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Analytic continuation around the pole at s = 1 leads to a region of negative values, including ζ(−1) = − + 1 / 12 . In zeta function regularization , the series ∑ n = 1 ∞ n {\textstyle \sum _{n=1}^{\infty }n} is replaced by the series ∑ n = 1 ∞ n − s . {\textstyle \sum _{n=1}^{\infty }n^{-s}.}
The electric charge Q, third component of weak isospin T 3 (also called T z, I 3 or I z) and weak hypercharge Y W are related by = +, (or by the alternative convention Q = T 3 + Y W). The first convention, used in this article, is equivalent to the earlier Gell-Mann–Nishijima formula .
Scientists. v. t. e. Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. This was first proven by British mathematician Samuel Earnshaw in 1842. It is usually cited in reference to magnetic fields, but was first ...
Bessel's correction. In statistics, Bessel's correction is the use of n − 1 instead of n in the formula for the sample variance and sample standard deviation, [1] where n is the number of observations in a sample. This method corrects the bias in the estimation of the population variance. It also partially corrects the bias in the estimation ...
In his 1911 paper , Rutherford assumed that the central charge of the atom was positive, but a negative charge would have fitted his scattering model just as well. [34] In a 1913 paper, [ 35 ] Rutherford declared that the "nucleus" (as he now called it) was indeed positively charged, based on the result of experiments exploring the scattering ...
The rms charge radius is a measure of the size of an atomic nucleus, particularly the proton distribution. The proton radius is about one femtometre = 10−15 metre. It can be measured by the scattering of electrons by the nucleus. Relative changes in the mean squared nuclear charge distribution can be precisely measured with atomic spectroscopy .
July 23, 2024 at 3:31 PM. Rep. Gregory Meeks (D-N.Y.) on Tuesday said he believes the candidacy of Vice President Harris will drive Black voter excitement to levels higher than what was seen in ...
Negative refraction. Negative refraction is the electromagnetic phenomenon where light rays become refracted at an interface that is opposite to their more commonly observed positive refractive properties. Negative refraction can be obtained by using a metamaterial which has been designed to achieve a negative value for (electric) permittivity ...