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For example, given a = f(x) = a 0 x 0 + a 1 x 1 + ··· and b = g(x) = b 0 x 0 + b 1 x 1 + ···, the product ab is a specific value of W(x) = f(x)g(x). One may easily find points along W(x) at small values of x, and interpolation based on those points will yield the terms of W(x) and the specific product ab. As fomulated in Karatsuba ...
4-2-0. Under the Whyte notation for the classification of steam locomotives, 4-2-0 represents the wheel arrangement of four leading wheels on two axles, two powered driving wheels on one axle and no trailing wheels. This type of locomotive is often called a Jervis type, the name of the original designer.
In mathematics, the associated Legendre polynomials are the canonical solutions of the general Legendre equation. or equivalently. where the indices ℓ and m (which are integers) are referred to as the degree and order of the associated Legendre polynomial respectively. This equation has nonzero solutions that are nonsingular on [−1, 1] only ...
The subsampling scheme is commonly expressed as a three-part ratio J:a:b (e.g. 4:2:2) or four parts, if alpha channel is present (e.g. 4:2:2:4), that describe the number of luminance and chrominance samples in a conceptual region that is J pixels wide and 2 pixels high. The parts are (in their respective order):
Andy Mac and 49-year-old South African Dallas Oberholzer are the older guys in a men's Olympic competition where the youngest entrant is 16-year-old Viktor Solmunde of Denmark. Macdonald finished ...
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, [ 1] and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. [ 2] Since the problem had withstood the attacks ...
X-2 #10: April 25, 1956 Frank Everest 46-674 USAF 8 1.40 15,250 Third powered flight. First supersonic flight. Both chambers ignited. X-2 #11: May 1, 1956 Frank Everest 46-674 USAF 9 1.683 16,378 Fourth powered flight. X-2 #12: May 11, 1956 Frank Everest 46-674 USAF 10 1.8 18,300 Fifth powered flight. X-2 #13: May 22, 1956 Frank Everest 46-674 ...
For this purpose, we consider for each x i the y i which is in the same residue class modulo m and between (–m + 1)/2 and m/2 (possibly included). It follows that y 1 2 + y 2 2 + y 3 2 + y 4 2 = mr, for some strictly positive integer r less than m. Finally, another appeal to Euler's four-square identity shows that mpmr = z 1 2 + z 2 2 + z 3 2 ...