Results 11 to 20 of about 766 (61)
Multivariable dimension polynomials and new invariants of differential field extensions
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 4, Page 201-214, 2001., 2001 We introduce a special type of reduction in the ring of differential polynomials and develop the appropriate technique of characteristic sets that allows to generalize the classical Kolchin′s theorem on differential dimension polynomial and find new differential birational invariants of a finitely generated differential field extension.
Alexander B. Levin
wiley +1 more source
Differential Invariants of Conformal and Projective Surfaces [PDF]
, 2007 We show that, for both the conformal and projective groups, all the differential invariants of a generic surface in three-dimensional space can be written as combinations of the invariant derivatives of a single differential invariant. The proof is based
Hubert, Evelyne, Olver, Peter J.
core +8 more sources
Rings and fields of constants of cyclic factorizable derivations
Analytic and Algebraic Geometry 3, 2019 We present a survey of the research on rings of polynomial constants and fields of rational constants of cyclic factorizable derivations in polynomial rings over fields of characteristic zero. 1.
J. Zieliński
semanticscholar +1 more source
Completeness of Finite-Rank Differential Varieties
Bulletin of Symbolic Logic, 2019 In this dissertation, I focus on a program in the philosophy of mathematics known as neo-logicism that is a direct descendant of Frege’s logicist project.
William D. Simmons
semanticscholar +1 more source
Algebraic and qualitative remarks about the family yy′ = (αxm+k–1 + βxm–k–1)y + γx2m–2k–1
Open Mathematics, 2019 The aim of this paper is the analysis, from algebraic point of view and singularities studies, of the 5-parametric family of differential ...
Rodríguez-Contreras Jorge +2 more
doaj +1 more source
A Note on Schanuel's Conjectures for Exponential Logarithmic Power Series Fields
, 2012 In [1], J. Ax proved a transcendency theorem for certain differential fields of characteristic zero: the differential counterpart of the still open Schanuel's conjecture about the exponential function over the field of complex numbers [11, page 30].
Kuhlmann, Salma +2 more
core +3 more sources
Algorithms yield upper bounds in differential algebra
, 2020 Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing.
Li, Wei +3 more
core +2 more sources
Nonautonomous Hamiltonian Systems and Morales-Ramis Theory I. The Case $\ddot{x}=f(x,t)$
, 2012 In this paper we present an approach towards the comprehensive analysis of the non-integrability of differential equations in the form $\ddot x=f(x,t)$ which is analogous to Hamiltonian systems with 1+1/2 degree of freedom.
Morales-Ruiz J. J. +3 more
core +1 more source
Classical nonintegrability of a quantum chaotic SU(3) Hamiltonian system
, 2009 We prove nonintegrability of a model Hamiltonian system defined on the Lie algebra $\mathfrak{su}_3$ suitable for investigation of connections between classical and quantum characteristics of chaos.Comment: 17 ...
Adam Sawicki +30 more
core +1 more source
Amitsur's theorem, semicentral idempotents, and additively idempotent semirings
Open MathematicsThe article explores research findings akin to Amitsur’s theorem, asserting that any derivation within a matrix ring can be expressed as the sum of an inner derivation and a hereditary derivation.
Rachev Martin, Trendafilov Ivan
doaj +1 more source