binomial

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Related to Binomials: Monomials

binomial

(bī'nō`mēəl), polynomial expression (see polynomialpolynomial,
mathematical expression which is a finite sum, each term being a constant times a product of one or more variables raised to powers. With only one variable the general form of a polynomial is a0xn+a1x
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) containing two terms, for example, x+y. The binomial theorem, or binomial formula, gives the expansion of the nth power of a binomial (x+y) for n=1, 2, 3, … , as follows:

where the ellipsis (…) indicates a continuation of terms following the same pattern. For example, using the formula and reducing fractions, one obtains (x+y)5=x5+5x4y+10x3y2+10x2y3+5xy4+y5. The coefficients 1, n, n (n−1)/1·2, etc., of x and y may also be found from an array known as Pascal's triangle (for Blaise PascalPascal, Blaise
, 1623–62, French scientist and religious philosopher. Studying under the direction of his father, a civil servant, Pascal showed great precocity, especially in mathematics and science.
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), formed by adding adjacent numbers to find the number below them as follows:

binomial

[bī′nō·mē·əl]
(mathematics)
A polynomial with only two terms.

binomial

1. a mathematical expression consisting of two terms, such as 3x + 2y
2. a two-part taxonomic name for an animal or plant
3. referring to two names or terms
References in periodicals archive ?
Thus, the optimal phrasing for a binomial expression should be one that preserves an alternating, preferably trochaic, stress structure.
Presumably an optimally formed binomial phrase, as its own prosodic unit, will display some of the same properties that words do and, accordingly, be subject to preferred syllabification principles.
This generalization is supported by Cooper and Ross's claim that second position words in binomial pairs tend to have "fewer final consonants.
Drawing together the literature with the above generalizations relating to English words, we can begin to make some fairly robust predictions about the "optimal" phonology of binomial pairs.
ICTV at the Paris ICV: Results of the plenary session and the binomial ballot.
Then the binomial (or polynomial) must be reinvented, as the PhyloCode taxonomic address, because, of course, no one is going to memorize unique species epithets for everything.
j] is small, the negative binomial is almost the same as the Poisson distribution.
Figure 1d shows a negative binomial distribution for one individual with mean 0.
ij] for each of the 5,000 individuals is negative binomial with mean 0.
A common approach used for analyzing comparative fishing data is binomial regression with an adjustment for over-dispersion.
and [beta] can be estimated as the intercept with a logit link function by using software for binomial regression.
The first was SAS/STAT PROC NLMIXED, which fits nonlinear mixed models, including binomial logistic regression, using marginal MLE.