Symmetries in Projective Multiresolution Analyses

We give an equivariant version of Packer and Rieffel’s theorem on sufficient conditions for the existence of orthonormal wavelets in projective multiresolution analysis. Suppose that the scaling functions are invariant with respect to some finite group action. We give sufficient conditions for the existence of wavelets with similar invariance. Research supported in part by the Research Council of Norway, project number NFR 154077/420. Some of the final work was also done with the support from the project NFR 170620/V30.     

Marcus contextual languages consisting of primitive words

In this paper we prove that the language of all primitive (strongly primitive) words over a nontrivial alphabet can be generated by certain types of Marcus contextual grammars.     

Quantifying the value of buyer–vendor coordination: Analytical and numerical results under different replenishment cost structures

Despite a growing interest in channel coordination, no detailed analytical or numerical results measuring its impact on system performance have been reported in the literature. Hence, this paper aims to develop analytical and numerical results documenting the system-wide cost improvement rates that are due to coordination. To this end, we revisit the classical buyer–vendor coordination problem introduced by Goyal [S.K. Goyal, An integrated inventory model for a single-supplier single-customer problem. International Journal of Production Research 15 (1976) 107–111] and extended by Toptal et al. [A. Toptal, S. Çetinkaya, C.-Y. Lee, The buyer–vendor coordination problem: modeling inbound and outbound cargo capacity and costs, IIE Transactions on Logistics and Scheduling 35 (2003) 987–1002] to consider generalized replenishment costs under centralized decision making. We analyze (i) how the counterpart centralized and decentralized solutions differ from each other, (ii) under what circumstances their implications are similar, and (iii) the effect of generalized replenishment costs on the system-wide cost improvement rates that are due to coordination. First, considering Goyal’s basic setting, we show that the improvement rate depends on cost parameters. We characterize this dependency analytically, develop analytical bounds on the improvement rate, and identify the problem instances in which considerable savings can be achieved through coordination. Next, we analyze Toptal et al.’s [A. Toptal, S. Çetinkaya, C.-Y. Lee, The buyer–vendor coordination problem: modeling inbound and outbound cargo capacity and costs, IIE Transactions on Logistics and Scheduling 35 (2003) 987–1002] extended setting that considers generalized replenishment costs representing inbound and outbound transportation considerations, and we present detailed numerical results quantifying the value of coordination. We report significant improvement rates with and without explicit transportation considerations, and we present numerical evidence which suggests that larger rates are more likely in the former case.     

Stochastic PAC models for vacancy motions with trapping and detrapping

In order to explain PAC data for tetragonal zirconia at temperatures between 900 and 1300oC, we have developed a four-state stochastic model. The model simulates vacancies which trap and detrap at a PAC probe nucleus. While trapped, the vacancies hop around the probe in equivalent sites. The four states in this Winkler–Gerdau stochastic theory are three trapped states with equivalent electric field gradients (EFGs) of different orientations and a detrapped state with a weaker EFG whose axis of symmetry is oriented along the diagonal between the three trapped EFGs. There are three hopping rates in this model: w, the rate a trapped vacancy hops around the probe, w_D, the detrapping rate, and w_t, the trapping rate. We report results of calculations for values of these hopping rates implied by our tetragonal zirconia data, and we report heuristic fitting functions which summarize the computer results and can be used to fit data efficiently for a wide range of parameters. This revised version was published online in August 2006 with corrections to the Cover Date.     

Acetone,butanone, pentanone,hexanone and heptanone in the headspace of aqueous solution and urine studied by selected ion flow tube mass spectrometry

Urine is commonly analysed in clinical practice by a variety of liquid‐phase techniques to check for excessive ketone bodies, proteins and salts to name just a few compounds. However, little work has been carried out to measure the volatile compounds emitted by urine since these do not yet have an established role in clinical diagnosis. There is, however, a growing body of evidence that these volatile compounds can be indicators of adverse physiological conditions and disease and with the advent of sensitive gas‐phase analytical methods they can be quickly quantified in urine headspace and potentially provide valuable support for clinical diagnosis. Thus, we are developing selected ion flow tube mass spectrometry, SIFT‐MS, for the real‐time analysis of urine headspace, ultimately to support rapid diagnosis in the clinical environment. In this paper we focus on volatile ketones in the headspace of aqueous solutions and urine donated by three healthy volunteers. Using SIFT‐MS, we have unambiguously quantified in urine headspace acetone, by far the most abundant ketone, butanone, pentanone, hexanone and heptanone using NO⁺ precursor ions. Further to this, we have determined the Henry's Law coefficients, HLC, for these ketones in aqueous solution to allow the liquid‐phase concentrations in urine to be estimated from headspace levels of their vapours. In addition, the influence of the addition of physiological amounts of dissolved urea, sodium chloride and hydrochloric acid on the partitioning of these ketones between the aqueous phase and gas phase has been investigated and found to be small, which gives greater credence to the use of the HLC obtained using aqueous solutions for the estimation of ketone concentrations in urine. Finally, parallel measurements of the levels of acetone in exhaled breath and urine headspace have been obtained and shown to be very similar, which gives support to the previous deduction from breath analysis that acetone is a truly systemic compound. Copyright © 2009 John Wiley & Sons, Ltd.