Results 41 to 50 of about 16,850 (158)

Biases towards the zero residue class for quadratic forms in arithmetic progressions

Mathematika, Volume 72, Issue 2, April 2026.
Abstract We prove a bias towards the zero residue class in the distribution of the integers represented by binary quadratic forms. In most cases, we prove that the bias comes from a secondary term in an associated asymptotic expansion. This is unlike Chebyshev's bias, which exists somewhere at the level of O(x1/2+ε)$O(x^{1/2+\varepsilon })$.
Jeremy Schlitt
wiley   +1 more source

Algebraic D-groups and differential Galois theory [PDF]

Pacific Journal of Mathematics, 2004
The author gives another exposition of his new differential Galois theory. As he thinks, a previous presentation [Ill. J. Math. 42, No. 4, 678--699 (1998; Zbl 0916.03028)] was too model-theoretic and so somewhat obscure to differential algebraists. This new representation is based on some generalization of \(G\)-primitive extensions of \textit{E.
openaire   +2 more sources

Attribute Implication Bases From Galois Connection Structures

Mathematical Methods in the Applied Sciences, Volume 49, Issue 4, Page 2729-2753, 15 March 2026.
ABSTRACT Modeling knowledge systems by determining relationships among key variables have been and currently is a fundamental and nontrivial challenge in real‐world scenarios. Many approaches have been developed to reach this goal, but many of them are heuristic and require of alternative procedures to provide robust and tractable rules.
M. Eugenia Cornejo, Jesús Medina, Francisco José Ocaña   +2 more
wiley   +1 more source

Galois differential algebras and categorical discretization of dynamical systems [PDF]

, 2015
A categorical theory for the discretization of a large class of dynamical systems with variable coefficients is proposed. It is based on the existence of covariant functors between the Rota category of Galois differential algebras and suitable categories
Tempesta, Piergiulio
core  

Galois theory of aigebraic and differential equations [PDF]

Nagoya Mathematical Journal, 1996
This paper will be the first part of our works on differential Galois theory which we plan to write. Our goal is to establish a Galois Theory of ordinary differential equations. The theory isinfinite dimensionalby nature and has a long history. The pioneer of this field is S. Lie who tried to apply the idea of Abel and Galois to differential equations.
openaire   +3 more sources

Simplification of exponential factors of irregular connections on P1${\mathbb {P}}^1$

Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.
Abstract We give an explicit algorithm to reduce the ramification order of any exponential factor of an irregular connection on P1$\mathbb {P}^1$, using the same types of basic operations as in the Katz–Deligne–Arinkin algorithm for rigid irregular connections.
Jean Douçot
wiley   +1 more source

Projective module description of the q-monopole

, 1998
The Dirac q-monopole connection is used to compute projector matrices of quantum Hopf line bundles for arbitrary winding number. The Chern-Connes pairing of cyclic cohomology and K-theory is computed for the winding number -1.
Hajac, P. M., Majid, S.
core   +2 more sources

Differential Galois theory III: Some inverse problems

Illinois Journal of Mathematics, 1997
[For Part I see ibid. 42, No. 4, 678-699 (1998; Zbl 0916.03028). Part II is reviewed above.] In Part I, the author developed a theory of differential Galois extensions, generalizing Kolchin's theory of strongly normal extensions. It was shown that arbitrary finite-dimensional differential algebraic groups can arise as differential Galois groups for ...
Marker, David, Pillay, Anand
openaire   +3 more sources

Hyperderivatives of the deformation series associated with arithmetic gamma values and characteristic p$p$ multiple zeta values

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract Number theory for positive characteristic contains analogues of the special values that were introduced by Carlitz; these include the Carlitz gamma values and Carlitz zeta values. These values were further developed to the arithmetic gamma values and multiple zeta values by Goss and Thakur, respectively.
Ryotaro Harada, Daichi Matsuzuki
wiley   +1 more source

Liouvillian propagators, Riccati equation and differential Galois theory [PDF]

Journal of Physics A: Mathematical and Theoretical, 2013
In this paper a Galoisian approach to build propagators through Riccati equations is presented. The main result corresponds to the relationship between the Galois integrability of the linear Schr dinger equation and the virtual solvability of the differential Galois group of its associated characteristic equation.
Acosta-Humánez, Primitivo B., Suazo, Erwin   +1 more
openaire   +2 more sources