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In meta-substitution, the substituents occupy positions 1 and 3 (corresponding to R and meta in the diagram). In para-substitution, the substituents occupy the opposite ends (positions 1 and 4, corresponding to R and para in the diagram). The toluidines serve as an example for these three types of substitution.
The substitution is described in most integral calculus textbooks since the late 19th century, usually without any special name. [5] It is known in Russia as the universal trigonometric substitution , [ 6 ] and also known by variant names such as half-tangent substitution or half-angle substitution .
A single-displacement reaction, also known as single replacement reaction or exchange reaction, is an archaic concept in chemistry.It describes the stoichiometry of some chemical reactions in which one element or ligand is replaced by an atom or group.
Where ψ and φ represent formulas of propositional logic, ψ is a substitution instance of φ if and only if ψ may be obtained from φ by substituting formulas for propositional variables in φ, replacing each occurrence of the same variable by an occurrence of the same formula. For example: ψ: (R → S) & (T → S) is a substitution ...
Arrow pushing or electron pushing is a technique used to describe the progression of organic chemistry reaction mechanisms. [1] It was first developed by Sir Robert Robinson.In using arrow pushing, "curved arrows" or "curly arrows" are drawn on the structural formulae of reactants in a chemical equation to show the reaction mechanism.
Change of variables is an operation that is related to substitution. However these are different operations, as can be seen when considering differentiation or integration (integration by substitution). A very simple example of a useful variable change can be seen in the problem of finding the roots of the sixth-degree polynomial:
Euler substitution is a method for evaluating integrals of the form (, + +), where is a rational function of and + +. In such cases, the integrand can be changed to a rational function by using the substitutions of Euler.
For example, if ⊕ is associative, the unification problem { x ⊕ a ≐ a ⊕ x} has the solutions {x ↦ a}, {x ↦ a ⊕ a}, {x ↦ a ⊕ a ⊕ a}, etc., while the problem { x ⊕ a ≐ a} has no solution. For a given unification problem E, a set S of unifiers is called complete if each solution substitution is subsumed by some substitution ...