“term”的概念、定义、翻译、参考文献-科学参考

term

Mathematics

See sequence, series.

Chemistry

An electronic energy level in an atom. A term is characterized by a term symbol, which is given by a capital letter indicating the total orbital angular momentum L of the atom, with a left superscript that gives the value of 2S + 1, where S is the total spin angular momentum of the atom. Analogously to the letters used for single electron angular momentum the letters S, P, D, F correspond to L = 0, 1, 2, 3 respectively. For example, a term for which L = 1 and S = 1 has the term symbol ³P.
In the absence of spin–orbit coupling the degeneracy of a term is (2L + 1)(2S + 1). In the presence of spin–orbit coupling a term splits up into several closely spaced energy levels, with this set of closely spaced energy levels being called a multiplet. The multiplicity of a multiplet is given by (2S + 1) since the number of atomic energy levels a term splits into because of spin–orbit coupling is (2S + 1). This is the case because the total electronic angular momentum J of an atom can have the (2S + 1) possible values: L + S, L + S–1, etc. Each level in a multiplet has the value of J written as a right subscript to the term symbol. The degeneracy of a level in a multiplet is 2J + 1. The names given to multiplets with 2S + 1 = 1, 2, 3, 4 are singlet, doublet, triplet, quartet, respectively, to correspond to the number of atomic levels in the multiplet. For example, ³P₁ is the J = 1 level in a P triplet.

Computer

An expression formed from symbols for functions, constants, and variables. An example is
$f (a, g (h (b), c, d))$
Terms are defined recursively as follows: a term is either a variable symbol, a constant symbol, or else has the form ϕ‎(τ‎₁,…,τ‎_k), where ϕ‎ is a function symbol and each of τ‎₁,…,τ‎_k is itself a term. The example above thus has the overall form f(τ‎₁,τ‎₂): in this case ϕ‎ = f and k = 2. Another constraint is that different occurrences of the same symbol ϕ‎ cannot occur with different values of k, i.e. each ϕ‎ must have a fixed arity (number of arguments). Thus
$f (a, f (h (b), c, d))$
would not be a term since the first f has arity 2 while the second has arity 3; neither would
$f (a, g (h (b), c, h))$
since the first h has arity 1 while the second has arity 0.
Terms are often built using signatures. A Σ‎-term is a term in which each constant and function symbol used is in a signature Σ‎, and has the arity associated with it by Σ‎ and, if Σ‎ is a many-sorted signature, all the sorts match properly. A Σ‎-term is also called a term over signature Σ‎. Often a Σ‎-term is allowed to contain variables (of arity 0) in addition to symbols in Σ‎. Terms containing variables are called open terms; terms containing only symbols of the signature are called closed or ground terms. Terms can also be viewed as trees (see tree language). Terms (whether as expressions or as trees) are important in the construction of virtually all syntactic concepts. Terms as defined here are sometimes called first-order terms, to distinguish them from the higher-order terms (such as those involved in lambda calculus). See also equation, initial algebra, predicate calculus.

Philosophy

A singular term is any expression that refers to an object. Singular terms include names, indexicals, and definite descriptions, and in the interpretation of logical calculi, bound variables are treated like singular terms, by being assigned objects in the evaluation of sentences containing them. General terms are those things that, added to singular terms, make sentences: predicates. In the traditional theory of the syllogism no such distinction is made, but terms include all the common nouns occurring in the forms of sentence of which the theory treats.

单词	term
释义	term Mathematics See sequence, series. Chemistry An electronic energy level in an atom. A term is characterized by a term symbol, which is given by a capital letter indicating the total orbital angular momentum L of the atom, with a left superscript that gives the value of 2S + 1, where S is the total spin angular momentum of the atom. Analogously to the letters used for single electron angular momentum the letters S, P, D, F correspond to L = 0, 1, 2, 3 respectively. For example, a term for which L = 1 and S = 1 has the term symbol ³P. In the absence of spin–orbit coupling the degeneracy of a term is (2L + 1)(2S + 1). In the presence of spin–orbit coupling a term splits up into several closely spaced energy levels, with this set of closely spaced energy levels being called a multiplet. The multiplicity of a multiplet is given by (2S + 1) since the number of atomic energy levels a term splits into because of spin–orbit coupling is (2S + 1). This is the case because the total electronic angular momentum J of an atom can have the (2S + 1) possible values: L + S, L + S–1, etc. Each level in a multiplet has the value of J written as a right subscript to the term symbol. The degeneracy of a level in a multiplet is 2J + 1. The names given to multiplets with 2S + 1 = 1, 2, 3, 4 are singlet, doublet, triplet, quartet, respectively, to correspond to the number of atomic levels in the multiplet. For example, ³P₁ is the J = 1 level in a P triplet. Computer An expression formed from symbols for functions, constants, and variables. An example is $f (a, g (h (b), c, d))$ Terms are defined recursively as follows: a term is either a variable symbol, a constant symbol, or else has the form ϕ‎(τ‎₁,…,τ‎_k), where ϕ‎ is a function symbol and each of τ‎₁,…,τ‎_k is itself a term. The example above thus has the overall form f(τ‎₁,τ‎₂): in this case ϕ‎ = f and k = 2. Another constraint is that different occurrences of the same symbol ϕ‎ cannot occur with different values of k, i.e. each ϕ‎ must have a fixed arity (number of arguments). Thus $f (a, f (h (b), c, d))$ would not be a term since the first f has arity 2 while the second has arity 3; neither would $f (a, g (h (b), c, h))$ since the first h has arity 1 while the second has arity 0. Terms are often built using signatures. A Σ‎-term is a term in which each constant and function symbol used is in a signature Σ‎, and has the arity associated with it by Σ‎ and, if Σ‎ is a many-sorted signature, all the sorts match properly. A Σ‎-term is also called a term over signature Σ‎. Often a Σ‎-term is allowed to contain variables (of arity 0) in addition to symbols in Σ‎. Terms containing variables are called open terms; terms containing only symbols of the signature are called closed or ground terms. Terms can also be viewed as trees (see tree language). Terms (whether as expressions or as trees) are important in the construction of virtually all syntactic concepts. Terms as defined here are sometimes called first-order terms, to distinguish them from the higher-order terms (such as those involved in lambda calculus). See also equation, initial algebra, predicate calculus. Philosophy A singular term is any expression that refers to an object. Singular terms include names, indexicals, and definite descriptions, and in the interpretation of logical calculi, bound variables are treated like singular terms, by being assigned objects in the evaluation of sentences containing them. General terms are those things that, added to singular terms, make sentences: predicates. In the traditional theory of the syllogism no such distinction is made, but terms include all the common nouns occurring in the forms of sentence of which the theory treats.
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