Density of States of Disordered Two-Dimensional Crystals with Half-Filled Band

A diagrammatic method is applied to study the effects of commensurability in two-dimensional disordered crystalline metals by using the particle-hole symmetry with respect to the nesting vector P_0={\pm{\pi}/a, {\pi}/a} for a half-filled electronic band. The density of electronic states (DoS) is shown to have nontrivial quantum corrections due to both nesting and elastic impurity scattering processes, as a result the van Hove singularity is preserved in the center of the band. However, the energy dependence of the DoS is strongly changed. A small offset from the middle of the band gives rise to disappearence of quantum corrections to the DoS .Comment: to be published in Physical Review Letter

Effect of Substitutional Impurities on the Electronic States and Conductivity of Crystals with Half-filled Band

Low temperature quantum corrections to the density of states (DOS) and the conductivity are examined for a two-dimensional(2D) square crystal with substitutional impurities. By summing the leading logarithmic corrections to the DOS its energy dependence near half-filling is obtained. It is shown that substitutional impurities do not suppress the van Hove singularity at the middle of the band, however they change its energy dependence strongly. Weak disorder due to substitutional impurities in the three-dimensional simple cubic lattice results in a shallow dip in the center of the band. The calculation of quantum corrections to the conductivity of a 2D lattice shows that the well-known logarithmic localization correction exists for all band fillings. Furthermore the magnitude of the correction increases as half-filling is approached. The evaluation of the obtained analytical results shows evidence for delocalized states in the center of the band of a 2D lattice with substitutional impurities

Receptor activator NF kB ligand (RANKL) and osteoprotegerin (OPG) protein expression in periodontitis

The definitive version is available at www.blackwell-synergy.com Article first published online: 26 JUN 2003Objectives and background: This study investigated the expression of key mediators that regulate differentiation of osteoclasts, receptor activator of nuclear factor κB ligand (RANKL), and its natural inhibitor, osteoprotegerin (OPG), in periodontitis. We aimed to compare the levels of the RANKL and OPG in the granulomatous tissue adjacent to areas of alveolar bone loss from patients with periodontitis to that present in tissue from patients without periodontitis. In addition, we aimed to determine the types of cells expressing these factors in these tissues and to demonstrate the expression of the osteoclastic markers, RANK and tartrate-resistant acid phosphatase (TRAP), in periodontitis. Materials and methods: Frozen biopsy specimens were analysed using specific monoclonal antibodies and were evaluated by semiquantitative analysis and digital image analysis to compare levels of RANKL and OPG protein expression. Double labelling of frozen sections with antibodies to different cell lineage specific markers was used to determine the types of cells expressing these proteins. In situ hybridization was used to detect cells expressing RANK mRNA. Results: Semiquantitative image analysis demonstrated that significantly higher levels of RANKL protein (P < 0.05) were expressed in the periodontitis tissue. Conversely, OPG protein was significantly lower (P < 0.05) in the periodontitis tissues. RANKL protein was associated with lymphocytes and macrophages. OPG protein was associated with endothelial cells in both tissues. Many leukocytes expressing RANK mRNA and TRAP were observed in periodontitis tissues. Conclusion: The change in the levels of these key regulators of osteoclast differentiation may play a major role in the bone loss seen in periodontitis.Tania Crotti, Malcolm D. Smith, Robert Hirsch, Steven Soukoulis, Helen Weedon, Maria Capone, Michael J. Ahern, David Hayne

Receptor activator NF kB ligand (RANKL) and osteoprotegerin (OPG) protein expression in periodontitis

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