Spatial asymptotic expansions in the Navier-Stokes equation

We prove that the Navier-Stokes equation for a viscous incompressible fluid in $\mathbb{R}^d$ is locally well-posed in spaces of functions allowing spatial asymptotic expansions with log terms as $|x|\to\infty$ of any a priori given order. The solution depends analytically on the initial data and time so that for any $0<\vartheta<\pi/2$ it can be holomorphically extended in time to a conic sector in $\mathbb{C}$ with angle $2\vartheta$ at zero. We discuss the approximation of solutions by their asymptotic parts

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 solution of a problem of Sophus Lie: Normal forms of 2-dim metrics admitting two projective vector fields

We give a complete list of normal forms for the 2-dimensional metrics that admit a transitive Lie pseudogroup of geodesic-preserving transformations and we show that these normal forms are mutually non-isometric. This solves a problem posed by Sophus Lie.Comment: This is an extended version of the paper that will appear in Math. Annalen. Some typos were corrected, references were updated, title was changed (as in the journal version). 31 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