Rigid analytic spaces
Rings of constants of four-variable Lotka-Volterra systems
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.
Rings of constants of generic 4D Lotka-Volterra systems
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 systems...
Rings of integers of type .
Rings of Real-Valued Continuous Functions. II.
Ringtopologien auf nichtalgebraischen Körpern.
Ringtopologien auf Z und Q.
Ritt's Second Theorem in arbitrary characteristic.
Root arrangements of hyperbolic polynomial-like functions.
A real polynomial P of degree n in one real variable is hyperbolic if its roots are all real. A real-valued function P is called a hyperbolic polynomial-like function (HPLF) of degree n if it has n real zeros and P(n) vanishes nowhere. Denote by xk(i) the roots of P(i), k = 1, ..., n-i, i = 0, ..., n-1. Then in the absence of any equality of the formxi(j) = xk(i) (1)one has∀i < j xk(i) < xk(j) < xk+j-i(i) (2)(the Rolle theorem). For n ≥ 4 (resp....
Root continuity theorems in valued fields.
Root continuity theorems in valued fields. II.
Roots of Unity over Large Algebraic Fields.
Round Quadratic Forms.
Safe convergence of Chebyshev-like method.
Safe convergence of Tanabe's method.
Salomon's Theorem for polynomials with several parameters
Schanuel Nullstellensatz for Zilber fields
We characterize the unsolvable exponential polynomials over the exponential fields introduced by Zilber, and deduce Picard's Little Theorem for such fields.
Schiefkörper über diskret bewerteten Körpern.
Schinzel's problem: Imprimitive covers and the monodromy method
Schnitt und Verbindung in projektiven Hjelmsleveschen Räumen.