On the Mathematical and Geometrical Structure of the Determining Equations for Shear Waves in Nonlinear Isotropic Incompressible Elastodynamics

Using the theory of $1+1$ hyperbolic systems we put in perspective the mathematical and geometrical structure of the celebrated circularly polarized waves solutions for isotropic hyperelastic materials determined by Carroll in Acta Mechanica 3 (1967) 167--181. We show that a natural generalization of this class of solutions yields an infinite family of \emph{linear} solutions for the equations of isotropic elastodynamics. Moreover, we determine a huge class of hyperbolic partial differential equations having the same property of the shear wave system. Restricting the attention to the usual first order asymptotic approximation of the equations determining transverse waves we provide the complete integration of this system using generalized symmetries.Comment: 19 page

Whole-body somatotopic maps in the cerebellum revealed with 7T fMRI

The cerebellum is known to contain a double somatotopic body representation. While the anterior lobe body map has shown a robust somatotopic organization in previous fMRI studies, the representations in the posterior lobe have been more difficult to observe and are less precisely characterized. In this study, participants went through a simple motor task asking them to move either the eyes (left-right guided saccades), tongue (left-right movement), thumbs, little fingers or toes (flexion). Using high spatial resolution fMRI data acquired at ultra-high field (7T), with special care taken to obtain sufficient B1 over the entire cerebellum and a cerebellar surface reconstruction facilitating visual inspection of the results, we were able to precisely map the somatotopic representations of these five distal body parts on both subject- and group-specific cerebellar surfaces. The anterior lobe (including lobule VI) showed a consistent and robust somatotopic gradient. Although less robust, the presence of such a gradient in the posterior lobe, from Crus II to lobule VIIIb, was also observed. Additionally, the eyes were also strongly represented in Crus I and the oculomotor vermis. Overall, crosstalk between the different body part representations was negligible. Taken together, these results show that multiple representations of distal body parts are present in the cerebellum, across many lobules, and they are organized in an orderly manner

``Good Propagation'' Constraints on Dual Invariant Actions in Electrodynamics and on Massless Fields

We present some consequences of non-anomalous propagation requirements on various massless fields. Among the models of nonlinear electrodynamics we show that only Maxwell and Born-Infeld also obey duality invariance. Separately we show that, for actions depending only on the F_\mn^2 invariant, the permitted models have $L \sim \sqrt{1 + F^2}$. We also characterize acceptable vector-scalar systems. Finally we find that wide classes of gravity models share with Einstein the null nature of their characteristic surfaces.Comment: 11 pages, LaTeX, no figure

Congruences of lines in P5\mathbb{P}^5, quadratic normality, and completely exceptional Monge-Amp\`ere equations

The existence is proved of two new families of locally Cohen-Macaulay sextic threefolds in $\mathbb{P}^5$, which are not quadratically normal. These threefolds arise naturally in the realm of first order congruences of lines as focal loci and in the study of the completely exceptional Monge-Amp\`ere equations. One of these families comes from a smooth congruence of multidegree $(1,3,3)$ which is a smooth Fano fourfold of index two and genus 9.Comment: 16 page

When Sales Meet Process Mining: A Scientific Approach to Sales Process and Performance Management

Selling has long been considered as an “art” driven by personal intuition and native sales talent. However, significant changes have occurred over the past 30 years, as a result of technological advances and changing customer expectations. As one answer to these changes, practitioners and scholars have promoted the idea of “sales as a science”, relying on documented, repeatable ways of selling that reflect scientific methods. We argue that process mining is a relevant candidate f or empowering “sales as a science” via its capacity to analyze, discover, and enhance end-to-end processes. Through a design science approach, we propose a framework for applying process mining to sales, comprising a refined notation and seven process min ing analysis scenarios. Our study represents a first step towards gaining a better un derstanding of real-world sales processes based on digital traces from operational systems e.g., customer relationship management (CRM) systems, or emerging technologies e.g., smart watches

The Hydro-electro-thermal Performance of Air-cooled, Open-cathode Polymer Electrolyte Fuel Cells: Combined Localised Current Density, Temperature and Water Mapping

In situ diagnostic techniques provide a means of understanding the internal workings of fuel cells so that improved designs and operating regimes can be identified. Here, a novel metrology approach is reported that combines current and temperature mapping with water visualisation using neutron radiography. The approach enables a hydro-electro-thermal performance map to be generated that is applied to an air-cooled, open-cathode polymer electrolyte fuel cell. This type of fuel cell exhibits a particularly interesting coupled relationship between water, current and heat, as the air supply has the due role of cooling the stack as well as providing the cathode reactant feed via a single source. It is found that water predominantly accumulates under the cooling channels (thickness of 70-100 μm under the cooling channels and 5-25 μm in the active channels at 0.5 A cm−2), in a similar fashion to the lands in a closed-cathode design, but contrary to passive open-cathode systems. The relationship between current, temperature and water accumulation is complex and highly dependent on location within the cell. However, there is a general trend that higher currents and cooling limitations, especially above 0.7 A cm−2 and below 3.9 × 10−3 m3 s−1, leads to temperatures above 60 °C, which dehydrate the membrane (water thickness of 10-25 um) and the cell operates below 0.5 V