The idea is simple (for these who know funcoids theory). But to find exact formulations about this is notoriously difficult. Below are attempts to formulate things about the theory of singularities. Definition 2. Singularity level is a transitive, T 2-separable endofuncoid. Let ν be a singularity level. Let ∆ be a filter.

The Ricci curvature at an isolated singularity of an immersed hypersurface exhibits a local behaviour echoing a global property of the Ricci curvature on a complete hypersurface in euclidean space (i.e., the Efimov theorem [12], that sup Ric ≥ 0). This local behaviour takes the form of a near universal bound on the decay of the Ricci curvature at a simple singularity (eg. a cone singularity) in...

The topology of a normal surface singularity does not determine the analytical invariants of its equisingularity class, but recent partial results indicated that this should be true under two restrictions, a topological one, that the link of the singularity is a rational homology sphere, and an analytical one, that the singularity is Q-Gorenstein. Neumann and Wahl conjectured that the singulari...

A finite subgroup of the conformal group SL(2,C) can be related to invariant polynomials on a hypersurface in C. The latter then carries a simple singularity, which resolves by a finite iteration of basic cycles of deprojections. The homological intersection graph of this cycles is the Dynkin graph of an ADE Lie group. The deformation of the simple singularity corresponds to ADE symmetry breaki...

The asymptotic analysis of a class of binomial sums that arise in information theory can be performed in a simple way by means of singularity analysis of generating functions. The method developed extends the range of applicability of singularity analysis techniques to combinatorial sums involving transcendental elements like logarithms or fractional powers. Analyse de singularit e et asymptoti...

Abstract-In this article, the authors first introduce four special singularity integral identities that involve the impulse, the doublet and the unit step functions, and provide a simple proof for each integral identity. Next, to demonstrate the use of these singularity integral identities, the authors consider the impulse response of two second-order RLC circuits and use these integrals to cal...

The analytic properties of the energy density ρ(t) of the cosmic fluid, and the Hubble parameter H(t), are investigated near to the future singularity t = ts assuming different forms for the equation of state. First, it is shown that the inclusion of quantum effects coming from the conformal anomaly modifies the singularity. Thereafter, we consider the effect coming from a bulk viscosity in the...