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Hyperbolic unit groups and quaternion algebras
(INDIAN ACAD SCIENCES, 2009)
We classify the quadratic extensions K = Q[root d] and the finite groups G for which the group ring o(K)[G] of G over the ring o(K) of integers of K has the property that the group U(1)(o(K)[G]) of units of augmentation 1 ...
Analysis of Computational Efficiency applied to forward and Inverse Kinematics of Robotic Manipulators using Homogeneous Transformation Matrixes and Dual Quaternions
(Universidade Tecnológica Federal do Paraná (UTFPR), 2019)
Free groups in quaternion algebras
(Amsterdam, 2013-04-01)
In Juriaans et al. (2009) [9] we constructed pairs of units u,v in Z-orders of a quaternion algebra over View the MathML source, d a positive and square free integer with View the MathML source, such that 〈un,vn〉 is free ...
Dos números complexos aos quatérnions: desenvolvimento algébrico, interpretação geométrica e aplicações
(Universidade Tecnológica Federal do ParanáCuritibaMestrado Profissional em Matemática em Rede Nacional, 2013-11-26)
This work was developed after observing the difficulties and unmotivated of the high school students to learning complex numbers. The development consisted in create a timeline in the study of complex numbers since Cardano ...
Computing ideal classes representatives in quaternion algebras
(American Mathematical Society, 2014-06)
Let K be a totally real number field and let B be a totally definite quaternion algebra over K. Given a set of representatives for ideal classes for a maximal order in B, we show how to construct in an efficient way a set ...
On some branches of the Bruhat-Tits tree
(WORLD SCIENTIFIC PUBL, 2016)
We explicitly compute the largest subtree, in the local Bruhat-Tits tree for PSL2(k), whose vertices correspond to maximal orders containing a fixed order generated by a pair of orthogonal pure quaternions. In other words, ...
Control de un quadrotor usando cuaternión unitario
(Instituto Nacional de Astrofísica, Óptica y Electrónica, 2013)
Control de un quadrotor usando cuaternión unitario
(Instituto Nacional de Astrofísica, Óptica y Electrónica, 2013)
Movimentos regulares e caóticos de rotação de corpos rígidosRegular and chaotic rotation movements of rigid bodies
(Universidade Estadual Paulista (Unesp), 2016)
Whole-body control of a mobile manipulator using feedback linearization and dual quaternion algebra
(Universidade Federal de Minas GeraisUFMG, 2017-06-14)
This master thesis presents the whole-body control of a nonholonomic mobile manipulator using feedback linearization and dual quaternion algebra. The controller, whose reference is a unit dual quaternion representing the ...