A model for the pinching of an inviscid liquid column, originally developed by Lee, is considered. We find that Lee’s model has a singularity in the curvature at a finite thread radius, and therefore does not describe breakup. However, the observed steepening of the profile corresponds to experiments with fluids at low viscosity. The singularity has similarity form, which we compute analyticall...

We study the self-tuning of general brane junctions and brane networks on the 6-dimensional space-time. For the general brane junctions, there may exist one fine-tuning among the brane tensions. For the brane networks, similar to the 5-dimensional self-tuning brane models, the brane tensions can be set arbitrarily and there exists the singularity for the metric and bulk scalar. And if we want t...

We study singular real-analytic Levi-flat hypersurfaces in complex projective space. We give necessary and sufficient conditions for such a hypersurface to be a pullback of a real-analytic curve in C via a meromorphic function. We define the rank of a real hypersurface and study the connections between rank, degree, and the type and size of the singularity for Levi-flat hypersurfaces. Finally, ...

We study the multiplicity modulo 2 of real analytic hypersurfaces. We prove that, under some assumptions on the singularity, the multiplicity modulo 2 is preserved by subanalytic bi-Lipschitz homeomorphisms of R. In the first part of the paper, we find a subset of the tangent cone which determines the multiplicity mod 2 and prove that this subset of S is preserved by the antipodal map. The stud...

The quotient-cusp singularities are isolated complex surface singularities that are double-covered by cusp singularities. We show that the universal abelian cover of such a singularity, branched only at the singular point, is a complete intersection cusp singularity of embedding dimension 4. This supports a general conjecture that we make about the universal abelian cover of a Q-Gorenstein sing...

in this paper, we obtain a suitable mathematical model for the seismic response of dams. by using the shear beam model (sb model), we give a mathematical formulation that it is a partial differential equation and transform it to the sturm-liouville equation.

Conditions under which gravity coupled to self interacting scalar field determines singularity formation are found and discussed. It is shown that, under a suitable matching with an external space, the boundary, if collapses completely, may give rise to a naked singularity. Issues related to the strength of the singularity are discussed.

We construct a non-decreasing pure jump Markov process, whose jump measure heavily depends on the values taken by the process. We determine the singularity spectrum of this process, which turns out to be random and to depend locally on the values taken by the process. The result relies on fine properties of the distribution of Poisson point processes and on ubiquity theorems.

Let π : X → S be a holomorphic map from a compact Kähler manifold (X, gX) to a compact Riemann surface S. Let Σπ be the critical locus of π and let ∆ = π(Σπ) be the discriminant locus. Let (ξ, hξ) be a holomorphic Hermitian vector bundle on X. We determine the singularity of the Quillen metric on detRπ∗ξ near ∆ with respect to gX |TX/S and hξ.

The evolution of a small but nite three-dimensional disturbance on a at uniform vortex sheet is studied numerically on the basis of a Lagrangian representation of the motion. The numerical simulations connrm the asymptotic analysis by Ishihara and Kaneda (1995; J. Fluid Mech., 300, 339-366) for the spontaneous singularity formation in the shape of the vortex sheet. They also suggest that the si...