Wiener-hopf equations for waves scattered by a system of parallel sommerfeld half-planes

A scalar time-harmonic wave (governed by Helmholtz's equation) impinges on N semi-infinite half-planes. The scattered field is sought when first, second, and third-kind boundary conditions or even general linear transmission conditions on the plates ∑_m and their complementary parts ∑ are prescribed. Making use of the Fourier transform a representation formula for H¹ (Ω) solutions is presented. The boundary/transmission problem is shown to be equivalent to a (2N × 2N)-Wiener–Hopf (WH) system for jumps of the Dirichlet–and Neumann–Cauchy data across the semi-infinite screens ∑_m. The (2N × 2N)-Fourier symbol matrix ??_?? contains N block matrices on the diagonal corresponding to Sommerfeld boundary/transmission problems for a single plate. These (2 × 2)-symbol matrices are factorizable and thus the full WH system is invertible by a perturbation argument for not too small spacings of neighbouring screens ∑_m.     

Functionalization of bolalipid nanofibers by silicification and subsequent one-dimensional fixation of gold nanoparticles

In the present work, we describe the successful stabilization of bolalipid nanofibers by sol-gel condensation (silicification) of tetraethoxysilane (TEOS) or 3-mercaptopropyltriethoxysilane (MP-TEOS), respectively, onto the nanofibers. The conditions for an effective and reproducible silicification reaction were determined, and the silicification process was pursued by transmission electron microscopy (TEM). The resulting bolalipid-silica composite nanofibers were characterized by means of differential scanning calorimetry (DSC), TEM, (13)C, and (31)P NMR spectroscopy. Finally, the novel silicified bolalipid nanofibers were used as templates for the fixation of 5 and 2 nm AuNPs, respectively, resulting in one of the rare examples of one-dimensional AuNP arrangements in aqueous suspension.     

Random forests for functional covariates

We propose a form of random forests that is especially suited for functional covariates. The method is based on partitioning the functions' domain in intervals and using the functions' mean values across those intervals as predictors in regression or classification trees. This approach appears to be more intuitive to applied researchers than usual methods for functional data, while also performing very well in terms of prediction accuracy. The intervals are obtained from randomly drawn, exponentially distributed waiting times. We apply our method to data from Raman spectra on boar meat as well as near‐infrared absorption spectra. The predictive performance of the proposed functional random forests is compared with commonly used parametric and nonparametric functional methods and with a nonfunctional random forest using the single measurements of the curve as covariates. Further, we present a functional variable importance measure, yielding information about the relevance of the different parts of the predictor curves. Our variable importance curve is much smoother and hence easier to interpret than the one obtained from nonfunctional random forests.     

Synthese und spektroskopische Charakterisierung einiger Pentacarbonylwolfram(0)-Komplexe mit verschiedenen 1H-Phosphiren-Liganden,Kristallstrukturen von,und

Synthesis and Spectroscopic Characterization of some Pentacarbonyltungsten(0) Complexes with Various 1H-Phosphirene Ligands: Crystal Structures of , and The tungsten(0) complex 1 reacts upon heating with acetylene derivatives 2a–f in toluene to form benzonitrile and the complexes 4a–f ( 4a : R¹ ? Ph, R² ? H; 4b : R¹ ? Ph, R² ? CH₃; 4c : R¹ ? OEt, R² ? H; 4d : R¹ ? Ph, R² ? CO₂Et; 4e : R¹, R² ? CO₂Me; 4f : R¹, R² ? SiMe₃), which have been isolated by chromatography. Spectroscopic and mass spectrometric data are discussed. The crystal structures of the compounds 4a, b and d were determined by X-ray single crystal structure analysis ( 4a : space group P2₁/n, Z = 4, a = 937,5(2) pm, b = 2202,4(6) pm, c = 1266,3(4) pm, β = 108,94(4)°; 4b : space group P2₁/c, Z = 4, a = 1293,9(2) pm, b = 923,5(1) pm, c = 2223,4(3) pm, β = 92,385(6)°; 4d : space group P2₁/c, Z = 4, a = 955,2(2) pm, b = 3190,9(4) pm, c = 930,7(2) pm, β = 99,64(1)°).     

Analysing fluorobenzoate tracers in groundwater samples using liquid chromatography-tandem mass spectrometry. A tool for leaching studies and hydrology

A sensitive LC-MS-MS method for the direct determination and quantification of 15 fluorobenzoic acids (FBAs) was developed. FBAs are used as conservative tracers for hydrological modelling of water flow and in studies of pesticides and other xenobiotic compounds. The use of FBAs is discussed in relation to other tracers (bromide, chloride, uranine). The method covers mono-substituted fluorobenzoic acid, difluorobenzoic acid, trifluorobenzoic acid, and tetrafluorobenzoic acid. The general detection limit in ground water was 1 microg/l using electrospray ionisation and 20 microg/l using atmospheric pressure chemical ionisation. Analysis time was less than 10 min, small sample volumes were needed and no clean-up was required.