Results 11 to 20 of about 50 (49)
Powersum formula for differential resolvents
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 7, Page 365-371, 2004., 2004 We will prove that we can specialize the indeterminate α in a linear differential α‐resolvent of a univariate polynomial over a differential field of characteristic zero to an integer q to obtain a q‐resolvent. We use this idea to obtain a formula, known as the powersum formula, for the terms of the α‐resolvent.
John Michael Nahay
wiley +1 more source
COUNTING $S_5$ -FIELDS WITH A POWER SAVING ERROR TERM
Forum of Mathematics, Sigma, 2014 We show how the Selberg $\Lambda ^2$ -sieve can be used to obtain power saving error terms in a wide class of counting problems which are tackled using the ...
ARUL SHANKAR, JACOB TSIMERMAN
doaj +1 more source
On dependent elements in rings
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 54, Page 2895-2906, 2004., 2004 Let R be an associative ring. An element a ∈ R is said to be dependent on a mapping F : R → R in case F(x)a = ax holds for all x ∈ R. In this paper, elements dependent on certain mappings on prime and semiprime rings are investigated. We prove, for example, that in case we have a semiprime ring R, there are no nonzero elements which are dependent on ...
Joso Vukman, Irena Kosi-Ulbl
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Jordan Derivations on Lie Ideals of Prime T-Rings [PDF]
, 2013 The details of the research can be found in the full paper.Keywords: Derivation, Jordan derivation, Lie ideal, admissible Lie ideal, square closed Lie ideal,prime ????-ring.2010 AMS Subject Classication: Primary 13N15; Secondary 16W10 ...
Paul, A. C., Rahman, M. M.
core +1 more source
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 𝔽 of characteristic zero, and for any constant indeterminate α, there exists a nonunique nonzero linear ordinary differential operator ℜ of finite order such that the αth power of each root of P is a solution of ℜzα = 0, and the coefficient functions of ℜ 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 α‐power 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 author′s 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 Kolchin′s theorem on differential dimension polynomial and find new differential birational invariants of a finitely generated differential field extension.
Alexander B. Levin
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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
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Fine‐scale reconstruction of pelagic fish migration by iso‐logging of eye lens
Methods in Ecology and Evolution, Volume 17, Issue 1, Page 77-84, January 2026.Abstract Understanding lifetime space use by pelagic animals is pivotal for ecology and fisheries management, but electronic tags are costly, labour‐intensive and rarely able to capture juvenile movement. We implemented an iso‐logging workflow that converts stable isotope chronologies in eye lenses into continuous migration tracks, and demonstrate its ...
Jun Matsubayashi +8 more
wiley +1 more source