Quantization for an elliptic equation of order 2m with critical exponential non-linearity

On a smoothly bounded domain $\Omega\subset\R{2m}$ we consider a sequence of positive solutions $u_k\stackrel{w}{\rightharpoondown} 0$ in $H^m(\Omega)$ to the equation $(-\Delta)^m u_k=\lambda_k u_k e^{mu_k^2}$ subject to Dirichlet boundary conditions, where $0<\lambda_k\to 0$. Assuming that $$\Lambda:=\lim_{k\to\infty}\int_\Omega u_k(-\Delta)^m u_k dx<\infty,$$ we prove that $\Lambda$ is an integer multiple of \Lambda_1:=(2m-1)!\vol(S^{2m}), the total $Q$-curvature of the standard $2m$-dimensional sphere.Comment: 33 page

Immunolocalization of RANKL is Increased and OPG Decreased During Dietary Magnesium Deficiency in the Rat

BACKGROUND: Epidemiological studies have linked low dietary magnesium (Mg) to low bone mineral density and osteoporosis. Mg deficiency in animal models has demonstrated a reduction in bone mass and increase in skeletal fragility. One major mechanism appears to be an increase in osteoclast number and bone resorption. The final pathway of osteoclastogenesis involves three constituents of a cytokine system: receptor activator of nuclear factor kB ligand (RANKL); its receptor, receptor activator of nuclear factor kB (RANK); and its soluble decoy receptor, osteoprotegerin (OPG). The relative presence of RANKL and OPG dictates osteoclastogenesis. The objective of this study was to assess the presence of RANKL and OPG in rats on a low Mg diet. METHODS: RANKL and OPG were assessed by immunocytochemistry staining in the tibia for up to 6 months in control rats on regular Mg intake (0.5 g/kg) and experimental rats on reduction of dietary Mg (.04%, 25% and 50% of this Nutrient Requirement). RESULTS: At all dietary Mg intakes, alteration in the presence of immunocytochemical staining of RANKL and OPG was observed. In general, OPG was decreased and RANKL increased, reflecting an alteration in the RANKL/OPG ratio toward increased osteoclastogenesis. CONCLUSION: We have, for the first time demonstrated that a reduction in dietary Mg in the rat alters the presence of RANKL and OPG and may explain the increase in osteoclast number and decrease in bone mass in this animal model. As some of these dietary intake reductions in terms of the RDA are present in a large segment of or population, Mg deficiency may be another risk factor for osteoporosis

Group velocity control in the ultraviolet domain via interacting dark-state resonances

The propagation of a weak probe field in a laser-driven four-level atomic system is investigated. We choose mercury as our model system, where the probe transition is in the ultraviolet region. A high-resolution peak appears in the optical spectra due to the presence of interacting dark resonances. We show that this narrow peak leads to superluminal light propagation with strong absorption, and thus by itself is only of limited interest. But if in addition a weak incoherent pump field is applied to the probe transition, then the peak structure can be changed such that both sub- and superluminal light propagation or a negative group velocity can be achieved without absorption, controlled by the incoherent pumping strength

Nitrous oxide emission from highland winter wheat field after long-term fertilization

