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The rule can then be derived [2] either from the Poisson approximation to the binomial distribution, or from the formula (1−p) n for the probability of zero events in the binomial distribution. In the latter case, the edge of the confidence interval is given by Pr(X = 0) = 0.05 and hence (1−p) n = .05 so n ln(1–p) = ln .05 ≈ −2
Cyclooctadiene iridium methoxide dimer is an organoiridium compound with the formula Ir 2 (OCH 3) 2 (C 8 H 12) 2, where C 8 H 12 is the diene 1,5-cyclooctadiene. It is a yellow solid that is soluble in organic solvents. The complex is used as a precursor to other iridium complexes, some of which are used in homogeneous catalysis. [1]
Another example is the bicyclic OBO protecting group (4-methyl-2,6,7-trioxa-bicyclo[2.2.2]octan-1-yl) which is formed by the action of (3-methyloxetan-3-yl)methanol on activated carboxylic acids in the presence of Lewis acids. The group is base stable and can be cleaved in two steps under mild conditions, mildly acidic hydrolysis yields the ...
A Golomb ruler of order m with length n may be optimal in either of two respects: [11]: 237 It may be optimally dense, exhibiting maximal m for the specific value of n, It may be optimally short, exhibiting minimal n for the specific value of m. The general term optimal Golomb ruler is used to refer to the second type of optimality.
P(OCH 3) 3 → CH 3 P(O)(OCH 3) 2. As a ligand, trimethyl phosphite has a smaller cone angle and better acceptor properties relative to trimethylphosphine. A representative derivative is the colorless tetrahedral complex Ni(P(OMe) 3) 4 (m.p. 108 °C). [4] The tridentate ligand called the Kläui ligand is derived from trimethyl phosphite. The ...
It is named after Carl Johannes Thomae, but has many other names: the popcorn function, the raindrop function, the countable cloud function, the modified Dirichlet function, the ruler function (not to be confused with the integer ruler function), [2] the Riemann function, or the Stars over Babylon (John Horton Conway's name). [3]
If the null hypothesis is true, the likelihood ratio test, the Wald test, and the Score test are asymptotically equivalent tests of hypotheses. [8] [9] When testing nested models, the statistics for each test then converge to a Chi-squared distribution with degrees of freedom equal to the difference in degrees of freedom in the two models.
The calculator described above was called "Model No. 1" . [6] Model 2 had scales on the inner cylinder for calculating logs and sines.The "Fuller-Bakewell" model 3 had two scales of angles printed on the inner cylinder to calculate cosine² and sine ⋅ cosine [note 1] for use by engineers and surveyors for tacheometry calculations.