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Multiple comparisons arise when a statistical analysis involves multiple simultaneous statistical tests, each of which has a potential to produce a "discovery". A stated confidence level generally applies only to each test considered individually, but often it is desirable to have a confidence level for the whole family of simultaneous tests. [ 4 ]
Let be a regular language. Then there exists an integer depending only on such that every string in of length at least (is called the "pumping length") [4] can be written as = (i.e., can be divided into three substrings), satisfying the following conditions:
A closed subspace of a Banach space is said to be almost-invariant under an operator () if + for some finite-dimensional subspace ; equivalently, is almost-invariant under if there is a finite-rank operator such that (+), i.e. if is invariant (in the usual sense) under +.
The cross-section of the column is uniform throughout its length. The direct stress is very small as compared to the bending stress (the material is compressed only within the elastic range of strains). The length of the column is very large as compared to the cross-sectional dimensions of the column. The column fails only by buckling.
The string-search functions in Lua script can run extremely fast, comparing millions of characters per second. For example, a search of a 40,000-character article text, for 99 separate words (passed as 99 parameters in a template), ran within one second of Lua CPU clock time.
The test consists of four or five 20-minute nap opportunities set two hours apart, often following an overnight sleep study. During the test, data such as the patient's brain waves, EEG, muscle activity, and eye movements are monitored and recorded. The entire test normally takes about 7 hours during the course of a day.
Priority of conditional formatting rules can be changed with new up/down buttons; Extra sheet protection options have been added, to optionally allow insertion or deletion of rows and columns; CSV export settings are now remembered; Impress & Draw. Allowing specify fractional angles while duplicating an object; Core