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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. [1] [2] [3] It can be represented generically as:
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:
In calculus, integration by substitution, also known as u-substitution, reverse chain rule or change of variables, [1] is a method for evaluating integrals and antiderivatives. It is the counterpart to the chain rule for differentiation , and can loosely be thought of as using the chain rule "backwards."
Acyl substitution occurs when a nucleophile attacks a carbon that is doubly bonded to one oxygen and singly bonded to another oxygen (can be N or S or a halogen), called an acyl group. The nucleophile attacks the carbon causing the double bond to break into a single bond. The double can then reform, kicking off the leaving group in the process.
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.
The substitution instance tσ of a ground substitution is a ground term if all of t ' s variables are in σ ' s domain, i.e. if vars(t) ⊆ dom(σ). A substitution σ is called a linear substitution if tσ is a linear term for some (and hence every) linear term t containing precisely the variables of σ ' s domain, i.e. with vars(t) = dom(σ).
A double integral, on the other hand, is defined with respect to area in the xy-plane. If the double integral exists, then it is equal to each of the two iterated integrals (either "dy dx" or "dx dy") and one often computes it by computing either of the iterated integrals. But sometimes the two iterated integrals exist when the double integral ...
Substitution, written M[x := N], is the process of replacing all free occurrences of the variable x in the expression M with expression N. Substitution on terms of the lambda calculus is defined by recursion on the structure of terms, as follows (note: x and y are only variables while M and N are any lambda expression): x[x := N] = N