This paper presents a generic approach to analyze the singularity of robots with an articulated nacelle like the H4 robot. Using screw theory, the concept of equivalent twist graph is introduced in order to characterize the constraint wrenches and the actuation wrenches applied to the moving platform. Using Grassmann-Cayley Algebra, the geometric conditions associated with the dependency of six...

Lines classification is the central tool for visibility calculation in dimension n ≥ 2. It has been previously expressed in Grassmann Algebra, allowing to work with any couple of 2-vectors, which may represent two real lines or not. This article discusses about the nature of lines in the conformal model, searching if such a classification is still valid in Rn+1,1. First, it shows that the proje...

Starting with the Lagrangian formalism with N = 2 supersymmetry in terms of two Grassmann variables in Classical Mechanics, the Dirac canonical quantization method is implemented. The N = 2 supersymmetry algebra is associated to one-component and two-component eigenfunctions considered in the Schrödinger picture of Nonrelativistic Quantum Mechanics. Applications are contemplated. PACS numbers: ...

Polyhedral scene analysis studies whether a 2D line drawing of a 3D polyhedron is realizable in the space, and if so, parameterizing the space of all possible realizations. For generic 2D data, symbolic computation with Grassmann-Cayley algebra is needed in the analysis. In this paper, we propose a method called parametric calotte propagation to solve the realization and parameterization proble...

Products and coproducts may be recognized as morphisms in a monoidal tensor category of vector spaces. To gain invariant data of these morphisms, we can use singular value decomposition which attaches singular values, ie generalized eigenvalues, to these maps. We show, for the case of Grassmann and Clifford products, that twist maps significantly alter these data reducing degeneracies. Since no...

The work continues a presentation of modern quantum mathematics backgrounds started in [3]. A general approach to quantum holonomic computing based on geometric Lie algebraic structures on Grassmann manifolds and related with them Lax type flows is proposed. Making use of the differential geometric techniques like momentum mapping reduction, central extension and connection theory on Stiefel bu...

We study a family of complex representations of the group GL n (o), where o is the ring of integers of a non-archimedean local field F. These representations occur in the restriction of the Grassmann representation of GL n (F) to its maximal compact subgroup GL n (o). We compute explicitly the transition matrix between a geometric basis of the Hecke algebra associated with the representation an...

Non-anticommutative Grassmann coordinates in four-dimensional twistdeformed N = 1 Euclidean superspace are decomposed into geometrical ones and quantum shift operators. This decomposition leads to the mapping from the commutative to the non-anticommutative supersymmetric field theory. We apply this mapping to the Wess-Zumino model in commutative field theory and derive the corresponding non-ant...

In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal processing. In addition to the new algorithms, we show how the geometrical framework gives penetrating ne...

Given three partially overlapping views of a scene from which a set of point correspondences have been extracted, recover the three trifocal tensors between the three views. We give a new way of deriving the trifocal tensor based on Grassmann-Cayley algebra that sheds some new light on its structure. We show that our derivation leads to a complete characterization of its geometric and algebraic...