Characterization of a sCMOS‐based high‐resolution imaging system

The detection system is a key part of any imaging station. Here the performance of the novel sCMOS‐based detection system installed at the ID17 biomedical beamline of the European Synchrotron Radiation Facility and dedicated to high‐resolution computed‐tomography imaging is analysed. The system consists of an X‐ray–visible‐light converter, a visible‐light optics and a PCO.Edge5.5 sCMOS detector. Measurements of the optical characteristics, the linearity of the system, the detection lag, the modulation transfer function, the normalized power spectrum, the detective quantum efficiency and the photon transfer curve are presented and discussed. The study was carried out at two different X‐ray energies (35 and 50 keV) using both 2× and 1× optical magnification systems. The final pixel size resulted in 3.1 and 6.2 µm, respectively. The measured characteristic parameters of the PCO.Edge5.5 are in good agreement with the manufacturer specifications. Fast imaging can be achieved using this detection system, but at the price of unavoidable losses in terms of image quality. The way in which the X‐ray beam inhomogeneity limited some of the performances of the system is also discussed.     

Mechanism of Water Dynamics in Hyaluronic Dermal Fillers Revealed by Nuclear Magnetic Resonance Relaxometry

¹H spin−lattice nuclear magnetic resonance relaxation experiments were performed for five kinds of dermal fillers based on hyaluronic acid. The relaxation data were collected over a broad frequency range between 4 kHz and 40 MHz, at body temperature. Thanks to the frequency range encompassing four orders of magnitude, the dynamics of water confined in the polymeric matrix was revealed. It is demonstrated that translation diffusion of the confined water molecules exhibits a two-dimensional character and the diffusion process is slower than diffusion in bulk water by 3–4 orders of magnitude. As far as rotational dynamics of the confined water is concerned, it is shown that in all cases there is a water pool characterized by a rotational correlation time of about 4×10⁻⁹ s. In some of the dermal fillers a fraction of the confined water (about 10 %) forms a pool that exhibits considerably slower (by an order of magnitude) rotational dynamics. In addition, the water binding capacity of the dermal fillers was quantitatively compared.     

Generic hyperbolicity of stationary solutions for a reaction-diffusion system

In this paper, we study the generic hyperbolicity of equilibria of a reaction-diffusion system with respect to nonlinear terms in the set of C²-functions equipped with the Whitney Topology. To accomplish this, we combine Baire’s Lemma and the usual Transversality Theorem.     

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Group algebras whose units satisfy a Laurent polynomial identity

Let KG be the group algebra of a torsion group G over a field K. We show that if the units of KG satisfy a Laurent polynomial identity, which is not satisfied by the units of the relative free algebra \(K[\alpha ,\beta : \alpha ^2=\beta ^2=0]\), then KG satisfies a polynomial identity. This extends Hartley’s Conjecture which states that if the units of KG satisfy a group identity, then KG satisfies a polynomial identity. As an application we prove that if the units of KG satisfy a Laurent polynomial identity whose support has cardinality at most 3, then KG satisfies a polynomial identity.     

Unitary Units Satisfying a Group Identity

Let K be a nonabsolute field of characteristic p ≠ 2, G a locally finite group and KG its group algebra. Let ?: KG → KG denote the K-linear extension of an involution ? defined on G. In this article, we prove that if the subgroup 𝒰_?(KG), i.e., the ?-unitary units of KG, satisfies a group identity, then KG satisfies a polynomial identity. Moreover, in case the prime radical of KG is nilpotent, we characterize the groups G for which 𝒰_?(KG) satisfies a group identity.