相关论文: Equisingularity and EIDS

We investigate a class of horizonless solutions in Einstein-Weyl gravity, corresponding to the so-called attractive naked singularities of the (-2,2) type. In contrast to General Relativity, where naked singularities are generically…

In this paper, we investigate semilinear elliptic equations with general exponential-type nonlinearities in two dimensions. For such nonlinearities, we establish two main results. The first is the construction of a singular solution.…

We study singularities of Gauss maps of fronts and give characterizations of types of singularities of Gauss maps by geometric properties of fronts which are related to behavior of bounded principal curvatures. Moreover, we investigate…

We consider in this paper discrete improper affine spheres based on asymptotic nets. In this context, we distinguish the discrete edges and vertices that must be considered singular. The singular edges can be considered as discrete cuspidal…

The aim of this article is the classification of simple 0-dimensional isolated complete intersection singularities in positive characteristic. As usual, a singularity is called simple or 0-modal if there are only finitely many isomorphism…

We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…

In this work, we are interested in to study removability of a singular set in the boundary for some classes of quasilinear elliptic equations. We will approach this question in two different ways: through an asymptotic behavior at the…

The solvability and stability analysis of linear time invariant systems of delay differential-algebraic equations (DDAEs) is analyzed. The behavior approach is applied to DDAEs in order to establish characterizations of their solvability in…

The asymptotic behavior of the integrated density of states (IDS), \(N(E)\), is investigated for random Schr\"{o}dinger operators with a single-site potential \(V\) satisfying \(\mathrm{essinf}\, V = -\infty\). Under the assumption that the…

We study a class of elliptic problems, involving a $k$-Hessian and a very fast-growing nonlinearity, on a unit ball. We prove the existence of a radial singular solution and obtain its exact asymptotic behavior in a neighborhood of the…

We investigate exceptional points of degeneracy (EPDs) in electromagnetic scattering of a sphere dimer from the electroquasistatic limit to the fully retarded regime. In the quasistatic limit, we prove that $\parity\trev$-symmetric…

Starting from basic identities of the group E8, we perform progressive reductions, namely decompositions with respect to the maximal and symmetric embeddings of E7xSU(2) and then of E6xU(1). This procedure provides a systematic approach to…

We define the singular orbifold elliptic genus and $E$-function for all normal surfaces without strictly log-canonical singularities, and prove the analogue of the McKay correspondence in this setting. Our invariants generalize the stringy…

We classify entire positive singular solutions to a family of critical sixth order equations in the punctured space with a non-removable singularity at the origin. More precisely, we show that when the origin is a non-removable singularity,…

Exceptional points (EPs) are complex singularities of parametric linear operators where two or more eigenvalues and eigenvectors coalesce. EPs are attracting increasing interest in mechanical metamaterials due to their strong potentials for…

Sextic oscillator in D dimensions is considered as a typical quasi-exactly solvable (QES) model. Usually, its QES N-plets of bound states have to be computed using the coupled Magyari's nonlinear algebraic equations. We propose and describe…

The study of bifurcations of differential-algebraic equations (DAEs) is the topic of interest for many applied sciences, such as electrical engineering, robotics, etc. While some of them were investigated already, the full classification of…

We can associate with any irreducible curve singularity (ics) a numerical semigroup. Two ics are said to be equisingular if they have the same semigroup. Two equisingular ics have the same Milnor number. Conversely, The set of ics with a…

In the well-studied genus zero case, bases of $\mathrm{d}\log$ integrands with integer leading singularities define Feynman integrals that automatically satisfy differential equations in canonical form. Such integrand bases can be…

This paper continues the investigation of the formation of naked singularities in the collapse of collisionless matter initiated in [RV]. There the existence of certain classes of non-smooth solutions of the Einstein-Vlasov system was…