Albanese Maps and Off Diagonal Long Time Asymptotics for the Heat Kernel

We discuss long time asymptotic behaviors of the heat kernel on a non-compact Riemannian manifold which admits a discontinuous free action of an abelian isometry group with a compact quotient. A local central limit theorem and the asymptotic power series expansion for the heat kernel as the time parameter goes to infinity are established by employing perturbation arguments on eigenvalues and eigenfunctions of twisted Laplacians. Our ideas and techniques are motivated partly by analogy with Floque–Bloch theory on periodic Schr?dinger operators. For the asymptotic expansion, we make careful use of the classical Laplace method. In the course of a discussion, we observe that the notion of Albanese maps associated with the abelian group action is closely related to the asymptotics. A similar idea is available for asymptotics of the transition probability of a random walk on a lattice graph. The results obtained in the present paper refine our previous ones [4]. In the asymptotics, the Euclidean distance associated with the standard realization of the lattice graph, which we call the Albanese distance, plays a crucial role. Received: 20 September 1998 / Accepted: 19 August 1999     

Stress-strain behavior of segmented polyurethaneureas under pure shear deformation

Elastic properties of segmented polyurethaneureas (SPUs) under pure shear deformation were investigated. Data were analyzed by using strain energy density function (W). The values of the derivatives of W with respect to the invariants of the strain tensor (I _i ; i = 1, 2, 3 ) at zero strain limit were also estimated theoretically and were compared with those estimated by experiment. The limiting value of the derivative with respect to I ₁ (W/I ₁) was shown theoretically to be 5 G/8, while the derivatives with respect to I ₂ and I ₃ (W/I ₂ and W/I ₃ were respectively-G/8 and -3G/8. The theoretical prediction could explain the asymptotic behavior of the derivatives of SPUs as well as isoprene rubber (IR) reported by Kawabata et al. at small I ₁ limit.     

In situ Raman imaging of osteoblastic mineralization

Hydroxyapatite (HA) is synthesized at early stages of bone formation by osteoblasts. Nondestructive observation of early stages of osteoblastic mineralization provides crucial information for biological mechanism of bone formation. Raman microscopy serves as an ideal tool to observe the osteoblastic mineralization process because it shows the chemical information of the sample at a minimally invasive level. In addition, HA is a marker for osteoblastic mineralization, and HA Raman signal is strong enough to identify mineralized spots in osteoblasts. In this research, we visualized the distribution of HA in cultured mouse osteoblasts by Raman imaging and observed the location of the mineralized spots in the culture. We monitored HA Raman signal from osteoblast culture for 3 days after administrating the osteogenic differentiation medium and observed Raman signal associated with HA. We identified mineralized spots of KUSA‐A1 by Raman imaging constructed from the distribution of HA Raman signal. We successfully visualized the distribution of the mineralized spots in the culture of KUSA‐A1. We compared our Raman images with Alizarin red S staining assay, which was a conventional method to evaluate the mineralization process. Raman imaging of the KUSA‐A1 culture visualized the mineralized spots more accurately than Alizarin red S staining assay. Raman imaging of HA serves as a powerful tool to identify the mineralized spots in an in vitro culture of osteogenic lineage cells. Copyright © 2014 John Wiley & Sons, Ltd.     

Adsorption of ytterbium onto Saccharomyces cerevisiae fungal cells: A pH-dependent contribution of phosphoryl functional group

The adsorption of ytterbium on the cells of yeast Saccharomyces cerevisiae has been studied by batch type experiment by changing solution pH. The Yb adsorption species on the yeast cell wall of the S. cerevisiae was determined by extended X-ray absorption fine structure spectroscopy combined with a linear combination analysis at various pHs. The results indicated that the contribution of Yb-phosphoryl species was constant between pH 3 and 5, strongly suggesting that most of the Yb was associated with undeprotonated phosphoryl functional groups.     

Improved efficiency and product selectivity in the photo-Claisen-type rearrangement of an aryl naphthylmethyl ether using a microreactor/flow system

Ultraviolet (UV) irradiation of 2-[(2,4,6-trimethylphenoxy)methyl]-1-(methoxycarbonyl)naphthalene promotes a photochemical reaction that gives a cyclohexa-2,4-dienone product arising from a photo-Claisen-type ortho-rearrangement and a phenol derivative arising from a meta-rearrangement, along with 1-methoxycarbonyl-2-methylnaphthalene and 1,2-bis[1-(methoxycarbonyl)naphthalen-2-yl]ethane. When this process is carried out in a microreactor/flow system, its efficiency is dramatically enhanced and selectivity of products is improved. The effects on efficiency and product selectivity caused by the microreactor/flow system are attributed to more efficient light absorption and the suppression of secondary reactions.     

