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Isomonodromic deformations were first studied by Richard Fuchs, with early pioneering contributions from Lazarus Fuchs, Paul Painlevé, René Garnier, and Ludwig Schlesinger. Inspired by results in statistical mechanics , a seminal contribution to the theory was made by Michio Jimbo , Tetsuji Miwa , and Kimio Ueno , who studied cases involving ...
It says that the propagation of singularities follows the bicharacteristic flow of the principal symbol of . The theorem appeared 1972 in a work on Fourier integral operators by Johannes Jisse Duistermaat and Lars Hörmander and since then there have been many generalizations which are known under the name propagation of singularities.
Essential singularities approach no limit, not even if valid answers are extended to include . In real analysis, a singularity or discontinuity is a property of a function alone. Any singularities that may exist in the derivative of a function are considered as belonging to the derivative, not to the original function.
Penrose–Hawking singularity theorems, in general relativity theory, theorems about how gravitation produces singularities such as in black holes; Prandtl–Glauert singularity, the point at which a sudden drop in air pressure occurs; Singularity (climate), a weather phenomenon associated with a specific calendar date
An important reason why singularities cause problems in mathematics is that, with a failure of manifold structure, the invocation of Poincaré duality is also disallowed. A major advance was the introduction of intersection cohomology, which arose initially from attempts to
It is still an open question whether (classical) general relativity predicts spacelike singularities in the interior of realistic charged or rotating black holes, or whether these are artefacts of high-symmetry solutions and turn into null or timelike singularities when perturbations are added. [citation needed]
WASHINGTON ‒ Rep. Bennie Thompson, who led a House committee investigating the Jan. 6 riot, said there's been an "uptick" in threating calls against members of Congress since President Donald ...
As predicted by catastrophe theory, singularities are generic, and stable under perturbation. This explains how the bright lines and surfaces are stable under perturbation. The caustics one sees at the bottom of a swimming pool, for example, have a distinctive texture and only has a few types of singular points, even though the surface of the ...