2,269 research outputs found
Robot's hand and expansions in non-integer bases
We study a robot hand model in the framework of the theory of expansions in
non-integer bases. We investigate the reachable workspace and we study some
configurations enjoying form closure properties.Comment: 22 pages, 10 figure
A Fibonacci control system with application to hyper-redundant manipulators
We study a robot snake model based on a discrete linear control system
involving Fibonacci sequence and closely related to the theory of expansions in
non-integer bases. The present paper includes an investigation of the reachable
workspace, a more general analysis of the control system underlying the model,
its reachability and local controllability properties and the relation with
expansions in non-integer bases and with iterated function systems
Quantum entanglement and the Bell Matrix
We present a class of maximally entangled states generated by a
high-dimensional generalisation of the \textsc{cnot} gate. The advantage of our
approach is the simple algebraic structure of both entangling operator and
resulting entangled states. In order to show that the method can be applied to
any dimension, we introduce new sufficient conditions for global and maximal
entanglement with respect to Meyer and Wallach's measure.Comment: 11 pages, 3 figure
Geometrical aspects of expansions in complex bases
We study the set of the representable numbers in base
with and and with digits in
a arbitrary finite real alphabet . We give a geometrical description of the
convex hull of the representable numbers in base and alphabet and an
explicit characterization of its extremal points. A characterizing condition
for the convexity of the set of representable numbers is also shown.Comment: 23 pages, 5 figure
Internal observability of the wave equation in tiled domains
We investigate the internal observability of the wave equation with Dirichlet
boundary conditions in tilings. The paper includes a general result relating
internal observability problems in general domains to their tiles, and a
discussion of the case in which the domain is the 30-60-90 triangle.Comment: arXiv admin note: substantial text overlap with arXiv:1807.1053
Optimal expansions of Kakeya sequences
We investigate optimal expansions of Kakeya sequences for the representation
of real numbers. Expansions of Kakeya sequences generalize the expansions in
non-integer bases and they display analogous redundancy phenomena. In this
paper, we characterize optimal expansions of Kakeya sequences, and we provide
conditions for the existence of unique expansions with respect to Kakeya
sequences
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