Tensor products and dimensions of simple modules for symmetric groups

LetK be an algebraically closed field of characteristic,p>0 and letD ^λ be the simple modules of the symmetric groupS _r overK where λ is a p-regular partition ofr. The dimensions ofD ^λ for λ with at mostn parts are the same as the multiplicities of direct summands ofD ^⊗r whereE is the natural module for the groupGL _n (K). Whenn=2 we determine generating functions for these multiplicities and hence for the dimensions ofD ^λ for all partitions λ with two parts. These can be expressed as rational functions of Chebyshev polynomials; and we obtain explicit formulae for the coefficients.     

Theoretical and computational aspects of scattering from rough surfaces: one-dimensional perfectly reflecting surfaces

We discuss the scattering of acoustic or electromagnetic waves from one-dimensional rough surfaces. We restrict the discussion in this report to perfectly reflecting Dirichlet surfaces (TE polarization). The theoretical development is for both infinite and periodic surfaces, the latter equations being derived from the former. We include both derivations for completeness of notation. Several theoretical developments are presented. They are characterized by integral equation solutions for the surface current or normal derivative of the total field. All the equations are discretized to a matrix system and further characterized by the sampling of the rows and columns of the matrix which is accomplished in either coordinate space (C) or spectral space (S). The standard equations are referred to here as CC equations of either the first (CC1) or second kind (CC2). Mixed representation, or SC-type, equations are solved as well as SS equations fully in spectral space.

Computational results are presented for scattering from various periodic surfaces. The results include examples with grazing incidence, a very rough surface and a highly oscillatory surface. The examples vary over a parameter set which includes the geometrical optics regime, physical optics or resonance regime, and a renormalization regime.

The objective of this study was to determine the best computational method for these problems. Briefly, the SC method was the fastest, but it did not converge for large slopes or very rough surfaces for reasons we explain. The SS method was slower and had the same convergence difficulties as SC. The CC methods were extremely slow but always converged. The simplest approach is to try the SC method first. Convergence, when the method works, is very fast. If convergence does not occur with SC, then SS should be used, and failing that CC.     

Retention-indices on OV-1 of approximately 170 commonly used pesticides

A screening program is reported for approximately 170 pesticides which are regularly encountered in toxicological analysis (organophosphates, carbamates, triazines, halogenated carbohydrates, phenoxycarbonic acid derivatives, and others). It is based on the retention index according to Kovats. Temperature dependence of the retention index and derivatization procedures are also studied.Dedicated in honour to Prof. Dr. Wolfgang Arnold (Hamburg) on the occasion of his 75th birthday.We are indebted to PD Dr. Hans H. Maurer (Homburg/Saar) for stimulating discussions     

Synthesis of 4′-C-Acylated Thymidines

Two synthetic pathways towards 4′-C-acylthymidines are presented. These modified mononucleosides are precursors of the 2′-deoxyribonucleotide 4′-C-radical. They were converted into their corresponding 3′-O-[(2-cyanoethyl) N,N-diisopropylphosphoramidites] 3a–c and incorporated in oligonucleotides by solid-phase synthesis. The structure of some modified nucleosides was revealed by X-ray crystal-structure analysis.     

Defect Engineering of Two-Dimensional Molybdenum Disulfide

Two-dimensional (2D) molybdenum disulfide (MoS₂) holds great promise in electronic and optoelectronic applications owing to its unique structure and intriguing properties. The intrinsic defects such as sulfur vacancies (SVs) of MoS₂ nanosheets are found to be detrimental to the device efficiency. To mitigate this problem, functionalization of 2D MoS₂ using thiols has emerged as one of the key strategies for engineering defects. Herein, we demonstrate an approach to controllably engineer the SVs of chemically exfoliated MoS₂ nanosheets using a series of substituted thiophenols in solution. The degree of functionalization can be tuned by varying the electron-withdrawing strength of substituents in thiophenols. We find that the intensity of 2LA(M) peak normalized to A_1g peak strongly correlates to the degree of functionalization. Our results provide a spectroscopic indicator to monitor and quantify the defect engineering process. This method of MoS₂ defect functionalization in solution also benefits the further exploration of defect-free MoS₂ for a wide range of applications.     

23W peak power picosecond pulses from a single-stage all-semiconductor master oscillator power amplifier

Using a single-stage all-semiconductor master oscillator-power amplifier, we generate narrow-band laser pulses of 23?W peak power at 1063?nm wavelength. These pulses of 40?ps length FWHM have a variable repetition rate and pulse energies around 2?nJ, which exceeds previous realizations and makes them ideally suited for second harmonic generation. With a spectral filter, an extinction ratio above 36?dB could be achieved at nearly 10?W peak power. We use a novel spectral method to reliably determine pulse energies independently of the background level.     

Application of pyrolysis–mass spectrometry and pyrolysis–gas chromatography–mass spectrometry with electron-ionization or resonance-enhanced-multi-photon ionization for characterization of crude oils

A novel analytical system for gas-chromatographic investigation of complex samples has been developed, that combines the advantages of several analytical principles to enhance the analytical information. Decomposition of high molecular weight structures is achieved by pyrolysis and a high separation capacity due to the chromatographic step provides both an universal as well as a selective and sensitive substance detection. The latter is achieved by simultaneously applying electron ionization quadrupole mass spectrometry (EI-QMS) for structural elucidation and [1 + 1]-resonance-enhanced-multi-photon ionization (REMPI) combined with time-of-flight mass spectrometry (ToFMS). The system has been evaluated and tested with polycyclic aromatic hydrocarbon (PAH) standards. It was applied to crude oil samples for the first time. In such highly complex samples several thousands of compounds are present and the identification especially of low concentrated chemical species such as PAH or their polycyclic aromatic sulfur containing heterocyclic (PASH) derivatives is often difficult. Detection of unalkylated and alkylated PAH together with PASH is considerably enhanced by REMPI–ToFMS, at times revealing aromatic structures which are not observable by EI-QMS due to their low abundance. On the other hand, the databased structure proposals of the EI-QMS analysis are needed to confirm structural information and isomers distinction. The technique allows a complex structure analysis as well as selective assessment of aromatic substances in one measurement. Information about the content of sulfur containing compounds plays a significant role for the increase of efficiency in the processing of petroleum.