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R ∗ = 8.314 32 × 10 3 N⋅m⋅kmol −1 ⋅K −1 = 8.314 32 J⋅K −1 ⋅mol −1. Note the use of the kilomole, with the resulting factor of 1000 in the constant. The USSA1976 acknowledges that this value is not consistent with the cited values for the Avogadro constant and the Boltzmann constant. [ 13 ]
Renard series are a system of preferred numbers dividing an interval from 1 to 10 into 5, 10, 20, or 40 steps. [1] This set of preferred numbers was proposed ca. 1877 by French army engineer Colonel Charles Renard [ 2 ] [ 3 ] [ 4 ] and reportedly published in an 1886 instruction for captive balloon troops, thus receiving the current name in ...
In the Cambridge Structural Database of small-molecule structures, more than 95% of the 500,000+ crystals have an R-factor lower than 0.15, and 9.5% have an R-factor lower than 0.03. Crystallographers also use the Free R-Factor ( R F r e e {\displaystyle R_{Free}} ) [ 3 ] to assess possible overmodeling of the data.
The entry 4+2i = −i(1+i) 2 (2+i), for example, could also be written as 4+2i= (1+i) 2 (1−2i). The entries in the table resolve this ambiguity by the following convention: the factors are primes in the right complex half plane with absolute value of the real part larger than or equal to the absolute value of the imaginary part.
Any real number can be written in the form m × 10 ^ n in many ways: for example, 350 can be written as 3.5 × 10 2 or 35 × 10 1 or 350 × 10 0. In normalized scientific notation (called "standard form" in the United Kingdom), the exponent n is chosen so that the absolute value of m remains at least one but less than ten ( 1 ≤ | m | < 10 ).
for all x and y such that −1 < x < 1 (otherwise the denominator f X (x) vanishes) and < < (otherwise the conditional probability degenerates to 0 or 1). One may also treat the conditional probability as a random variable, — a function of the random variable X , namely,
Then let x and y be ordered 5-element vectors containing the above data: x = (1, 2, 3, 5, 8) and y = (0.11, 0.12, 0.13, 0.15, 0.18). By the usual procedure for finding the angle θ between two vectors (see dot product ), the uncentered correlation coefficient is
Ordinary least squares regression of Okun's law.Since the regression line does not miss any of the points by very much, the R 2 of the regression is relatively high.. In statistics, the coefficient of determination, denoted R 2 or r 2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s).