Volumetric q-space imaging by 3D diffusion-weighted MRI

High b-value diffusion magnetic resonance imaging (MRI) enables us to detect far smaller architectures, by using q-space analysis, than the resolution in conventional MRI. Average displacement, one of the q-space parameters, quantitatively reflects architecture size and is very useful in observing small changes in microstructures in vivo (e.g., neurodegeneration, tumor heterogeneity, and others). Diffusion-weighted imaging (DWI) is performed by a two-dimensional (2D) multislice method; however, due to finite slice thickness and slice gap, there is a partial-volume effect that makes it difficult to detect the net q-space signal. On the other hand, three-dimensional (3D) MRI, having the advantages of very thin slice thickness and no slice gap (contiguous slices), allows volumetric evaluation acquired in a small isotropic voxel, as compared to 2D multislice imaging. Little is known about the isotropic high-resolution 3D DWI application to q-space analysis. In this study, we have developed and implemented a high b-value 3D DWI sequence, applied q-space analysis to study the reliability of high b-value 3D DWI and obtained a microscopic analytical map with isotropic high resolution and less contamination.     

On the cellular decomposition of the exceptional Lie group

The present note is to give a cellular decomposition of the compact connected exceptional Lie group .

     

Kinetic stability of hematite nanoparticles: the effect of particle sizes

Nanoparticles are ubiquitous in environment and are potentially important in many environmental processes such as sorption, coprecipitation, redox reactions, and dissolution. To investigate particle size effects on nanoparticle aggregation and stability, this study tested aggregation behavior of 12(±2), 32(±3), and 65(±3) nm (hydrated radius) hematite particles under environmental relevant pH and ionic strength conditions. The results showed that at the same ionic strength and pH conditions, different particle sizes show different tendency to aggregate. At the same ionic strength, aggregation rates are higher for smaller particles. The critical coagulation concentration also depends on particle size, and decreases as particle size decreases. As the particle size decreases, fast aggregation shifted to lower pH. This may be related to a dependence of PZC on particle size originating from change of structure and surface energy characteristics as particle size decreases. Under the same conditions, aggregation occurs faster as particle concentration increases. Even though the nanoparticles of different sizes show different response to the same pH and ionic strength, DLVO theory can be used to qualitatively understand hematite nanoparticle aggregation behavior.     

The asymptotic behavior of solutions to the Kirchhoff equation with a viscous damping term

We study the asymptotic behavior of solutions to an equation describing non-linear vibration of a string with viscosity. In the case when the string is unstretched (the degenerate case), we determine the decay order of solutions by investigating the dynamics near an infinite-dimensional center manifold. Moreover, we classify the asymptotic behavior of all solutions from a dynamical systems point of view. We also deal with the case where the string is stretched (the nondegenerate case).     

Comparison of the accuracy of periodic reaction field methods in molecular dynamics simulations of a model liquid crystal system

A periodic reaction field (PRF) method is a technique to estimate long‐range interactions. The method has the potential to effectively reduce the computational cost while maintaining adequate accuracy. We performed molecular dynamics (MD) simulations of a model liquid‐crystal system to assess the accuracy of some variations of the PRF method in low‐charge‐density systems. All the methods had adequate accuracy compared with the results of the particle mesh Ewald (PME) method, except for a few simulation conditions. Furthermore, in all of the simulation conditions, one of the PRF methods had the same accuracy as the PME method. © 2015 Wiley Periodicals, Inc.     

On the Umemura polynomials for the Painlevé III equation

A determinant expression of Jacobi–Trudi type for the rational solutions of the Painlevé III (P_III) equation is presented. Entries of determinant are given by the Laguerre polynomials. Degeneration of this determinant expression to that for the rational solutions of P_II is discussed by applying the coalescence procedure.     

Gagliardo–Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces

The aim of this paper is to give a Gagliardo–Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces over spaces of homogeneous type.