Related papers: Bounds on the degrees of vector fields
This work aims to bridge the gap between pure and applied research on scalar, linear Volterra equations by examining five major classes: integral and integro-differential equations with completely monotone kernels, such as linear…
The degree-constrained subgraph problem asks for a subgraph of a given graph such that the degree of each vertex is within some specified bounds. We study the following reconfiguration variant of this problem: Given two solutions to a…
The paper studies a general inverse eigenvalue problem which contains as special cases many well studied pole placement and matrix extension problems. It is shown that the studied problem corresponds on the geometric side to a central…
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…
The classical Center-Focus Problem posed by H. Poincar\'e in 1880's is concerned on the characterization of planar polynomial vector fields $X=(-y+P(x,y))\dfrac{\partial}{\partial x}+(x+Q(x,y))\dfrac{\partial}{\partial y},$ with…
In this paper we consider the normal map of a closed plane curve as a vector field on the cylinder. We interpret the critical points geometrically and study their Poincar\'{e} index, including the points at infinity. After projecting the…
We construct the space of vector fields on a generic quantum group. Its elements are products of elements of the quantum group itself with left invariant vector fields. We study the duality between vector fields and 1-forms and generalize…
We give an optimal upper bound of the degree of quasi-smooth hypersurfaces which are invariant by a one-dimensional holomorphic foliation on a compact toric orbifold, i.e. on a complete simplicial toric variety. This bound depends only on…
We prove the optimal regularity for some class of vector-valued variational inequalities with gradient constraints. We also give a new proof for the optimal regularity of some scalar variational inequalities with gradient constraints. In…
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
We present a geometric proof of the Poincar\'e-Dulac Normalization Theorem for analytic vector fields with singularities of Poincar\'e type. Our approach allows us to relate the size of the convergence domain of the linearizing…
We solve the problem of characterizing the existence of a polynomial matrix of fixed degree when its eigenstructure (or part of it) and some of its rows (columns) are prescribed. More specifically, we present a solution to the row (column)…
The purpose of this paper is to put into a noncommutative context basic notions related to vector fields from classical differential geometry. The manner of exposition is an attempt to make the material as accessible as possible to…
In this article, we consider weak del Pezzo surfaces defined over a finite field, and their associated, singular, anticanonical models. We first define arithmetic types for such surfaces, by considering the Frobenius actions on their Picard…
We introduce and study a generalized concept of boundedness of a subset of a normed vector space with respect to a cone, which is defined as lower boundedness of the images of the underlying set through all the positive functionals of the…
We give an attempt to build a classification of planar integral point sets. For two obtained classes, we provide general constructions of upper bounds for minimal diameter of integral point sets in higher dimensions of certain cardinality.…
In this note, we provide a important considerations of a familiar topic: the gradient of a vector field. The gradient of a vector field is a common quantity represented in continuum mechanics. However, even for Cartesian coordinate systems,…
In this paper, we studied integrals involving both real and complex Hessian operators over bounded domain. Poincare type inequalities were proved in both cases which generalized a early results of Trudinger and Wang.
We extend the Poincare'-Lyapounov-Nekhoroshev theorem from torus actions and invariant tori to general (non-abelian) involutory systems of vector fields and general invariant manifolds.
Invariant coordinate selection is an unsupervised multivariate data transformation useful in many contexts such as outlier detection or clustering. It is based on the simultaneous diagonalization of two affine equivariant and positive…