“index”的概念、定义、翻译、参考文献-科学参考

index

Mathematics

Suppose that a is a real number. When the product a×a×a×a×a is written as a⁵, the number 5 is called the index. When the index is a positive integer p, then a^p means a×a×⋯×a, where there are p occurrences of a. It can then be shown that
1. (i) a^p×a^q = a^p + q
2. (ii) a^p/a^q = a^p−q (a ≠ 0),
3. (iii) (a^p)^q = a^pq,
4. (iv) (ab)^p = a^pb^p,
  
  where, in (ii), for the moment, it is required that p>q. The meaning of a^p can be extended for a general integer p by the following definitions:
5. (v) a⁰ = 1,
6. (vi) a^−p = 1/a^p (a ≠ 0),
  
  noting (i)–(vi) still hold. And if a > 0, m,n are integers with n > 0, we define
7. (vii) $a^{m / n} = \sqrt[n]{a^{m}}$
For a > 0 and x a real number, we define

$a^{x} = exp (x ln a)$

and again rules (i)–(vii) hold. The same notation is used in other contexts; for example, to define z^p, where z is a complex number, to define A^p, where A is a square matrix, or to define g^p, where g is an element of a multiplicative group. In such cases, some of the above rules may hold and others may not.

Statistics

In the term a^x, the index is x. The plural is indices.

Computer

A list of values of some particular data item contained in a record, enabling it to be retrieved more rapidly than by simple serial search. For example, a subscript indexes a particular element of an array. The B+ tree (see B-tree) is an efficient form of multilevel index. See also indexed file.

Internet

1 An Internet entity which contains references to other documents or to sections of itself. Most Web sites contain pages which function as an index; sometimes the home page or sometimes a special index page which is embedded in a frame.
2 A term used to describe the collection of files which are used by a search engine.

单词	index
释义	index Mathematics Suppose that a is a real number. When the product a×a×a×a×a is written as a⁵, the number 5 is called the index. When the index is a positive integer p, then a^p means a×a×⋯×a, where there are p occurrences of a. It can then be shown that (i) a^p×a^q = a^p + q (ii) a^p/a^q = a^p−q (a ≠ 0), (iii) (a^p)^q = a^pq, (iv) (ab)^p = a^pb^p, where, in (ii), for the moment, it is required that p>q. The meaning of a^p can be extended for a general integer p by the following definitions: (v) a⁰ = 1, (vi) a^−p = 1/a^p (a ≠ 0), noting (i)–(vi) still hold. And if a > 0, m,n are integers with n > 0, we define (vii) $a^{m / n} = \sqrt[n]{a^{m}}$ For a > 0 and x a real number, we define $a^{x} = exp (x ln a)$ and again rules (i)–(vii) hold. The same notation is used in other contexts; for example, to define z^p, where z is a complex number, to define A^p, where A is a square matrix, or to define g^p, where g is an element of a multiplicative group. In such cases, some of the above rules may hold and others may not. Statistics In the term a^x, the index is x. The plural is indices. Computer A list of values of some particular data item contained in a record, enabling it to be retrieved more rapidly than by simple serial search. For example, a subscript indexes a particular element of an array. The B+ tree (see B-tree) is an efficient form of multilevel index. See also indexed file. Internet 1 An Internet entity which contains references to other documents or to sections of itself. Most Web sites contain pages which function as an index; sometimes the home page or sometimes a special index page which is embedded in a frame. 2 A term used to describe the collection of files which are used by a search engine.
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