Search results
Results From The WOW.Com Content Network
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.
The singularities of solutions of these equations are The point , and; The point 0 for types III, V and VI, and; The point 1 for type VI, and; Possibly some movable poles; For type I, the singularities are (movable) double poles of residue 0, and the solutions all have an infinite number of such poles in the complex plane.
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
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.
The attributes of singularities include the following in various degrees, according to context: Instability: because singularities tend to produce effects out of proportion to the size of initial causes. System relatedness: the effects of a singularity are characteristic of the system.
Trying to find a complete and precise definition of singularities in the theory of general relativity, the current best theory of gravity, remains a difficult problem. [1] [2] A singularity in general relativity can be defined by the scalar invariant curvature becoming infinite [3] or, better, by a geodesic being incomplete. [4]
Null singularities: These singularities occur on light-like or null surfaces. An example might be found in certain types of black hole interiors, such as the Cauchy horizon of a charged (Reissner–Nordström) or rotating black hole. A singularity can be either strong or weak: