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.     

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.     

Novel Optical Vibration Sensor Using External Cavity Feedback: Novel Optical Vibration Sensor Using External Cavity Feedback

A novel low cost, non-contact optical vibration sensor requiring only a single optoelectronic component has been developed. It consists of a continuous wave semiconductor laser operating with external optical feedback. Vibrations have been measured at frequencies of up to 600 Hz with target reflectivities lower than 5%. When calibrated, the sensor demonstrates satisfactory output for submicron vibration amplitudes. Accuracies of 0.2% have been obtained over a range of 1 mm.     

Qurves and quivers

In this paper we associate to a -qurve A (formerly known as a quasi-free algebra [J. Cuntz, D. Quillen, Algebra extensions and nonsingularity, J. Amer. Math. Soc. 8 (1995) 251–289] or formally smooth algebra [M. Kontsevich, A. Rosenberg, Noncommutative smooth spaces, math.AG/9812158, 1998]) the one-quiver Q₁(A) and dimension vector α₁(A). This pair contains enough information to reconstruct for all the GL_n-étale local structure of the representation scheme rep_nA. In an appendix we indicate how one might extend this to qurves over non-algebraically closed fields. Further, we classify all finitely generated groups G such that the group algebra kG is a k-qurve. If char(k)=0 these are exactly the virtually free groups. We determine the one-quiver setting in this case and indicate how it can be used to study the finite-dimensional representations of virtually free groups. As this approach also applies to fundamental algebras of graphs of separable k-algebras, we state the results in this more general setting.     

Flexible and adaptive use of strategies and representations in mathematics education

The flexible and adaptive use of strategies and representations is part of a cognitive variability, which enables individuals to solve problems quickly and accurately. The development of these abilities is not simply based on growing experience; instead, we can assume that their acquisition is based on complex cognitive processes. How these processes can be described and how these can be fostered through instructional environments are research questions, which are yet to be answered satisfactorily. This special issue on flexible and adaptive use of strategies and representations in mathematics education encompasses contributions of several authors working in this particular field. They present recent research on flexible and adaptive use of strategies or representations based on theoretical and empirical perspectives. Two commentary articles discuss the presented results against the background of existing theories.     

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.     

Homogeneity and Curvatures of Geodesic Spheres

We study some scalar curvature invariants on geodesic spheres and use them to characterize several kinds of Riemannian manifolds such as homogenous manifolds and in particular, the two-point homogeneous spaces and the Damek-Ricci spaces.     

Three- and Four-Dimensional Einstein-like Manifolds and Homogeneity

The aim of this paper is to study three- and four-dimensional Einstein-like Riemannian manifolds which are Ricci-curvature homogeneous, that is, have constant Ricci eigenvalues. In the three-dimensional case, we present the complete classification of these spaces while, in the four-dimensional case, this classification is obtained in the special case where the manifold is locally homogeneous. We also present explicit examples of four-dimensional locally homogeneous Riemannian manifolds whose Ricci tensor is cyclic-parallel (that is, are of type A) and has distinct eigenvalues. These examples are invalidating an expectation stated by F. Podestá and A. Spiro, and illustrating a striking contrast with the three-dimensional case (where this situation cannot occur). Finally, we also investigate the relation between three- and four-dimensional Einstein-like manifolds of type A and D'Atri spaces, that is, Riemannian manifolds whose geodesic symmetries are volume-preserving (up to sign).