The nonmembership detection is based on Lagrange

interpolation formula. That is, with t or more than t coordinate points of a polynomial can uniquely determine this polynomial and the secret; however, if there is any invalid value in the set of coordinate points, it cannot determine the original polynomial and the secret.

According to the

interpolation formula, it can be derived that

Our approach is based on Newton's divided differences

interpolation formula. We show that the sums in formulas (1.3) and (1.4) are indeed two direct consequences of a specific

interpolation formula of Newton type and their corresponding remainders must obey the residue of a Newton

interpolation formula.

* - Having the fragments {[F.sub.i]/i [member of] A }, for some group A with |A | = k, the polynomial f (x) and, thus, the information S, can be obtained using Lagrange's

interpolation formula as in equations (2, 3).

In our approach the derivatives of the velocity potential are calculated by employing the Lagrange

interpolation formula through five points.

We now consider the

interpolation formula given in Corollary 7.

To calculate an IRR, two net present values should be calculated and then be used in the

interpolation formula to derive the rate.

Most of the time, the

interpolation formula depends on the values of the spectrum, through the values of [S.sub.t] ([omega]) and [V.sub.t] ([omega]).

It can be easily seen that the polynomial enclosed in the first square brackets fits the curve y(x) satisfying the given data, which is the Newton's forward difference

interpolation formula. And hence, the other part of (2.4) can be directly equated to zero.

Between these fixed points, standard platinum resistance thermometers (SPRTs) are used as interpolating devices with a prescribed

interpolation formula. At any temperature between the fixed-point values, the temperature indicated by an SPRT may depend on the physical or chemical characteristics of that particular SPRT.

We consider the initial value problem (1.1) and the Newton's forward

interpolation formula for a real analytic P(x) for these derivations, where P(x) is given by