A novel one-pot synthesis of carbazole-1,4-quinones through Pd-catalyzed cyclocarbonylation,desilylation and oxidation processes from 3-iodo-2-propenylindoles

A novel one-pot synthesis of carbazole-1,4-quinone by consecutive Pd-catalyzed cyclocarbonylation, desilylation, and oxidation reactions is described. We propose a possible mechanism of the cyclocarbonylation reaction between 3-iodo-2-propenylindole and CO (1 atm) in the presence of a tributyl(vinyl)tin and Pd-catalyst and the resulting acylpalladium species was directly coupled with a terminal alkene to produce the carbazole-1,4-quinone. To our knowledge, this is the first example of this type of reaction. A new formal total synthesis of a carbazole-1,4-quinone alkaloid, murrayaquinone A was established using this reaction.     

Straightforward synthesis of fucoxanthin short-chain derivatives via modified-Julia olefination

Fucoxanthin is an essential pigment for the light-harvesting of aquatic algae. It exhibits high energy transfer efficiencies to Chl a (>80%) as well as peridinin (>95%). In order to verify the generality and specificity of the noticeable observation on the ICT excited energy state character, which was found in the study of peridinin, we achieved the straightforward synthesis of a series of fucoxanthin short-chain derivatives via the modified-Julia olefination with the aldehyde half segment possessing a β,γ-epoxyketone function. The established method was successfully applied to the synthesis of the epoxy olefin derivative as an allene modified fucoxanthin analogue.     

Consequence analysis of blast wave from accidental gas explosions

Recently, consequence analyses of accidental gas explosions are often carried out to assess the risk of chemical plants, hazardous-materials sites and new energy systems. In these consequence analyses, it is indispensable to adequately predict the blast-wave (pressure-wave) intensity from gas deflagrations. Some prediction models already exist; however, most of them are based on the theory for explosives and adjusting parameters are needed for evaluating gas deflagrations. In this study, new prediction methods for gas deflagrations were developed. From theoretical analysis of blast-wave generation by a gas deflagration, an evaluation equation of the blast-wave intensity was derived. As the scale of gas deflagration becomes larger, flame front instability (especially hydrodynamic instability) would be more effective and the flame propagating velocity starts to be accelerated. Therefore, the equation was modified considering the effect of flame instability. The evaluations by this modified equation agreed well with the results of large scale experiments. By this analysis, it was found that not only total energy release but also combustion reaction rate has to be introduced into the prediction of gas deflagrations. Using this concept, a modified scale model to predict the blast-wave intensity was developed by improving the previous scale model introducing the term of combustion reaction rate as burning velocity. Furthermore, scale analysis was performed to develop the new scaling law. The universal relationship between scaled distance and overpressure has been realized by this new scaling law for gas deflagrations. In summary, these results provide new methods for accurate prediction of the blast-wave intensity from gas deflagrations.     

Spin nematic state as a candidate of the hidden order phase of URu2Si2

Motivated by the recent discovery of broken fourfold symmetry in the hidden order phase of URu2Si2 [R. Okazaki et al., Science 331, 439 (2011)], we examine a scenario of a spin nematic state as a possible candidate of the hidden order phase. We demonstrate that the scenario naturally explains most of experimental observations, and furthermore, reproduces successfully the temperature dependence of the spin anisotropy detected by the above-mentioned experiment in a semiquantitative way. This result provides strong evidence for the realization of the spin nematic order.     

Total synthesis of gelsemoxonine

The first total synthesis of gelsemoxonine (1) has been accomplished. Divinylcyclopropane-cycloheptadiene rearrangement of the highly functionalized substrate was successfully applied to assemble the spiro-quaternary carbon center connected to the bicyclic seven-membered core structure. A one-pot isomerization reaction of the α,β-unsaturated aldehyde to the saturated ester via the TMSCN-DBU reagent combination allowed a facile diastereoselective introduction of the latent nitrogen functionality of the unique azetidine moiety.