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Transition-metal dichalcogenide (TMD) semiconductors have been widely studied due to their distinctive electronic and optical properties. The property of TMD flakes is a function of their thickness, or layer number (N). How to determine the N of ultrathin TMD materials is of primary importance for fundamental study and practical applications. Raman mode intensity from substrates has been used t...

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Let be a binary relation in which is a real vector space of vector-valued discrete-time Ð ¤ ß Z Ñ Z stochastic processes with as the sequence of zero vectors. If satisfies four axioms, then ! Ð ¤ ß Z Ñ there are unique discount factors such that preferences regarding stochastic processes induce prefences among present value random vectors. Three of the axioms are familiar: weak ordering, contin...

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A fast introduction to the the construction of the cohomology of sheaves pioneered by A. Grothendieck and J.L. Verdier. The approach is from the point of view of derived categories, though this concept is never mentioned. 1. Sheaves Let R commutative ring with 1. We denote by RMod the category of R-modules. For any topological space X we denote by OpenpXq the collection of open subsets. It can ...

Shock wave Hugoniot data have been obtained for almandine-garnet of composition (Fe•.7•, Mgo.14, Ca•.•, Mno.•) Al,iaO• to pressures of >650 kb. The Hugoniot data indicate the onset of a high-pressure phase at 195 ñ 20 kb. Equation-of-state systematics and crystal chemical data (stemming largely from analog compounds) suggest that the high-pressure phase occurs in an 'ilmenitelike' structure wit...