Spectral analysis and zeta determinant on the deformed spheres

We consider a class of singular Riemannian manifolds, the deformed spheres $S^N_k$, defined as the classical spheres with a one parameter family $g[k]$ of singular Riemannian structures, that reduces for $k=1$ to the classical metric. After giving explicit formulas for the eigenvalues and eigenfunctions of the metric Laplacian $\Delta_{S^N_k}$, we study the associated zeta functions $\zeta(s,\Delta_{S^N_k})$. We introduce a general method to deal with some classes of simple and double abstract zeta functions, generalizing the ones appearing in $\zeta(s,\Delta_{S^N_k})$. An application of this method allows to obtain the main zeta invariants for these zeta functions in all dimensions, and in particular $\zeta(0,\Delta_{S^N_k})$ and $\zeta'(0,\Delta_{S^N_k})$. We give explicit formulas for the zeta regularized determinant in the low dimensional cases, $N=2,3$, thus generalizing a result of Dowker \cite{Dow1}, and we compute the first coefficients in the expansion of these determinants in powers of the deformation parameter $k$.Comment: 1 figur

MicroRNA-196b is an independent prognostic biomarker in patients with pancreatic cancer

microRNA-196bは膵癌において異常高発現しており，多変量解析で不良な予後に相関した．その阻害剤は膵癌細胞株において抗腫瘍効果を示すことから，microRNA-196bは診断バイオマーカーおよび治療標的となることが示唆された

Composting of rice straw with effective microorganisms (EM) and its influence on compost quality.

This study aims to assess the effect of EM application on the composting process of rice straw with goat manure and green waste and to evaluate the quality of both compost treatments. There are two treatment piles in this study, in which one pile was applied with EM and another pile without EM. Each treatment was replicated three times with 90 days of composting duration. The parameters for the temperature, pH, TOC and C/N ratio, show that decomposition of organic matter occurs during the 90-day period. The t-test conducted shows that there is a significant difference between compost with EM and compost without EM. The application of EM in compost increases the macro and micronutrient content. The following parameters support this conclusion: compost applied with EM has more N, P and K content (P < 0.05) compared to compost without EM. Although the Fe in compost with EM is much higher (P < 0.05) than in the compost without EM, for Zn and Cu, there is no significant difference between treatments. This study suggests that the application of EM is suitable to increase the mineralization in the composting process. The final resultant compost indicated that it was in the range of the matured level and can be used without any restriction