Related papers: On the Center Problem for Ordinary Differential Eq…

Let L be a finite dimensional Lie algebra over an algebraically closed field k of characteristic zero. We provide necessary and also some sufficient conditions in order for its Poisson center and semi-center to be polynomial algebras over…

We explicitly describe the Jacquet-Langlands correspondence at the level of modular forms. This gives a simpler and more flexible solution to Eichler's basis problem for general level than earlier work of Hijikata-Pizer-Shemanske for…

We will make the case that \textit{pedal coordinates} (instead of polar or Cartesian coordinates) are more natural settings in which to study force problems of classical mechanics in the plane. We will show that the trajectory of a test…

The general term of the Poincare normalizing series is explicitly constructed for non-resonant systems of ODE's in a large class of equations. In the resonant case, a non-local transformation is found, which exactly linearizes the ODE's and…

This note presents a method to study center families of periodic orbits of complex holomorphic differential equations near singularities, based on some iteration properties of fixed point indices. As an application of this method, we will…

In the paper, we investigate Poincare type inequalities for the functions having zero mean value on the whole boundary of a Lipschitz domain or on a measurable part of the boundary. We derive exact and easily computable constants for some…

This paper contributes to the solution of the Poincare problem, which is to bound the degree of a (generalized algebraic) leaf of a (singular algebraic) foliation of the complex projective plane. The first theorem gives a new sort of bound,…

Given a planar differential system with a first integral, we show how to find a normalizer. For systems with a center, we give an integral formula for the derivative of its period function.

We apply a heuristic method based on counting points over finite fields to the Poincar\'e center problem. We show that this method gives the correct results for homogeneous non linearities of degree 2 and 3. Also we obtain new evidence for…

This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for…

In this work we propose a discretization of the second boundary condition for the Monge-Ampere equation arising in geometric optics and optimal transport. The discretization we propose is the natural generalization of the popular…

Point transformations of the 3-rd order ordinary differential equations are considered. Special classes of ordinary differential equations that are invariant under the general point transformations are constructed.

Indices of singular points of a vector field or of a 1-form on a smooth manifold are closely related with the Euler characteristic through the classical Poincar\'e--Hopf theorem. Generalized Euler characteristics (additive topological…

The Zariski closure of the central path which interior point algorithms track in convex optimization problems such as linear, quadratic, and semidefinite programs is an algebraic curve. The degree of this curve has been studied in relation…

We describe dualities and complexes of logarithmic forms and differentials for central affine and corresponding projective arrangements. We generalize the Borel-Serre formula from vector bundles to sheaves on projective d-space with locally…

We give a complete classification of all simple current modular invariants, extending previous results for $(\Zbf_p)^k$ to arbitrary centers. We obtain a simple explicit formula for the most general case. Using orbifold techniques to this…

The notion of center of mass, which is very useful in kinematics, proves to be very handy in geometry (see [1]-[2]). Countless applications of center of mass to geometry go back to Archimedes. Unfortunately, the center of mass cannot be…

We discuss different generalizations of the classical notion of the index of a singular point of a vector field to the case of vector fields or 1-forms on singular varieties, describe relations between them and formulae for their…

A first order differential equation with a periodic operator coefficient acting in a pair of Hilbert spaces is considered. This setting models both elliptic equations with periodic coefficients in a cylinder and parabolic equations with…

We introduce the notion of 'centre' for pomonoid-graded strong monads which generalizes some previous work that describes the centre of (not graded) strong monads. We show that, whenever the centre exists, this determines a pomonoid-graded…