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The associated grammatical category is degree of comparison. [1] The usual degrees of comparison are the positive , which simply denotes a property (as with the English words big and fully ); the comparative , which indicates great er degree (as bigger and more fully ); and the superlative , which indicates great est degree (as biggest and most ...
In mathematics, a positive polynomial (respectively non-negative polynomial) on a particular set is a polynomial whose values are positive (respectively non-negative) on that set. Precisely, Let p {\displaystyle p} be a polynomial in n {\displaystyle n} variables with real coefficients and let S {\displaystyle S} be a subset of the n ...
A line bundle is ample if some positive power is very ample. An ample line bundle on a projective variety has positive degree on every curve in . The converse is not quite true, but there are corrected versions of the converse, the Nakai–Moishezon and Kleiman criteria for ampleness.
Given a homogeneous polynomial of degree with real coefficients that takes only positive values, one gets a positively homogeneous function of degree / by raising it to the power /. So for example, the following function is positively homogeneous of degree 1 but not homogeneous: ( x 2 + y 2 + z 2 ) 1 2 . {\displaystyle \left(x^{2}+y^{2}+z^{2 ...
As for general fields, a non-constant polynomial f in F[x] is said to be irreducible over F if it is not the product of two polynomials of positive degree. A polynomial of positive degree that is not irreducible over F is called reducible over F. Irreducible polynomials allow us to construct the finite fields of non-prime order.
Both pleasure and pain come in degrees and have been thought of as a dimension going from positive degrees through a neutral point to negative degrees. This assumption is important for the possibility of comparing and aggregating the degrees of pleasure of different experiences, for example, in order to perform the Utilitarian calculus .
The fact that every polynomial equation of positive degree has solutions, possibly non-real, was asserted during the 17th century, but completely proved only at the beginning of the 19th century. This is the fundamental theorem of algebra , which does not provide any tool for computing the solutions, although several methods are known for ...
However, the degree sequence does not, in general, uniquely identify a graph; in some cases, non-isomorphic graphs have the same degree sequence. The degree sequence problem is the problem of finding some or all graphs with the degree sequence being a given non-increasing sequence of positive integers. (Trailing zeroes may be ignored since they ...