In this paper, a novel design point approach in generalized random space (DPG method) associated with the method of divided difference is proposed and applied to analyze the probability of gravity dam foundation instability over multiple sliding planes.

Hence, if a partial derivative of g(X) is calculated by divided difference mathematically, the value of the derivative at any design point [x.

n] corresponds a

divided difference [[partial derivative].

The Schubert classes classes are constructed by

divided difference operators

alpha]] is convex for [alpha] [less than or equal to] 1/3, hence its

divided difference [t.

2] in it domain the first

divided difference is defined by

Comparing "old" and "new"

divided difference operators for z = n c N, yields

The condition in Theorem 3 is equivalent to non-negativity of the second

divided difference [[[y.

jk]] be a

divided difference (DD) of order k - 1 of a function f constructed by the points [[lambda].

integral operators,

divided difference operators, the continuous q-Hermite polynomials, generating functions, Poisson kernel, bilinear generating functions, q-harmonic oscillators

2), the mth degree Newton

divided difference for [S.

Among those are the endpoint interpolation property, the shape-preserving properties in the case 0 < q < 1, and the representation via

divided differences.