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A solution in radicals or algebraic solution is an expression of a solution of a polynomial equation that is algebraic, that is, relies only on addition, subtraction, multiplication, division, raising to integer powers, and extraction of n th roots (square roots, cube roots, etc.). A well-known example is the quadratic formula
Ideally the radicals are shared equally, causing chains to have equal opportunities for growth and a narrow PDI. Termination: Chains in their active form react via a process known as bi-radical termination to form chains that cannot react further, known as dead polymer. Ideally, the RAFT adduct radical is sufficiently hindered such that it does ...
The radical cyclization step usually involves the attack of a radical on a multiple bond. After this step occurs, the resulting cyclized radicals are quenched through the action of a radical scavenger, a fragmentation process, or an electron-transfer reaction. Five- and six-membered rings are the most common products; formation of smaller and ...
The nested radicals in this solution cannot in general be simplified unless the cubic equation has at least one rational solution. Indeed, if the cubic has three irrational but real solutions, we have the casus irreducibilis, in which all three real solutions are written in terms of cube roots of complex numbers. On the other hand, consider the ...
Radicals can undergo a disproportionation reaction through a radical elimination mechanism (See Fig. 1). Here a radical abstracts a hydrogen atom from another same radical to form two non-radical species: an alkane and an alkene. Radicals can also undergo an elimination reaction to generate a new radical as the leaving group.
Radical 108 or radical dish (皿部) meaning "dish" is one of the 23 Kangxi radicals (214 radicals in total) composed of 5 strokes. In the Kangxi Dictionary , there are 129 characters (out of 49,030) to be found under this radical .
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One of the most widely recognized examples of the synthetic utility of radical cascades is the cyclization sequence employed in the total synthesis of (±)-hirsutene, in 1985 (Scheme 6). [4] [16] Herein, alkyl iodide 28 was converted to the primary radical intermediate 29, which underwent a 5-exo-trig cyclization to afford reactive species 30.