Symmetry-break in Voronoi tessellations

We analyse in a common framework the properties of the Voronoi tessellations resulting from regular 2D and 3D crystals and those of tessellations generated by Poisson distributions of points, thus joining on symmetry breaking processes and the approach to uniform random distributions of seeds. We perturb crystalline structures in 2D and 3D with a spatial Gaussian noise whose adimensional strength is α and analyse the statistical properties of the cells of the resulting Voronoi tessellations using an ensemble approach. In 2D we consider triangular, square and hexagonal regular lattices, resulting into hexagonal, square and triangular tessellations, respectively. In 3D we consider the simple cubic (SC), body-centred cubic (BCC), and face-centred cubic (FCC) crystals, whose corresponding Voronoi cells are the cube, the truncated octahedron, and the rhombic dodecahedron, respectively. In 2D, for all values α>0, hexagons constitute the most common class of cells. Noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α=0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise with α0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α>2, results converge to those of Poisson-Voronoi tessellations. In 2D, while the isoperimetric ratio increases with noise for the perturbed hexagonal tessellation, for the perturbed triangular and square tessellations it is optimised for specific value of noise intensity. The same applies in 3D, where noise degrades the isoperimetric ratio for perturbed FCC and BCC lattices, whereas the opposite holds for perturbed SCC lattices. This allows for formulating a weaker form of the Kelvin conjecture. By analysing jointly the statistical properties of the area and of the volume of the cells, we discover that also the cells shape heavily fluctuates when noise is introduced in the system. In 2D, the geometrical properties of n-sided cells change with α until the Poisson-Voronoi limit is reached for α>2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established, which agrees with exact asymptotic results. Anomalous scaling relations are observed between the perimeter and the area in the 2D and between the areas and the volumes of the cells in 3D: except for the hexagonal (2D) and FCC structure (3D), this applies also for infinitesimal noise. In the Poisson-Voronoi limit, the anomalous exponent is about 0.17 in both the 2D and 3D case. A positive anomaly in the scaling indicates that large cells preferentially feature large isoperimetric quotients. As the number of faces is strongly correlated with the sphericity (cells with more faces are bulkier), in 3D it is shown that the anomalous scaling is heavily reduced when we perform power law fits separately on cells with a specific number of faces

An investigation of the colorimetric methods for the determination of fluorine by the zirconium alizarin sulfonate method

There has been a need for a rapid and an accurate method for the determination of fluorine in its compounds. Both gravimetric and volumetric methods have been studied, but both methods were time consuming or inaccurate or both. Colorimetric methods had been studied before F. Richter developed his method but none had been reported to be as satisfactory as his method. This method was investigated because it was thought that F. Richter\u27s method would be a satisfactory colorimetric determination for fluorine in its compounds --Introduction, page 1

Analysis of Interventions for Improving Cervical-Cancer Screening Uptake among Nigerian Women

Cervical-cancer is preventable through early detection of cervical intraepithelial neoplasia that heralds the disease via cervical-cancer screening, yet its mortality is still high especially in developing countries. In Nigeria, researchers have attributed the high cervical-cancer mortality to low uptake of cervical-cancer screening predicated on wrong perception and low knowledge of cervical-cancer and cervical-cancer screening; lack of cervical-cancer screening programme; inadequate community support for cervical-cancer screening and gap in screening skills among health-workers where opportunistic cervical-cancer screening exists. This study aims to identify context-specific interventions for improving cervical-cancer screening uptake and reducing cervical-cancer burden in Nigeria. Secondary data was used for the study. Literature were obtained from Global Health, Popline and PubMed databases; WHO and other relevant websites using Eldis search engine; and from libraries in the University of Leeds and WHO in Geneva. Interventions for improving cervical-cancer screening uptake were analyzed using a set of appraisal criteria which include; technical and cost effectiveness, organizational, gender, cultural and political feasibility to determine their applicability and transferability in Nigeria. Broad interventions identified are; intervention aimed at correcting perception, improving knowledge and increasing access to cervical-cancer screening. Reducing the burden and impact of cervical-cancer in Nigeria will depend on implementation of these interventions by stakeholders