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Radical addition of a bromine radical to a substituted alkene. In free-radical additions, a radical adds to a spin-paired substrate. When applied to organic compounds, the reaction usually entails addition to an alkene. This addition generates a new radical, which can add to yet another alkene, etc.
Free-radical addition. In organic chemistry, free-radical addition is an addition reaction which involves free radicals. Radical additions are known for a variety of unsaturated substrates, both olefinic or aromatic and with or without heteroatoms. Free-radical reactions depend on one or more relatively weak bonds in a reagent.
In mathematics, a sum of radicals is defined as a finite linear combination of n th roots: =, where , are natural numbers and , are real numbers.. A particular special case arising in computational complexity theory is the square-root sum problem, asking whether it is possible to determine the sign of a sum of square roots, with integer coefficients, in polynomial time.
n. th root. In mathematics, an nth root of a number x is a number r (the root) which, when raised to the power of the positive integer n, yields x: The integer n is called the index or degree, and the number x of which the root is taken is the radicand. A root of degree 2 is called a square root and a root of degree 3, a cube root.
The hydroxyl radical, •HO, is the neutral form of the hydroxide ion (HO – ). Hydroxyl radicals are highly reactive and consequently short-lived; however, they form an important part of radical chemistry. Most notably hydroxyl radicals are produced from the decomposition of hydroperoxides (ROOH) or, in atmospheric chemistry, by the reaction ...
Definition. A simple radical extension is a simple extension F / K generated by a single element satisfying for an element b of K. In characteristic p, we also take an extension by a root of an Artin–Schreier polynomial to be a simple radical extension. A radical series is a tower where each extension is a simple radical extension.
In ring theory, a branch of mathematics, the radical of an ideal of a commutative ring is another ideal defined by the property that an element is in the radical if and only if some power of is in . Taking the radical of an ideal is called radicalization. A radical ideal (or semiprime ideal) is an ideal that is equal to its radical.
Solution in radicals. A solution in radicals or algebraic solution is a closed-form expression, and more specifically a closed-form algebraic expression, that is the solution of a polynomial equation, and relies only on addition, subtraction, multiplication, division, raising to integer powers, and the extraction of n th roots (square roots ...