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The electronic band structure of MoS 2 single crystals has been investigated using angle-resolved photoelectron spectroscopy and first-principles calculations. The orbital symmetry and k dispersion of these electronic states responsible for the direct and the indirect electronic band gaps have been unambiguously determined. By experimentally probing an increase of the electronic band gap, we conclude that a MoS 2 (0002) surface localized state exists just below the valence band maximum at the point. This electronic state originates from the sulfur planes within the topmost layer. Our comprehensive study addresses the surface electronic structure of MoS 2 and the role of van der Waals interlayer interactions.

The electronic structure of spinel FeV 2 O 4 , which contains two Jahn-Teller active Fe and V ions, has been investigated by employing soft x-ray absorption spectroscopy (XAS), soft x-ray magnetic circular dichroism (XMCD), and nuclear magnetic resonance (NMR). XAS indicates that V ions are trivalent and Fe ions are nearly divalent. The signs of V and Fe 2p XMCD spectra are opposite to each other. It is found that the effect of the V 3d spin-orbit interaction on the V 2p XMCD spectrum is negligible, indicating that the orbital ordering of V t 2g states occurs from the real orbital states and that the orbital moment of a V 3+ ion is mostly quenched. NMR shows that V spins are canted to have a Yafet-Kittel-type triangular spin configuration.

We investigated how the opportunity to learn (OTL) with different types of mathematics tasks are related to mathematical literacy and the role of perceived control in the relationship between OTL and mathematical literacy. The structural equation modeling was applied to the data of 1,649 Korean students from the PISA 2012 database. OTL with the four different types of tasks – algebraic word problems, procedural tasks, pure mathematics reasoning, and applied mathematics reasoning – were measured via student survey on how often they have encountered each type of task in their mathematics lessons and tests. The results showed that OTL with the procedural tasks was likely to increase mathematical literacy directly and indirectly through internal perceived control. Engaging in the applied reasoning tasks is positively related to external perceived control, but negatively to mathematical literacy.