-aryl-linked bis-beta-diketonato ligands

Uncharged complexes, formulated as trimeric metallocycles of type [M3(L(1))3(Py)6] (where M = cobalt(II), nickel(II) and zinc(II) and L(1) is the doubly deprotonated form of a 1,4-phenylene linked bis-beta-diketone ligand of type 1,4-bis(RC(O)CH2C(O))C6H4 (R = t-Bu)) have been synthesised, adding to related, previously reported complexes of these metals with L(1) (R = Ph) and copper(ii) with L(1) (R = Me, Et, Pr, t-Bu, Ph). New lipophilic ligand derivatives with R = hexyl, octyl or nonyl were also prepared for use in solvent extraction experiments. The X-ray structures of H2L(1) (R = t-Bu) and of its trinuclear (triangular) nickel(II) complex [Ni3(L(1))3(Py)6].3.5Py (R = t-Bu) are also presented. Electrochemical studies of H2L(1), [Co3(L(1))3(Py)6], [Ni3(L(1))3(Py)6], [Cu3(L(1))3], [Zn3(L(1))3(Py)6] and [Fe4(L(1))6] (all with R = t-Bu) show that oxidative processes for the complexes are predominantly irreversible, but several examples of quasireversible behaviour also occur and support the assignment of an anodic process, seen between +1.0 and +1.6 V, as involving metal-centred oxidations. The reduction behaviour for the respective metal complexes is not simple, being irreversible in most cases. Solvent extraction studies (water/chloroform) involving the systematic variation of the metal, bis-beta-diketone and heterocyclic base concentrations have been performed for cobalt(II) and zinc(II) using a radiotracer technique in order to probe the stoichiometries of the respective extracted species. Significant extraction synergism was observed when 4-ethylpyridine was also present with the bis-beta-diketone ligand in the chloroform phase. Competitive extraction studies demonstrated a clear uptake preference for copper(II) over cobalt(II), nickel(II), zinc(II) and cadmium(II).     

Automated modular preparative HPLC-MS purification laboratory with enhanced efficiency

Automated parallel synthesis as tool to increase productivity in chemical synthesis is well-established. However, even more time-consuming than the synthesis process is the following purification of the resulting crude products. To enhance efficiency of the lead optimization process at Bayer CropScience, a high-throughput HPLC/MS-laboratory for the purification of up to 48 crude products per day in the range of 200-400 mg each in one injection per sample has been set up. The use of Covaris technology for HPLC sample preparation, automated aliquotation during fractionation, and a novel evaporation process by combination with freeze-drying are new key technologies applied successfully for the first time in this purification unit facilitating to achieve the targeted efficiency. The whole process is supported by a specially designed IT-landscape covering each step of the workflow. Both the technical instruments used within the laboratory and the workflow and IT platform are described in this article.     

Analysis of amino acids without derivatization in barley extracts by LC-MS-MS

A method has been developed for quantification of 20 amino acids as well as 13 (15)N-labeled amino acids in barley plants. The amino acids were extracted from plant tissues using aqueous HCl-ethanol and directly analyzed without further purification. Analysis of the underivatized amino acids was performed by liquid chromatography (LC)-electrospray ionization (ESI) tandem mass spectrometry (MS-MS) in the positive ESI mode. Separation was achieved on a strong cation exchange column (Luna 5micro SCX 100A) with 30 mM ammonium acetate in water (solvent A) and 5% acetic acid in water (solvent B). Quantification was accomplished using d (2)-Phe as an internal standard. Calibration curves were linear over the range 0.5-50 microM, and limits of detection were estimated to be 0.1-3.0 microM. The mass-spectrometric technique was employed to study the regulation of amino acid levels in barley plants grown at 15 degrees C uniform root temperature (RT) and 20-10 degrees C vertical RT gradient (RTG). The LC-MS-MS results demonstrated enhanced concentration of free amino acids in shoots at 20-10 degrees C RTG, while total free amino acid concentration in roots was similarly low for both RT treatments. (15)NO(3) (-) labeling experiments showed lower (15)N/(14)N ratios for Glu, Ser, Ala and Val in plants grown at 20-10 degrees C RTG compared with those grown at 15 degrees C RT.     

ADSA-TRIS: a new method to study interfacial phenomena at polymer–aqueous solution interfaces

Axisymmetric drop shape analysis-profile (ADSA-P) was combined with total reflectometric interference spectroscopy (TRIS) in one experimental setup to study the interfacial phenomena at solid–liquid and liquid–vapor interfaces caused by adsorption/desorption (dissolution) of surface-active substances. Using sessile liquid droplets on polymer film/chromium-coated glass substrates that were optically matched with an immersion oil to a TRIS reflection prism, the optical thickness (product of physical thickness d and refractive index n) of the polymer film can be estimated by evaluating the wavelength-dependent intensity of reflected light. The sessile droplet is analyzed simultaneously by an ADSA setup arranged in a transverse direction to the path of the white-light beam of TRIS. From this analysis, the solid–vapor interfacial tension γ _lv(t), contact angle θ(t), contact radius r(t), drop volume V(t), and solid–liquid interfacial tension γ _sl(t) can be monitored as a function of time. The new method was applied to study polystyrene and poly(4-hydroxystyrene) surfaces in contact with aqueous buffer solutions and with protein solutions. The time-dependent changes in the optical film thickness caused by the adsorption of human serum albumin (HSA) and lysozyme (LSZ) were accompanied by changes in the solid–liquid interfacial tension. From the detailed study of both parameters, conclusions can be drawn with regard to the adsorption kinetics of the proteins on the hydrophobic polystyrene surfaces and to conformational changes occurring within the adsorbed protein layers. Figure Photo of the ADSA-TRIS setup     

