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Chain propagation: A radical reacts with a non-radical to produce a new radical species; Chain termination: Two radicals react with each other to create a non-radical species; In a free-radical addition, there are two chain propagation steps. In one, the adding radical attaches to a multiply-bonded precursor to give a radical with lesser bond ...
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Free-radical intermediate is stabilized by hyperconjugation; adjacent occupied sigma C–H orbitals donate into the electron-deficient radical orbital. A new method of anti-Markovnikov addition has been described by Hamilton and Nicewicz, who utilize aromatic molecules and light energy from a low-energy diode to turn the alkene into a cation ...
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.
In the case of two nested square roots, the following theorem completely solves the problem of denesting. [2]If a and c are rational numbers and c is not the square of a rational number, there are two rational numbers x and y such that + = if and only if is the square of a rational number d.
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.
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.
A user will input a number and the Calculator will use an algorithm to search for and calculate closed-form expressions or suitable functions that have roots near this number. Hence, the calculator is of great importance for those working in numerical areas of experimental mathematics. The ISC contains 54 million mathematical constants.