In this paper we revisit the subject of stationary flows Lax hierarchies a coupled KdV class. We explain main ideas in standard case and then consider dispersive water waves (DWW) case, with respectively 2 3 Hamiltonian representations. Each representation gives us different form flow. Comparing these, construct Poisson maps, which, being non-canonical, give rise to bi-Hamiltonian representatio...

Many specific problems ranging from theoretical probability to applications in statistical physics, combinatorial optimization and communications can be formulated as an optimal tuning of local parameters large systems interacting particles. Using the framework stationary point processes Euclidean space, we pose it a problem marking given process. The quality is evaluated terms scores calculate...

The feature map represented by the set of weight vectors of the basic SOM (Self-Organizing Map) provides a good approximation to the input space from which the sample vectors come. But the timedecreasing learning rate and neighborhood function of the basic SOM algorithm reduce its capability to adapt weights for a varied environment. In dealing with non-stationary input distributions and changi...

The existence of shift for periodically correlated processes and its boundedness are investigated. Spectral criteria for these non-stationary processes to have such shifts are obtained.