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...

Given a large number N of copies of a qubit state of which we wish to estimate its purity, we prove that separable-measurement protocols can be as efficient as the optimal joint-measurement one if classical communication is used. This shows that the optimal estimation of the entanglement of a two-qubit state can also be achieved asymptotically with fully separable measurements. Thus, quantum me...

We emphasize the role of the choice of vocabulary in formalization of a mathematical area and remark that this is a particular preoccupation of logicians. We use this framework to discuss Kennedy’s notion of ‘formalism freeness’ in the context of various schools in model theory. Then we clarify some of the mathematical issues in recent discussions of purity in the proof of the Desargues proposi...

In the last 15 years NMR has become a reference technique for the determination of purity for organic standards containing NMR active nuclei [1, 2]. The puzzle proposed for this Analytical Challenge was focused on the use of 1H-NMR for the characterization of a phenylbutazone standard. Such material was purchased from Sigma-Aldrich and analyzed in parallel by HPLC-UV and 1H-NMR. Initially, appl...

Logical inferentialism claims that the meaning of the logical constants should be given, not model-theoretically, but by the rules of inference of a suitable calculus. It has been claimed that certain proof-theoretical systems, most particularly, labelled deductive systems for modal logic, are unsuitable, on the grounds that they are semantically polluted and suffer from an untoward intrusion o...

We show that entanglement can always arise in the interaction of an arbitrarily large system in any mixed state with a single qubit in a pure state. This small initial purity is enough to enforce entanglement even when the total entropy is close to maximum. We demonstrate this feature using the Jaynes-Cummings interaction of a two-level atom in a pure state with a field in a thermal state at an...

We experimentally and theoretically demonstrate the purity (polarization) control of qubits entangled with multiple spins, using induced dephasing in nuclear magnetic resonance setups to simulate repeated quantum measurements. We show that one may steer the qubit ensemble towards a quasiequilibrium state of a certain purity by choosing suitable time intervals between dephasing operations. These...