Geodesic equivalence and integrability

We suggest a construction that, given a trajectorial diffeomorphism between two Hamiltonian systems, produces integrals of them. As the main example we treat geodesic equivalence of metrics. We show that the existence of a non-trivially geodesically equivalent metric leads to Liouville integrability, and present explicit formulae for integrals.Comment: 19 pages; LaTe

Qualitative features of periodic solutions of KdV

In this paper we prove new qualitative features of solutions of KdV on the circle. The first result says that the Fourier coefficients of a solution of KdV in Sobolev space $H^N,\, N\geq 0$, admit a WKB type expansion up to first order with strongly oscillating phase factors defined in terms of the KdV frequencies. The second result provides estimates for the approximation of such a solution by trigonometric polynomials of sufficiently large degree

Cut loci and conjugate loci on Liouville surfaces

In the earlier paper (Itoh and Kiyohara, Manuscr Math 114:247–264, 2004), we showed that the cut locus of a general point on two-dimensional ellipsoid is a segment of a curvature line and proved "Jacobi’s last geometric statement" on the singularities of the conjugate locus. In the present paper,we showthat a wider class of Liouville surfaces possess such simple cut loci and conjugate loci. The results include the determination of cut loci and the set of poles on two-sheeted hyperboloids and elliptic paraboloids

A few things I learnt from Jurgen Moser

A few remarks on integrable dynamical systems inspired by discussions with Jurgen Moser and by his work.Comment: An article for the special issue of "Regular and Chaotic Dynamics" dedicated to 80-th anniversary of Jurgen Mose

Investigation on Parameters Affecting the Effectiveness of Photocatalytic Functional Coatings to Degrade NO: TiO 2

This paper deals with the degradation of NO by photocatalytic oxidation using TiO2-based coatings. Tests are conducted at a laboratory scale through an experimental setup inspired from ISO 22197-1 standard. Various parameters are explored to evaluate their influence on photocatalysis efficiency: TiO2 dry matter content applied to the surface, nature of the substrate, and illumination conditions (UV and visible light). This article points out the different behaviors between three kinds of substrates which are common building materials: normalized mortar, denser mortar, and commercial wood. The illumination conditions are of great importance in the photocatalytic process with experiments under UV light showing the best results. However, a significant decrease in NO concentration under visible light is also observed provided that the TiO2 dry matter content on the surface is high enough. The nature of the substrate plays an important role in the photocatalytic activity with rougher substrates being more efficient to degrade NO. However, limiting the roughness of the substrate seems to be of utmost interest to obtain the highest exposed surface area and thus the optimal photocatalytic efficiency. A higher roughness promotes the surface contact between TiO2 and NO but does not necessarily increase the photochemical oxidation

Light-bending in Schwarzschild-de-Sitter: projective geometry of the optical metric

We interpret the well known fact that the equations for light rays in the Kottler or Schwarzschild-de Sitter metric are independent of the cosmological constant in terms of the projective equivalence of the optical metric for any value of \Lambda. We explain why this does not imply that lensing phenomena are independent of \Lambda. Motivated by this example, we find a large collection of one-parameter families of projectively equivalent metrics including both the Kottler optical geometry and the constant curvature metrics as special cases. Using standard constructions for geodesically equivalent metrics we find classical and quantum conserved quantities and relate these to known quantities.Comment: 8 page

Synthesis and Characterization of Rutile TiO2Nanopowders Doped with Iron Ions

Titanium dioxide nanopowders doped with different amounts of Fe ions were prepared by coprecipitation method. Obtained materials were characterized by structural (XRD), morphological (TEM and SEM), optical (UV/vis reflection and photoluminescence, and Raman), and analytical techniques (XPS and ICP-OES). XRD analysis revealed rutile crystalline phase for doped and undoped titanium dioxide obtained in the same manner. Diameter of the particles was 5–7 nm. The presence of iron ions was confirmed by XPS and ICP-OES. Doping process moved absorption threshold of TiO2into visible spectrum range. Photocatalytic activity was also checked. Doped nanopowders showed normal and up-converted photoluminescence

Proof of projective Lichnerowicz conjecture for pseudo-Riemannian metrics with degree of mobility greater than two

We prove an important partial case of the pseudo-Riemannian version of the projective Lichnerowicz conjecture stating that a complete manifold admitting an essential group of projective transformations is the round sphere (up to a finite cover).Comment: 32 pages, one .eps figure. The version v1 has a misprint in Theorem 1: I forgot to write the assumption that the degree of mobility is greater than two. The versions v3, v4 have only cosmetic changes wrt v

Unemployment benefits : discursive convergence, distant realities

Production of INCASI Project H2020-MSCA-RISE-2015 GA 691004Unemployment protection systems have certain characteristics in common in Argentina, Uruguay, Spain and Italy: they are compulsory and contributory-proportional, although in Uruguay, it also has a capitalisation supplement. Despite the similarities, they work differently because the context of informal employment chiefly, and unemployment, low salaries and precariousness differ greatly. Consequently, the unemployment protection coverage rate varies. Theories of the Active Welfare State, the Investor State and the reforms of unemployment protection systems have led to a certain modernising language being adopted in these countries: activation, employability, conditionality, lifelong learning, flexibility, which are, among others, words shared with Europe. However, the meanings of these words differ according to the institutional context of each country. In Latin America the welfare state is low institutionalised even almost non-existent, while in Europe it is a diverse institution. Despite this, the four countries share an upward trend in benefit policies, in accordance with the increase in poverty risk