In this paper, a reaction-diffusion prey-predator system including the fear effect of predator on prey population and group defense has been considered. The conditions for the onset of cross-diffusion-driven instability are obtained by linear stability analysis. The technique of multiple time scales is employed to deduce the amplitude equation near Turing bifurcation threshold by choosing the cross-diffusion coefficient as a bifurcation parameter.

The computation of the eigenvalue decomposition of matrices is one of the most investigated problems in numerical linear algebra. In particular, real nonsymmetric tridiagonal eigenvalue problems arise in a variety of applications. In this paper the problem of computing an eigenvector corresponding to a known eigenvalue of a real nonsymmetric tridiagonal matrix is considered, developing an algorithm that combines part of a QR sweep and part of a QL sweep, both with the shift equal to the known eigenvalue. The numerical tests show the reliability of the proposed method.

A full ODE model for the transmission of cholera is investigated, includ- ing both direct and indirect transmission and a nonlinear growth for pathogens. The direct problem is preliminarily studied and characterized in terms of reproduction number, endemic and disease free equilibria. The inverse problem is then discussed in view of parameter estimation and model identification via a Least Squares Approximation approach. The procedure is applied to real data coming from the recent Yemen cholera outbreak of 2017-2018.

A major neglected weakness of many ecological models is the numerical method used to solve the governing systems of differential equations. Indeed, the discrete dynamics described by numerical integrators can provide spurious solution of the corresponding continuous model. The approach represented by the geometric numerical integration, by preserving qualitative properties of the solution, leads to improved numerical behaviour expecially in the long-time integration.

In recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers have been studied, and several integer sequences related to them have been introduced. In this article other types of Sheffer polynomials are considered, by introducing the adjoint Poisson-Charlier and the adjoint Related polynomials.

The discoveries of the last thirty years in Apulia have highlighted the leading role of this region, and especially ancient Peucetia, in the evolution of Lucanian and Apulian red-figured pottery. In fact, from the last decades of the fifth century BC onwards the aristocratic classes of Apulia (in the fourth century also those of the Daunian district) were the main patrons and consumers of the products of Italic workshops. As the most complex elements of the funerary assemblage there was a specific demand for those objects.

The archaeological discoveries of recent years and the latest studies about the uses and customs of Italic aristocracies of the Apulian-Lucanian area have added some relevant data concerning to the class of personal adornments and symbolic objects, fundamental elements underpinning the phenomenon of the birth of aristocracies between the eighth and seventh century BC.

The study takes up some issues relating to the location of the workshops that produced the valuable figured ambers that marked the aristocratic burials of southern Italy from the eighth to fifth century BC. The contribution of findings and recent studies enabled us to assign some groups of artifacts to the activity of different workshops and even to identify outstanding artistic personalities, highlighting the undeniable stylistic connections between them.