In this paper, the function approximation of Gelenbe Neural Network (GNN) is discussed and it is proved that GNN can approximate any G-type polynomial by using constructional method.

Based on the classical GMDH algorithm and other several improved GMDH algorithms, the paper studies the GMDH s theory, especial the K-G polynomial and the transfer function which induce the problems of mass and redundant polynomial variables in the output model.

In this paper we have investigated the constructing method of the axial stiffness in polynomial form for arbitrary supported rod with homogeneous cross-section from the fundamental mode and corresponding frequency when rods density distribution in polynomial form is given.

Furthermore, the functional matrix Pn,λ[x] with polynomial of binomial type related to [ n+λ n-k ] and its properties are studied.

The properties of the lower triangular functional matrix Ln[x] associated with a polynomial of binomial type are discussed in this paper, in which the entry-(i,j) of Ln[x] is equal to lij =(?)i-j(x)l(i,j)if i≥j and equal to 0 otherwise, with l(i, k)l(k,j) = l(i,j)(k-j i-j) and for integers n,k,i,j and real numbers x,y.

At first,risk-neutral probabilities of option pricing were obtained which with asymmetrical multinomial model of two assets,then the American option price of two assets were gotten,which volatility followed Markov process.

OFDM blind channel estimation based on polynomial models;

To improve the precision of short stroke control in hot mill, the broken line model is converted into the slick curve model,a polynomial model and a RBF neural network model are studied,which have been simulated and applied to online controlling.

Using the polynomial model as the dynamics model of magneto-rheological damper,the bad effect of the damping force jump with the "on-off" semi-active control on vibration acceleration of vehicle sprung mass is investigated.