Abstract:
Ethics without morality and morality without ethics are the characteristics of two distinct eras: modernity and post-modernity. The duty to obey the law is an ethical act, but not always moral. Morality in fact is something more: a principle of responsibility and an index of humanity. This paper aims to explain the historical relationship between morality, ethics and politics up to the present day. The erosion of the nation-state, global capitalism, bio-economy leads us to rethink the meaning of ethics, morality and politics. A utilitarian ethics and a necessary morality may be the new frontiers of our contemporary world.

Abstract:
Starting with service robotics and industrial robotics, this paper aims to suggest philosophical reflections about the relationship between body and machine, between man and technology in our contemporary world. From the massive use of the cell phone to the robots which apparently “feel” and show emotions like humans do. From the wearable exoskeleton to the prototype reproducing the artificial sense of touch, technological progress explodes to the extent of embodying itself in our nakedness. Robotics, indeed, is inspired by biology in order to develop a new kind of technology affecting human life. This is a bio-robotic approach, which is fulfilled in the figure of the cyborg and consequently in the loss of human nature. Today, humans have reached the possibility to modify and create their own body following their personal desires. But what is the limit of this achievement? For this reason, we all must question ourselves whether we have or whether we are a body.

Abstract:
We associate a tower with an infinitesimal algebraic skeleton to the (2+1)-dimensional (compact and noncompact) Heisenberg spin model. In particular, we construct the absolute parallelism defining the tower and the corresponding extension of the adjoint Lie algebra representation defining its skeleton.

Abstract:
The B\"acklund problem is solved for both the compact and noncompact versions of the Ishimori (2+1)-dimensional nonlinear spin model. In particular, a realization of the arising B\"acklund algebra in the form of an infinite-dimensional loop Lie algebra of the Ka\v{c}--Moody type is provided.

Abstract:
We shall construct a class of nonlinear reaction-diffusion equations starting from an infinitesimal algebraic skeleton. Our aim is to explore the possibility of an algebraic foundation of integrability properties and of stability of equilibrium states associated with nonlinear models describing patterns formation.

Abstract:
In this work we consider the non linear stability of a chemicalequilibrium of a thermally conducting two component reactive viscousmixture which is situated in a horizontal layer heated from belowand experiencing a catalyzed chemical reaction at the bottom plate.The evolution equation for the perturbation energy is deduced withan approach which generalizes the Joseph’s parametric differentiationmethod. Moreover, the nonlinear stability bound for the chemical equilibrium of the fluid mixture is derived in terms of thermal and concentrational non dimensional numbers.

Abstract:
A tower for a (2+1)-dimensional Toda type system is constructed in terms of a series expansion of operators which can be interpreted as generalized Bessel coefficients; the result is formulated as an analog of the Baker-Campbell-Hausdorff formula. We tackle the problem of the construction of infinitesimal algebraic skeletons for such a tower and discuss some open problems arising along our approach. In particular, we realize the prolongation skeleton as a Kac-Moody algebra.

Abstract:
We derive both {\em local} and {\em global} generalized {\em Bianchi identities} for classical Lagrangian field theories on gauge-natural bundles. We show that globally defined generalized Bianchi identities can be found without the {\em a priori} introduction of a connection. The proof is based on a {\em global} decomposition of the {\em variational Lie derivative} of the generalized Euler--Lagrange morphism and the representation of the corresponding generalized Jacobi morphism on gauge-natural bundles. In particular, we show that {\em within} a gauge-natural invariant Lagrangian variational principle, the gauge-natural lift of infinitesimal principal automorphism {\em is not} intrinsically arbitrary. As a consequence the existence of {\em canonical} global superpotentials for gauge-natural Noether conserved currents is proved without resorting to additional structures.

Abstract:
We show that the nonlinear 2+1--dimensional Three--Wave Resonant Interaction equations, describing several important physical phenomena, can be generated starting from incomplete Lie algebras in the framework of multidimensional prolongation structures. We make use of an {\em ansatz} involving the structure equations of a principal prolongation connection induced by an admissible B\"acklund map.

Abstract:
When a gauge-natural invariant variational principle is assigned, to determine {\em canonical} covariant conservation laws, the vertical part of gauge-natural lifts of infinitesimal principal automorphisms -- defining infinitesimal variations of sections of gauge-natural bundles -- must satisfy generalized Jacobi equations for the gauge-natural invariant Lagrangian. {\em Vice versa} all vertical parts of gauge-natural lifts of infinitesimal principal automorphisms which are in the kernel of generalized Jacobi morphisms are generators of canonical covariant currents and superpotentials. In particular, only a few gauge-natural lifts can be considered as {\em canonical} generators of covariant gauge-natural physical charges.