12,704 research outputs found
Bis(4-(3,4-dimethylenepyrrolidyl)-phenyl) methane
It is the primary object of the present invention to prepare high temperature polymeric materials, especially linear aromatic polyimides, which maintain their integrity and toughness during long exposure times at elevated temperatures. According to the present invention, this object is achieved, and the attending benefits are obtained, by first providing the bis(exocyclodiene) bis(4-(3,4-dinethylene pyrrolidyl) phenyl) methane, which is formed from the monomer N-phenyl 3,4-dimethylene pyrrolidine. This bis-(exocyclodiene) undergoes Diels-Alder reaction with a bismaleimide without the evolution of gaseous by-products, to form the aromatic polyimide
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The Asian drivers and SSA: MFA quota removal and the portents for African industrialisation
The Panopticon under the Light of Politics and Technology
This paper focuses on Foucault's concept of the Panopticon. The Panopticon since time immemorial has been used as a concept in order to control society. Since this is being used as a tool to control society, this then is considered to be a form of technology of which is being used by individuals who hold power
On the Finiteness Property for Rational Matrices
We analyze the periodicity of optimal long products of matrices. A set of
matrices is said to have the finiteness property if the maximal rate of growth
of long products of matrices taken from the set can be obtained by a periodic
product. It was conjectured a decade ago that all finite sets of real matrices
have the finiteness property. This conjecture, known as the ``finiteness
conjecture", is now known to be false but no explicit counterexample to the
conjecture is available and in particular it is unclear if a counterexample is
possible whose matrices have rational or binary entries. In this paper, we
prove that finite sets of nonnegative rational matrices have the finiteness
property if and only if \emph{pairs} of \emph{binary} matrices do. We also show
that all {pairs} of binary matrices have the finiteness property.
These results have direct implications for the stability problem for sets of
matrices. Stability is algorithmically decidable for sets of matrices that have
the finiteness property and so it follows from our results that if all pairs of
binary matrices have the finiteness property then stability is decidable for
sets of nonnegative rational matrices. This would be in sharp contrast with the
fact that the related problem of boundedness is known to be undecidable for
sets of nonnegative rational matrices.Comment: 12 pages, 1 figur
Observable Graphs
An edge-colored directed graph is \emph{observable} if an agent that moves
along its edges is able to determine his position in the graph after a
sufficiently long observation of the edge colors. When the agent is able to
determine his position only from time to time, the graph is said to be
\emph{partly observable}. Observability in graphs is desirable in situations
where autonomous agents are moving on a network and one wants to localize them
(or the agent wants to localize himself) with limited information. In this
paper, we completely characterize observable and partly observable graphs and
show how these concepts relate to observable discrete event systems and to
local automata. Based on these characterizations, we provide polynomial time
algorithms to decide observability, to decide partial observability, and to
compute the minimal number of observations necessary for finding the position
of an agent. In particular we prove that in the worst case this minimal number
of observations increases quadratically with the number of nodes in the graph.
From this it follows that it may be necessary for an agent to pass through
the same node several times before he is finally able to determine his position
in the graph. We then consider the more difficult question of assigning colors
to a graph so as to make it observable and we prove that two different versions
of this problem are NP-complete.Comment: 15 pages, 8 figure
Resonance and marginal instability of switching systems
We analyse the so-called Marginal Instability of linear switching systems,
both in continuous and discrete time. This is a phenomenon of unboundedness of
trajectories when the Lyapunov exponent is zero. We disprove two recent
conjectures of Chitour, Mason, and Sigalotti (2012) stating that for generic
systems, the resonance is sufficient for marginal instability and for
polynomial growth of the trajectories. We provide a characterization of
marginal instability under some mild assumptions on the sys- tem. These
assumptions can be verified algorithmically and are believed to be generic.
Finally, we analyze possible types of fastest asymptotic growth of
trajectories. An example of a pair of matrices with sublinear growth is given
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