As CMAC neural network could not be used to approximate the multi-valued mapping of an inverse hysteresis directly,an inverse hysteretic operator was proposed to transform the multi-valued mapping into a one-to-one mapping which could enable neural networks to approximate the behavior of an inverse hysteresis.

The continuous transfor-mation technique is used to construct an elementary inverse hysteresis operator (EIHO), which extracts the elementary information of inverse hysteresis.

A novel dynamic bandwidth allocation algorithm named the hysteresis algorithm is presented based on VBR video traffic prediction in this paper, The buffer size requirement and cell loss rate are both improved significantly compared with threshold algorithm presented by Girish and the allocation scheme based on GOP scene detection presented by Youssef.

By means of the causal operator determined by the initial pmblem of the differentio-integral equation, the class of the noulinear diffusion model of the biological population was translated into the initia-boundary problem of the parabolic equation with the causal operator.

A mathematical model describing memory effects, the causal operator is introduced, the ordinary differential equation and the parabolic equation with the causal operator are discussed and sufficient conditions of existence, positiveness and uniqueness for their solutions are given.