Abstract. A special class of recurrent neural network, termed Zhang neural network (ZNN) depicted in the implicit dynamics, has recently been proposed for online solution of time-varying matrix square roots. Such a ZNN model can be constructed by using monotonically-increasing odd activation functions to obtain the theoretical time-varying matrix square roots in an error-free manner. Different ...

We present an analytic study of the finite size effects in Sine–Gordon model, based on the semiclassical quantization of an appropriate kink background defined on a cylindrical geometry. The quasi–periodic kink is realized as an elliptic function with its real period related to the size of the system. The stability equation for the small quantum fluctuations around this classical background is ...

We argue that, contrary to previous claims, the supersymmetric sine-Gordon model with boundary has a two-parameter family of boundary interactions which preserves both integrability and supersymmetry. We also propose the corresponding boundary S matrix for the first supermultiplet of breathers.

Local cosine/sine basis is a localized version of co-sine/sine basis with a smooth window function. It has orthogonality and good time and frequency localization properties. Adaptive local cosine/sine basis is a best-basis based on a cost-functional obtained from an overabundant library of cosine/sine packets. In this paper, we apply the 2-D semi-adaptive (time-adaptive or space-adaptive) local...