Nitrous oxide (N&lt;sub&gt;2&lt;/sub&gt;O) is an important greenhouse gas. N&lt;sub&gt;2&lt;/sub&gt;O emissions from soils vary with fertilization and cropping practices. The response of N&lt;sub&gt;2&lt;/sub&gt;O emission to fertilization of agricultural soils plays an important role in global N&lt;sub&gt;2&lt;/sub&gt;O emission. The objective of this study was to assess the seasonal pattern of N&lt;sub&gt;2&lt;/sub&gt;O fluxes and the annual N&lt;sub&gt;2&lt;/sub&gt;O emissions from a rain-fed winter wheat (&lt;i&gt;Triticum aestivum&lt;/i&gt; L.) field in the Loess Plateau of China. A static flux chamber method was used to measure soil N&lt;sub&gt;2&lt;/sub&gt;O fluxes from 2006 to 2008. The study included 5 treatments with 3 replications in a randomized complete block design. Prior to initiating N&lt;sub&gt;2&lt;/sub&gt;O measurements the treatments had received the same fertilization for 22 years. The fertilizer treatments were unfertilized control (CK), manure (M), nitrogen (N), nitrogen + phosphorus (NP), and nitrogen + phosphorus + manure (NPM). Soil N&lt;sub&gt;2&lt;/sub&gt;O fluxes in the highland winter wheat field were highly variable temporally and thus were fertilization dependent. The highest fluxes occurred in the warmer and wetter seasons. Relative to CK, m slightly increased N&lt;sub&gt;2&lt;/sub&gt;O flux while N, NP and NPM treatments significantly increased N&lt;sub&gt;2&lt;/sub&gt;O fluxes. The fertilizer induced increase in N&lt;sub&gt;2&lt;/sub&gt;O flux occurred mainly in the first 30 days after fertilization. The increases were smaller in the relatively warm and dry year than in the cold and wet year. Combining phosphorous and/or manure with mineral N fertilizer partly offset the nitrogen fertilizer induced increase in N&lt;sub&gt;2&lt;/sub&gt;O flux. N&lt;sub&gt;2&lt;/sub&gt;O fluxes at the seedling stage were mainly controlled by nitrogen fertilization, while fluxes at other plant growth stages were influenced by plant and environmental conditions. The cumulative N&lt;sub&gt;2&lt;/sub&gt;O emissions were always higher in the fertilized treatments than in the non-fertilized treatment (CK). Mineral and manure nitrogen fertilizer enhanced N&lt;sub&gt;2&lt;/sub&gt;O emissions in wetter years compared to dryer years. Phosphorous fertilizer offset 0.50 and 1.26 kg N&lt;sub&gt;2&lt;/sub&gt;O-N ha&lt;sup&gt;−1&lt;/sup&gt; increases, while manure + phosphorous offset 0.43 and 1.04 kg N&lt;sub&gt;2&lt;/sub&gt;O-N ha&lt;sup&gt;−1&lt;/sup&gt; increases by N fertilizer for the two observation years. Our results suggested that the contribution of single N fertilizer on N&lt;sub&gt;2&lt;/sub&gt;O emission was larger than that of NP and NPM and that manure and phosphorous had important roles in offsetting mineral N fertilizer induced N&lt;sub&gt;2&lt;/sub&gt;O emissions. Relative to agricultural production and N&lt;sub&gt;2&lt;/sub&gt;O emission, manure fertilization (M) should be recommended while single N fertilization (N) should be avoided for the highland winter wheat due to the higher biomass and grain yield and lower N&lt;sub&gt;2&lt;/sub&gt;O flux and annual emission in m than in N

De novo glomerular osteopontin expression in rat crescentic glomerulonephritis

De novo glomerular osteopontin expression in rat crescentic glomerulonephritis. Osteopontin (OPN) is a secreted acidic glycoprotein that has potent monocyte chemoattractant and adhesive properties. Up-regulation of tubular OPN expression is thought to promote interstitial macrophage infiltration in experimental nephritis; however, the role of OPN in glomerular lesions, particularly crescent formation, is unknown. The present study used Northern blotting, in situ hybridization and immunohistochemistry to examine OPN expression in a rat model of accelerated anti-GBM glomerulonephritis. Osteopontin mRNA and protein is expressed by some parietal epithelial cells, thick ascending limbs of Henle and medullary tubules and collecting ducts in normal rat kidney. De novo OPN mRNA and protein expression was evident in glomerular visceral and parietal epithelial cells in anti-GBM glomerulonephritis. Glomerular OPN expression preceded and correlated with macrophage infiltration in the development of hypercellularity, focal and segmental lesions and, notably, crescent formation. There was marked up-regulation of OPN expression by tubular epithelial cells that also preceded and correlated with interstitial macrophage (r = 0.93, P < 0.001) and T-cell infiltration (r = 0.85, P < 0.001). Both glomerular and tubular OPN expression correlated significantly with proteinuria (P < 0.001) and a reduction in creatinine clearance (P < 0.01). In addition, double immunohistochemistry showed co-expression of osteopontin and one of its ligands, CD44, in intrinsic renal cells. CD44 and OPN expression by parietal epithelial cells was evident in crescent formation, while virtually all OPN-positive tubules expressed CD44. Infiltrating macrophages and T-cells were CD44-positive, but only a small proportion of T-cells and few macrophages showed OPN expression. Interestingly, strong OPN mRNA and protein expression was seen in macrophage multinucleated giant cells. In summary, this study suggests that OPN promotes macrophage and T-cell infiltration in the development of renal lesions in rat anti-GBM glomerulonephritis, including glomerular crescent and multinucleated giant cell formation