Then A(x) [approximately equal to] B(x), where B(x) has the form (2) in which co deg [b.sub.2] = co deg [a.sub.2], co deg [b.sub.3] [greater than or equal to] co deg [b.sub.2] and in [b.sub.1] (x) the monomial
of degree 2co deg [b.sub.1] = 2co deg [a.sub.1] is absent.
According to the basic characteristics of (3), the monomial
coefficient is related to the reciprocal of the square of the fracture aperture.
geometric programming with fuzzy relation equation constraints," Fuzzy Optimization and Decision Making.
For comparison of efficiency, we also do some evaluation using the direct algorithm [mathematical expression not reproducible] represents each monomial
for polynomial F and w = [([2.sup.s] + 1).sup.m].
where [C.sub.0](v) is the sum of all the monomials
that do not contain u and [C.sub.1] (u, v) is the result of dividing all u-containing monomials
Before we proceed to this result, discussed in Section 3, we will illustrate our combinatorial methodology on a simpler case of the action on monomials
and provide a link with combinatorial model of Hermite polynomials (cf.
We divide the monomials
of some rde[t.sub.i]A into two subsets.
Specifically, consider the monomial
basis of Po[l.sub.n]([R.sup.2]):
However, this requires cost functions and basic equations to be posynomial and/or monomial
But here we use the Chebyshev polynomial of the first kind to replace the monomial
term [s.sup.n], instead of the Chebyshev polynomial of the second kind as shown in .
Substituting S(r) with the Zth-degree monomial
[r.sup.l], we obtain
where [x.sup.i] s are monomial
bases and ats are real coefficients to be determined.