相关论文: Teissier singularities

This paper demonstrates some connections between the coefficients of a Taylor series $f(z)=\ds\sum_{n=0}^\infty a_n z^n$ and singularities of the function. There are many known results of this type, for example, counting the number of poles…

In this note, we relax the hypothesis of the main results in Kellner-Shelah-T\v{a}nasie's "Another ordering of the ten cardinal characteristics in Cicho\'n's diagram".

Spectral singularities are among generic mathematical features of complex scattering potentials. Physically they correspond to scattering states that behave like zero-width resonances. For a simple optical system, we show that a spectral…

We give a description of the equisingularity of a family of normal surface singularities by numerical invariants belonging to them. By equisingularity we mean Whitney regularity or a more restrictive condition using the Nash modification.

The purpose of this note is to describe limiting shapes (as introduced by Mayes) of symbolic generic initial systems of star configurations in projective spaces over a field of characteristic 0.

We address the open problem of existence of singularities for the complex Ginzburg-Landau equation. Using a combination of rigourous results and numerical computations, we describe a countable family of self-similar singularities. Our…

We derive new identities involving zeros of the Bessel function $J_{\nu}$ and some related functions. These are special cases of more general identities obtained in this note, which might also be of interest.

In this note, we introduce arithmetic Heilbronn supercharacters that generalize the notions of arithmetic Heilbronn characters and Heilbronn supercharacters and discuss several properties of them.

This paper is devoted to give all the technical constructions and definitions that will lead to the construction of an algorithm of resolution of singularities for binomial ideals. We construct a resolution function that will provide a…

In this note, we study the arithmetic nature of values of modular functions, meromorphic modular forms and meromorphic quasi-modular forms with respect to arbitrary congruence subgroups, that have algebraic Fourier coefficients. This…

In this note, we address the following question: Why certain nonassociative algebra structures emerge in the regularity theory of elliptic type PDEs and also in constructing nonclassical and singular solutions? The aim of the paper is…

We give an overview of the fundamental definitions and results concerning hypersurface singularities, defined by convergent power series over an arbitrary real valued field. This approach combines, on the one hand, the classical case of…

The aim of these notes is to give an overview of the current results about existence and uniqueness of solutions for the stochastic Euler equation driven by a Brownian noise in a two-dimensional bounded domain.

The main purpose of this paper is to propose some interesting number theory problems related to the Legendre's symbol and the two-term exponential sums.

We study a boundary value elliptic problem having a lower order nonlinear term with subquadratic growth in the gradient of the solution and possibly singular when the solution vanishes. If the singularity is mild enough (and even in the…

The Bernstein-Sato polynomial is an important invariant of an element or an ideal in a polynomial ring or power series ring of characteristic zero, with interesting connections to various algebraic and topological aspects of the…

The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…

The purpose of this article is to develop an algebraic approach to the problem of integrable classification of differential-difference equations with one continuous and two discrete variables. As a classification criterion, we put forward…

We present some results on character degree sums in connection with certain characteristics of finite groups such as p-solvability, solvability, supersolvability, and nilpotency. Some of them strengthen known results in the literature.

We show that suitable congruences between polarized automorphic forms over a CM field always produce elements in the Selmer group for exactly the +/--Asai (aka tensor induction) representation that is critical in the sense of Deligne. For…