Optical properties of Fe-doped silica films on Si

Optical properties of Fe-doped silica films on Si were investigated by ellipsometric technique in the region 1-5 eV. Samples were produced by sol-gel method. Precursors were prepared by mixing tetraethoxysilane (TEOS) solution in ethanol and water with aqueous solution of Fe-chloride or Fe-acetate. The coating solution was deposited on Si substrates by spin on technique. The size of Fe-containing nanometric-sized particles depended on technology and varied from 20 to 100 nm. Optical response of complex hybrid samples SiO₂:Fe/Si was interpreted in a multi-layer model. In the inverse problem, the Maxwell equations were solved by transfer matrix technique. Dielectric function of Fe-doped silica layers was calculated in the model of effective media. Analysis of optical data has shown that various Fe-oxides formed. Experimental data for films obtained from precursors with Fe-acetate and annealed in hydrogen were well described by the model calculations taking into account a small contribution 1-5% of metal Fe imbedded in silica. The Fe/Fe-O contribution to optical response increased for samples grown from FeCl₃-precursor. Ellipsometric data for Fe-doped silica films on Si were interpreted taking into account the structural AFM studies as well as the results of magnetic measurements.     

On deformations of Hamiltonian actions

In this paper we generalize to coisotropic actions of compact Lie groups a theorem of Guillemin on deformations of Hamiltonian structures on compact symplectic manifolds. We show how one can reconstruct from the moment polytope the symplectic form on the manifold. Received: 21 March 2006     

Commutative idempotent residuated lattices

We investigate the variety of residuated lattices with a commutative and idempotent monoid reduct.     

On potentially <Emphasis Type="Italic">H</Emphasis>-graphic sequences

For given a graph H, a graphic sequence π = (d ₁, d ₂,..., d _n) is said to be potentially H-graphic if there is a realization of π containing H as a subgraph. In this paper, we characterize the potentially (K ₅ − e)-positive graphic sequences and give two simple necessary and sufficient conditions for a positive graphic sequence π to be potentially K ₅-graphic, where K _r is a complete graph on r vertices and K _r-e is a graph obtained from K _r by deleting one edge. Moreover, we also give a simple necessary and sufficient condition for a positive graphic sequence π to be potentially K ₆-graphic. Project supported by National Natural Science Foundation of China (No. 10401010).     

The continuity of superposition operators on some sequence spaces defined by moduli

Let λ and μ be solid sequence spaces. For a sequence of modulus functions Φ = (ϕ k) let λ(Φ) = {x = (x _k ): (ϕk(|x _k |)) ∈ λ}. Given another sequence of modulus functions Ψ = (ψ_k), we characterize the continuity of the superposition operators P _f from λ(Φ) into μ (Ψ) for some Banach sequence spaces λ and μ under the assumptions that the moduli ϕk (k ∈ ℕ) are unbounded and the topologies on the sequence spaces λ(Φ) and μ(Ψ) are given by certain F-norms. As applications we consider superposition operators on some multiplier sequence spaces of Maddox type. This research was supported by Estonian Science Foundation Grant 5376.     

Sudoku’s french ancestors

This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, suprising, or appealing that one has an urge to pass them on. Contributions are most welcome.