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In the empirical sciences, the so-called three-sigma rule of thumb (or 3 σ rule) expresses a conventional heuristic that nearly all values are taken to lie within three standard deviations of the mean, and thus it is empirically useful to treat 99.7% probability as near certainty.
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James K. Freericks (born 1963) is an American physicist and endowed chair at Georgetown University. He has worked in fields of condensed matter physics, mathematical physics, atomic physics, nonequilibrium physics, quantum computation, and quantum mechanics pedagogy.
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Most analytical instruments produce a signal even when a blank (matrix without analyte) is analyzed.This signal is referred to as the noise level. The instrument detection limit (IDL) is the analyte concentration that is required to produce a signal greater than three times the standard deviation of the noise level.
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An odd number is an indication of the involvement of a charged C atom or of a heteroatom lone pair replacing a CC double bond. Thus, [1,5] and [3,3] shifts become [1,4] and [2,3] shifts with heteroatoms, while preserving symmetry considerations. Hydrogens are omitted in the third example for clarity.
Gift giving can be monetarily stressful if that’s how you want to cheer people up after a tough year, but frugal alternatives could show that appreciation, too.