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Several Problems in Global Singularity Theory (Singularity Theory and its Applications)

open access: yesSeveral Problems in Global Singularity Theory (Singularity Theory and its Applications)
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Singular Cardinals and the PCF Theory

Bulletin of Symbolic Logic, 1995
§1. Introduction. Among the most remarkable discoveries in set theory in the last quarter century is the rich structure of the arithmetic of singular cardinals, and its deep relationship to large cardinals. The problem of finding a complete set of rules describing the behavior of the continuum function 2ℵαfor singular ℵα's, known as theSingular ...
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A Singular Problem in Electrolytes Theory

Mathematical Methods in the Applied Sciences, 1997
Existence and nonexistence of solutions for a parabolic-elliptic system describing the electrodiffusion of ions are studied. This system is of the form: \[ u_t= \nabla\cdot(\nabla u- u\nabla\varphi),\quad \Delta(\varphi+ V)= u, \] where \(u,\varphi: \Omega\times\mathbb{R}^+\to \mathbb{R}\), \(V:\Omega\to \mathbb{R}\), and \(\Omega\) is a bounded smooth
Biler, Piotr, Nadzieja, Tadeusz
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Theory and Reduction of Singularities

1948
Let x1, x2,…, xr+1 be homogeneous point coordinates in a complex projective γ-dimensional space Sr. An algebraic variety V in S γ is the locus of point (x) satisfiying a system of algebraic equations, $${f_1}\left( {{x_{1,}} \ldots ,{x_\gamma }_{ + 1}} \right) = 0, \ldots ,{f_n}\left( {{x_1}, \ldots ,{x_{\gamma + 1}}} \right) = 0$$ (1) , where
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Canonical quantization of singular theories

Soviet Physics Journal, 1983
We construct here a formal operator formulation of a singular theory. In tackling this problem we shall bear in mind that there are many physically equivalent classical theories which can describe a physical system. Hence one may believe that all the quantum theories corresponding to these classical theories must also be physically equivalent and that ...
Dmitriy M. Gitman, Igor V. Tyutin
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NAIVE SINGULAR PERTURBATION THEORY

Mathematical Models and Methods in Applied Sciences, 2001
The paper demonstrates, via extremely simple examples, the shocks, spikes, and initial layers that arise in solving certain singularly perturbed initial value problems for first-order ordinary differential equations. As examples from stability theory, they are basic to many asymptotic techniques.
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Spacetime singularities in string theory

Physical Review Letters, 1990
Summary: It is shown that a large class of time-dependent solutions to Einstein's equation are classical solutions to string theory. These include metrics with large curvature and some with spacetime singularities. Unlike the case of orbifold singularities, it is shown that string propagation through the singluar region is not well behaved.
Horowitz, Gary T., Steif, Alan R.
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