We study the group of automorphisms of Shimura curves X0(D,N) attached to an Eichler order of square-free level N in an indefinite rational quaternion algebra of discriminant D > 1. We prove that, when the genus g of the curve is greater than or equal to 2, Aut(X0(D,N)) is a 2-elementary abelian group which contains the group of Atkin-Lehner involutions W0(D,N) as a subgroup of index 1 or 2. It...

This note is devoted to the study of families quaternionic modular forms arising from orders defined by Pizer. In this situation, Hecke eigenspaces are 2-dimensional contrary classical case Eichler orders. The main result a Control Theorem in spirit Hida, interpolating these eigenspaces. We restrict our attention definite rational quaternion algebra ramified at single odd prime [Formula: see te...

In this paper we will construct a lattice-based public-key cryptosystem using non-commutative quaternion algebra, and since its lattice does not fully fit within Circular and Convolutional Modular Lattice (CCML), we prove it is arguably more secure than the existing lattice-based cryptosystems such as NTRU. As in NTRU, the proposed public-key cryptosystem relies for its inherent securi...

an involution or anti-involution is a self-inverse linear mapping. in this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. moreover, properties and geometrical meanings of these matrices will be given as reflections in r^3.

A structure preserving Sort-Jacobi algorithm for computing eigenvalues or singular values is presented. The proposed method applies to an arbitrary semisimple Lie algebra on its (−1)-eigenspace of the Cartan involution. Local quadratic convergence for arbitrary cyclic schemes is shown for the regular case. The proposed method is independent of the representation of the underlying Lie algebra an...

Spatial audio methods are gaining a growing interest due to the spread of immersive experiences and applications, such as virtual augmented reality. For these purposes, 3D signals often acquired through arrays Ambisonics microphones, each comprising four capsules that decompose sound field in spherical harmonics. In this paper, we propose dual quaternion representation spatial an array two Firs...

In the literature we find a variety of mathematical approaches for solving problems in robotics which we will review now briefly. Denavit and Hartenberg [60] introduced the mostly used kinematic notation for lower pair mechanisms based on matrix algebra, Walker [243] used the epsilon algebra for the treatment of the manipulator kinematics, Gu and Luh [99] utilized dual– matrices for computing t...

The widespread use of unmanned aerial vehicles during warfare has intensified the problem their management, especially when they are used in large groups. One main tasks is to ensure coordinated movement group's aircraft space. Optimizing each device group three-dimensional space expedient mathematical models. any vehicle can be presented as a combination translational and rotational movements,...