We study equi-singular strata of curves with two singular points of prescribed types. The method of our previous work [Kerner04] is generalized to this case. This allows to solve the enumerative problem for plane curves with two singular points of linear singularity types. In the general case this reduces the enumerative questions to the problem of collision of the two singular points. The meth...

Under certain conditions, we give an estimate from above on the number of differential equations of order r+1 with prescribed regular singular points, prescribed exponents at singular points, and having a quasi-polynomial flag of solutions. The estimate is given in terms of a suitable weight subspace of the tensor power U(n−) , where n is the number of singular points in C and U(n−) is the enve...

We study the parabolic obstacle problem ∆u− ut = fχ{u>0}, u ≥ 0, f ∈ L with f(0) = 1 and obtain two monotonicity formulae, one that applies for general free boundary points and one for singular free boundary points. These are used to prove a second order Taylor expansion at singular points (under a pointwise Dini condition), with an estimate of the error (under a pointwise double Dini condition...

In this paper, we investigate infinite product representation of the solution of a Sturm- Liouville equation with an indefinite weight function which has two zeros and/or singularities in a finite interval. First, by using of the asymptotic estimates provided in [W. Eberhard, G. Freiling, K. Wilcken-Stoeber, Indefinite eigenvalue problems with several singular points and turning points, Math. N...

The numerical analysis of boundary layer effect is one of the major concerned problems in boundary element method (BEM). The accuracy of this problem depends on the precision of the evaluation of the nearly singular integrals. In the boundary element analysis with direct formulation, the hyper-singular integral will arise from the potential derivative boundary integral equations (BIEs). Thus th...

This paper aims to present a fingerprint singular point detection algorithm and a rule-based fingerprint classification method. The singular point detection algorithm uses a quantization approach on the orientation field of the fingerprint image and seeks to locate the core and delta points via the changes of the gray levels around a 2x2 window. It has been found that with the application of an...

Because of the hairy ball theorem, the only closed 2-manifold that supports a lattice in its tangent space is T . But, if singular points (i.e. points whose tangent space is not endowed with 2 distinct coordinate directions) are allowed, then it becomes possible to give the tangent space a lattice. Because the lattice is well defined everywhere around the points, the effect of moving around the...