Valence‐to‐core X‐ray emission spectroscopy of titanium compounds using energy dispersive detectors

X‐ray emission spectroscopy (XES) of transition metal compounds is a powerful tool for investigating the spin and oxidation state of the metal centers. Valence‐to‐core (vtc) XES is of special interest, as it contains information on the ligand nature, hybridization, and protonation. To date, most vtc‐XES studies have been performed with high‐brightness sources, such as synchrotrons, due to the weak fluorescence lines from vtc transitions. Here, we present a systematic study of the vtc‐XES for different titanium compounds in a laboratory setting using an X‐ray tube source and energy dispersive microcalorimeter sensors. With a full‐width at half‐maximum energy resolution of approximately 4 eV at the Ti Kβ lines, we measure the XES features of different titanium compounds and compare our results for the vtc line shapes and energies to previously published and newly acquired synchrotron data as well as to new theoretical calculations. Finally, we report simulations of the feasibility of performing time‐resolved vtc‐XES studies with a laser‐based plasma source in a laboratory setting. Our results show that microcalorimeter sensors can already perform high‐quality measurements of vtc‐XES features in a laboratory setting under static conditions and that dynamic measurements will be possible in the future after reasonable technological developments.     

Volume-based thermoelasticity: consequences of the (near) proportionality of isothermal compressibility to formula-unit volume

Groups of structurally related materials, including the alkali halides, exhibit a proportionality of isothermal compressibility to formula-unit volume. The relationship has recently been explored by Glasser and by Recio et al. In this paper, we present the consequences of such proportionality on the relationships of Born-Lande? and Born-Mayer parameters to the formula-unit volume. These relationships have then been tested separately on (i) alkali (excluding cesium) halides and (ii) cesium halides. We conclude that the equations fit the NaCl-type materials satisfactorily, but less well for the CsCl-type materials, and that the Born-Mayer equation is more applicable. These results confirm the conclusion that volume is intimately linked to thermodynamic quantities, as already demonstrated by our development of volume-based thermodynamics (VBT).     

Saxophonists tune vocal tract resonances in advanced performance techniques

The acoustical impedance spectrum was measured in the mouths of saxophonists while they played. During bugling and while playing in the very high or altissimo range, experienced players tune a strong, but relatively broad, peak in the tract impedance to select which peak in the bore impedance will determine the note. Less experienced players are unable to produce resonances with impedance peaks comparable in magnitude to those of the bore and consequently are unable to play these notes. Experienced players can also tune their tracts to select which combinations of notes are played simultaneously in multiphonics or chords, and to produce pitch bending, a technique in which notes are produced at frequencies far from those of the peak of impedance of the instrument bore. However, in normal playing in the standard range, there is no consistent tuning of the tract resonances. The playing frequency, in all cases, lies close to the peak in the impedance of the reed in parallel with the series combination of the impedances measured in the mouth and the instrument bore on either side of the reed (ZMouth+ZBore)∥ZReed.     

Evaluating Binomial Character Sums Modulo Powers of Two

We show that for any mod 2m characters, χ1, χ2, the complete exponential sum,∑~(2m)_(x=1)χ1(x)χ2(Ax~k+ B) has a simple explicit evaluation.     

A decision support tool for Public Rights of Way officers based on the Analytic Hierarchy Process

Local Government Authorities (LGA) in England and Wales have statutory responsibility for the maintenance of Public Rights of Way (PROW), such as pathways and byways open to non-motorised traffic. The departments responsible have to compete for budgets and justify their expenditure in terms of councils’ priorities, such as well-being and environment. A need was identified for a simple decision support tool to provide a consistent and transparent framework for assessing the range of possible social and economic benefits from expenditure on PROW. The tool uses the Analytic Hierarchy Process to elicit weights forming the links from path attributes to users and usage to benefits, with a final stage to combine the benefits according to LGA priorities. It was successfully tested through case studies, where improving signage was generally found to be the most cost effective option, giving moderate benefits at low cost, whereas improving the physical conditions of the surface gave greater benefits at relatively high cost.     

Best cooperative partner selection and input resource reallocation using DEA

Reallocation of input resources (RIR) is a process by which certain decision making units (DMUs) reallocate resources among themselves; a process that occurs frequently in many enterprises. In this paper, a new data envelopment analysis (DEA) approach is developed to select the best cooperative partner DMU. Context-dependent DEA is used to identify the different levels of best-practice frontiers. Two DEA-based models are established for two cooperative scenarios, namely, resources pooling only and best-practice sharing. A cooperative method is applied to determine how to reallocate the input resources, and Shapley value is used to estimate the revenue changes that the various DMUs should expect after RIR. Two different situations with different objectives are considered. One objective is to maximize total revenue for the partnership, while the other is to maximize the Shapley value. The proposed approaches are illustrated with two examples.     

The structure of the unit group of the group algebra $mathbb{F}_{2^k } A_4 $

The structure of the unit group of the group algebra of the group A4 over any finite field of characteristic 2 is established in terms of split extensions of cyclic groups.     

On Bateman's method for second kind integral equations

Summary Under suitable conditions, we prove the convergence of the Bateman method for integral equations defined over bounded domains inR ^d ,d1. The proof makes use of Hilbert space methods, and requires the integral operator to be non-negative definite. For one-dimensional integral equations over finite intervals, estimated rates of convergence are obtained which depend on the smoothness of the kernel, but are independent of the inhomogeneous term. In particular, for aC kernel andn reasonably spaced Bateman points, the convergence is shown to be faster than any power of 1/n. Numerical calculations support this result.