On the geometries of the rational unfoldings of X k

With a view to applications to self-regulating dynamical processes in biology, we determine the geometric structure of what we call isotangent curves, i.e. curves parametrized by the slopes of their points. They come up naturally as bifurcation curves of rational unfoldings of X ^k, and we classify them according to degree and number of cusps. They, as well as their isotangent involute curves, turn up in simulations of these processes.     

Curvature invariants, differential operators and local homogeneity

We first prove that a Riemannian manifold with globally constant additive Weyl invariants is locally homogeneous. Then we use this result to show that a manifold whose Laplacian commutes with all invariant differential operators is a locally homogeneous space.

     

High resolution orbitrap mass spectrometry in comparison with tandem mass spectrometry for confirmation of anabolic steroids in meat

A prominent trend which has been observed in recent years in the analysis of veterinary drugs and growth-promoting agents is the shift from target-oriented procedures, mainly based on liquid chromatography coupled to triple-quadrupole mass spectrometry (LC-QqQ-MS), towards accurate mass full scan MS (such as time of flight (ToF) and Fourier Transform (FT) Orbitrap MS). In this study the applicability of high resolution single-stage-Orbitrap-MS for confirmatory analysis of growth-promoting agents in meat was compared to that of a QqQ-MS. Validation according to CD 2002/657/EC demonstrated that steroid analysis based on Orbitrap MS, operating at a resolution of 50,000 FWHM, is indeed capable to compete with QqQ-MS in terms of selectivity/specificity, while providing excellent linearity (for most compounds >0.99) but somewhat inferior sensitivity. Indeed, CC_αs reached from 0.04–0.88 μg kg⁻¹ for the 34 anabolic steroids upon MS/MS detection, while upon Orbitrap MS detection a range of 0.07–2.50 μg kg⁻¹ was observed. Using QqQ-MS adequate precision was obtained since relative standard deviations, associated with the repeatability and intra-laboratory reproducibility, were below 20%. In the case of Orbitrap MS, for some compounds (i.e. some estrogens) this threshold was exceeded and thus poor precision was observed, which is possibly caused by the lack in sensitivity. Overall, it may be concluded that Orbitrap-MS offers an adequate performance in terms of linearity and precision but lacks in sensitivity for some of the compounds.     

High-resolution Orbitrap mass spectrometry for the analysis of carotenoids in tomato fruit: validation and comparative evaluation towards UV–VIS and tandem mass spectrometry

In this study, a generic extraction protocol and full-scan high-resolution Orbitrap-mass spectrometry (MS) detection method were developed, enabling the metabolomic screening for carotenoids in tomato fruit tissue. To this end, the carotenoids lutein, zeaxanthin, α-carotene, β-carotene, and lycopene (representing both xanthofylls and carotenes) were considered. The extraction procedure was optimized by means of a D-optimal design and consisted of a liquid–liquid extraction with methanol/tert-butyl methyl ether (1:1, v/v). The considered compounds were detected by a single-stage Exactive^TM mass spectrometer, operating at a mass resolution of 100,000 full width at half maximum. The validation study demonstrated excellent performance in terms of linearity (R ²?>?0.99), repeatability (CV?≤?10.6 %), within-laboratory reproducibility (CV?≤?12.2 %), and mean corrected recovery (ranging from 85 to 106 %). Additionally, a comparative evaluation towards well-established detection techniques, i.e., tandem mass spectrometry (MS/MS) and ultraviolet-visible spectroscopy (UV–VIS) photodiode array, indicated superior performance of high-resolution Orbitrap-MS with regard to specificity/selectivity and sensitivity (with limits of detection ranging from 1.0 to 3.8 pg μL^?1). As a result, it may be concluded that high-resolution Orbitrap-MS is a suited alternative for UV–VIS or MS/MS in analyzing carotenoids and may offer significant value in carotenoid research because of the metabolomic screening possibilities.

Validation of a confirmatory method for lipophilic marine toxins in shellfish using UHPLC-HR-Orbitrap MS

Lipophilic marine toxins are produced by harmful microalgae and can accumulate in edible filter feeders such as shellfish, leading to an introduction of toxins into the human food chain, causing different poisoning effects. During the last years, analytical methods, based on liquid chromatography coupled to tandem mass spectrometry (LC-MS/MS), have been consolidated by interlaboratory validations. However, the main drawback of LC-MS/MS methods remains the limited number of compounds that can be analyzed in a single run. Due to the targeted nature of these methods, only known toxins, previously considered during method optimization, will be detected. Therefore in this study, a method based on ultra-high-performance liquid chromatography coupled to high-resolution Orbitrap mass spectrometry (UHPLC-HR-Orbitrap MS) was developed. Its quantitative performance was evaluated for confirmatory analysis of regulated lipophilic marine toxins in shellfish flesh according to Commission Decision 2002/657/EC. Okadaic acid (OA), dinophysistoxin-1 (DTX-1), pectenotoxin-2 (PTX-2), azaspiracid-1 (AZA-1), yessotoxin (YTX), and 13-desmethyl spirolide C (SPX-1) were quantified using matrix-matched calibration curves (MMS). For all compounds, the reproducibility ranged from 2.9 to 4.9 %, repeatability from 2.9 to 4.9 %, and recoveries from 82.9 to 113 % at the three different spiked levels. In addition, confirmatory identification of the compounds was effectively performed by the presence of a second diagnostic ion (¹³C). In conclusion, UHPLC-HR-Orbitrap MS permitted more accurate and faster detection of the target toxins than previously described LC-MS/MS methods. Furthermore, HRMS allows to retrospectively screen for many analogues and metabolites using its full-scan capabilities but also untargeted screening through the use of metabolomics software. Figure

?     

Identification and updating of loading in frameworks using dynamic measurements

This paper is concerned with the effect of structural loading on dynamic performance. This topic is recognised as being of importance when validating finite element (FE) models with experimental data. A strategy for including axial load effects in a model updating procedure is developed. The method can be used to identify loading in structural frameworks using measured dynamic data.The effectiveness of the new method is demonstrated by means of case studies involving both simulated and experimental data. The theoretical study allows aspects of the sensitivity of the method to realistic levels of experimental noise to be studied as well as the way in which dynamic load identification can be enhanced with static measurements. The experimental case study proves the practical success of the technique. Updated axial load parameters are compared with static measurements of the same quantities.     

Local structure of Schelter-Procesi smooth orders

In this paper we give the étale local classification of Schelter-Procesi smooth orders in central simple algebras. In particular, we prove that if is a central simple -algebra of dimension , where is a field of trancendence degree , then there are only finitely many étale local classes of smooth orders in . This result is a non-commutative generalization of the fact that a smooth variety is analytically a manifold, and so has only one type of étale local behaviour.