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Pyridinium refers to the cation [C 5 H 5 NH] +. It is the conjugate acid of pyridine. Many related cations are known involving substituted pyridines, e.g. picolines ...
Casus irreducibilis (from Latin 'the irreducible case') is the name given by mathematicians of the 16th century to cubic equations that cannot be solved in terms of real radicals, that is to those equations such that the computation of the solutions cannot be reduced to the computation of square and cube roots.
An ylide (/ ˈ ɪ l aɪ d /) [1] or ylid (/ ˈ ɪ l ɪ d /) is a neutral dipolar molecule containing a formally negatively charged atom (usually a carbanion) directly attached to a heteroatom with a formal positive charge (usually nitrogen, phosphorus or sulfur), and in which both atoms have full octets of electrons.
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 ...
Pyridinium p-toluenesulfonate (PPTS) is a colourless solid salt of pyridine and p-toluenesulfonic acid. Uses. In organic synthesis, PPTS is used as a weakly acidic ...
Galois theory allows proving that when the three roots are real, and none is rational (casus irreducibilis), one cannot express the roots in terms of real radicals. Nevertheless, purely real expressions of the solutions may be obtained using trigonometric functions, specifically in terms of cosines and arccosines. [25]
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Pyridinium chlorochromate in a vial. Pyridinium chlorochromate (PCC) is a yellow-orange salt with the formula [C 5 H 5 NH] + [CrO 3 Cl] −. It is a reagent in organic synthesis used primarily for oxidation of alcohols to form carbonyls. A variety of related compounds are known with similar reactivity.