Even cycle decompositions of complete graphs minus a 1-factor

Some sufficient conditions are proven for the complete graph of even order with a 1-factor removed to be decomposable into even length cycles. © 1994 John Wiley & Sons, Inc.     

The Cantor-Lebesgue property

If the terms of a trigonometric series tend to zero at each point of a set and if the smallest additive group containing that set has positive outer Lebesgue measure, then the coefficients of that series tend to zero. This result generalizes the well known Cantor-Lebesgue Theorem. Several other extensions of the Cantor-Lebesgue Theorem as well as some examples to demonstrate scope and sharpness are also given. Dedicated to the memory of Antoni Zygmund     

Near-infrared absorptions of monomethylhydrazine

The peak absorption coefficients for two near-infrared absorptions of monomethylhydrazine, CH₃-N₂H₃, (MMH) were measured. Absorption bands located at 1.524 μm (6560 cm^-1), 1.557 μm (6423 cm^-1), and 1.583 μm (6316 cm^-1) are assigned to the υ = 2 overtones of the infrared N-H stretching fundamentals at 3317, 3245 and 3177 cm^-1. An absorption band located at 1.04 μm (9620±100 cm^-1) is assigned to the υ = 3 overtone of one of these fundamentals. The peak absorption coefficients (₁₀) at 1.524 μm (6560±20 cm^-1) and 1.04 μm (9620±100 cm^-1) are 31 × 10^-3 and 0.97 × 10^-3 (cm atm)^-1, respectively. Uncertainties in these coefficients were estimated to be less than ±20% due primarily to uncertainties in the partial vapor pressure of MMH.     

Modelling nationwide hospital length of stay: opening the black box

Hospital length of stay is considered to be a reliable and valid proxy for measuring the consumption of hospital resources. Average length of stay, however, albeit easy to quantify and calculate, does not suitably reflect the nature of such underlying distributions and may therefore mask the effects that the different streams of patients have on the system. This paper uses routinely collected and readily available nationwide data on stroke-related patients, aged 65 years and over, who were discharged from English hospitals over a 1-year period. This will be the basis for a running example illustrating the alternative methods of analysis and models of patients' length of stay. The methods include statistical methods: survival analysis, mixed exponential and phase-type distributions; and decision modelling techniques: compartmental and simulation models. The paper concludes by summarizing these various modelling techniques and by highlighting the similarity of the estimated parameters of patient flow as calculated by the phase-type distribution and compartmental modelling techniques.     

Intensive voice treatment in parkinson disease: Laryngostroboscopic findings

As part of ongoing research to investigate and document the efficacy of intensive voice therapy to improve functional communication in patients with idiopathic Parkinson disease, 45 patients were enrolled in a controlled, randomized, prospective study. Pre- to posttreatment comparisons are presented here on 22 of those patients who underwent laryngeal imaging examination. Of the 22 patients, 13 patients received intensive therapy aimed at increasing vocal and respiratory effort (VR), whereas nine received intensive therapy aimed at increasing respiratory effort (R) only. All patients had a pretreatment evaluation that included two (but sometimes only one) voice recordings and an otolaryngologic examination with laryngostroboscopy. At the completion of 4 weeks of therapy (16 sessions), two voice recordings were made, and laryngostroboscopy was again performed. The pre- and posttherapy videolaryngostroboscopy tapes were then randomized and rated by four judges. Raters' findings were then compared with vocal intensity measured before and after therapy. The VR therapy group showed improvements on laryngostroboscopic variables: less glottal incompetence and no significant change in supraglottal hyperfunction after therapy. No differences were observed in the R-only group. The mean intensity increase in the VR therapy group was 12.5 dB, compared with a decrease of 1.9 dB in the R-only group. These findings suggest that in patients with Parkinson disease, intensive therapy focusing on phonatory effort improves adduction of the vocal folds as assessed by laryngostroboscopy. Differences in laryngeal function in these patients observed with fiberoptic laryngoscopy and rigid telescopic laryngoscopy are discussed.     

Sums of corestrictions of cyclic algebras

By a cyclic layer of a finite Galois extension,E/K, of fields one means a cyclic extension,L/F, of fields whereE⊇L⊇F⊇K. LetC(E/K) denote the subgroup of the relative Brauer group, Br(E/K), generated by the various subgroups cor(Br(L/F)) asL/F ranges over all cyclic layers ofE/K and where cor denotes the corestriction map into Br(E/K). We show that forK global, [Br(E/K) :C(E/K)]<∞ and we produce examples whereC(E/K)≠Br(E/K). In memory of S.A. Amitsur, our teacher, friend, collaborator, and inspiration. Supported in part by NSA Grant No. MDA904-95-H-1054. Supported in part by NSA Grant No. MDA904-95-H-1022.     

Spectral curves and the ADHM method

For a general monopole the algebraic curves defined by Nahm are shown to be the same as the spectral curves.