“substitution”的概念、定义、翻译、参考文献-科学参考

substitution

Mathematics

The replacement of a term in an expression or equation with another which is known to have the same value. This includes replacing variables with their numerical value to evaluate a formula. See also integration.

Chemical Engineering

The process of solving mathematical problems by replacing one variable with another. For example, for the simultaneous equations: $x - y = 1$ and $2 x - y = 3$ , in the first equation y = x−1 can be substituted into the second as 2x−(x−1)=3 and be readily solved to show $x = 2$ and so $y = 1$ .

Computer

1. A particular kind of mapping on formal languages. Let Σ‎₁ and Σ‎₂ be alphabets. For each symbol a in Σ‎₁ let s(a) be a Σ‎₂-language. The function s is a substitution. A homomorphism occurs where each s(a) is a single word. s is Λ‎-free if no s(a) contains the empty word.
The function s can be extended to map Σ‎₁-words to Σ‎₂-languages:
$s (a_{1} \dots a_{n}) = s (a_{1}) \dots s (a_{n})$
i.e. the concatenation of the languages s(a₁),…,s(a_n). s can then be further extended to map Σ‎₁-languages to Σ‎₂-languages:
$s (L) = {s (w) | w \in L}$
s(L) is called the substitution image of L under s.
2. See substitution cipher.

Economics

The switching of consumption from one good or service to another in response to a change in the ratio of prices. Holding utility constant, the elasticity of substitution between two goods or services is the ratio of the proportional change in relative quantities consumed to the proportional change in relative prices. If the price of one good changes, the prices of all other goods being held constant, the change in demand can be divided into a substitution effect and an income effect. The substitution effect is the change in consumption holding the utility level constant: it shows how consumption would have changed if consumers had been compensated for the change in prices. See also elasticity of substitution; import substitution; marginal rate of substitution; substitution effect.

单词	substitution
释义	substitution Mathematics The replacement of a term in an expression or equation with another which is known to have the same value. This includes replacing variables with their numerical value to evaluate a formula. See also integration. Chemical Engineering The process of solving mathematical problems by replacing one variable with another. For example, for the simultaneous equations: $x - y = 1$ and $2 x - y = 3$ , in the first equation y = x−1 can be substituted into the second as 2x−(x−1)=3 and be readily solved to show $x = 2$ and so $y = 1$ . Computer 1. A particular kind of mapping on formal languages. Let Σ‎₁ and Σ‎₂ be alphabets. For each symbol a in Σ‎₁ let s(a) be a Σ‎₂-language. The function s is a substitution. A homomorphism occurs where each s(a) is a single word. s is Λ‎-free if no s(a) contains the empty word. The function s can be extended to map Σ‎₁-words to Σ‎₂-languages: $s (a_{1} \dots a_{n}) = s (a_{1}) \dots s (a_{n})$ i.e. the concatenation of the languages s(a₁),…,s(a_n). s can then be further extended to map Σ‎₁-languages to Σ‎₂-languages: $s (L) = {s (w) \| w \in L}$ s(L) is called the substitution image of L under s. 2. See substitution cipher. Economics The switching of consumption from one good or service to another in response to a change in the ratio of prices. Holding utility constant, the elasticity of substitution between two goods or services is the ratio of the proportional change in relative quantities consumed to the proportional change in relative prices. If the price of one good changes, the prices of all other goods being held constant, the change in demand can be divided into a substitution effect and an income effect. The substitution effect is the change in consumption holding the utility level constant: it shows how consumption would have changed if consumers had been compensated for the change in prices. See also elasticity of substitution; import substitution; marginal rate of substitution; substitution effect.
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