An explicit bound of the number of vanishing double moments forcing composition
نویسندگان
چکیده
We give two new characterizations of pairs of polynomials or trigonometric polynomials that form a composition pair. One of them proves that the cancellation of a given number of double moments implies that they form a composition pair. This number only depends on the maximum degree of both polynomials. This is the first time that composition is characterized in terms of the cancellation of an explicit number of double moments. Our results allow to recognize the composition centers for polynomial and trigonometric Abel differential equations. 2000 Mathematics Subject Classification: 39C25, 37C27.
منابع مشابه
Some new families of definite polynomials and the composition conjectures
The planar polynomial vector fields with a center at the origin can be written as an scalar differential equation, for example Abel equation. If the coefficients of an Abel equation satisfy the composition condition, then the Abel equation has a center at the origin. Also the composition condition is sufficient for vanishing the first order moments of the coefficients. The composition conjectur...
متن کاملComplete forcing numbers of polyphenyl systems
The idea of “forcing” has long been used in many research fields, such as colorings, orientations, geodetics and dominating sets in graph theory, as well as Latin squares, block designs and Steiner systems in combinatorics (see [1] and the references therein). Recently, the forcing on perfect matchings has been attracting more researchers attention. A forcing set of M is a subset of M contained...
متن کاملOn Construction of Multivariate Wavelets with Vanishing Moments
Wavelets with matrix dilation are studied. An explicit formula for masks providing vanishing moments is found. The class of interpolatory masks providing vanishing moments is also described. For an interpolatory mask, formulas for a dual mask which also provides vanishing moments of the same order and for wavelet masks are given explicitly. An example of construction of symmetric and antisymmet...
متن کاملLocal stabilization for a class of nonlinear impulsive switched system with non-vanishing uncertainties under a norm-bounded control input
Stability and stabilization of impulsive switched system have been considered in recent decades, but there are some issues that are not yet fully addressed such as actuator saturation. This paper deals with expo-nential stabilization for a class of nonlinear impulsive switched systems with different types of non-vanishing uncertainties under the norm-bounded control input. Due to the constraine...
متن کاملGlobal Forcing Number for Maximal Matchings under Graph Operations
Let $S= \{e_1,\,e_2, \ldots,\,e_m\}$ be an ordered subset of edges of a connected graph $G$. The edge $S$-representation of an edge set $M\subseteq E(G)$ with respect to $S$ is the vector $r_e(M|S) = (d_1,\,d_2,\ldots,\,d_m)$, where $d_i=1$ if $e_i\in M$ and $d_i=0$ otherwise, for each $i\in\{1,\ldots , k\}$. We say $S$ is a global forcing set for maximal matchings of $G$ if $...
متن کامل