Abstract:
We study how the paradigm of Newton’s science, based on the organization of scientific knowledge as a series of mathematical laws, was definitively accepted in science courses—in the last decades of the XVIII century, in England as well as in the Continent—by means of the “universal” dynamical machine invented by George Atwood in late 1770s just for this purpose. The spreading of such machine, occurring well before the appearance of Atwood’s treatise where he described the novel machine and the experiments to be performed with it, is a quite interesting historical case, which we consider in some detail. In particular, we focus on the “improvement” introduced by the Italian Giuseppe Saverio Poli and the subsequent “simplifications” of the machine, underlying the ongoing change of perspective after the definitive success of Newtonianism. The case studied here allows recognizing the relevant role played by a properly devised instrument in the acceptance of a new paradigm by nonerudite scholars, in addition to the traditional ways involving erudite scientists, and thus the complementary role of machine philosophy with respect to mathematical, philosophical or even physical reasoning.

Abstract:
An historical overview is given of the relevant steps that allowed the genesis of the quantum
theory of the chemical bond, starting from the appearance of the new quantum mechanics and
following later developments till approximately 1931. General ideas and some important details
are discussed concerning molecular spectroscopy, as well as quantum computations for simple
molecular systems performed within perturbative and variational approaches, for which the Born-
Oppenheimer method provided a quantitative theory accounting for rotational, vibrational and
electronic states. The novel concepts introduced by the Heitler-London theory, complemented by
those underlying the method of the molecular orbitals, are critically analyzed along with some of
their relevant applications. Further improvements in the understanding of the nature of the
chemical bond are also considered, including the ideas of one-electron and three-electron bonds
introduced by Pauling, as well as the generalizations of the Heitler-London theory firstly performed
by Majorana, which allowed the presence of ionic structures into homopolar compounds and
provided the theoretical proof of the stability of the helium molecular ion. The study of intermolecular interactions, as developed by London, is finally examined.

Abstract:
We report on an original method, due to Majorana, leading to a semi-analytical series solution of the Thomas-Fermi equation, with appropriate boundary conditions, in terms of only one quadrature. We also deduce a general formula for such a solution which avoids numerical integration, but is expressed in terms of the roots of a given polynomial equation.

Abstract:
We present a method for reducing the order of ordinary differential equations satisfying a given scaling relation (Majorana scale-invariant equations). We also develop a variant of this method, aimed to reduce the degree of non-linearity of the lower-order equation. Some applications of these methods are carried out and, in particular, we show that second-order Emden-Fowler equations can be transformed into first-order Abel equations. The work presented here is a generalization of a method used by Majorana in order to solve the Thomas-Fermi equation.

Abstract:
Relevant contributions by Majorana regarding Compton scattering off free or bound electrons are
considered in detail, where a (full quantum) generalization of the Kramers-Heisenberg dispersion
formula is derived. The role of intermediate electronic states is appropriately pointed out in recovering
the standard Klein-Nishina formula (for free electron scattering) by making recourse to a
limpid physical scheme alternative to the (then unknown) Feynman diagram approach. For bound
electron scattering, a quantitative description of the broadening of the Compton line was obtained
for the first time by introducing a finite mean life for the excited state of the electron system. Finally,
a generalization aimed to describe Compton scattering assisted by a non-vanishing applied
magnetic field is as well considered, revealing its relevance for present day research.

Abstract:
We describe a geometric picture for the pattern of fermion masses of the three generations which is invariant with respect to the renormalization group below the electroweak scale. Moreover, we predict the upper limit for the ratio between the Dirac masses of the $\mu$ and $\tau$ neutrinos, $m_{\nu_{\mu}}/ m_{\nu_{\tau}} < (9.6 \pm 0.6) 10^{-3}$.

Abstract:
We present a panoramic view of the main scientific manuscripts left unpublished by the brightest Italian theoretical physicist of the XX century, Ettore Majorana. We deal in particular: (i) with his very original "study" notes (the so-called "Volumetti"), already published by us in English, in 2003, c/o Kluwer Acad.Press, Dordrecht & Boston, and in the original Italian language, in 2006, c/o Zanichelli pub., Bologna, Italy; and (ii) with a selection of his research notes (the so-called "Quaderni"), that we shall publish c/o Springer, Berlin. We seize the present opportunity for setting forth also some suitable -scarcely known- information about Majorana's life and work, on the basis of documents (letters, testimonies, different documents...) discovered or collected by ourselves during the last decades. [A finished, enlarged version of this paper will appear as the editors' Preface, at the beginning of the coming book "Ettore Majorana - Unpublished Research Notes on Theoretical Physics", edited by S.Esposito, E.Recami, A.van der Merwe and R.Battiston, to be printed by Springer verlag, Berlin].

Abstract:
Gravitational waves are considered as metric perturbations about a curved background metric, rather than the flat Minkowski metric since several situations of physical interest can be discussed by this generalization. In this case, when the de Donder gauge is imposed, its preservation under infinitesimal spacetime diffeomorphisms is guaranteed if and only if the associated covector is ruled by a second-order hyperbolic operator which is the classical counterpart of the ghost operator in quantum gravity. In such a wave equation, the Ricci term has opposite sign with respect to the wave equation for Maxwell theory in the Lorenz gauge. We are, nevertheless, able to relate the solutions of the two problems, and the algorithm is applied to the case when the curved background geometry is the de Sitter spacetime. Such vector wave equations are studied in two different ways: i) an integral representation, ii) through a solution by factorization of the hyperbolic equation. The latter method is extended to the wave equation of metric perturbations in the de Sitter spacetime. This approach is a step towards a general discussion of gravitational waves in the de Sitter spacetime and might assume relevance in cosmology in order to study the stochastic background emerging from inflation.

Abstract:
The biochemical and cellular changes that occur following treatment with 1-methyl-4-phenyl-1,2,3,6-tetrahyropyrid？ine(MPTP) are remarkably similar to that seen in idiopathic Parkinson's disease (PD). PD is characterized by the degeneration of dopaminergic nigrostriatal neurons, which results in disabling motor disturbances. Activation of glial cells and the consequent neuroinflammatory response is increasingly recognized as a prominent neuropathological feature of PD. There is currently no effective disease-modifying therapy. Targeting the signaling pathways in glial cells responsible for neuroinflammation represents a promising new therapeutic approach designed to preserve remaining neurons in PD. Chronic treatment with palmitoylethanolamide (PEA, 10 mg/kg, i.p.), initiated 24 hr after MPTP injection (20 mg/kg), protected against MPTP-induced loss of tyrosine hydroxylase positive neurons in the substantia nigra pars compacta. Treatment with PEA reduced MPTP-induced microglial activation, the number of GFAP-positive astrocytes and S100β overexpression, and protected against the alterations of microtubule-associated protein 2a,b-, dopamine transporter-, nNOS- positive cells in the substantia nigra. Furthermore, chronic PEA reversed MPTP-associated motor deficits, as revealed by the analysis of forepaw step width and percentage of faults. Genetic ablation of peroxisome proliferator activated receptor (PPAR)-α in PPAR-αKO mice exacerbated MPTP systemic toxicity, while PEA-induced neuroprotection seemed be partially PPARα-dependent. The effects of PEA on molecules typically involved in apoptotic pathways were also analyzed. Our results indicate that PEA protects against MPTP-induced neurotoxicity and the ensuing functional deficits even when administered once the insult has been initiated.