Automorphisms of Cartan modular curves of prime and composite level

We study the automorphisms of modular curves associated to Cartan subgroups of $\mathrm{GL}_2(\mathbb Z/n\mathbb Z)$ and certain subgroups of their normalizers. We prove that if $n$ is large enough, all the automorphisms are induced by the ramified covering of the complex upper half-plane. We get new results for non-split curves of prime level $p\ge 13$: the curve $X_{\text{ns}}^+(p)$ has no non-trivial automorphisms, whereas the curve $X_{\text{ns}}(p)$ has exactly one non-trivial automorphism. Moreover, as an immediate consequence of our results we compute the automorphism group of $X_0^*(n):=X_0(n)/W$, where $W$ is the group generated by the Atkin-Lehner involutions of $X_0(n)$ and $n$ is a large enough square.Comment: 31 pages, 2 tables. Some proofs rely on MAGMA scripts available at https://github.com/guidoshore/automorphisms_of_Cartan_modular_curve

Rupi Kaur's Poetry: Trauma and Healing

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Study of propagation along the body at 60 GHz with analytical models and skin-equivalent phantoms

International audiencePropagation on the surface of the human body is investigated for the first time in the mm-wave frequency range. The study, motivated by the increasing number of applications of body area networks, is performed through an accurate analytical model for the fields excited by a small source in the proximity of the human body. New asymptotic expressions are derived for the fields, uniformly valid for the range of values of the physical and geometrical parameters of interest. The theoretical analysis leads to the rigorous estimation of important parameters of the communication link. Moreover, an experimental setup is built in order to validate the approach and to obtain further physical insight into aspects not modeled by the theoretical analysis

Wild-Type and mutated laccases for a green industry

In the frame of white biotechnology, enzymes attract an enormous attention both for their potential and for the recent social and economical interest in green chemistry. Thanks to the improved knowledge of production biochemistry, fermentation processes, and recovery methods, an increasing number of enzymes can be affordably produced. The majority of currently used industrial enzymes are the hydrolytic ones, being used for the degradation of various natural substances. Also, various oxidative enzymes, primarily laccases are used in industries such as the starch, textile, detergent and baking industries, and they represent a second important group of enzymes. This project has been focused on the recombinant expression of the industrially attractive laccase POXA1b from Pleurotus ostreatus in Pichia pastoris and on exploiting its industrial application in order to substitute some chemical industrial processes with a better eco-friendly ones. An economical analysis of the recombinant POXA1b laccase production process, in terms of productivity and cost has been evaluated. Furthermore, computational analysis and site-specific mutagenesis of the POXA1b were performed to increase the enzymatic performances towards selected substrates. A POXA1b laccase immobilization process was optimized by statistic methods (Response Surface Methodology) in order to increment the operational stability of the enzyme in specific processes. Applications of the recombinant enzyme were then developed: (i) reduction of the phenol contents inside the fruit juices by immobilized laccase POXA1b; (ii) synthesis of a new eco-friendly dyes for the staining of different textile materials (nylon, cotton and wool) and (iii) synthesis of a new eco-friendly dye for proteins visualization on the polyacrilamide gels; (iv) cotton fiber functionalization with an anti-adhesive and anti-oxidant dye polymer

Characterization of on-body communications at millimeter waves

International audienceThis paper presents a the study of on-body communications at millimeter waves. An analytical formulation is proposed by assuming a dipole source radiating on a flat skin, whose permittivity is suitably chosen to model human tissues at those frequencies, according to previous investigation. An experimental setup, consisting of two open-ended waveguides placed on the top of a skin-equivalent phantom, is then discussed in order to validate the theoretical analysis

A millimeter-wave Bessel beam launcher through the excitation of higher-order leaky modes

International audienceWe present a Bessel beam launcher based on a radial leaky-wave antenna operating at millimeter waves. With respect to a design method proposed by one of the Authors in a lower frequency range, a new approach is chosen here, as an alternative to a simple scaling of all the geometrical parameters. In order to avoid inacceptable levels of losses and possible fabrication issues due to an extremely thin substrate, our design is based on the suitable excitation of a higher-order leaky mode. Closed-form equations are derived in order to simplify the design, providing reliable values for the physical parameters once the near-field characteristics are assigned. Simulated results are shown to validate the proposed procedure