Zobrazeno 1 - 10
of 23
pro vyhledávání: '"William F Keigher"'
Differential algebra explores properties of solutions to systems of (ordinary or partial, linear or nonlinear) differential equations from an algebraic point of view. It includes as special cases algebraic systems as well as differential systems with
Publikováno v:
Applied Categorical Structures. 26:747-765
In a previous study, the algebraic formulation of the First Fundamental Theorem of Calculus (FFTC) is shown to allow extensions of differential and Rota-Baxter operators on the one hand, and to give rise to categorical explanations using the ideas of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a7e2ae572e6b34b81287d58a04d5ff95
https://doi.org/10.1007/s10485-018-9517-3
https://doi.org/10.1007/s10485-018-9517-3
Publikováno v:
Journal of Pure and Applied Algebra. 221:2525-2556
An integro-differential algebra of arbitrary characteristic is given the structure of a uniform topological space, such that the ring operations as well as the derivation (= differentiation operator) and Rota–Baxter operator (= integral operator) a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::499cfbe5afac5b3e0cb9b6d164583463
https://doi.org/10.1016/j.jpaa.2017.01.001
https://doi.org/10.1016/j.jpaa.2017.01.001
Generalizing the algebraic formulation of the First Fundamental Theorem of Calculus (FFTC), a class of constraints involving a pair of operators was considered in \cite{ZGK2}. For a given constraint, the existences of extensions of differential and R
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2ab2d7410d3a9a103f19afbf61e437f8
Autor:
William F. Keigher, Xing Gao
Publikováno v:
Communications in Algebra. 45:2163-2185
In this paper, we introduce the notion of interlacing of Hurwitz series. We begin by reviewing some important properties of the ring of Hurwitz series over a commutative ring A of arbitrary characteristic, and we introduce and investigate properties
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::90e5e03e039d3b63f0a2b4ecd474ce8b
https://doi.org/10.1080/00927872.2016.1226885
https://doi.org/10.1080/00927872.2016.1226885
Publikováno v:
Advances in Applied Mathematics. 72:139-165
In recent years, algebraic studies of the differential calculus and integral calculus in the forms of differential algebra and Rota-Baxter algebra have been merged together to reflect the close relationship between the two calculi through the First F
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5f07011179021afbb29d8cadb09bdf49
https://doi.org/10.1016/j.aam.2015.09.014
https://doi.org/10.1016/j.aam.2015.09.014
Publikováno v:
Homology Homotopy Appl. 14, no. 2 (2012), 91-99
In this article we will define the notions of Hurwitz automorphism and comorphism of the ring of Hurwitz series. A Hurwitz automorphism is the analog of a Seidenberg automorphism of a power series ring when the characteristic of the underlying ring i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a57b5fd0b5b58655b60f6defbf74ea2f
https://doi.org/10.4310/hha.2012.v14.n2.a6
https://doi.org/10.4310/hha.2012.v14.n2.a6
Autor:
William F. Keigher, F. Leon Pritchard
Publikováno v:
Journal of Algebra and Its Applications. :425-441
A differential quasifield is a natural generalization of a differential field in characteristic p > 0. Elementary properties of differential quasifields are considered, and a generalized version of the theorem on the connection between linear indepen
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::99d50f120163a35171c13888a1d3feb1
https://doi.org/10.1142/s0219498808002849
https://doi.org/10.1142/s0219498808002849
Autor:
Li Guo, William F. Keigher
Publikováno v:
Journal of Pure and Applied Algebra. 212(3):522-540
A Rota–Baxter operator of weight λ is an abstraction of both the integral operator (when λ = 0 ) and the summation operator (when λ = 1 ). We similarly define a differential operator of weight λ that includes both the differential operator (whe
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2a52b9ca1062870bba233776e2c39ecd
Autor:
Li Guo, William F. Keigher
Publikováno v:
Advances in Mathematics. 150:117-149
In this paper we generalize the well-known construction of shuffle product algebras by using mixable shuffles, and prove that any free Baxter algebra is isomorphic to a mixable shuffle product algebra. This gives an explicit construction of the free
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4da749d2d3f3109c8ff6c72b1df3842c
https://doi.org/10.1006/aima.1999.1858
https://doi.org/10.1006/aima.1999.1858