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In mathematics, a binary quadratic form is a quadratic homogeneous polynomial in two variables (,) = + +,where a, b, c are the coefficients.When the coefficients can be arbitrary complex numbers, most results are not specific to the case of two variables, so they are described in quadratic form.
In the absence of protic solvent, this dimer collapses to form 1,2-diols. In the presence of a proton source, however, the dimer may undergo either disproportionation to form a samarium alkoxide and carbonyl compound, or protonation to form a carbinol radical ii followed by a second reduction and protonation, yielding an alcohol. (5)
Samarium(II) iodide is an inorganic compound with the formula SmI 2. When employed as a solution for organic synthesis, it is known as Kagan's reagent. SmI 2 is a green solid and forms a dark blue solution in THF. [1] It is a strong one-electron reducing agent that is used in organic synthesis.
Schwartz's reagent is the common name for the organozirconium compound with the formula (C 5 H 5) 2 ZrHCl, sometimes called zirconocene hydrochloride or zirconocene chloride hydride, and is named after Jeffrey Schwartz, a chemistry professor at Princeton University.
Fix some value k that is a non-square positive integer. Assume there exist positive integers (a, b) for which k = a 2 + b 2 / ab + 1 . Let (A, B) be positive integers for which k = A 2 + B 2 / AB + 1 and such that A + B is minimized, and without loss of generality assume A ≥ B. Fixing B, replace A with the variable x to yield x ...
The CBS reduction has proven to be an effective and powerful method to reduce a wide range of different types of ketones in both a stereoselective and chemoselective manner. Substrates include a large variety of aryl-aliphatic, di-aliphatic, di-aryl, α,β unsaturated enone and ynone systems, as well as ketones containing heteroatoms .
If none of the terms are 0, then the form is called nondegenerate; this includes positive definite, negative definite, and isotropic quadratic form (a mix of 1 and −1); equivalently, a nondegenerate quadratic form is one whose associated symmetric form is a nondegenerate bilinear form.
Marcus' formula shows a quadratic dependence of the Gibbs free energy of activation on the Gibbs free energy of reaction. It is general knowledge from the host of chemical experience that reactions usually are the faster the more negative is . In many cases even a linear free energy relation is found.