Heegaard 分解の距離と Goeritz 群

広島大学(Hiroshima University)博士(理学)Doctor of Philosophy in Sciencedoctora

Thick isotopy property and the mapping class groups of Heegaard splittings

Let $M$ be a closed orientable $3$-manifold and $S$ a Heegaard surface of $M$. The space of Heegaard surfaces $\mathcal{H}(M,S)$ is defined to be the space of left cosets $\mathrm{Diff}(M)/\mathrm{Diff}(M,S)$. We prove that the fundamental group $\pi_{1}(\mathcal{H}(M,S))$ is finitely generated if and only if any element of $\pi_{1}(\mathcal{H}(M,S))$ can be represented by a "thick" isotopy. As an application, we prove that the mapping class group of a strongly irreducible Heegaard splitting of a closed hyperbolic $3$-manifold is finitely generated.Comment: 8 pages, 1 figur

High levels of soluble C5b-9 complex in dialysis fluid may predict poor prognosis in peritonitis in peritoneal dialysis patients

Background We searched for indicators to predict the prognosis of infectious peritonitis by measuring levels of complement proteins and activation products in peritoneal dialysis (PD) fluid (PDF) of patients at early stages of peritonitis. We retrospectively analyzed the relationship between the levels of sC5b-9, C3 and C4 in PDF and the subsequent clinical prognosis. Methods We measured levels of sC5b-9, C3 and C4 in PDF on days 1, 2 and 5 post-onset of peritonitis in 104 episodes of infectious peritonitis in PD patients from 2008 and retrospectively compared levels with clinical outcomes. Further analysis for the presence of causative microorganisms or to demonstrate bacterial culture negative peritonitis was performed and correlated with change of levels of sC5b-9 in PDF. Results When PD patients with peritonitis were divided into groups that either failed to recover from peritonitis and were finally withdrawn from PD (group 1; n = 25) or recovered (group 2; n = 79), levels of sC5b-9, C3 and C4 in PDF were significantly higher in group 1 patients compared to those in group 2 on day5. Analysis of microorganisms showed significantly higher sC5b-9 levels in PDF of peritonitis cases caused by culture negative peritonitis in group 1 compared with group 2 when we analyzed for individual microorganisms. Of note, on day5, the sC5b-9 levels in PDF were similarly high in peritonitis caused by fungi or other organisms. Conclusion Our results suggested that levels of complement markers in PDF, especially sC5b-9, have potential as surrogate markers to predict prognosis of PD-related peritonitis

X-ray absorption fine structure studies on nickel phosphide catalysts for the non-oxidative coupling of methane reaction using a theoretical model

SiO2-supported Ni phosphide catalysts are highly active toward the non-oxidative coupling of methane (NOCM) reaction, and their catalytic activity is strongly dependent on their Ni:P ratio. We analyzed Ni phosphide catalysts using X-ray absorption fine structure (XAFS) to elucidate the structure-catalytic activity relationship. Because only Ni2P was available as a reference material, we calculated the theoretical XAFS based on the reference crystal structures using the FEFF program and compared them with the experimental spectra of Ni phosphide catalysts. We demonstrated that catalysts with Ni to P ratios of 1:1, 2:1, and 3:1 consisted mainly of the Ni2P, Ni12P5, and Ni3P, respectively. We found that Ni2P exhibited the highest activity toward NOCM because of its optimum balance of C-H cleavage activity and coke formation. This analysis demonstrated that the theoretical XAFS simulation could be used to identify the structure of supported catalysts based on the crystal structure of reference compounds