Morphisms and Inverse Problems
نویسندگان
چکیده
In order to investigate polynomial vector fields admitting a prescribed Darboux integrating factor, we show that it is helpful to employ morphisms of the affine plane. In particular, such morphisms may be used to remove degeneracies of the underlying curve. Our main result states that the space of vector fields admitting a prescribed Darboux integrating factor modulo a well understood subspace has finite dimension. This extends earlier work for the case of nondegenerate geometric setting. In addition, we present a number of explicit examples with degenerate underlying curve.
منابع مشابه
Morphisms and Inverse Problems for Darboux Integrating Factors
Polynomial vector fields which admit a prescribed Darboux integrating factor are quite well-understood when the geometry of the underlying curve is nondegenerate. In the general setting morphisms of the affine plane may remove degeneracies of the curve, and thus allow more structural insight. In the present paper we establish some properties of integrating factors subjected to morphisms, and we...
متن کاملOn morphisms of crossed polymodules
In this paper, we prove that the category of crossed polymodules (i.e. crossed modules of polygroups) and their morphisms is finitely complete. We, therefore, generalize the group theoretical case of this completeness property of crossed modules.
متن کاملIll-Posed and Linear Inverse Problems
In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.
متن کاملToroidalization of locally toroidal morphisms of 3-folds
A toroidalization of a dominant morphism $varphi: Xto Y$ of algebraic varieties over a field of characteristic zero is a toroidal lifting of $varphi$ obtained by performing sequences of blow ups of nonsingular subvarieties above $X$ and $Y$. We give a proof of toroidalization of locally toroidal morphisms of 3-folds.
متن کاملInverse and Reverse 2-facility Location Problems with Equality Measures on a Network
In this paper we consider the inverse and reverse network facility location problems with considering the equity on servers. The inverse facility location with equality measure deals with modifying the weights of vertices with minimum cost, such that the difference between the maximum and minimum weights of clients allocated to the given facilities is minimized. On the other hand, the reverse c...
متن کامل