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Geodesics orbiting a singularity
We study the behaviour of geodesics on a Riemannian manifold near a generalized conical or cuspidal singularity. We show that geodesics entering a...
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On deformations of isolated singularity functions
We study multi-parameter deformations of isolated singularity function-germs on either a subanalytic set or a complex analytic space. We prove that...
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A Family of Dicritical Foliations with One Singularity
We give an example of a family of dicritical foliations over the projective plane with one singularity and prove that it contains foliations with...
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Reconstructions of the Asymptotics of an Integral Determined by a Hyperbolic Unimodal Singularity
AbstractThe asymptotic behavior of an exponential integral is studied in which the phase function has the form of a special deformation of the germ...
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Singularity swap quadrature for nearly singular line integrals on closed curves in two dimensions
This paper presents a quadrature method for evaluating layer potentials in two dimensions close to periodic boundaries, discretized using the...
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Axisymmetric self-similar finite-time singularity solution of the Euler equations
Self-similar finite-time singularity solutions of the axisymmetric Euler equations in an infinite system with a swirl are provided. Using the Elgindi...
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The Singularity Set of Optimal Transportation Maps
AbstractOptimal transportation plays an important role in many engineering fields, especially in deep learning. By the Brenier theorem, computing...
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Singularity properties of Lorentzian Darboux surfaces in Lorentz–Minkowski spacetime
In this paper, by virtue of unfolding theory in singularity theory, we investigate the singularities of five special surfaces generated by a regular...
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Optimal Control for Suppression of Singularity in Chemotaxis via Flow Advection
This work focuses on the optimal control design for suppressing the singularity formation in chemotaxis governed by the parabolic-elliptic...
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Integrable Cross-Field Generation Based on Imposed Singularity Configuration—The 2D Manifold Case
This work presents the mathematical foundations for the generation of integrable cross-field on 2D manifolds based on user-imposed singularity...
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Finiteness Conditions and Relative Singularity Categories
We introduce the n -pure projective (resp., injective) dimension of complexes in n -pure derived categories, and give some criteria for computing these...
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Formation of Singularity for Full Compressible Magnetohydrodynamic Equations with Zero Resistivity in Two Dimensional Bounded Domains
We are concerned with singularity formation of strong solutions to the two-dimensional (2D) full compressible magnetohydrodynamic equations with zero...
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The Singularity Theorems of General Relativity and Their Low Regularity Extensions
On the occasion of Sir Roger Penrose’s 2020 Nobel Prize in Physics, we review the singularity theorems of General Relativity, as well as their recent...
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Equivalence–Singularity Dichotomy in Markov Measures
We establish an equivalence–singularity dichotomy for a large class of one-dimensional Markov measures. Our approach is new in that we deal with...
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Potential Singularity of the 3D Euler Equations in the Interior Domain
Whether the 3D incompressible Euler equations can develop a finite time singularity from smooth initial data is one of the most challenging problems...
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Rational Spectral Collocation Combined with Singularity Separation Method for Second-Order Singular Perturbation Problems
Novel rational spectral collocation is presented in combination with singularity separation method for the second-order singularly perturbed...
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Singularity Formation in an Incompressible Boundary Layer on an Upstream Moving Wall under Given External Pressure
AbstractThe two-dimensional laminar flow of a viscous incompressible fluid over a flat surface is considered at high Reynolds numbers. The influence...
