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Rutherford scattering cross-section is strongly peaked around zero degrees, and yet has nonzero values out to 180 degrees. This formula predicted the results that Geiger measured in the coming year. The scattering probability into small angles greatly exceeds the probability in to larger angles, reflecting the tiny nucleus surrounded by empty ...
This family overlaps with the first: when one of the two "factor" polygons is a square, the product is equivalent to a hyperprism whose base is a three-dimensional prism. The symmetry number of a duoprism whose factors are a p -gon and a q -gon (a " p,q -duoprism") is 4 pq if p ≠ q ; if the factors are both p -gons, the symmetry number is 8 p 2 .
More formulas of this nature can be given, as explained by Ramanujan's theory of elliptic functions to alternative bases. Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function τ {\displaystyle \tau } and the Fourier coefficients j {\displaystyle \mathrm {j} } of the J-invariant ...
New data from Freddie Mac shows average mortgage rates for 30-year terms sliding closer to 6.00% as of Friday, September 20, 2024, rounding out a week in which the Federal Reserve announced a long ...
Sam Darnold & Justin Jefferson (97-yd TD) Two plays after the Vikings defense forced a turnover on downs near their own goal line, Darnold & Jefferson connect deep to put Minnesota up two scores.
A 27-year-old Nebraska man who posed as someone a decade younger and attended high school for more than 50 days was sentenced to at least 85 years in prison in connection with sex crimes charges ...
Calculus. In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative.
Isaac Barrow. Succeeded by. William Whiston. Signature. Sir Isaac Newton FRS (25 December 1642 – 20 March 1726/27 [a]) was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author who was described in his time as a natural philosopher. [7] He was a key figure in the Scientific Revolution and the ...