Yet another proof of Marstrand’s theorem

In a paper from 1954 Marstrand proved that if K ⊂ ℝ² is a Borel set with Hausdorff dimension greater than 1, then its one-dimensional projection has positive Lebesgue measure for almost-all directions. In this article, we give a combinatorial proof of this theorem, extending the techniques developed in our previous paper [9].     

An analysis of Y2O3:Eu thin films for thermographic phosphor applications

A comparative study of the luminescent properties of Y₂O₃:Eu³⁺ phosphor powders and thin films sputtered from targets prepared from combustion synthesized powders is reported. Thin films of (Y_0.96Eu_0.04)₂O₃ were deposited on silicon substrates. Films deposited at 600 °C had both monoclinic and cubic phases of Y₂O₃, which developed to an oriented cubic phase after annealing. Films and powders showed a linear dependence of the intensity of the ⁵D₇→⁷F₂ (611 nm) transition with temperature in the range 26-660 °C with an average rate of change of 1.8×10⁻⁴ °C⁻¹. The rate of change appears to be dependent on the Eu³⁺ concentration. This work shows that these thin films can be used as thermographic phosphors for remote temperature measurements.     

Self-imaging by a volume grating

The self-image phenomenon by a volume grating is proposed and theoretically analyzed. A theoretical model based on a path integral formulation to describe wave propagation through the grating inhomogeneous medium is applied. A modified version of the scalar diffraction theory Fresnel propagator is obtained which allows calculating the diffracted field amplitude by the grating. The proposed model is applied to amplitude and/or phase volume gratings. Remarkable features appear, in particular at the fractional Talbot distance 0.125z_T. In this case, if an in-phase real and imaginary grating modulation is considered a self-image intensity profile is observed for determined values of the absorptive and refractive parameters. On the other hand, a spatial comb intensity profile for a near half period shift between the real and imaginary grating modulations is found.     

The finite <Emphasis Type="Italic">p</Emphasis>-groups with <Emphasis Type="Italic">p</Emphasis> conjugacy classes of non-normal subgroups

Let ν(G) be the number of conjugacy classes of non-normal subgroups of a finite group G. The finite groups for which ν(G) ≤ 2 were determined by Dedekind and by Schmidt in the early times of group theory. On the other hand, if G is a finite p-group, La Haye and Rhemtulla have proved that either ν(G) ≤ 1 or ν(G) ≥ p. In this note, we determine all finite p-groups satisfying ν(G) = p for p > 2.     

Immobilized ruthenium complexes and aspects of their reactivity

Methodologies for the immobilization and characterization of ruthenium complexes into/onto functionalized silica gel, zeolites, polymers, dendrimers, sol–gel, nano and microparticles are described. The corresponding spectroscopic, electrochemical, and photochemical properties as well as chemical reactivities are used for their characterization and study. Comparison between the reactivities of immobilized and in solution species is presented. Some biological applications are also described.     

The crystal structure of 3-methyluracil from X-ray powder diffraction data

The crystal structure of 3-methyluracil has been determined ab initio by conventional monochromatic X-ray powder diffraction data. The crystal data are: orthorombic, a=6.6294(1), b=13.1816(3), c=6.53938(9) (Å), V=571.45(3) (ų), space group Pbnm, Z=8. The structure was solved by direct methods and the final Rietveld refinement converged to R_p=0.0398, R_wp=0.0528, R_Bragg=0.0294. The crystal structure exhibits endless chains of planar molecules, connected via head-to-tail N-H?O hydrogen bonds.     

Impurity-stabilized zinc-blende phase of wurtzite compounds

We propose here a new approach to stabilizing the cubic zinc blende phase of semiconductors that are usually more stable in the hexagonal wurtzite phase. We show that this can be done by taking advantage of the valence and conduction band offsets between the cubic and the hexagonal phases. Due to this band offset, it will cost less energy to insert electrons by shallow donors, or insert holes by 3d acceptors in the zinc blende structure, thus stabilizing the cubic phase.