2,513 research outputs found
Permutations Containing Many Patterns
It is shown that the maximum number of patterns that can occur in a
permutation of length is asymptotically . This significantly improves
a previous result of Coleman
Simulation Studies of Nanomagnet-Based Architecture
We report a simulation study on interacting ensembles of Co nanomagnets that
can perform basic logic operations and propagate logic signals, where the state
variable is the magnetization direction. Dipole field coupling between
individual nanomagnets drives the logic functionality of the ensemble and
coordinated arrangements of the nanomagnets allow for the logic signal to
propagate in a predictable way. Problems with the integrity of the logic signal
arising from instabilities in the constituent magnetizations are solved by
introducing a biaxial anisotropy term to the Gibbs magnetic free energy of each
nanomagnet. The enhanced stability allows for more complex components of a
logic architecture capable of random combinatorial logic, including horizontal
wires, vertical wires, junctions, fanout nodes, and a novel universal logic
gate. Our simulations define the focus of scaling trends in nanomagnet-based
logic and provide estimates of the energy dissipation and time per nanomagnet
reversal
Synchronization versus stability of the invariant distribution for a class of globally coupled maps
We study a class of globally coupled maps in the continuum limit, where the
individual maps are expanding maps of the circle. The circle maps in question
are such that the uncoupled system admits a unique absolutely continuous
invariant measure (acim), which is furthermore mixing. Interaction arises in
the form of diffusive coupling, which involves a function that is discontinuous
on the circle. We show that for sufficiently small coupling strength the
coupled map system admits a unique absolutely continuous invariant
distribution, which depends on the coupling strength .
Furthermore, the invariant density exponentially attracts all initial
distributions considered in our framework. We also show that the dependence of
the invariant density on the coupling strength is Lipschitz
continuous in the BV norm.
When the coupling is sufficiently strong, the limit behavior of the system is
more complex. We prove that a wide class of initial measures approach a point
mass with support moving chaotically on the circle. This can be interpreted as
synchronization in a chaotic state
Ancient Maya Beekeeping (ca. 1000-1520 CE)
Articlehttp://deepblue.lib.umich.edu/bitstream/2027.42/96996/1/UMURJ-Issue07_2010-DMImre.pd
Highly Selective Hydroformylation of the Cinchona Alkaloids
The four naturally occurring cinchona alkaloids were subjected to hydroformylation to create an extra functional group that allows immobilization. Cinchonidine, quinine, and quinidine, could be hydroformylated with virtually complete terminal selectivity, using a rhodium/tetraphosphite catalyst. The cinchonidine aldehyde was reduced to the alcohol and subjected to reductive amination with benzylamine.
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