Scheduling precedence graphs of bounded height

The existence of a schedule for a partially ordered set of unit length tasks on m identical processors is known to be NP-complete (J. D. Ullman, NP-complete scheduling problems, J. Comput. System Sci., 10 (1975), 384–393). The problem remains NP-complete even if we restrict the precedence graph to be of height bounded by a constant. (J. K. Lenkstra and A. H. G. Rinnooy Kan, Complexity of scheduling under precedence constraints, Operations Res., 26 (1978), 22–35; D. Dolev and M. K. Warmuth, “Scheduling Flat Graphs,” IBM Research Report RJ 3398, 1982). In these NP-completeness proofs the upper bound on the number of available processors varies with the problem instance. We present a polynomial algorithm for the case where the upper bound on the number of available processors and the height of the precedence graph are both constants.     

Influence of a TiCl4 post-treatment on nanocrystalline TiO2 films in dye-sensitized solar cells

In this study, the influence of the TiCl(4) post-treatment on nanocrystalline TiO(2) films as electrodes in dye-sensitized solar cells is investigated and compared to nontreated films. As a result of this post-treatment cell efficiencies are improved, due to higher photocurrents. On a microscopic scale TiO(2) particle growth on the order of 1 nm is observed. Despite a corresponding decrease of BET surface area, more dye is adsorbed onto the oxide surface. Although it seems trivial to match this finding with the improved photocurrent, this performance improvement cannot be attributed to higher dye adsorption only. This follows from comparison between incident photon to current conversion efficiency (IPCE) and light absorption characteristics. Since the charge transport properties of the TiO(2) films are already more than sufficient without treatment, the increase in short circuit current density J(SC) cannot be related to improvements in charge transport either. Transient photocurrent measurements indicate a shift in the conduction band edge of the TiO(2) upon TiCl(4) treatment. It is concluded that the main contribution to enhanced current originates from this shift in conduction band edge, resulting in improved charge injection into the TiO(2).     

Oxoneptunium(v) as part of the framework of a polyoxometalate

(NH4)14Na4[(Np3W4O15)(H2O)3(BiW9O33)3].62H2O (1) and (NH4)14.5Na3.5[(Np3W4O15)(H2O)3(SbW9O33)3].40.5H2O (2) each contain three neptunyl(v) moieties encapsulated within heteropolyoxotungstate frameworks in which axial {NpO2}+ oxygens form one face of a WO6 octahedron.     

The energy transfer mechanism in Ce,Tb co-doped LaF3 nanoparticles

LaF₃ pure host, LaF₃:Ce, LaF₃:Tb as well as LaF₃:Ce,Tb phosphors were synthesized by the hydrothermal method. X-ray diffraction measurements were in good agreement with the standard data of LaF₃ from JCPDS card No. 32-0483 and indicated that the material was nanocrystalline with an average particle size of about 36 nm. Photoluminescence spectra of co-doped samples revealed that the Ce³⁺ emission was quenched while Tb³⁺ emission was enhanced, implying that energy was transferred from Ce³⁺ (the donor) to Tb³⁺ (the acceptor) in this system. The luminescence intensities and lifetimes of the donor for different concentrations of the acceptor were fitted to theoretical models in order to investigate the energy transfer mechanism. The quadrupole–quadrupole and exchange interaction mechanisms gave the best fit between the experimental data and the theoretical curves. The effective average Bohr radius from the fit to the exchange model is 0.095 nm. Since this is close to the ionic radii of the Ce³⁺ and Tb³⁺ ions, it suggests that the exchange interaction mechanism contributes to the energy transfer.     

Avoided-crossing-based liquid-crystal photonic-bandgap notch filter

We demonstrate a highly tunable deep notch filter realized in a liquid-crystal photonic-bandgap (LCPBG) fiber. The filter is realized without inducing a long-period grating in the fiber but simply by filling a solid-core photonic-crystal fiber with a liquid crystal and exploiting avoided crossings within the bandgap of the LCPBG fiber. The filter is demonstrated experimentally and investigated using numerical simulations. A high degree of tuning of the spectral position of the deep notch is also demonstrated.     

Injective dimension of sheaves of rational vector spaces

The Cantor–Bendixson rank of a topological space X is a measure of the complexity of the topology of X. We will be interested primarily in the case that the space is profinite: Hausdorff, compact and totally disconnected. In this paper, we prove that the injective dimension of the abelian category of sheaves of $\mathbb{Q}$-modules over a profinite space X is determined by the Cantor–Bendixson rank of X.