substitutionen

Substitutionen (substitutions) is a term used across disciplines to describe the replacement of one element with another according to a defined rule. The concept appears in chemistry, mathematics, cryptography, and computer science, among other fields, and serves to transform, simplify, or encode information.

In chemistry, substitution reactions involve replacing an atom or group in a molecule with a different atom or group. Classic categories include nucleophilic substitution (SN1 and SN2) in organic chemistry and electrophilic substitution in aromatic compounds. Reaction mechanisms, rates, and product structures depend on the substrate, leaving groups, and conditions.

In mathematics, substitution is a method for simplifying problems by replacing variables or expressions with equivalent ones. It is used to solve systems of linear equations by expressing one variable in terms of another and substituting into the remaining equations. In calculus, u-substitution transforms integrals into more manageable forms. Substitution is also used in probability to transform random variables and their distributions.

In cryptography, substitution refers to schemes that replace plaintext symbols with ciphertext symbols according to a fixed mapping, such as substitution ciphers. Monoalphabetic substitutions use a single fixed mapping, while polyalphabetic schemes vary the mapping to thwart frequency analysis.

In computer science and logic, substitution is the operation of replacing variables with expressions within formal systems, as seen in lambda calculus, term rewriting, and unification in automated reasoning. Substitution provides a foundational mechanism for expression manipulation, problem solving, and encoding information across diverse domains.