### ${\mathbb{A}}^{1}$-homotopy theory.

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It is known ([1], [2]) that a construction of equivariant finiteness obstructions leads to a family ${w}_{\alpha}^{H}\left(X\right)$ of elements of the groups ${K}_{0}\left(\mathbb{Z}\left[{\pi}_{0}{\left(WH\left(X\right)\right)}_{\alpha}^{*}\right]\right)$. We prove that every family ${w}_{\alpha}^{H}$ of elements of the groups ${K}_{0}\left(\mathbb{Z}\left[{\pi}_{0}{\left(WH\left(X\right)\right)}_{\alpha}^{*}\right]\right)$ can be realized as the family of equivariant finiteness obstructions ${w}_{\alpha}^{H}\left(X\right)$ of an appropriate finitely dominated G-complex X. As an application of this result we show the natural equivalence of the geometric construction of equivariant finiteness obstruction ([5], [6]) and equivariant generalization of Wall’s obstruction...

In this paper the control of robotic manipulation is investigated. Manipulation system analysis and control are approached in a general framework. The geometric aspect of manipulation system dynamics is strongly emphasized by using the well developed techniques of geometric multivariable control theory. The focus is on the (functional) control of the crucial outputs in robotic manipulation, namely the reachable internal forces and the rigid-body object motions. A geometric control procedure is outlined...

This paper deals with the problem of controlling contact forces in robotic manipulators with general kinematics. The main focus is on control of grasping contact forces exerted on the manipulated object. A visco-elastic model for contacts is adopted. The robustness of the decoupling controller with respect to the uncertainties affecting system parameters is investigated. Sufficient conditions for the invariance of decoupling action under perturbations on the contact stiffness and damping parameters...

The aim of this note is to offer a summary of the definitions and properties of arithmetic symbols on the linear group Gl(n, F) -F being an arbitrary discrete valuation field- and to show that the natural generalizations of the Parshin symbol on an algebraic surface S to the linear group Gl(n, ΣS) do not allow us to define new 2-dimensional symbols on S.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].

We extend the definition of Hochschild and cyclic homologies of a scheme over a commutative ring k to define the Hochschild homologies HH⁎(X/S) and cyclic homologies HC⁎(X/S) of a scheme X with respect to an arbitrary base scheme S. Our main purpose is to study product structures on the Hochschild homology groups HH⁎(X/S). In particular, we show that $HH\u204e(X/S)={\u2a01}_{n\in \mathbb{Z}}HH\u2099(X/S)$ carries the structure of a graded algebra.