Dirichlet-Ford domains and Double Dirichlet domains E. Jespers, S. O. Juriaans, A. Kiefer, A. de A. e Silva, A. C. Souza Filho Bulletin of the Belgian Mathematical Society Simon Stevin, 2016 We continue investigations started by Lakeland on Fuchsian and Kleinian groups which have a Dirichlet fundamental domain that also is a Ford domain in the upper half-space model of hyperbolic $2$- and $3$-space, or which have a Dirichlet domain with multiple centers. Such domains are called DF-domains and Double Dirichlet domains respectively. Making use of earlier obtained concrete formulas for the bisectors defining the Dirichlet domain of center $i \\in \\HQ^2$ or center $j \\in \\HQ^3$, we obtain a simple condition on the matrix entries of the side-pairing transformations of the fundamental domain of a Fuchsian or Kleinian group to be a DF-domain. Using the same methods, we also complement a result of Lakeland stating that a cofinite Fuchsian group has a DF domain (or a Dirichlet domain with multiple centers) if and only if it is an index $2$ subgroup of the discrete group G of reflections in a hyperbolic polygon.
Traces of Torsion Units S. O. Juriaans, A. De A. E Silva, A. C. Souza Filho Communications in Algebra, 2015 A conjecture due to Zassenhaus asserts that if G is a finite group then any torsion unit in ℤG is conjugate in ℚG to an element of G. Here, a weaker form of this conjecture is proved for some infinite groups.
Locally convex topological algebras of generalized functions: Compactness and nuclearity in a nonlinear context J. Aragona, S. O. Juriaans, J. F. Colombeau Transactions of the American Mathematical Society, 2015 In this paper we introduce Hausdorff locally convex algebra topologies on subalgebras of the whole algebra of nonlinear generalized functions. These topologies are strong duals of Frechet-Schwartz space topologies and even strong duals of nuclear Frechet space topologies. In particular any bounded set is relatively compact and one benefits from all deep properties of nuclearity. These algebras of generalized functions contain most of the classical irregular functions and distributions. They are obtained by replacing the mathematical tool of C∞ functions in the original version of nonlinear generalized functions by the far more evolved tool of holomorphic functions. This paper continues the nonlinear theory of generalized functions in which such locally convex topological properties were strongly lacking up to now.
From the Poincaré theorem to generators of the unit group of integral group rings of finite groups E. Jespers, S. O. Juriaans, A. Kiefer, A. de A. e Silva, A. C. Souza Filho Mathematics of Computation, 2015 We give an algorithm to determine finitely many generators for a subgroup of finite index in the unit group of an integral group ring $\\mathbb{Z} G$ of a finite nilpotent group $G$, this provided the rational group algebra $\\mathbb{Q} G$ does not have simple components that are division classical quaternion algebras or two-by-two matrices over a classical quaternion algebra with centre $\\mathbb{Q}$. The main difficulty is to deal with orders in quaternion algebras over the rationals or a quadratic imaginary extension of the rationals. In order to deal with these we give a finite and easy implementable algorithm to compute a fundamental domain in the hyperbolic three space $\\mathbb{H}^3$ (respectively hyperbolic two space $\\mathbb{H}^2$) for a discrete subgroup of ${\\rm PSL}_2(\\mathbb{C})$ (respectively ${\\rm PSL}_2(\\mathbb{R})$) of finite covolume. Our results on group rings are a continuation of earlier work of Ritter and Sehgal, Jespers and Leal.
