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In the differential form formulation on arbitrary space times, F = 1 / 2 F αβ dx α ∧ dx β is the electromagnetic tensor considered as a 2-form, A = A α dx α is the potential 1-form, = is the current 3-form, d is the exterior derivative, and is the Hodge star on forms defined (up to its orientation, i.e. its sign) by the ...
Many easily stated number problems have solutions that require sophisticated methods, often from across mathematics. A prominent example is Fermat's Last Theorem . This conjecture was stated in 1637 by Pierre de Fermat, but it was proved only in 1994 by Andrew Wiles , who used tools including scheme theory from algebraic geometry , category ...
In the late 17th century, Sir Isaac Newton had advocated that light was corpuscular (particulate), but Christiaan Huygens took an opposing wave description. While Newton had favored a particle approach, he was the first to attempt to reconcile both wave and particle theories of light, and the only one in his time to consider both, thereby anticipating modern wave-particle duality.
[W 1] As of November 2024, over 25% of Wikipedia's traffic was from the United States, followed by Japan at 6.2%, the United Kingdom at 5.6%, Russia at 5.0%, Germany at 4.8%, and the remaining 53.3% split among other countries. [8]
[1] [4] [33] To elaborate, in trying to find the length of a wavy non-fractal curve, one could find straight segments of some measuring tool small enough to lay end to end over the waves, where the pieces could get small enough to be considered to conform to the curve in the normal manner of measuring with a tape measure. But in measuring an ...
[1]: 1–2 Its discovery was a significant landmark in the development of quantum mechanics. It is named after Erwin Schrödinger , an Austrian physicist, who postulated the equation in 1925 and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933.
The eminent historian of mathematics Carl Boyer once called Euler's Introductio in analysin infinitorum the greatest modern textbook in mathematics. [32] Published in two volumes, [ 33 ] [ 34 ] this book more than any other work succeeded in establishing analysis as a major branch of mathematics, with a focus and approach distinct from that ...
The racial composition of the city was 39.3% Black alone (42.0% Black alone or in combination), 36.3% White alone (41.9% White alone or in combination), 8.7% Asian alone, 0.4% American Indian and Alaska Native alone, 8.7% some other race, and 6.9% multiracial. 14.9% of residents were Hispanic or Latino.