Acceleration of generalized hypergeometric functions through precise remainder asymptotics

We express the asymptotics of the remainders of the partial sums {s _n } of the generalized hypergeometric function \({\ensuremath{{}_{q+1}F_q\!\left(\left.\begin{smallmatrix}\alpha_1,\ldots,\alpha_{q+1}\\ \beta_1,\ldots,\beta_q\end{smallmatrix}\right|z\right)}}\) through an inverse power series \(z^n n^{\lambda} \sum \frac{c_k}{n^k}\), where the exponent λ and the asymptotic coefficients {c _k } may be recursively computed to any desired order from the hypergeometric parameters and argument. From this we derive a new series acceleration technique that can be applied to any such function, even with complex parameters and at the branch point z?=?1. For moderate parameters (up to approximately ten) a C implementation at fixed precision is very effective at computing these functions; for larger parameters an implementation in higher than machine precision would be needed. Even for larger parameters, however, our C implementation is able to correctly determine whether or not it has converged; and when it converges, its estimate of its error is accurate.     

High‐performance X‐ray detectors for the new powder diffraction beamline I11 at Diamond

The design and performance characterization of a new light‐weight and compact X‐ray scintillation detector is presented. The detectors are intended for use on the new I11 powder diffraction beamline at the third‐generation Diamond synchrotron facility where X‐ray beams of high photon brightness are generated by insertion devices. The performance characteristics of these detection units were measured first using a radioactive source (efficiency of detection and background count rate) and then synchrotron X‐rays (peak stability, light yield linearity and response consistency). Here, the results obtained from these tests are reported, and the suitability of the design for the Diamond powder beamline is demonstrated by presenting diffraction data obtained from a silicon powder standard using a prototype multicrystal analyser stage.     

Structure and oil repellency: Textiles with liquid repellency to hexane

Combining structure and liquid repellent coatings to optimise non-wettability is a well-established field. However, the area in recent years has been dominated by data on water repellency. The work here provides data on how certain plant structures can be used to develop surfaces that provide repellency towards both polar and non-polar, low surface tension fluids. Combining fluoropolymer coatings with ‘hairy’ fibres is particularly beneficial for providing liquid-repellent textiles. None of these surfaces can however be regarded as super-repellent to low surface tension liquids (i.e. with little difference in advancing and receding contact angles).     

Angular-resolved secondary-electron-emission spectroscopy of clean and adsorbate covered tungsten single-crystal surfaces

Energy-distribution measurements are reported for secondary electrons back-scattered into a narrow angle about the normal direction to three low-index tungsten single-crystal surfaces, viz. (100), (110) and (111). Improved spectral resolution provides unambiguous evidence for scattering out of excited “final” states located above the vacuum level; the results for all three faces correlate closely with high-energy states of a calculated energy band structure, the intensity of emission being directly related to features in the one-dimensional density of unfilled states along the corresponding low-index symmetry directions. In the presence of ordered adsorbate monolayers, additional SEE spectral fine-structure is observed at energies which lie within finalstate band gaps of the crystal. Results are presented for the specific case of CO adsorption on W(110), which shows a distinct disorder-order structural transition after exposure of the clean surface to 10 L of gas at 300 K and subsequent annealing to temperatures ?1000 K. We interpret these adsorbate surface resonances to be due to two-dimensional Bloch-like surface states produced by the periodicity of the adsorbate layer, which manifest themselves as a direct consequence of the special circumstances associated with “band-gap emission”.     

New protocols for the assembly of the tetracyclic framework associated with the aromatic erythrina alkaloids

[reaction: see text] Treatment of the anion derived from the ring-fused gem-dichlorocyclopropane 4c with silver tetrafluoroborate afforded the spirocyclic compound 17 in 74% yield. Product 17 was readily converted, over three steps, into the beta-iodoethyl derivative 20 and treatment of this latter compound with n-Bu(3)SnH then afforded, in 93% yield and via a radical addition/elimination sequence, compound 2 incorporating the ABCD framework of the aromatic erythrina alkaloids.     

Intermediates in the synthesis of nitrogen heterocycles: addition of acylated camphorsultams to nitroalkenes

Reaction of acylated camphorsultam 7 with nitroalkenes in the presence of TiCl₄ and Et₃N gave addition products in good yields (>70%) and with excellent stereocontrol. Addition of propionylated camphorsultam 15 to nitrostyrene gave the addition product 16 in which two new asymmetric centres were created, the stereochemical outcome of the reaction was confirmed by X-ray cystallography.     

Electron states in amorphous solids studied by higher derivative secondary-electron and photoemission spectroscopy

Subtle changes in the density of conduction-band states of vapor-deposited, amorphous Ge films, due to thermally activated, microstructural reordering processes, has been resolved in the photoelectron and secondary-electron energy distribution curves using electronic modulation techniques. Second-derivative spectra relate the energy distribution and density of electron states to the microstructure, and define the degree of short-range ordering in these films. The results provide evidence for “ideal” amorphous Ge films, which approach closely the completely random network. Polk structure.     

A hydrodynamic injection approach for capillary electrophoresis using rotor–stator valves

Sample injection is a critical step in a capillary electrophoresis (CE) analysis. Electrokinetic injection is the simplest approach and is often selected for implementation in portable CE instruments. However, in order to minimize the effect of sample matrix upon the results of a CE analysis, hydrodynamic injection is preferred. Although portable CE instruments with hydrodynamic injection have been reported, injection has always been performed at the grounded end of the capillary. This simplifies fluidic handling but limits coupling with electrochemical detectors and electrospray ionization–mass spectrometry (ESI–MS). We demonstrated previously that injection at the high-voltage (HV) end of the capillary could be performed using an HV-compatible rotary injection valve (fixed-volume injection). However, the mismatch between the bore sizes of the channels on the rotor–stator valve and the separation capillary caused peak tailing and undesired mixing, impairing analytical performance. In this work, we present an HV-compatible hydrodynamic injection approach that overcomes the issues associated with the fixed-volume injection approach reported previously. The performance of the CE instrument was demonstrated by analyzing a mixture of 13 amino acids by CE coupled to laser-induced fluorescence, which showed relative standard deviations for peak area and migration time below 5% and 1%, respectively, for triplicate analysis. Additionally, replicate measurements of a mixture of amino acids, peptides, nucleobases, and nucleosides by CE coupled to electrospray ionization–mass spectrometry (CE–ESI–MS) were performed to evaluate peak tailing, and results were similar to those obtained with a commercial CE–ESI–MS setup.