In this case, in the left reducible matrix (see (12)) we define [s.sub.12] from the condition [s.sub.12][c.sup.2.sub.0] = [c.sub.1], where [c.sub.0] and [c.sub.1] are junior coefficient and coefficient of the monomial
of degree 2co deg [a.sub.1] in [a.sub.1](x), respectively.
Clearly, due to the influence of roughness, the relationship between the monomial
coefficient a and the fracture aperture b in (3) changes.
geometric programming with fuzzy relation inequality constraints with max-product composition," Computers & Industrial Engineering, vol.
Then the polynomial has totally l = [(d + 1).sup.m] monomials
. Index them with tuple ([i.sub.1], ..., [i.sub.m]), 0 [less than or equal to] [i.sub.j] [less than or equal to] d.
As t(q) = 2m+n[square root of (2)] with m, n [member of] Z, if det A = [s.sub.2] + [r.sub.2], [square root of (2)] then the parity of [s.sub.1] is determined by the monomials
of the first subset.
In order to evaluate [P.sub.n], we first need to compute monomials
of [G.sub.n] that can be written as
In the following we show that the monomial
[s.sup.n] can be replaced by the nth-order orthogonal polynomial, such that the HL consistency conditions are tractable to use in reconstruction.
Since the resultant spherical simplex-radial cubature rule is fully symmetric, we only need to match the even degree monomials
. Matching different even-degree monomials
yields different quadrature points and weights.
where [a.sub.[alpha]] [member of] C, [alpha] = ([[alpha].sub.1], ..., [[alpha].sub.n)], and [mathematical expression not reproducible] is a monomial
. Then the multidegree of f is
In our designed model, the data transmission time is divided into T slots (from T to 1) and we adopt a monomial
energy-bit function in   and  to demonstrate the energy consumed per transmission time slot.
Duffin (1970) condensed the posynomial functions to a monomial
form (by a logarithmic transformation, it became linear), and particularly showed that a "duality gap" function could not occur in geometric programming.
We also initiate the investigation of dendriform coalgebra structures on matroids and introduce a monomial
invariant which satisfy a convolution identity with respect to restriction and deletion.