in this paper, we investigate the canonical property of solutions of a system of differentialequations having a singularity and turning point of even order. first, by a replacement, we transform thesystem to the sturm-liouville equation with a turning point. using the asymptotic estimates for a specialfundamental system of solutions of sturm-liouville equation, we study the infinite product rep...

This work analyses the link between Western Europe large-scale circulation and precipitation variability in Northern French Alps from 1950 to 2017. We consider simple descriptors characterizing daily 500 hPa geopotential height fields. They are maximum pressure difference (MPD)—representing range of heights over Europe, singularity—representing mean distance a shape its closest analogs, that is...

We present a simple and new method of constructing superdistributions on superspace over a Grassmann-Banach algebra, which close to the de Rham’s “currents” defined as dual objects to differential forms. The paper also contains the extension of the Hörmander’s description of the singularity structure (wavefront set) of a distribution to include the supersymmetric case. PACS numbers: 11.10.-z, 1...

It was shown by J.N. Mather and S.S.-T. Yau that an isolated complex hypersurface singularity is completely determined by its moduli algebra. In this article it is shown, for the simple elliptic singularities, how to construct continuous invariants from the moduli algebras and, hence, associate invariants to the singularities themselves.

A generic geodesic on a finite area, hyperbolic 2-orbifold exhibits an infinite sequence of penetrations into a neighborhood of a cone singularity of order k ≥ 3, so that the sequence of depths of maximal penetration has a limiting distribution. The distribution function is the same for all such surfaces and is described by a fairly simple formula.

In this paper we describe the Garnier systems as isomonodromic deformation equations of a linear system with a simple pole at 0 and a Poincaré rank two singularity at infinity. We discuss the extension of Okamoto’s birational canonical transformations to the Garnier systems in more than one variable and to the Schlesinger systems.

It is proved that the diffeomorphism type of the minimal symplectic fillings of the link of a simple singularity is unique. In the proof, the uniqueness of the diffeomorphism type of CP 2 \D, where D is a pseudo holomorphic rational curve with one (2, 3)cusp, is discussed.

Let Σ ⊂ C be a 2-dimensional subvariety with an isolated simple (rational double point) singularity at the origin. The main objective of this paper is to solve the ∂-equation on a neighbourhood of the origin in Σ, demanding a Hölder condition on the solution.

The form of the propagating electrostatic Bernstein mode in a relativistic electron-positron plasma is markedly different from that in the classical plasma, once the momentum-dependent cyclotron frequency is accounted for in full inside the integrations. Given that particles in different parts of momentum space "see" a different cyclotron frequency, there is no simple global singularity which r...

Let M and N be two representations of an extended Dynkin quiver such that the orbit O N of N is contained in the orbit closure O M and has codimension two. We show that the pointed variety (O M , N) is smoothly equivalent to a simple surface singularity of type A n , or to the cone over a rational normal curve.