## Displaying similar documents to “The constants of the Volterra derivation”

### The five-variable Volterra system

Open Mathematics

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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

Czechoslovak Mathematical Journal

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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...

### Rings of constants of four-variable Lotka-Volterra systems

Open Mathematics

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Lotka-Volterra systems appear in population biology, plasma physics, laser physics and derivation theory, among many others. We determine the rings of constants of four-variable Lotka-Volterra derivations with four parameters C 1, C 2, C 3, C 4 ∈ k, where k is a field of characteristic zero. Thus, we give a full description of polynomial first integrals of the respective systems of differential equations.

### A characterization of p-bases of rings of constants

Open Mathematics

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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

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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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,...

### Powersum formula for polynomials whose distinct roots are differentially independent over constants.

International Journal of Mathematics and Mathematical Sciences

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### Set-polynomials and polynomial extension of the Hales-Jewett theorem.

Annals of Mathematics. Second Series

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### Irreducible Jacobian derivations in positive characteristic

Open Mathematics

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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.

### Polynomial algebra of constants of the four variable Lotka-Volterra system

Colloquium Mathematicae

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We describe the ring of constants of a specific four variable Lotka-Volterra derivation. We investigate the existence of polynomial constants in the other cases of Lotka-Volterra derivations, also in n variables.

### Multivariable dimension polynomials and new invariants of differential field extensions.

International Journal of Mathematics and Mathematical Sciences

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### Powersum formula for differential resolvents.

International Journal of Mathematics and Mathematical Sciences

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