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Employment record book. An employment record book is an official personal document recording the employment status of its owner over time. Some European countries issue such documents, others did earlier. The first employment record books are said to have been issued in German Reich in 1892 in the mining industry. [1]
A minimal element of a subset of some preordered set is defined dually as an element of that is not greater than any other element in . The notions of maximal and minimal elements are weaker than those of greatest element and least element which are also known, respectively, as maximum and minimum. The maximum of a subset of a preordered set is ...
one of the longest increasing subsequences is. 0, 2, 6, 9, 11, 15. This subsequence has length six; the input sequence has no seven-member increasing subsequences. The longest increasing subsequence in this example is not the only solution: for instance, are other increasing subsequences of equal length in the same input sequence.
Hausdorff maximal principle. In mathematics, the Hausdorff maximal principle is an alternate and earlier formulation of Zorn's lemma proved by Felix Hausdorff in 1914 (Moore 1982:168). It states that in any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset, where "maximal" is with respect to ...
A maximal order for ω ( n) is ln n / ln ln n. [1] : 83. For the number of prime factors counted with multiplicity Ω ( n) we have a trivial lower bound 1 ≤ Ω ( n ), in which equality occurs when n is prime. A maximal order for Ω ( n) is ln n / ln 2 [1] : 83. It is conjectured that the Mertens function, or summatory function of the Möbius ...
In mathematical analysis, the maximum and minimum[ a ] of a function are, respectively, the largest and smallest value taken by the function. Known generically as extremum, [ b ] they may be defined either within a given range (the local or relative extrema) or on the entire domain (the global or absolute extrema) of a function. [ 1 ][ 2 ][ 3 ...
It is an important tool in algebraic geometry, because it allows local data on algebraic varieties, in the form of modules over local rings, to be studied pointwise as vector spaces over the residue field of the ring. The lemma is named after the Japanese mathematician Tadashi Nakayama and introduced in its present form in Nakayama (1951 ...
For a locally integrable function f on Rn, the sharp maximal function is defined as. for each x in Rn, where the supremum is taken over all balls B and is the integral average of over the ball . [2] The sharp function can be used to obtain a point-wise inequality regarding singular integrals. Suppose we have an operator T which is bounded on L2 ...