Finite conjugacy in algebras and orders M. A. Dokuchaev, S. O. Juriaans, C. Polcino Milies, M. L. Sobral Singer Proceedings of the Edinburgh Mathematical Society, 2001
Units of integral group rings of Frobenius groups Journal of Group Theory, 2000
Transition probabilities and almost periodic functions in colombeau algebras SO Juriaans, PC Queiroz Monatshefte für Mathematik , 2025 2025
Generalized Differential Geometry SO Juriaans, PC Queiroz arXiv preprint arXiv:2309.07239 , 2023 2023
Transition Probabilities and Almost Periodic Functions SO Juriaans, PC Queiroz arXiv preprint arXiv:2305.08862 , 2023 2023 Citations: 1
Generalized geometry and transition probabilities OS Juriaans, PCQ Moraes Anais , 2023 2023
On geometrically uniform codes and topological quantum MDS codes VL Vieira, OS Juriaans Journal of Mathematical Physics 63 (9) , 2022 2022 Citations: 1
Off-diagonal condition W Rodrigues, ARG Garcia, SO Juriaans, JC Silva Monatshefte für Mathematik 198 (2), 465-482 , 2022 2022 Citations: 3
A nonlinear theory of generalized functions ARG Garcia, SO Juriaans, J Oliveira, WM Rodrigues São Paulo Journal of Mathematical Sciences 16 (1), 396-405 , 2022 2022 Citations: 5
Fixed Point Theorems for Hypersequences and the Foundation of Generalized Differential Geometry I: The Simplified Algebra SO Juriaans, J Oliveira arXiv preprint arXiv:2205.00114 , 2022 2022 Citations: 7
Multiplication of Distributions and Nonperturbative Calculations of Transition Probabilities J Aragona, P Catuogno, JF Colombeau, SO Juriaans, C Olivera arXiv preprint arXiv:1801.03527 , 2018 2018
Multiplication of distributions and nonperturbative calculations of transition probabilities JF Colombeau, J Aragona, P Catuogno, SO Juriaans, C Olivera Quantum Theory And Symmetries, 393-401 , 2017 2017 Citations: 3
Dirichlet-Ford domains and Double Dirichlet domains E Jespers, SO Juriaans, A Kiefer, AA e Silva, AC Souza Filho Bulletin of the Belgian Mathematical Society-Simon Stevin 23 (3), 465-479 , 2016 2016 Citations: 1
The origin of felsic microgranitoid enclaves: Insights from plagioclase crystal size distributions and thermodynamic models A Alves, G de Souza Pereira, V de Assis Janasi, M Higgins, LA Polo, ... Lithos 239, 33-44 , 2015 2015 Citations: 19
Traces of Torsion Units SO Juriaans, A De A. E Silva, AC Souza Filho Communications in Algebra 43 (9), 3925-3933 , 2015 2015
Locally convex topological algebras of generalized functions: compactness and nuclearity in a nonlinear context J Aragona, S Juriaans, J Colombeau Transactions of the American Mathematical Society 367 (8), 5399-5414 , 2015 2015 Citations: 6
Multiplication of distributions in mathematical physics J Aragona, P Catuogno, JF Colombeau, SO Juriaans, C Olivera International Workshop on Lie Theory and Its Applications in Physics, 583-589 , 2015 2015 Citations: 1
From the Poincaré theorem to generators of the unit group of integral group rings of finite groups E Jespers, S Juriaans, A Kiefer, A de A e Silva, A Souza Filho Mathematics of Computation 84 (293), 1489-1520 , 2015 2015 Citations: 12
Nonlinear generalized functions and jump conditions for a standard one pressure liquid–gas model J Aragona, JF Colombeau, SO Juriaans Journal of Mathematical analysis and Applications 418 (2), 964-977 , 2014 2014 Citations: 17
Algebraic theory of Colombeauʼs generalized numbers J Aragona, ARG Garcia, SO Juriaans Journal of Algebra 384, 194-211 , 2013 2013 Citations: 17
Free groups in quaternion algebras SO Juriaans, AC Souza Filho Journal of Algebra 379, 314-321 , 2013 2013 Citations: 4
