Representations of solutions of the wave equation based on relativistic wavelets

A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine Poincar\'e group, i.e., with the help of translations, dilations in space and time and Lorentz transformations. The representation can be interpreted in terms of the initial-boundary value problem for the wave equation in a half-plane. It gives the solution as an integral representation of two types of solutions: propagating localized solutions running away from the boundary under different angles and packet-like surface waves running along the boundary and exponentially decreasing away from the boundary. Properties of elementary solutions are discussed. A numerical investigation of coefficients of the decomposition is carried out. An example of the field created by sources moving along a line with different speeds is considered, and the dependence of coefficients on speeds of sources is discussed.Comment: submitted to J. Phys. A: Math. Theor., 20 pages, 6 figure

Broadband impedance spectroscopy of some Li+ and Vo** conducting solid electrolytes

The solid electrolyte Li3Ti1.5(PO4)3 compound has been synthesized by solid state reaction and studied by X-ray diffraction. At room temperature the compound belongs to rhombohedral symmetry (space group R3 ̅c) with six formula units in the unit cell. Li3Ti1.5(PO4)3, Li3xLa2/3–xTiO3 (where x = 0.12) Li+-ion conducting, Ce0.8Gd0.2O1.9, (ZrO2)92(Y2O3)8 with fast oxygen vacancy transport ceramic samples were investigated in the frequency range from 1 Hz to 3 GHz in the temperature interval (300-700) K by impedance spectroscopy methods. Two dispersion regions in ionic conductivity spectra for investigated ceramic samples have been found. The dispersions have been attributed to relaxation processes in grain boundaries and in grains of the ceramics

Impact of Optimized Breastfeeding on the Costs of Necrotizing Enterocolitis in Extremely Low Birthweight Infants

To estimate risk of NEC for ELBW infants as a function of preterm formula and maternal milk (MM) intake and calculate the impact of suboptimal feeding on NEC incidence and costs

Fast H+/Li+ ion exchange in Li0.30La0.57TiO3 nanopowder and films in water and in ambient air

International audienceThe H+/Li+ ion exchange reaction of lithium lanthanum titanate (LLTO) nanopowders and films with water and CO2 contained in air, leads to the formation of a partially protonated titanates and carbonates at the surface of the oxide. A mechanism of surface reaction is proposed: the titanate undergoes reaction with water, then a topotactic exchange reaction of H+ for Li+ takes place into the perovskite structure, lithium hydroxide (or lanthanum oxyhydroxide) is then formed on the grain surface and reacts with CO2 contained in air to form Li2CO3 (or lanthanum carbonate). This surface reaction occurs rapidly after synthesis under ambient atmosphere and is greatly enhanced by the use of nanomaterials or films. It is reversible if the material is heat-treated around 300–400 °C. Rutherford Backscattering Spectroscopy (RBS), Nuclear Reaction Analysis (RNA) and Elastic Recoil Detection Analysis (ERDA) are used to determine the composition of the films after storage in ambient air and to confirm the occurrence of an exchange reaction at the surface of the oxide stored under ambient atmospher

Critical behaviour of the electrical resistivity in amorphous ferromagnetic alloys

Electrical resistivity ρ of the amorphous FexNi80-xB19Si1 (χ = 10, 13, 16), Fe20Ni60B20 and Fe20Ni60P14B6 alloys has been measured in a wide temperature range which embraces the second-order magnetic phase transition at the Curie point TC. Analysis of the data reveals that in these systems critical region has a much wider range compared with that in crystalline ferromagnets even though dρ/dT for T≥TC decreases at a rate that is comparable in both the cases. For the glassy ribbons coming from the same alloy batch, TC and the specific heat critical exponent a have the same values as those determined from our previous magnetic measurements. a for all the investigated alloys possesses values that are typical of a Heisenberg ferromagnet