A subset S of vertices in a graph G is called a geodetic set if every vertex not in S lies on a shortest path between two vertices from S. A subset D of vertices in G is called dominating set if every vertex not in D has at least one neighbor in D. A geodetic dominating set S is both a geodetic and a dominating set. The geodetic (domination, geodetic domination) number g(G)(γ(G), γg(G)) of G is...

The single wheel, gyroscopically stabilized robot Gyrover, is a dynamically stable but statically unstable, underactuated system. In this paper, based on the dynamic model of the robot, we investigate two classes of nonholonomic constraints associated with the system. Then, based on the backstepping technology, we propose a control law for balance control of Gyrover. Next, through transferring ...

In this work, a cartesian impedance controller purposely designed for dexterous manipulation is described. Based on the main features of the DLR Hand II, concerning kinematic structure and sensory equipment of fingers, this control strategy allows to overcome the main problems encountered in fine manipulation, namely: effects of the friction (and unmodeled dynamics) on robot performances and oc...

Rotagraphs generalize all standard products of graphs in which one factor is a cycle. A computer based approach for searching graph invariants on rotagraphs is proposed and two of its applications are presented. First, the-numbers of the Cartesian product of a cycle and a path are computed, where the-number of a graph G is the minimum number of colors needed in a (2,1)-coloring of G. The indepe...

This paper presents the experimental identification of the dynamic parameters of the Orthoglide [1], a 3-DOF parallel. The dynamic identification model is based on the inverse dynamic model, which is linear in the parameters. The model is computed in a closed form in terms of the Cartesian dynamic model elements of the legs and of the Newton-Euler equation of the platform. The base inertial par...

This paper presents the experimental identification of the dynamic parameters of the Orthoglide [1], a 3-DOF parallel. The dynamic identification model is based on the inverse dynamic model, which is linear in the parameters. The model is computed in a closed form in terms of the Cartesian dynamic model elements of the legs and of the Newton-Euler equation of the platform. The base inertial par...

The definition of $L$-fuzzy Q-convergence spaces is presented by Pang and Fang in 2011. However, Cartesian-closedness of the category of $L$-fuzzy Q-convergence spaces is not investigated. This paper focuses on Cartesian-closedness of the category of $L$-fuzzy Q-convergence spaces, and it is shown that  the category $L$-$mathbf{QFCS}$ of $L$-fuzzy Q-convergence spaces is Cartesian-closed.

A category $mathbf{C}$ is called Cartesian closed  provided that it has finite products and for each$mathbf{C}$-object $A$ the functor $(Atimes -): Ara A$ has a right adjoint. It is well known that the category $mathbf{TopFuzz}$  of all topological fuzzes is both complete  and cocomplete, but it is not Cartesian closed. In this paper, we introduce some Cartesian closed subcategories of this cat...