Hoppeld networks are neural architectures remarkable by architectural simplicity and exibility in usage. There are many areas in which Hoppeld networks have been successfully applied, including associative memories, pattern recognition and artiicial intelligence. This paper proposes a novel application of Hoppeld networks in image processing, as morphologic lters, and illustrates the concept wi...

Macroscopic models for spatially extended systems under random influences are often described by stochastic partial differential equations (SPDEs). Some techniques for understanding solutions of such equations, such as estimating correlations, Liapunov exponents and impact of noises, are discussed. They are relevant for understanding predictability in spatially extended systems with model uncer...

We study linear and nonlinear instability of steady incompressible inviscid flows. First, some sufficient conditions of linear instability for a class of shear flows are given. Second, nonlinear instability in the L2-norm of velocity is proved under the assumption that the growth rate exceeds half of the Liapunov exponent of the steady flow, for any bounded domain. We also estimate the growth o...

The convergence to steady states of non-negative solutions u to the one-dimensional viscous Hamilton-Jacobi equation ∂tu − ∂2 xu = |∂xu|, (t, x) ∈ (0,∞)× (−1, 1) with homogeneous Dirichlet boundary conditions is investigated. For that purpose, a Liapunov functional is constructed by the approach of Zelenyak (1968). Instantaneous extinction of ∂xu on a subinterval of (−1, 1) is also shown for su...

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