PROBLEM Historically, hydrogen has been employed in a variety of industrial chemical processes. Typically, the purity requirements for this hydrogen have tolerated contaminant levels ranging from ppm to low percentages, depending upon the application. The use of hydrogen has now expanded into novel applications such as alternative fuel for use in transportation and stationary electrical generat...

We classify the entanglement of two-mode Gaussian states according to their degree of total and partial mixedness. We derive exact bounds that determine maximally and minimally entangled states for fixed global and marginal purities. This characterization allows for an experimentally reliable estimate of continuous variable entanglement based on measurements of purity.

Let κ = Fq be a finite field of characteristic p > 0, and k be a fixed algebraic closure of κ. We fix a prime ` 6= p, and an isomorphism τ : Q` → C. Whenever we want to denote something (e.g. scheme, sheaf, morphism, etc.) defined over κ, we will put a subscript 0 (e.g. X0 is a scheme over κ, F0 is a Weil sheaf defined over X0, etc.), and when the subscript is dropped, this means the correspond...

Three recrystallization technics were used to fractionate five commercial cholesterol products and one artificial mixture. One technic involved the recrystallization of cholesterol from absolute ethyl alcohol, the second technic involved the recrystallization of cholesterol from glacial acetic acid, and the third technic used the dibromide derivative method. The molar absorptivities for the var...

Restricting destructive update to values of a distinguished reference type prevents functions from being polymorphic in the mutability of their arguments. This restriction makes it easier to reason about program behaviour during transformation, but the lack of polymorphism reduces the expressiveness of the language. We present a System-F style core language that uses dependently kinded proof wi...