Displaying similar documents to “Rings of constants of four-variable Lotka-Volterra systems”

The five-variable Volterra system

Janusz Zieliński (2011)

Open Mathematics

Similarity:

We give a description of all polynomial constants of the five-variable Volterra derivation, hence of all polynomial first integrals of its corresponding Volterra system of differential equations. The Volterra system plays a significant role in plasma physics and population biology.

Rings of constants of generic 4D Lotka-Volterra systems

Janusz Zieliński, Piotr Ossowski (2013)

Czechoslovak Mathematical Journal

Similarity:

We show that the rings of constants of generic four-variable Lotka-Volterra derivations are finitely generated polynomial rings. We explicitly determine these rings, and we give a description of all polynomial first integrals of their corresponding systems of differential equations. Besides, we characterize cofactors of Darboux polynomials of arbitrary four-variable Lotka-Volterra systems. These cofactors are linear forms with coefficients in the set of nonnegative integers. Lotka-Volterra...

The constants of the Volterra derivation

Pál Hegedűs (2012)

Open Mathematics

Similarity:

The ring of constants of the Volterra derivation is found. Confirming a conjecture of Zielinski, it is always a polynomial ring.

Irreducible Jacobian derivations in positive characteristic

Piotr Jędrzejewicz (2014)

Open Mathematics

Similarity:

We prove that an irreducible polynomial derivation in positive characteristic is a Jacobian derivation if and only if there exists an (n-1)-element p-basis of its ring of constants. In the case of two variables we characterize these derivations in terms of their divergence and some nontrivial constants.

Linear gradings of polynomial algebras

Piotr Jędrzejewicz (2008)

Open Mathematics

Similarity:

Let k be a field, let G be a finite group. We describe linear G -gradings of the polynomial algebra k[x 1, ..., x m] such that the unit component is a polynomial k-algebra.

A characterization of p-bases of rings of constants

Piotr Jędrzejewicz (2013)

Open Mathematics

Similarity:

We obtain two equivalent conditions for m polynomials in n variables to form a p-basis of a ring of constants of some polynomial K-derivation, where K is a unique factorization domain of characteristic p > 0. One of these conditions involves Jacobians while the other some properties of factors. In the case m = n this extends the known theorem of Nousiainen, and we obtain a new formulation of the Jacobian conjecture in positive characteristic.

Polynomials over the reals in proofs of termination : from theory to practice

Salvador Lucas (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Similarity:

This paper provides a framework to address termination problems in term rewriting by using orderings induced by algebras over the reals. The generation of such orderings is parameterized by concrete monotonicity requirements which are connected with different classes of termination problems: termination of rewriting, termination of rewriting by using dependency pairs, termination of innermost rewriting, top-termination of infinitary rewriting, termination of context-sensitive rewriting,...

Positive characteristic analogs of closed polynomials

Piotr Jędrzejewicz (2011)

Open Mathematics

Similarity:

The notion of a closed polynomial over a field of zero characteristic was introduced by Nowicki and Nagata. In this paper we discuss possible ways to define an analog of this notion over fields of positive characteristic. We are mostly interested in conditions of maximality of the algebra generated by a polynomial in a respective family of rings. We also present a modification of the condition of integral closure and discuss a condition involving partial derivatives.