A new type of MISO(Multiple-Input,Single-Output) multivariate generalized polynomials neural network is constructed based on multivariate function approximation theory.

In this paper,we prove that the Descartes\' law of signs for generalized polynomials holds.

In this paper,the eigenvalue statistical analysis was performed for the horizontal deformation of Wanjiazhai dam,and a deformation statistical model is constructed with generalized linear polynomial stepwise regression.

In this paper, the trend of thedeformation of the Wanjiazhai dam is analyzed by means of physical deducibility and graphology, and a deformation model isconstructed with generalized linear polynomial stepwise regression.

Iterative learning control algorithm based on general orthogonal polynomials;

For the numerical solution of switching law related to system state which is difficult to be obtained, the general orthogonal polynomials was used to get approximate switching law and the simulation was realized.

By semigroup theory and general orthogonal polynomials (GOP), the stability of a class of distributed parameter hybrid systems (DPHS) and a class of distributed parameter switched systems (DPSS), the stabilization for a class of DPSS and the approximate analysis for distributed parameter control systems were discussed in this dissertation.

To be specific,its generalized characteristic polynomial has positive double roots,which we proved further has only a double,root by using the affine transformation and inverse affine transformation.

We derive an algebraic condition (based on the generalized characteristic polynomial) for detecting the positional relationship of a planar ellipse and a planar parabola (hyperbola) by considering all the cases: separation, exterior contact, intersection, interior contact and inclusion.