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In elementary algebra, root rationalisation (or rationalization) is a process by which radicals in the denominator of an algebraic fraction are eliminated.. If the denominator is a monomial in some radical, say , with k < n, rationalisation consists of multiplying the numerator and the denominator by , and replacing by x (this is allowed, as, by definition, a n th root of x is a number that ...
The mass fraction of isotactic (mm) triads is a common quantitative measure of tacticity. When the stereochemistry of a macromolecule is considered to be a Bernoulli process, the triad composition can be calculated from the probability P m of a diad being m type. For example, when this probability is 0.25 then the probability of finding:
The process of blood fractionation involves separation of blood into its main components. Blood fractionation refers generally to the process of separation using a centrifuge (centrifugation), after which three major blood components can be visualized: plasma, buffy coat and erythrocytes (blood cells). These separated components can be analyzed ...
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. [1]
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers ; they may be taken in any field K .
The radical symbol refers to the principal value of the square root function called the principal square root, which is the positive one. The two square roots of a negative number are both imaginary numbers , and the square root symbol refers to the principal square root, the one with a positive imaginary part.
Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator = (),
Perhaps the simplest example application of linear fractional transformations occurs in the analysis of the damped harmonic oscillator. Another elementary application is obtaining the Frobenius normal form, i.e. the companion matrix of a polynomial.