On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution $\{u,p\}$ of the Navier–Stokes equation such that $|{?}^j{u(t,x)|=O(|x|}^{1?n?j})$ and $|{?}^j{p(t,x)|=O(|x|}^{?n?j})(j=0,1,\dots )$ uniformly in $t\in \mathbb{R}$ as $|x|\to \infty$. Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described.     

Conformity and precision of CO2 densimetry in CO2 inclusions: microthermometry versus Raman microspectroscopic densimetry

To assess the ability of densimetry for CO₂ fluid in CO₂ inclusions, we compare two methods, microthermometry and Raman microspectroscopic densimetry for CO₂. The comparative experiment was performed for nine CO₂ inclusions in three mantle xenoliths. The results are as follows: (1) microthermometry precisely determines CO₂ density with the range of 0.65 to 1.18 g/cm³ compared with Raman microspectroscopic densimetry; (2) CO₂ density obtained by Raman microspectroscopic densimetry is fairly consistent with that by microthermometry; (3) it is hard to determine CO₂ density in CO₂ inclusion with diameter of less than around 3 µm using microthermometry; and (4) microthermometry can be applied only to the CO₂ inclusion whose CO₂ density ranges from around 0.65 to 1.18 g/cm³, whereas the Raman microspectroscopic densimetry is applicable to CO₂ density ranging from 0.1 to 1.24 g/cm³. The above features carry the potential for estimation of depth origin of mantle‐derived rocks. The depth where the rocks were trapped by host magma can be estimated using both geothermometric data and CO₂ fluid density in CO₂ inclusions in the rocks. Typical precisions of density of CO₂ in CO₂ inclusions obtained by the Raman microspectroscopic densimetry (~0.01 g/cm³) and by the microthermometry (< 0.001 g/cm³) correspond to uncertainties in the depth origin of 2.4 km and < 1.7 km, respectively, at 1000 ± 50 °C. In case of the mantle under 750–1250 °C and 1 GPa, the CO₂ fluid has a density ranging from 1.06 g/cm³ to 1.21 g/cm³, which are well measured by the Raman microspectroscopic densimetry. Combination of both densimetries for CO₂ in mantle minerals elucidates the deep structure of the Earth. Copyright © 2012 John Wiley & Sons, Ltd.     

On the space curves with the same image under the gauss maps

From an irreducible complete immersed curveX in a projective space ? other than a line, one obtains a curveX ^′ in a Graasmann manifoldG of lines in ? that is the image ofX under the Gauss map, which is defined by the embedded tangents ofX. The main result of this article clarifies in case of positive characteristic what curvesX have the sameX′: It is shown thatX is uniquely determined byX′ ifX, or equivalentlyX′, has geometric genus at least two, and that for curvesX ₁ andX ₂ withX ₁ ≠X ₂ in ?, ifX′₁ =X′₂ inG and eitherX ₁ orX ₂ is reflexive, then bothX ₁ andX ₂ are rational or supersingular elliptic; moreover, examples of smoothX ₁ andX ₂ in that case are given.     

On canonicity of poset expansions

In this paper, we discuss the canonical extension of poset expansions. To obtain canonicity results on poset expansions, we study Ghilardi and Meloni’s canonicity methodology for Heyting algebras with unary modalities, raise the problem of extending the technique to poset expansions, and give a possible solution for the problem. Finally, we obtain a syntactic account of canonical inequalities on poset expansions consisting of constants, e_^{\epsilon_{\bot}} -additive operations, e^T{\epsilon^{\top}} -multiplicative operations, diamond, box, and strict adjoint pairs, and bounded poset expansions consisting of constants, e{\epsilon} -join preserving operations, e{\epsilon} -meet preserving operations, e{\epsilon} -additive operations, e{\epsilon} -multiplicative operations and adjoint pairs, which are more restricted than the case of lattice expansions, but can still account for Sahlqvist-like canonicity results.     

On Default Priors for Robust Bayesian Estimation with Divergences

This paper presents objective priors for robust Bayesian estimation against outliers based on divergences. The minimum γ-divergence estimator is well-known to work well in estimation against heavy contamination. The robust Bayesian methods by using quasi-posterior distributions based on divergences have been also proposed in recent years. In the objective Bayesian framework, the selection of default prior distributions under such quasi-posterior distributions is an important problem. In this study, we provide some properties of reference and moment matching priors under the quasi-posterior distribution based on the γ-divergence. In particular, we show that the proposed priors are approximately robust under the condition on the contamination distribution without assuming any conditions on the contamination ratio. Some simulation studies are also presented.     

Translational medicine of the glutamate AMPA receptor

Psychiatric and neurological disorders severely hamper patient’s quality of life. Despite their high unmet needs, the development of diagnostics and therapeutics has only made slow progress. This is due to limited evidence on the biological basis of these disorders in humans. Synapses are essential structural units of neurotransmission, and neuropsychiatric disorders are considered as “synapse diseases”. Thus, a translational approach with synaptic physiology is crucial to tackle these disorders. Among a variety of synapses, excitatory glutamatergic synapses play central roles in neuronal functions. The glutamate α-amino-3-hydroxy-5-methyl-4-isoxazole propionic acid receptor (AMPAR) is a principal component of glutamatergic neurotransmission; therefore, it is considered to be a promising translational target. Here, we review the limitations of current diagnostics and therapeutics of neuropsychiatric disorders and advocate the urgent need for the promotion of translational medicine based on the synaptic physiology of AMPAR. Furthermore, we introduce our recent translational approach to these disorders by targeting at AMPARs.     

Network images of drainage channels in sea spray icing by MR microscopy

An MR imaging system was developed to visualize brine drainage channels in sea spray icing. Brine pockets trapped in spray-ice matrices during ice growth are structural features of sea spray icing. Brine in the spray ice sample had drained out; therefore, using a suction pump, we filled the air gaps in the drainage channels with dodecane. In the experiments, 0.5-1.0 h was necessary to accumulate signals sufficient to obtain a 3-D micro-image; the image matrix comprised 128(3) voxels (each voxel was 200 microm per side). The MIP view showed that sea spray icing has a developed drainage-channel network structure.     

Observation of increase in Raman intensity of surface phonon polaritons on rough surfaces of ZnTe

An increase in Raman intensity of surface phonon polaritons has been observed in free-standing thin slabs (thickness ～ 7 μm) of single- crystal ZnTe with rough surfaces by a conventional Raman-scattering technique at room temperature. The samples with various root-mean- square roughness heights have been prepared by making use of final polishing powders with different mean-grit sizes, and the surface roughness has been confirmed by measuring the intensities of the diffuse scattering of the laser light. The increase of the Raman intensity is proportional to the mean-square height of the surface roughness, and the shift of the dispersion relation is also proportional to it. The frequency shift is explained by a perturbation theory of the surface-roughness-induced scattering.     

Detection of macroscopic entanglement by correlation of local observables

We propose a correlation of local observables on many sites in macroscopic quantum systems. By measuring the correlation one can detect, if any, superposition of macroscopically distinct states, which we call macroscopic entanglement, in arbitrary quantum states that are (effectively) homogeneous. Using this property, we also propose an index of macroscopic entanglement.