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Nondimensionalization is the partial or full removal of physical dimensions from an equation involving physical quantities by a suitable substitution of variables.This technique can simplify and parameterize problems where measured units are involved.
In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by the equivalent sum of products, continuing until the expression becomes a ...
The names for the degrees may be applied to the polynomial or to its terms. For example, the term 2x in x 2 + 2x + 1 is a linear term in a quadratic polynomial. The polynomial 0, which may be considered to have no terms at all, is called the zero polynomial. Unlike other constant polynomials, its degree is not zero.
Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include:
Since taking the square root is the same as raising to the power 1 / 2 , the following is also an algebraic expression: 1 − x 2 1 + x 2 {\displaystyle {\sqrt {\frac {1-x^{2}}{1+x^{2}}}}} An algebraic equation is an equation involving polynomials , for which algebraic expressions may be solutions .
The full eigenvalues are approximately [9],, (). For m < s {\displaystyle m<s} when the atomic ensemble, and not the photon field, is averaged, then the off-diagonal elements in H ^ T C {\displaystyle {\hat {H}}_{TC}} approximate as g c 2 n s ( m − n + 1 ) {\displaystyle g_{c}{\sqrt {2ns(m-n+1)}}} , smearing over the atomic degrees of freedom ...
the system is equivalent to solving X = 2 ξ t ξ C for the undetermined spinor ξ. A fortiori, if the roles of ξ and x are now reversed, the form Q(ξ) = x defines, for each spinor ξ, a vector x quadratically in the components of ξ. If this quadratic form is polarized, it determines a bilinear vector-valued form on spinors Q(μ, ξ). This ...
The polynomial x 2 + cx + d, where a + b = c and ab = d, can be factorized into (x + a)(x + b).. In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.