I codici dell'Archivio storico vescovile di Senigallia (secoli XIV-XV)

This research presents a thorough description of physical and codicological characteristics and information on the contents of 17 codes preserved by the clergy of the Senigallia\u2019s Diocese, in order to produce a kind of inventory. Manuscripts contain some of the documents produced between XIV and XV centuries by the bishops of Senigallia, who played the parts of both the community\u2019s spiritual leaders that of country lords. Therefore, these codes present a wide variety of documents, in particular emphyteutic agreements, leases, purchases of animals and lands, castles\u2019 councils, elections of notaries alongside pastoral visits, inquisitional proceedings, excommunications, synods and tax collections. Some manuscripts are included in the category of notarial registers or \u201cbastardelli\u201d, others have an unambiguous content (e.g. the Codex Gladii is a liber inquisitionum whereas the Miscellaneorum \uabM\ubb Codex III is also called \u201ccode of tithes\u201d), while still others have a miscellaneous content

Pattern formation for reactive species undergoing anisotropic diffusion

Turing instabilities for a two species reaction-diffusion systems is studied under anisotropic diffusion. More specifically, the diffusion constants which characterize the ability of the species to relocate in space are direction sensitive. Under this working hypothesis, the conditions for the onset of the instability are mathematically derived and numerically validated. Patterns which closely resemble those obtained in the classical context of isotropic diffusion, develop when the usual Turing condition is violated, along one of the two accessible directions of migration. Remarkably, the instability can also set in when the activator diffuses faster than the inhibitor, along the direction for which the usual Turing conditions are not matched

Turing patterns in multiplex networks

The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The intra-layer diffusion constants act as small parameter in the expansion and the unperturbed state coincides with the limiting setting where the multiplex layers are decoupled. The interaction between adjacent layers can seed the instability of an homogeneous fixed point, yielding self-organized patterns which are instead impeded in the limit of decoupled layers. Patterns on individual layers can also fade away due to cross-talking between layers. Analytical results are compared to direct simulations

Existence and uniqueness of limit cycles in a class of second order ODE's with inseparable mixed terms

We prove a uniqueness result for limit cycles of the second order ODE $\ddot x + \dot x \phi(x,\dot x) + g(x) = 0$. Under mild additional conditions, we show that such a limit cycle attracts every non-constant solution. As a special case, we prove limit cycle's uniqueness for an ODE studied in \cite{ETA} as a model of pedestrians' walk. This paper is an extension to equations with a non-linear $g(x)$ of the results presented in \cite{S}

Resonant, broadband and highly efficient optical frequency conversion in semiconductor nanowire gratings at visible and UV wavelengths

Using a hydrodynamic approach we examine bulk- and surface-induced second and third harmonic generation from semiconductor nanowire gratings having a resonant nonlinearity in the absorption region. We demonstrate resonant, broadband and highly efficient optical frequency conversion: contrary to conventional wisdom, we show that harmonic generation can take full advantage of resonant nonlinearities in a spectral range where nonlinear optical coefficients are boosted well beyond what is achievable in the transparent, long-wavelength, non-resonant regime. Using femtosecond pulses with approximately 500 MW/cm2 peak power density, we predict third harmonic conversion efficiencies of approximately 1% in a silicon nanowire array, at nearly any desired UV or visible wavelength, including the range of negative dielectric constant. We also predict surface second harmonic conversion efficiencies of order 0.01%, depending on the electronic effective mass, bistable behavior of the signals as a result of a reshaped resonance, and the onset fifth order nonlinear effects. These remarkable findings, arising from the combined effects of nonlinear resonance dispersion, field localization, and phase-locking, could significantly extend the operational spectral bandwidth of silicon photonics, and strongly suggest that neither linear absorption nor skin depth should be motivating factors to exclude either semiconductors or metals from the list of useful or practical nonlinear materials in any spectral range.Comment: 12 pages, 4 figure