The application of threefold theory to deformations of rational singularities
as found in [Kollar-Shepherd-Barron] was important both for discovering M-resolutions and for the proofs of their properties.
131102) a study published in the latest edition of Physical Review Letters, a team of researchers has argued that naked singularities
cannot exist because when quantum-mechanical effects are included in the description of singularities
, they smooth out space-time, removing some of the problematic features stemming from general relativity alone.
The difficulties of obtaining accurate numerical solutions to Poisson's problems containing boundary singularities
are well known.
It is easy to see that exceptional singularities
of R-join-type curves can be only node singularities
45) may contain singularities
, and they can be divided into three categories that respectively correspond to three different types of wave front arrivals: 1) The body waves relevant to the regular reflected rays which are determined from the singularities
of [partial][phi]/[partial]y = 0,2) The interface waves, including Rayleigh surface waves, Stoneley interface waves, and the other possible leaky waves, which are determined from the singularities
Witten and Seiberg found a way to eliminate certain singularities
in a four-dimensional quantum field theory known as supersymmetry--an extension of the standard model of particle physics that attempts to incorporate all the forces of nature except gravity.
In general, if a smooth quartic curve has n hyperflexes, then the singularities
of the dual curve are (28 - n)[A.
of functions, wave fronts, caustics and multidimensional integrals.
I; algebraic and analytic aspects; proceedings.
The mathematicla expressions obtained involve no simplifying approximations and are free of singularities
, except in the aperture plane itself.
The loop picture of quantum gravity may prove useful for studying the problem of what quantum theory has to say about singularities
, Smolin says.
Weingard  has discussed some of the analogies between vacuum black hole singularities
and the big bang singularity, and in Section 3 I use some of his ideas to show how interesting arguments from analog can be constructed for the conclusion that the big bang has a cause.