Poincar\'e Bisectors in Hyperbolic Spaces A Kiefer, SO Juriaans, E Jespers, ADAE Silva 2012
MOST CITED SCHOLAR PUBLICATIONS
A discontinuous Colombeau differential calculus J Aragona, R Fernandez, SO Juriaans Monatshefte für Mathematik 144 (1), 13-29 , 2005 2005 Citations: 58
Some structural properties of the topological ring of Colombeau's generalized numbers J Aragona, SO Juriaans Taylor & Francis Group 29 (5), 2201-2230 , 2001 2001 Citations: 58
Algebraic and geometric theory of the topological ring of Colombeau generalized functions J Aragona, SO Juriaans, ORB Oliveira, D Scarpalezos Proceedings of the Edinburgh Mathematical Society 51 (3), 545-564 , 2008 2008 Citations: 47
Finite subgroups in integral group rings MA Dokuchaev, SO Juriaans Canadian Journal of Mathematics 48 (6), 1170-1179 , 1996 1996 Citations: 44
Natural topologies on Colombeau algebras J Aragona, R Fernandez, SO Juriaans 2009 Citations: 37
Differential calculus and integration of generalized functions over membranes J Aragona, R Fernandez, SO Juriaans, M Oberguggenberger Monatshefte für Mathematik 166 (1), 1-18 , 2012 2012 Citations: 36
Automorphisms of finite groups SO Juriaans, JM De Miranda, JR Robério Communications in Algebra 32 (5), 1705-1714 , 2004 2004 Citations: 35
On the normalizer problem E Jespers, SO Juriaans, JM De Miranda, JR Rogério Journal of Algebra 247 (1), 24-36 , 2002 2002 Citations: 28
Integral group rings of Frobenius groups and the conjectures of HJ Zassenhaus MA Dokuchaev, SO Juriaans, C Polcino Milies Communications in Algebra 25 (7), 2311-2325 , 1997 1997 Citations: 28
Hyperbolic unit groups S Juriaans, I Passi, D Prasad Proceedings of the American Mathematical Society 133 (2), 415-423 , 2005 2005 Citations: 24
Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data J Aragona, ARG Garcia, SO Juriaans Nonlinear Analysis: Theory, Methods & Applications 71 (11), 5187-5207 , 2009 2009 Citations: 23
The origin of felsic microgranitoid enclaves: Insights from plagioclase crystal size distributions and thermodynamic models A Alves, G de Souza Pereira, V de Assis Janasi, M Higgins, LA Polo, ... Lithos 239, 33-44 , 2015 2015 Citations: 19
The sharp topology on the full Colombeau algebra of generalized functions J Aragona, R Fernandez, SO Juriaans Integral Transforms and Special Functions 17 (2-3), 165-170 , 2006 2006 Citations: 18
Nonlinear generalized functions and jump conditions for a standard one pressure liquid–gas model J Aragona, JF Colombeau, SO Juriaans Journal of Mathematical analysis and Applications 418 (2), 964-977 , 2014 2014 Citations: 17
Algebraic theory of Colombeauʼs generalized numbers J Aragona, ARG Garcia, SO Juriaans Journal of Algebra 384, 194-211 , 2013 2013 Citations: 17
Units of integral group rings of Frobenius groups OS Juriaans, FC Polcino Milies 1998 Citations: 17
Hyperbolic unit groups and quaternion algebras SO Juriaans, IBS Passi, AC Souza Filho Proceedings-Mathematical Sciences 119 (1), 9-22 , 2009 2009 Citations: 14
On hypercentral units in integral group rings. M Hertweck, E Iwaki, E Jespers, SO Juriaans, DJS Robinson Journal of Group Theory 10 (4) , 2007 2007 Citations: 14
Isomorphisms of integral group rings of infinite groups E Jespers, SO Juriaans Journal of Algebra 223 (1), 171-189 , 2000 2000 Citations: 14
From the Poincaré theorem to generators of the unit group of integral group rings of finite groups E Jespers, S Juriaans, A Kiefer, A de A e Silva, A Souza Filho Mathematics of Computation 84 (293), 1489-1520 , 2015 2015 Citations: 12