Mesoscale simulation of concrete spall failure

Although intensively studied, it is still being debated which physical mechanisms are responsible for the increase of dynamic strength and fracture energy of concrete observed at high loading rates, and to what extent structural inertia forces on different scales contribute to the observation. We present a new approach for the three dimensional mesoscale modelling of dynamic damage and cracking in concrete. Concrete is approximated as a composite of spherical elastic aggregates of mm to cm size embedded in an elastic cement stone matrix. Cracking within the matrix and at aggregate interfaces in the μm range are modelled with adaptively inserted—initially rigid—cohesive interface elements. The model is applied to analyse the dynamic tensile failure observed in Hopkinson-Bar spallation experiments with strain rates up to 100/s. The influence of the key mesoscale failure parameters of strength, fracture energy and relative weakening of the ITZ on macromechanic strength, momentum and energy conservation is numerically investigated.     

Exploring new 129Xe chemical shift ranges in HXeY compounds: hydrogen more relativistic than xenon

Among rare gases, xenon features an unusually broad nuclear magnetic resonance (NMR) chemical shift range in its compounds and as a non-bonded Xe atom introduced into different environments. In this work we show that (129)Xe NMR chemical shifts in the recently prepared, matrix-isolated xenon compounds appear in new, so far unexplored (129)Xe chemical shift ranges. State-of-the-art theoretical predictions of NMR chemical shifts in compounds of general formula HXeY (Y = H, F, Cl, Br, I, -CN, -NC, -CCH, -CCCCH, -CCCN, -CCXeH, -OXeH, -OH, -SH) as well as in the recently prepared ClXeCN and ClXeNC species are reported. The bonding situation of Xe in the studied compounds is rather different from the previously characterized cases as Xe appears in the electronic state corresponding to a situation with a low formal oxidation state, between I and II in these compounds. Accordingly, the predicted (129)Xe chemical shifts occur in new NMR ranges for this nucleus: ca. 500-1000 ppm (wrt Xe gas) for HXeY species and ca. 1100-1600 ppm for ClXeCN and ClXeNC. These new ranges fall between those corresponding to the weakly-bonded Xe(0) atom in guest-host systems (δ < 300 ppm) and in the hitherto characterized Xe molecules (δ > 2000 ppm). The importance of relativistic effects is discussed. Relativistic effects only slightly modulate the (129)Xe chemical shift that is obtained already at the nonrelativistic CCSD(T) level. In contrast, spin-orbit-induced shielding effects on the (1)H chemical shifts of the H1 atom directly bonded to the Xe center largely overwhelm the nonrelativistic deshielding effects. This leads to an overall negative (1)H chemical shift in the range between -5 and -25 ppm (wrt CH(4)). Thus, the relativistic effects induced by the heavy Xe atom appear considerably more important for the chemical shift of the neighbouring, light hydrogen atom than that of the Xe nucleus itself. The predicted NMR parameters facilitate an unambiguous experimental identification of these novel compounds.     

Oligonuclear Molecular Models of Intermetallic Phases: A Case Study on [Pd2Zn6Ga2(Cp*)5(CH3)3]

The synthesis, characterization, and theoretical investigation by means of quantum‐chemical calculations of an oligonuclear metal‐rich compound are presented. The reaction of homoleptic dinuclear palladium compound [Pd₂(μ‐GaCp*)₃(GaCp*)₂] with ZnMe₂ resulted in the formation of unprecedented ternary Pd/Ga/Zn compound [Pd₂Zn₆Ga₂(Cp*)₅(CH₃)₃] ( 1 ), which was analyzed by ¹H and ¹³C NMR spectroscopy, MS, elemental analysis, and single‐crystal X‐ray diffraction. Compound 1 consisted of two C_s‐symmetric molecular isomers, as revealed by NMR spectroscopy, at which distinct site‐preferences related to the Ga and Zn positions were observed by quantum‐chemical calculations. Structural characterization of compound 1 showed significantly different coordination environments for both palladium centers. Whilst one Pd atom sat in the central of a bi‐capped trigonal prism, thereby resulting in a formal 18‐valence electron fragment, {Pd(ZnMe)₂(ZnCp*)₄(GaMe)}, the other Pd atom occupied one capping unit, thereby resulting in a highly unsaturated 12‐valence electron fragment, {Pd(GaCp*)}. The bonding situation, as determined by atoms‐in‐molecules analysis (AIM), NBO partial charges, and molecular orbital (MO) analysis, pointed out that significant Pd? Pd interactions had a large stake in the stabilization of this unusual molecule. The characterization and quantum‐chemical calculations of compound 1 revealed distinct similarities to related M/Zn/Ga Hume–Rothery intermetallic solid‐state compounds, such as Ga/Zn‐exchange reactions, the site‐preferences of the Zn/Ga positions, and direct M? M bonding, which contributes to the overall stability of the metal‐rich compound.