10,468 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
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
Finite size scaling in three-dimensional bootstrap percolation
We consider the problem of bootstrap percolation on a three dimensional
lattice and we study its finite size scaling behavior. Bootstrap percolation is
an example of Cellular Automata defined on the -dimensional lattice
in which each site can be empty or occupied by a single
particle; in the starting configuration each site is occupied with probability
, occupied sites remain occupied for ever, while empty sites are occupied by
a particle if at least among their nearest neighbor sites are
occupied. When is fixed, the most interesting case is the one :
this is a sort of threshold, in the sense that the critical probability
for the dynamics on the infinite lattice switches from zero to one
when this limit is crossed. Finite size effects in the three-dimensional case
are already known in the cases : in this paper we discuss the case
and we show that the finite size scaling function for this problem is
of the form . We prove a conjecture proposed by
A.C.D. van Enter.Comment: 18 pages, LaTeX file, no figur
Polyimide from bis(n-isoprenyl)s of aryl diamides
A process and polyimide product formed by the reaction of a bismaleimide with a bis(amidediene) is disclosed wherein the bis(amidediene) is formed by reacting an excess of an acid chloride with 1,4-N,N'-diisoprenyl 2,3,5,6-tetramethy1 benzene
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