Adaptive neural Legendre orthogonal polynomial nonlinear channel equalization for chaos-based communications systems;

A method to estimate the failure probability of structures using Legendre orthogonal polynomial approximate method (LPAM) was presented.

Based on the maximum likelihood analysis principle for dynamic trait QTL mapping,selecting three orders Legendre polynomial as sub-model,the effects of the individual number,the frequency of test day,the marker density and heritability on detecting power are investigated by Monte-Carlo simulation.

Based on the idea about random regression test-day model for estimating breeding values in animal evaluation,a mathematic model was constructed for mapping dynamic trait loci by using Legendre polynomials to model dynamic changes of each genetic effect.

By assuming the warping displacement of the rectangular cross-section in the form of 3 order Legendre polynomial function, the governing differential equations, which are simple and can be solved easily, was derived using incomplete generalized Hellinger-Reissner variational principle of sub-item in the scope of elasticity theory for plane stress problems.

Fibonacci numbers and Legendre polynomials;

The best quadratic approximation by Legendre polynomials was used to develop a two-step method to identify systems with nonsymmetrical dead zone nonlinearities.

At first,we choose Legendre polynomials as basis and then estimate the convergence of the approximate solution.

A new method of plane magnetic field fitting based on orthogonal polynomials;

Application to harmonics statistic with orthogonal polynomials series based on least squares method;

Application of orthogonal polynomials with constraints to fitting of stage-discharge relation;

Applications of orthogonal polynomials in caculating GPS orbit with broadcast ephemeris;

Application of fitting orthogonal polynomial in standard compaction test;

Fuzzy control based on Chebyshev orthogonal polynomial prediction;