47,505 research outputs found
Nonlinear Boundary Value Problems via Minimization on Orlicz-Sobolev Spaces
We develop arguments on convexity and minimization of energy functionals on
Orlicz-Sobolev spaces to investigate existence of solution to the equation
\displaystyle -\mbox{div} (\phi(|\nabla u|) \nabla u) = f(x,u) + h \mbox{in}
\Omega under Dirichlet boundary conditions, where
is a bounded smooth domain, is a
suitable continuous function and
satisfies the Carath\'eodory conditions, while is a measure.Comment: 14 page
Symmetry Breaking Study with Deformed Ensembles
A random matrix model to describe the coupling of m-fold symmetry in
constructed. The particular threefold case is used to analyze data on
eigenfrequencies of elastomechanical vibration of an anisotropic quartz block.
It is suggested that such experimental/theoretical study may supply powerful
means to discern intrinsic symmetries in physical systems.Comment: 12 pages, 5 figure
Optimal network topologies for information transmission in active networks
This work clarifies the relation between network circuit (topology) and
behavior (information transmission and synchronization) in active networks,
e.g. neural networks. As an application, we show how to determine a network
topology that is optimal for information transmission. By optimal, we mean that
the network is able to transmit a large amount of information, it possesses a
large number of communication channels, and it is robust under large variations
of the network coupling configuration. This theoretical approach is general and
does not depend on the particular dynamic of the elements forming the network,
since the network topology can be determined by finding a Laplacian matrix (the
matrix that describes the connections and the coupling strengths among the
elements) whose eigenvalues satisfy some special conditions. To illustrate our
ideas and theoretical approaches, we use neural networks of electrically
connected chaotic Hindmarsh-Rose neurons.Comment: 20 pages, 12 figure
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