103 research outputs found

    On the minimal property of the Fourier projection

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    The turbulent structure and diurnal growth of the Saharan atmospheric boundary layer

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    The turbulent structure and growth of the remote Saharan atmospheric boundary layer (ABL) is described with in situ radiosonde and aircraft measurements and a large-eddy simulation model. A month of radiosonde data from June 2011 provides a mean profile of the midday Saharan ABL, which is characterized by a well-mixed convective boundary layer, capped by a small temperature inversion (<1K) and a deep, near-neutral residual layer. The boundary layer depth varies by up to 100% over horizontal distances of a few kilometers due to turbulent processes alone. The distinctive vertical structure also leads to unique boundary layer processes, such as detrainment of the warmest plumes across the weak temperature inversion, which slows down the warming and growth of the convective boundary layer. As the boundary layer grows, overshooting plumes can also entrain freetropospheric air into the residual layer, forming a second entrainment zone that acts to maintain the inversion above the convective boundary layer, thus slowing down boundary layer growth further.Asingle-column model is unable to accurately reproduce the evolution of the Saharan boundary layer, highlighting the difficulty of representing such processes in large-scale models. These boundary layer processes are special to the Sahara, and possibly hot, dry, desert environments in general, and have implications for the large-scale structure of the Saharan heat low. The growth of the boundary layer influences the vertical redistribution of moisture and dust, and the spatial coverage and duration of clouds, with large-scale dynamical and radiative implications

    Optimal functional outcome measures for assessing treatment for Dupuytren's disease: A systematic review and recommendations for future practice

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    This article is available through the Brunel Open Access Publishing Fund. Copyright © 2013 Ball et al.; licensee BioMed Central Ltd.Background: Dupuytren's disease of the hand is a common condition affecting the palmar fascia, resulting in progressive flexion deformities of the digits and hence limitation of hand function. The optimal treatment remains unclear as outcomes studies have used a variety of measures for assessment. Methods: A literature search was performed for all publications describing surgical treatment, percutaneous needle aponeurotomy or collagenase injection for primary or recurrent Dupuytren’s disease where outcomes had been monitored using functional measures. Results: Ninety-one studies met the inclusion criteria. Twenty-two studies reported outcomes using patient reported outcome measures (PROMs) ranging from validated questionnaires to self-reported measures for return to work and self-rated disability. The Disability of Arm, Shoulder and Hand (DASH) score was the most utilised patient-reported function measure (n=11). Patient satisfaction was reported by eighteen studies but no single method was used consistently. Range of movement was the most frequent physical measure and was reported in all 91 studies. However, the methods of measurement and reporting varied, with seventeen different techniques being used. Other physical measures included grip and pinch strength and sensibility, again with variations in measurement protocols. The mean follow-up time ranged from 2 weeks to 17 years. Conclusions: There is little consistency in the reporting of outcomes for interventions in patients with Dupuytren’s disease, making it impossible to compare the efficacy of different treatment modalities. Although there are limitations to the existing generic patient reported outcomes measures, a combination of these together with a disease-specific questionnaire, and physical measures of active and passive individual joint Range of movement (ROM), grip and sensibility using standardised protocols should be used for future outcomes studies. As Dupuytren’s disease tends to recur following treatment as well as extend to involve other areas of the hand, follow-up times should be standardised and designed to capture both short and long term outcomes

    Advances in structure elucidation of small molecules using mass spectrometry

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    The structural elucidation of small molecules using mass spectrometry plays an important role in modern life sciences and bioanalytical approaches. This review covers different soft and hard ionization techniques and figures of merit for modern mass spectrometers, such as mass resolving power, mass accuracy, isotopic abundance accuracy, accurate mass multiple-stage MS(n) capability, as well as hybrid mass spectrometric and orthogonal chromatographic approaches. The latter part discusses mass spectral data handling strategies, which includes background and noise subtraction, adduct formation and detection, charge state determination, accurate mass measurements, elemental composition determinations, and complex data-dependent setups with ion maps and ion trees. The importance of mass spectral library search algorithms for tandem mass spectra and multiple-stage MS(n) mass spectra as well as mass spectral tree libraries that combine multiple-stage mass spectra are outlined. The successive chapter discusses mass spectral fragmentation pathways, biotransformation reactions and drug metabolism studies, the mass spectral simulation and generation of in silico mass spectra, expert systems for mass spectral interpretation, and the use of computational chemistry to explain gas-phase phenomena. A single chapter discusses data handling for hyphenated approaches including mass spectral deconvolution for clean mass spectra, cheminformatics approaches and structure retention relationships, and retention index predictions for gas and liquid chromatography. The last section reviews the current state of electronic data sharing of mass spectra and discusses the importance of software development for the advancement of structure elucidation of small molecules

    On the minimal property of the Fourier projection

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    Let C be the space of real 27r-periodic continuous functions normed with the supremum norm. Let Pn denote the subspace of trigono-metric polynomials of degree ^n. It is known [l] that the Fourier projection F of C onto P » is minimal; i.e., if A is a projection of C onto Pn then \\F\ \ Û\\A\\. We prove that F is the only minimal projection of C onto P n. The proof is constructed by verifying the assertions listed below. Details will appear elsewhere. ASSERTION. If there exists a minimal projection different from F, then there exist minimal projections L and H, different from F such tha
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