Projector keystone correction based on image space transformation and image interpolation algorithm;

Nowadays the keystone correction has become the basic function of a projector.

First we apply Green s functions in special solution,simplifying the second order problems to the first order integral formulation,then we deal with its numerical solution by the compound trapezoidal formula.

The asymptotic behavior of the remainder mean value in the trapezoidal formula is discussed under main condition f(x) ∈C4(I).

The mid-rectangle formula and trapezoid formula are generalized,and as one of its application,a generalization of midpoint formula in numerical differentiation is obtained.

This paper intends to give a new integral trapezoid formula by using the asymptotic feature of mean value theorem of differential to conclude the estimated formula of definite integral.

Asymptotic behavior theorem of the "midpoint" of remainder in the trapezoidal rule and its application;

Performance characteristics of IKA C5000 calorimeter and the correction formula of gross calorific value;

in the orthogonal frequency division multiplexing(OFDM) channel estimation method based on expectation maximization(EM) algorithm,an acceleration EM OFDM channel estimation algorithm was proposed,which is complemented by quasi-Newton accelerate method and combines with Broyden symmetry rank one correction formulae with adjusted parameters.

we illustrate that once the numerical integral error formula is obtained,only using the concept of algebra accuracy one can determine the intermediate point of the error formula to obtain the higher order algebra accuracy correction formula.