On a question of Gromov about the Wirtinger inequalities

We prove that Gromov’s \(\mathrm {Cycl}_4(0)\) condition implies \(\mathrm {Wir}_k\) inequalities for any \(k \ge 4\), which answers a question of Gromov (J Math Sci N Y 119(2):178–200, 2004).     

Boundary Behavior of Monotone Sobolev Functions in Orlicz Spaces on John Domains in a Metric Space

This paper deals with weighted boundary limits of monotone Sobolev functions in Orlicz spaces on bounded s-John domains in a metric space.     

How many metal atoms are needed to dehydrogenate an ethylene molecule on metal clusters?: Correlation between reactivity and electronic structures of Fen+, Con+, and Nin+

The absolute cross section for dehydrogenation of an ethylene molecule on Mn+ [Fen+ (n = 2-28), Con+ (n = 8-29), and Nin+ (n = 3-30)] was measured as a function of the cluster size n in a gas-beam geometry at a collision energy of 0.4 eV in the center-of-mass frame in an apparatus equipped with a tandem-type mass spectrometer. It is found that (1) the dehydrogenation cross section increases rapidly above a cluster size of approximately 18 on Fen+, approximately 13 and approximately 18 on Con+, and approximately 10 on Nin+ and (2) the rapid increase of the cross section for Mn+ occurs at a cluster size where the 3d electrons start to contribute to the highest occupied levels of Mn+. These findings lead us to conclude that the 3d electrons of Mn+ play a central role in the dehydrogenation on Mn+.     

Pressure-induced phase transitions in the Cd-Yb periodic approximant to a quasicrystal

The phase study of a Cd-Yb 1/1 approximant crystal over a wide pressure and temperature range is crucial for the comparison study between periodic and quasiperiodic crystals. The Cd(4) tetrahedra, the most inner part of the atomic clusters, exhibited various structural ordering in the orientation sensitive to pressure and temperature. Five ordered phases appeared in a P-T span up to 5.2 GPa and down to 10 K. The propagation direction of ordering alternated from [110] to <111> to at about 1.0 GPa and again to [110] at 3.5-4.3 GPa. The primarily ordered phases that appeared by cooling to 210-250 K between 1.0-5.2 GPa further transformed to finely ordered ones at 120-155 K. Besides the original short-range type interaction, a long-range type interaction was likely developed under pressure to lead to the primary ordering of Cd(4) tetrahedra. Coexistence of these interactions is responsible for the complicated phase behavior.     

Mg segregation in a (1 1¯ 0 1) GaN grown on a 7° off-axis (0 0 1) Si substrate by MOVPE

Redistribution behavior of magnesium (Mg) in the N-terminated (1 1¯ 0 1) gallium nitride (GaN) has been investigated. A nominally undoped GaN layer was grown on a heavily Mg-doped GaN template by metalorganic vapor-phase epitaxy (MOVPE). Mg dopant profiles were measured by secondary ion mass spectrometry (SIMS) analysis. A slow decay of the Mg concentration was observed in the nominally undoped GaN layer due to the surface segregation. The calculated decay lengths of the (1 1¯ 0 1) GaN are ∼75–85 nm/decade. These values are shorter than the decay length determined in the sample grown on the Ga-terminated (0 0 0 1) GaN. This result indicates that Mg exhibited weak surface segregation in the (1 1¯ 0 1) GaN as compared to the (0 0 0 1) GaN. The weak surface segregation is in agreement with the high efficiency of Mg incorporation on the (1 1¯ 0 1) face. The high density of hydrogen was obtained in the (1 1¯ 0 1) GaN, which might enhance the Mg incorporation.     

Sobolev's inequality for Riesz potentials of functions in Morrey spaces of integral form

Morrey spaces have become a good tool for the study of existence and regularity of solutions of partial differential equations. Our aim in this paper is to give Sobolev's inequality for Riesz potentials of functions in Morrey spaces (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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 .