# monomial

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## monomial

1. Maths an expression consisting of a single term, such as 5ax
2. consisting of a single algebraic term
3. Biology of, relating to, or denoting a taxonomic name that consists of a single term
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Monomial

the simplest type of algebraic expression considered in elementary algebra. A product consisting of a numerical coefficient and one or several variables, each with some integral positive exponent, is called a monomial. An individual numeral without literal factors is also called a monomial. Examples of monomials are –5ax3, + a3c3xy, –7, + x3 and –a. In these examples, the coefficient +1 is implicit for the monomials +a3c3xy and +x3 and the coefficient –1 is implicit for the monomial –a.

In older algebra textbooks, an algebraic expression in which the last operation in the order of operations is not addition or subtraction is sometimes called a monomial. In this case, for example, the expressions 2(a + b) and x/(y + 1) are called monomials. However, even textbooks that start out by using this definition usually subsequently treat monomials in the narrower sense given above.

## monomial

[mə′nō·mē·əl]
(mathematics)
A polynomial of degree one.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
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.
Khorram, "Monomial 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 [9] [16] and [17] 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.

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