In Principia Mathematica, Whitehead and Russell were able to provide many detailed derivations of major theorems in set theory, finite and transfinite arithmetic, and elementary measure theory.
Although Principia succeeded in providing detailed derivations of many major theorems in finite and transfinite arithmetic, set theory, and elementary measure theory, two axioms in particular were arguably non-logical in character: the axiom of infinity and the axiom of reducibility.
Photon detectors are an elementary tool to measure electromagnetic waves at the quantum limit1,2 and are heavily demanded in the emerging quantum technologies such as communication3, sensing4 and computing5.
So there does appear a quasi-periodic tiling of the unit disk; it should not of course be forgotten that this quasi-periodicity holds only when the area of an "elementary cell" is measured in the appropriate hyperbolic units (see the previous section and the next).
Moving the car out of the way of an oncoming vehicle seems like a pretty elementary safety measure.
The time required to break the chemical bond in an elementary reaction has been measured and the characteristic repulsion length for the potential governing fragment separation has been obtained.
Leaf samples were crushed to powder with a ball mill (MM 200, Fisher Bioblock Scientific, France), then nitrogen content (Nm, %) was measured with an elementary analyser Eager 300 CHONS (FlashEA 1112, ThermoElectron Corporation, Waltham, MA, USA).
Then given the measure of information, an elementary general-purpose information processor is defined and used as a vehicle from which to estimate its overall performance based on the limiting transistor/interconnect parameters developed previously in.
While there, she brought her food-based curriculum into an elementary school in rural Trumansburg, New York, and carefully measured the results.
Topological helicity provides an elementary means of computing helicity for a magnetic flux rope by measuring its knotting, linking, and twisting.
Notions from measure theory and computability theory are used in the discussion below; an elementary presentation of the mathematics needed can be found in supplement B.2.
