Results 11 to 20 of about 689 (41)
Galois correspondence theorem for Picard-Vessiot extensions [PDF]
, 2015 In this paper, we generalize the definition of the differential Galois group and the Galois correspondence theorem established previously for Picard-Vessiot extensions of real differential fields with real closed field of constants to any Picard-Vessiot ...
Crespo, Teresa +2 more
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A partial factorization of the powersum formula
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 58, Page 3075-3101, 2004., 2004 For any univariate polynomial P whose coefficients lie in an ordinary differential field đœ of characteristic zero, and for any constant indeterminate α, there exists a nonunique nonzero linear ordinary differential operator â of finite order such that the αth power of each root of P is a solution of âzα = 0, and the coefficient functions of â all lie ...
John Michael Nahay
wiley +1 more source
Differential resolvents of minimal order and weight
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 54, Page 2867-2893, 2004., 2004 We will determine the number of powers of α that appear with nonzero coefficient in an αâpower linear differential resolvent of smallest possible order of a univariate polynomial P(t) whose coefficients lie in an ordinary differential field and whose distinct roots are differentially independent over constants.
John Michael Nahay
wiley +1 more source
Powersum formula for polynomials whose distinct roots are differentially independent over constants
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 12, Page 721-738, 2002., 2002 We prove that the authorâČs powersum formula yields a nonzero expression for a particular linear ordinary differential equation, called a resolvent, associated with a univariate polynomial whose coefficients lie in a differential field of characteristic zero provided the distinct roots of the polynomial are differentially independent over constants.
John Michael Nahay
wiley +1 more source
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 KolchinâČs 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.
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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
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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
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Divergence-free polynomial derivations [PDF]
, 2017 In this paper we present some new and old properties of divergences and divergence-free ...
Nowicki, Andrzej
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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
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