Is time the real line?

This paper is devoted to discussing the topological structure of the arrow of time. In the literature, it is often accepted that its algebraic and topological structures are that of a one-dimensional Euclidean space $\mathbb{E}^1$, although a critical review on the subject is not easy to be found. Hence, leveraging on an operational approach, we collect evidences to identify it structurally as a normed vector space $(\mathbb{Q}, |\cdot|)$, and take a leap of abstraction to complete it, up to isometries, to the real line. During the development of the paper, the space-time is recognized as a fibration, with the fibers being the sets of simultaneous events. The corresponding topology is also exposed: open sets naturally arise within our construction, showing that the classical space-time is non-Hausdorff. The transition from relativistic to classical regimes is explored too.Comment: 26 pages, 9 figures. Misprints corrected and minor adjustments according to the review proces

Generalization of the Extended Lagrangian Formalism on a Field Theory and Applications

Formalism of extended Lagrangian represent a systematic procedure to look for the local symmetries of a given Lagrangian action. In this work, the formalism is discussed and applied to a field theory. We describe it in detail for a field theory with first-class constraints present in the Hamiltonian formulation. The method is illustrated on examples of electrodynamics, Yang-Mills field and non-linear sigma model.Comment: 17 pages, to be published in Phys. Rev.

. Microwave-assisted solvothermal controlled synthesis of Fe-Co

Syntheses of bimetallic cobalt-iron-based nanoparticles starting from Co(acac)2 and Fe(acac)3 (acac = acetylacetonate) were carried out by microwave-assisted solvothermal process, using ethylene glycol as the solvent and (polyvinylpyrrolidone) PVP, as the stabilizer. Indeed, the reaction mechanism in the presence of ethylene glycol is well understood [1] with the role of PVP being the inhibition of nanoparticles growth [2]. However, the control of the morphology of the synthetized nanoparticles is still a great challenge. Herein, we demonstrated that by adding amines to the reaction mixture, it is possible to control the morphology of the prepared bimetallic cobalt-iron materials. Thus, different Co-Fe micro-composites were synthetized by an innovative microwave assisted solvothermal synthesis, which allows to considerably reduce reaction time from 12 h to 15 min, with respect to classical thermal methods. The procedure was optimized by varying several parameters, such as: amount of PVP, in the presence or in the absence of amines, reaction temperature. The dark brown obtained powders were characterized by scanning electron microscopy, infrared spectroscopy and thermogravimetric analysis, confirming the beneficial effect of the presence of the amine in the morphology of the obtained composites. The obtained results open a new scenario for further studies on the possibility to control the morphology of bimetallic composite materials. [1] Fievet F, Lagier J P and Figlarz M Mater. Res. Soc. Bull. 24 (1989) 29–34 [2] Teranishi T, Kurita R and Miyake M J. Inorg. Organometall. Polym. 10 (2000) 145–5

Microwave-assisted solvothermal synthesis of fe3o4/ceo2 nanocomposites and their catalytic activity in the imine formation from benzyl alcohol and aniline

Fe3O4/CeO2 nanocomposites were synthetized by coating magnetite seeds of different morphologies (hexagonal, spheroidal, quasi-spherical) with ceria, in ethylene glycol as solvothermal solvent. The synthesis was performed in the presence of microwave irradiation aiming to overcome the common disadvantages proper of the classic solvothermal/hydrothermal procedure. The obtained nanocomposites were calcined at the optimum temperature of 550 °C. The structure of the new nanomaterials was carefully investigated by IR, XRD, SEM, EDS and TEM analyses. The nanocomposites resulted to be constituted by CeO2 nanoparticles distributed onto Fe3O4 seeds, that kept their pristine morphology. The new materials were used as catalysts for imine synthesis from benzyl alcohol and aniline. The highest imine conversion rate was obtained with Fe3O4/CeO2, which was synthesized from Fe3O4 nanoparticles (hexagonal) obtained by microwave hydrothermal procedure in the absence of any organic additive (polyvinylpyrrolidone, trisodium citrate dihydrate or oleic acid). The catalyst could be easily removed from the reaction mixture with the help of an external magnet, and it was recycled for at least five runs with increasing catalytic activity